Technical Mathematics.

ERIC Educational Resources Information Center

Flannery, Carol A.

This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…

Basic Measurement and Related Careers: Level C.

ERIC Educational Resources Information Center

Ohio State Univ., Columbus. Center for Vocational and Technical Education.

The teaching guide, part of a series of four, consists of learning experiences for use at the levels of grades 3 and 4 in mathematics. It focuses on the basic concepts of measurement and developing measurement skills in the early grades. It progresses to the concept of measurement by comparison and to developing basic volume measurement skills.…

Getting a Bead on It

ERIC Educational Resources Information Center

Ferrucci, Beverly J.; McDougall, Jennifer; Carter, Jack

2009-01-01

One challenge that middle school teachers commonly face is finding insightful, hands-on applications when teaching basic mathematical concepts. One concept that is a foundation of middle school mathematics is the notion of "linear functions." Although a variety of models can be used for linear equations, such as temperature conversions,…

The effect of mathematics games to the student perception of mathematics subject: A case study in Sekolah Kebangsaan Bukit Kuda, Klang

NASA Astrophysics Data System (ADS)

Abdul Hadi, Normi; Mohd Noor, Norlenda; Abd Halim, Suhaila; Alwadood, Zuraida; Khairol Azmi, Nurul Nisa'

2013-04-01

Mathematics is a basic subject in primary and secondary schools. Early exposure to mathematics is very important since it will affect the student perception towards this subject for their entire life. Therefore, a program called 'Mini Hari Matematik' was conducted to expose the basic mathematics concept through some games which fit the knowledge of Standard four and five students. A questionnaire regarding student perception towards this subject was distributed before and after the program. From the analysis, the program has positively changed the student's perception towards mathematics.

General Mathematics; Part 1. Mathematics Curriculum Guide (Career Oriented).

ERIC Educational Resources Information Center

Nuschler, Alexandra; And Others

The curriculum guide for secondary level, career-oriented General Mathematics Part 1, correlates performance objectives in basic mathematics with career-oriented concepts and activities. The material is designed to lead the student in a systematic development that provides for continuous progress. The guide is in outline format, providing a…

Characterizing Reading Comprehension of Mathematical Texts

ERIC Educational Resources Information Center

Osterholm, Magnus

2006-01-01

This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the…

Using Five-Frames in Preschool Mathematics Instruction

ERIC Educational Resources Information Center

Rizer, Jennifer

2017-01-01

Mathematics education is a critical part of instruction for students around the globe. The foundation for understanding basic mathematical concepts begins early in life. Preschool classrooms can provide the early skills in mathematical reasoning that will be needed later in life. In this study, the author sought to determine if the use of…

Reflectiveness/Impulsiveness and Mathematics Achievement

ERIC Educational Resources Information Center

Cathcart, W. George; Liedtke, Werner

1969-01-01

Report of research to test the hypothesis that reflective students would be higher achievers in mathematics than impulsive pupils. An achievement test was developed to measure understanding of mathematical concepts and applications, ability to solve verbal problems and recall basic facts. Data suggest that reflective students obtain better…

Introduction to Probability, Part 1 - Basic Concepts. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Blakeslee, David W.; And Others

This book is designed to introduce the reader to some fundamental ideas about probability. The mathematical theory of probability plays an increasingly important role in science, government, industry, business, and economics. An understanding of the basic concepts of probability is essential for the study of statistical methods that are widely…

Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

ERIC Educational Resources Information Center

Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

2016-01-01

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

Video Based Developmental Mathematics Learning System For Community College Students.

ERIC Educational Resources Information Center

Gormley, Tyrone D.

The University of Maine at Augusta uses an individualized video-taped mathematics instructional system to eliminate students' math weaknesses before they attempt college math. The course, "1 Mth Developmental Mathematics," is part of the Educational Assistance Program and teaches basic skills and concepts of arithmetic and algebra. The…

Using Example Generation to Explore Students' Understanding of the Concepts of Linear Dependence/Independence in Linear Algebra

ERIC Educational Resources Information Center

Aydin, Sinan

2014-01-01

Linear algebra is a basic mathematical subject taught in mathematics and science depar-tments of universities. The teaching and learning of this course has always been difficult. This study aims to contribute to the research in linear algebra education, focusing on linear dependence and independence concepts. This was done by introducing…

Improving basic math skills through integrated dynamic representation strategies.

PubMed

González-Castro, Paloma; Cueli, Marisol; Cabeza, Lourdes; Álvarez-García, David; Rodríguez, Celestino

2014-01-01

In this paper, we analyze the effectiveness of the Integrated Dynamic Representation strategy (IDR) to develop basic math skills. The study involved 72 students, aged between 6 and 8 years. We compared the development of informal basic skills (numbers, comparison, informal calculation, and informal concepts) and formal (conventionalisms, number facts, formal calculus, and formal concepts) in an experimental group (n = 35) where we applied the IDR strategy and in a Control group (n = 37) in order to identify the impact of the procedure. The experimental group improved significantly in all variables except for number facts and formal calculus. It can therefore be concluded that IDR favors the development of the skills more closely related to applied mathematics than those related to automatic mathematics and mental arithmetic.

Teaching Early Knowledge of Whole Number Concepts through Technology: Findings from a Feasibility Study of an iPad Delivered Kindergarten Mathematics Intervention

ERIC Educational Resources Information Center

Shanley, Lina; Cary, Mari Strand; Clarke, Ben; Jungjohann, Kathy

2013-01-01

Children enter kindergarten with variable levels of mathematics skill and knowledge gained from informal learning opportunities at home, preschool, and daycare. Many perform well once they receive formal mathematics instruction. However, if students do not develop an initial understanding of the most basic aspects of formal mathematics, they are…

That Figures. A Mathematics Resource Package for Intermediate Grades. Revised.

ERIC Educational Resources Information Center

Hintz, Marilyn; Ziegler, Jerry

This resource package deals with elementary level mathematics in daily living, substituting newspapers as a refreshing change from mathematics texts. A total of 40 exercises are intended to provide review and reinforcement for skills previously taught in formal lessons. Skill or concept areas included are: reading large numbers; basic operations;…

Increasing Mathematical Computation Skills for Students with Physical and Health Disabilities

ERIC Educational Resources Information Center

Webb, Paula

2017-01-01

Students with physical and health disabilities struggle with basic mathematical concepts. The purpose of this research study was to increase the students' mathematical computation skills through implementing new strategies and/or methods. The strategies implemented with the students was utilizing the ten-frame tiles and technology with the purpose…

Remediation for Students With Mathematics Difficulties: An Intervention Study in Middle Schools.

PubMed

Moser Opitz, Elisabeth; Freesemann, Okka; Prediger, Susanne; Grob, Urs; Matull, Ina; Hußmann, Stephan

As empirical studies have consistently shown, low achievement in mathematics at the secondary level can often be traced to deficits in the understanding of certain basic arithmetic concepts taught in primary school. The present intervention study in middle schools evaluated whether such learning deficits can be reduced effectively and whether the type of instruction influences students' progress. The sample consisted of 123 students in 34 classes, split among one control group and two intervention groups: (a) small group instruction and (b) independent work partially integrated into regular classrooms. Over a period of 14 weeks, students were taught basic concepts, such as place value and basic operations. In addition, they practiced fact retrieval and counting (in groups). Multilevel regression analyses demonstrated that the interventions can be used to reduce given deficits.

Science and Mathematics

ERIC Educational Resources Information Center

Redlich, Otto

1972-01-01

The foundation of science, and of thermodynamics in particular, can be developed cogently and without arbitrariness. The goal of science, description of nature, is externally given; it requires a set of basic concepts as indispensable tools. Mathematics has no similar externally given goal. (Author/TS)

Learning Mathematics or Losing Money--Betting as a Topic for Mathematical Education

ERIC Educational Resources Information Center

Siller, Hans-Stefan; MaaB, Jurgen

2012-01-01

No risk, no fun--betting on sports events costs the gamblers a lot of money and brings excellent profits to those who offer the bets. Among the people who bet on a regular basis, the proportion of young adults is frighteningly high. We now suggest a concept (as part of a basic mathematics course) for acquiring the necessary mathematical knowledge…

Shop Math for the Metal Trades. Combination Welder Apprentice, Machinist Helper, Precision Metal Finisher, Sheet Metal Worker Apprentice. A Report on Metal Trades Industry Certified, Single-Concept, Mathematical Learning Projects to Eliminate Student Math Fears.

ERIC Educational Resources Information Center

Newton, Lawrence R.

This project (1) identifies basic and functional mathematics skills (shop mathematics skills), (2) provides pretests on these functional mathematics skills, and (3) provides student learning projects (project sheets) that prepare metal trades students to read, understand, and apply mathematics and measuring skills that meet entry-level job…

The Power of Algebra.

ERIC Educational Resources Information Center

Boiteau, Denise; Stansfield, David

This document describes mathematical programs on the basic concepts of algebra produced by Louisiana Public Broadcasting. Programs included are: (1) "Inverse Operations"; (2) "The Order of Operations"; (3) "Basic Properties" (addition and multiplication of numbers and variables); (4) "The Positive and Negative…

Differential Calculus: Concepts and Notation.

ERIC Educational Resources Information Center

Hobbs, David; Relf, Simon

1997-01-01

Suggests that many students with A-level mathematics, and even with a degree in mathematics or a related subject, do not have an understanding of the basic principles of calculus. Describes the approach used in three textbooks currently in use. Contains 14 references. (Author/ASK)

Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course

ERIC Educational Resources Information Center

Cook, John Paul

2015-01-01

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…

Mathematics and engineering in real life through mathematical competitions

NASA Astrophysics Data System (ADS)

More, M.

2018-02-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

Count on It: Congruent Manipulative Displays

ERIC Educational Resources Information Center

Morin, Joe; Samelson, Vicki M.

2015-01-01

Representations that create informative visual displays are powerful tools for communicating mathematical concepts. The National Council of Teachers of Mathematics encourages the use of manipulatives (NCTM 2000). Manipulative materials are often used to present initial representations of basic numerical principles to young children, and it is…

Approximation concepts for efficient structural synthesis

NASA Technical Reports Server (NTRS)

Schmit, L. A., Jr.; Miura, H.

1976-01-01

It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.

Processes and Pathways: How Do Mathematics and Science Partnerships Measure and Promote Growth in Teacher Content Knowledge?

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia S.; Westenskow, Arla

2012-01-01

Intense focus on student achievement results in mathematics and science has brought about claims that K-12 teachers should be better prepared to teach basic concepts in these disciplines. The focus on teachers' mathematics and science content knowledge has been met by efforts to increase teacher knowledge through funded national initiatives…

Digital Educational Games and Mathematics. Results of a Case Study in Primary School Settings

ERIC Educational Resources Information Center

Fokides, Emmanuel

2018-01-01

The study presents the results of a project in which a series of digital games were used for teaching Mathematics to first, fourth, and sixth-grade primary school students (ages 6-7, 8-9, and 11-12). Mathematics was selected as the teaching subject because of the difficulties students face in understanding basic math concepts. Although digital…

My Entirely Plausible Fantasy: Early Mathematics Education in the Age of the Touchscreen Computer

ERIC Educational Resources Information Center

Ginsburg, Herbert P.

2014-01-01

This paper offers an account of what early mathematics education could look like in an age of young digital natives. Each "Tubby," as the tablets are called, presents Nicole (our generic little child) with stimulating mathematics microworlds, from which, beginning at age 3, she can learn basic math concepts, as well as methods of…

Adults Learning Mathematics: What We Should Know about Betting and Bookkeeping?

ERIC Educational Resources Information Center

Maasz, Juergen; Siller, Hans-Stefan

2010-01-01

A lot of people risk money with bets on sport events or other events. Bookkeepers that offer such bets earn a lot of money. We are making a proposal (more exactly: a concept for a part of a basic mathematics course) for learning mathematics behind the screen (internet bets are very popular). Learners should organize a "sports event"…

Multiplicative Thinking: Much More than Knowing Multiplication Facts and Procedures

ERIC Educational Resources Information Center

Hurst, Chris; Hurrell, Derek

2016-01-01

Multiplicative thinking is accepted as a "big idea" of mathematics that underpins important mathematical concepts such as fraction understanding, proportional reasoning, and algebraic thinking. It is characterised by understandings such as the multiplicative relationship between places in the number system, basic and extended number…

Math Interventions for Students with Autism Spectrum Disorder: A Best-Evidence Synthesis

ERIC Educational Resources Information Center

King, Seth A.; Lemons, Christopher J.; Davidson, Kimberly A.

2016-01-01

Educators need evidence-based practices to assist students with disabilities in meeting increasingly rigorous standards in mathematics. Students with autism spectrum disorder (ASD) are increasingly expected to demonstrate learning of basic and advanced mathematical concepts. This review identifies math intervention studies involving children and…

Getting into Gear

ERIC Educational Resources Information Center

Cobbs, Georgia A.; Cranor-Buck, Edith

2011-01-01

This article describes a particular activity, the Motorized Toy unit, which supports science, technology, engineering, and mathematics (STEM) goals and teaches students the basic concept of ratio. The unit addresses both mathematics and science standards and is part of a team-teaching activity. The unit comes from a curriculum titled A World In…

Not Just for Computation: Basic Calculators Can Advance the Process Standards

ERIC Educational Resources Information Center

Moss, Laura J.; Grover, Barbara W.

2007-01-01

Simple nongraphing calculators can be powerful tools to enhance students' conceptual understanding of mathematics concepts. Students have opportunities to develop (1) a broad repertoire of problem-solving strategies by observing multiple solution strategies; (2) respect for other students' abilities and ways of thinking about mathematics; (3) the…

Mathematical Building-Blocks in Engineering Mechanics

ERIC Educational Resources Information Center

Boyajian, David M.

2007-01-01

A gamut of mathematical subjects and concepts are taught within a handful of courses formally required of the typical engineering student who so often questions the relevancy of being bound to certain lower-division prerequisites. Basic classes at the undergraduate level, in this context, include: Integral and Differential Calculus, Differential…

Cool's Clams Casino

ERIC Educational Resources Information Center

Cobey, Paul; Williams, David E.

1977-01-01

A mathematical game that reinforces basic multiplication facts, strengthens concepts of factors and multiples, and also provides arithmetic drill is described. Four variations of the game are also provided. (JT)

Remediation for Students with Mathematics Difficulties: An Intervention Study in Middle Schools

ERIC Educational Resources Information Center

Moser Opitz, Elisabeth; Freesemann, Okka; Prediger, Susanne; Grob, Urs; Matull, Ina; Hußmann, Stephan

2017-01-01

As empirical studies have consistently shown, low achievement in mathematics at the secondary level can often be traced to deficits in the understanding of certain basic arithmetic concepts taught in primary school. The present intervention study in middle schools evaluated whether such learning deficits can be reduced effectively and whether the…

White House Suggests Model Used in Reading to Elevate Math Skills

ERIC Educational Resources Information Center

Cavanagh, Sean

2006-01-01

This article discusses the Bush administration's aim to improve mathematics education through a suggested reading model. The White House is focusing on research to shape how students across the country are taught the most basic mathematical concepts. This undertaking would be modeled on the government's action toward reading, which includes the…

Everything You Always Wanted to Know About the Mathematics of Sex and Family Planning...But Were Afraid to Calculate

ERIC Educational Resources Information Center

Meyer, Rochelle Wilson

1978-01-01

The author uses mathematical models that involve only algebra and a few basic ideas in discrete probability to describe the frequency of conception in large human societies. A number of calculations which can be done by students as exercises are given. (MN)

Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method

ERIC Educational Resources Information Center

Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo

2012-01-01

This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)

Computer Systems for Teaching Complex Concepts.

ERIC Educational Resources Information Center

Feurzeig, Wallace

Four Programing systems--Mentor, Stringcomp, Simon, and Logo--were designed and implemented as integral parts of research into the various ways computers may be used for teaching problem-solving concepts and skills. Various instructional contexts, among them medicine, mathematics, physics, and basic problem-solving for elementary school children,…

Understanding Thermal Equilibrium through Activities

ERIC Educational Resources Information Center

Pathare, Shirish; Huli, Saurabhee; Nachane, Madhura; Ladage, Savita; Pradhan, Hemachandra

2015-01-01

Thermal equilibrium is a basic concept in thermodynamics. In India, this concept is generally introduced at the first year of undergraduate education in physics and chemistry. In our earlier studies (Pathare and Pradhan 2011 "Proc. episteme-4 Int. Conf. to Review Research on Science Technology and Mathematics Education" pp 169-72) we…

Multiple Solutions Approach (MSA): Conceptions and Practices of Primary School Teachers in Ghana

ERIC Educational Resources Information Center

Nabie, Michael Johnson; Raheem, Kolawole; Agbemaka, John Bijou; Sabtiwu, Rufai

2016-01-01

The study explored the curriculum guidelines and primary school teachers' conceptions and practices of the Multiple Solutions Approach (MSA) in teaching mathematics using basic qualitative research design. Informal conversation interviews (ICIs), observations, video and document analyses were used to collect data. Participants included a purposive…

Quantum Social Science

NASA Astrophysics Data System (ADS)

Haven, Emmanuel; Khrennikov, Andrei

2013-01-01

Preface; Part I. Physics Concepts in Social Science? A Discussion: 1. Classical, statistical and quantum mechanics: all in one; 2. Econophysics: statistical physics and social science; 3. Quantum social science: a non-mathematical motivation; Part II. Mathematics and Physics Preliminaries: 4. Vector calculus and other mathematical preliminaries; 5. Basic elements of quantum mechanics; 6. Basic elements of Bohmian mechanics; Part III. Quantum Probabilistic Effects in Psychology: Basic Questions and Answers: 7. A brief overview; 8. Interference effects in psychology - an introduction; 9. A quantum-like model of decision making; Part IV. Other Quantum Probabilistic Effects in Economics, Finance and Brain Sciences: 10. Financial/economic theory in crisis; 11. Bohmian mechanics in finance and economics; 12. The Bohm-Vigier Model and path simulation; 13. Other applications to economic/financial theory; 14. The neurophysiological sources of quantum-like processing in the brain; Conclusion; Glossary; Index.

On Access to Knowledge in the Social Sciences and Humanities, From the Viewpoint of Cybernetics and Information Science.

ERIC Educational Resources Information Center

Heilprin, Laurence B.

The literature of knowledge is a very large system in the cybernetic sense of intractibility to control. Improving access to it needs some simplifying theory. A step in this direction is a hypothesis constructed from basic concepts. These include cybernetic concepts of variety and requisite variety; a version of the mathematical concept of…

Suggestions for Teaching Mathematics Using Laboratory Approaches. 6. Probability. Experimental Edition.

ERIC Educational Resources Information Center

New York State Education Dept., Albany. Bureau of Elementary Curriculum Development.

This guide is the sixth in a series of publications to assist teachers in using a laboratory approach to mathematics. Twenty activities on probability and statistics for the elementary grades are described in terms of purpose, materials needed, and procedures to be used. Objectives of these activities include basic probability concepts; gathering,…

Learning and Teaching Mathematics through Real Life Models

ERIC Educational Resources Information Center

Takaci, Djurdjica; Budinski, Natalija

2011-01-01

This paper proposes modelling based learning as a tool for learning and teaching mathematics in high school. We report on an example of modelling real world problems in two high schools in Serbia where students were introduced for the first time to the basic concepts of modelling. Student use of computers and educational software, GeoGebra, was…

Types of Learning Problems

MedlinePlus

... Dyscalculia is defined as difficulty performing mathematical calculations. Math is problematic for many students, but dyscalculia may prevent a teenager from grasping even basic math concepts. Auditory Memory and Processing Disabilities Auditory memory ...

Aerodynamic mathematical modeling - basic concepts

NASA Technical Reports Server (NTRS)

Tobak, M.; Schiff, L. B.

1981-01-01

The mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers is reviewed. Bryan's original formulation, linear aerodynamic indicial functions, and superposition are considered. These concepts are extended into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well defined characteristic motions, reproducible in principle either in wind tunnel experiments or flow field computations. A further generalization leads to a form accommodating the discontinuous and double valued behavior characteristics of hysteresis in the steady state aerodynamic response.

Global differential geometry: An introduction for control engineers

NASA Technical Reports Server (NTRS)

Doolin, B. F.; Martin, C. F.

1982-01-01

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control.

Math Experiences for Preschool Children: Games and Cuisenaire Rods.

ERIC Educational Resources Information Center

Goetz, Elizabeth M.

Acquisition of the basic concepts of mathematics such as matching, number and counting, sets and classifying, comparing, measuring, shape, space, and parts and wholes, may be followed by two types of activities. First, the child may subsequently be presented activities that allow for practice and generalization of those acquired concepts.…

Demystifying Concepts of Epidemic and Causal Association for Public Health Students--A Pedagogical Approach to Promote Critical and Analytical Thinking

ERIC Educational Resources Information Center

Patil, Rajan R.

2011-01-01

Epidemiology is a difficult but an important subject in public health curriculum. As teachers, we need to be very innovative in teaching the core concepts in epidemiology since it is basically a research oriented subject that calls for enormous application of logic and mathematical skills. Very often, complex epidemiological concepts need to be…

Determining the Numeracy and Algebra Errors of Students in a Two-Year Vocational School

ERIC Educational Resources Information Center

Akyüz, Gözde

2015-01-01

The goal of this study was to determine the mathematics achievement level in basic numeracy and algebra concepts of students in a two-year program in a technical vocational school of higher education and determine the errors that they make in these topics. The researcher developed a diagnostic mathematics achievement test related to numeracy and…

Mathematical modeling of the aerodynamic characteristics in flight dynamics

NASA Technical Reports Server (NTRS)

Tobak, M.; Chapman, G. T.; Schiff, L. B.

1984-01-01

Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.

Relating the Learned Knowledge and Acquired Skills to Real Life: Function Sample

ERIC Educational Resources Information Center

Albayrak, Mustafa; Yazici, Nurullah; Simsek, Mertkan

2017-01-01

Considering that Mathematics is a multidimensional problem-solving method that can be effective in all areas of cultural life, it is of great importance because of its contribution to other sciences such as physical and social sciences. It is known that the basic concepts of mathematics, which can also be expressed as a way of life, have helped to…

Grass Grows, the Cow Eats: A Simple Grazing Systems Model with Emergent Properties

ERIC Educational Resources Information Center

Ungar, Eugene David; Seligman, Noam G.; Noy-Meir, Imanuel

2004-01-01

We describe a simple, yet intellectually challenging model of grazing systems that introduces basic concepts in ecology and systems analysis. The practical is suitable for high-school and university curricula with a quantitative orientation, and requires only basic skills in mathematics and spreadsheet use. The model is based on Noy-Meir's (1975)…

Teachers' Conceptions of Standards in South African Basic Education and Training: A Case Study

ERIC Educational Resources Information Center

Sosibo, Lungi; Nomlomo, Vuyokazi

2014-01-01

In South Africa, the Department of Basic Education and Training (DBE) is responsible for primary and secondary education (Grades R-12). In an effort to improve educational standards in literacy, numeracy and mathematics, especially in the Foundation Phase (FP) levels of education, the DBE has developed several initiatives and campaigns. To monitor…

Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development.

PubMed

Andersen, Morten; Sajid, Zamra; Pedersen, Rasmus K; Gudmand-Hoeyer, Johanne; Ellervik, Christina; Skov, Vibe; Kjær, Lasse; Pallisgaard, Niels; Kruse, Torben A; Thomassen, Mads; Troelsen, Jesper; Hasselbalch, Hans Carl; Ottesen, Johnny T

2017-01-01

The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.

What Works Clearinghouse Quick Review: "Academic Music: Music Instruction to Engage Third-Grade Students in Learning Basic Fraction Concepts"

ERIC Educational Resources Information Center

What Works Clearinghouse, 2012

2012-01-01

The study examined the effectiveness of an intervention designed to teach mathematical concepts through music. Specifically, it investigated the effect of the intervention on third-grade students' understanding of fractions. Sixty-seven students from one northern California elementary school participated in the study over a period of six weeks; of…

Three Concepts or One? Students' Understanding of Basic Limit Concepts

ERIC Educational Resources Information Center

Fernández-Plaza, José Antonio; Simpson, Adrian

2016-01-01

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of…

It's a Wonderful Life: Using Public Domain Cinema Clips To Teach Affective Objectives and Illustrate Real-World Algebra Applications.

ERIC Educational Resources Information Center

Palmer, Loretta

A basic algebra unit was developed at Utah Valley State College to emphasize applications of mathematical concepts in the work world, using video and computer-generated graphics to integrate textual material. The course was implemented in three introductory algebra sections involving 80 students and taught algebraic concepts using such areas as…

Do Vampires Exist? Using Spreadsheets To Investigate a Common Folktale.

ERIC Educational Resources Information Center

Drier, Hollylynne Stohl

1999-01-01

Describes the use of spreadsheets in a third grade class to teach basic mathematical concepts by investigating the existence of vampires. Incorporates addition and multiplication skills, patterning, variables, formulas, exponential growth, and proof by contradiction. (LRW)

Helping Students to Recognize and Evaluate an Assumption in Quantitative Reasoning: A Basic Critical-Thinking Activity with Marbles and Electronic Balance

ERIC Educational Resources Information Center

Slisko, Josip; Cruz, Adrian Corona

2013-01-01

There is a general agreement that critical thinking is an important element of 21st century skills. Although critical thinking is a very complex and controversial conception, many would accept that recognition and evaluation of assumptions is a basic critical-thinking process. When students use simple mathematical model to reason quantitatively…

Design of multiple representations e-learning resources based on a contextual approach for the basic physics course

NASA Astrophysics Data System (ADS)

Bakri, F.; Muliyati, D.

2018-05-01

This research aims to design e-learning resources with multiple representations based on a contextual approach for the Basic Physics Course. The research uses the research and development methods accordance Dick & Carey strategy. The development carried out in the digital laboratory of Physics Education Department, Mathematics and Science Faculty, Universitas Negeri Jakarta. The result of the process of product development with Dick & Carey strategy, have produced e-learning design of the Basic Physics Course is presented in multiple representations in contextual learning syntax. The appropriate of representation used in the design of learning basic physics include: concept map, video, figures, data tables of experiment results, charts of data tables, the verbal explanations, mathematical equations, problem and solutions example, and exercise. Multiple representations are presented in the form of contextual learning by stages: relating, experiencing, applying, transferring, and cooperating.

Image processing in forensic pathology.

PubMed

Oliver, W R

1998-03-01

Image processing applications in forensic pathology are becoming increasingly important. This article introduces basic concepts in image processing as applied to problems in forensic pathology in a non-mathematical context. Discussions of contrast enhancement, digital encoding, compression, deblurring, and other topics are presented.

On the Use of History of Mathematics: An Introduction to Galileo's Study of Free Fall Motion

ERIC Educational Resources Information Center

Ponce Campuzano, Juan Carlos; Matthews, Kelly E.; Adams, Peter

2018-01-01

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year…

The Mathematics of High School Physics

NASA Astrophysics Data System (ADS)

Kanderakis, Nikos

2016-10-01

In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and simplified models of these systems, constructed with the help of geometry. By analyzing these models, they were able to formulate new concepts, laws and theories of physics and then through models again, to apply these concepts and theories to new physical phenomena and check the results by means of experiment. Students' difficulties with the mathematics of high school physics are well known. Science education research attributes them to inadequately deep understanding of mathematics and mainly to inadequate understanding of the meaning of symbolic mathematical expressions. There seem to be, however, more causes of these difficulties. One of them, not independent from the previous ones, is the complex meaning of the algebraic concepts used in school physics (e.g. variables, parameters, functions), as well as the complexities added by physics itself (e.g. that equations' symbols represent magnitudes with empirical meaning and units instead of pure numbers). Another source of difficulties is that the theories and laws of physics are often applied, via mathematics, to simplified, and idealized physical models of the world and not to the world itself. This concerns not only the applications of basic theories but also all authentic end-of-the-chapter problems. Hence, students have to understand and participate in a complex interplay between physics concepts and theories, physical and mathematical models, and the real world, often without being aware that they are working with models and not directly with the real world.

Mathematics, thermodynamics, and modeling to address ten common misconceptions about protein structure, folding, and stability.

PubMed

Robic, Srebrenka

2010-01-01

To fully understand the roles proteins play in cellular processes, students need to grasp complex ideas about protein structure, folding, and stability. Our current understanding of these topics is based on mathematical models and experimental data. However, protein structure, folding, and stability are often introduced as descriptive, qualitative phenomena in undergraduate classes. In the process of learning about these topics, students often form incorrect ideas. For example, by learning about protein folding in the context of protein synthesis, students may come to an incorrect conclusion that once synthesized on the ribosome, a protein spends its entire cellular life time in its fully folded native confirmation. This is clearly not true; proteins are dynamic structures that undergo both local fluctuations and global unfolding events. To prevent and address such misconceptions, basic concepts of protein science can be introduced in the context of simple mathematical models and hands-on explorations of publicly available data sets. Ten common misconceptions about proteins are presented, along with suggestions for using equations, models, sequence, structure, and thermodynamic data to help students gain a deeper understanding of basic concepts relating to protein structure, folding, and stability.

Theory of the Decoherence Effect in Finite and Infinite Open Quantum Systems Using the Algebraic Approach

NASA Astrophysics Data System (ADS)

Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert

Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.

ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra

NASA Astrophysics Data System (ADS)

Dockendorff, Monika; Solar, Horacio

2018-01-01

This case study investigates the impact of the integration of information and communications technology (ICT) in mathematics visualization skills and initial teacher education programmes. It reports on the influence GeoGebra dynamic software use has on promoting mathematical learning at secondary school and on its impact on teachers' conceptions about teaching and learning mathematics. This paper describes how GeoGebra-based dynamic applets - designed and used in an exploratory manner - promote mathematical processes such as conjectures. It also refers to the changes prospective teachers experience regarding the relevance visual dynamic representations acquire in teaching mathematics. This study observes a shift in school routines when incorporating technology into the mathematics classroom. Visualization appears as a basic competence associated to key mathematical processes. Implications of an early integration of ICT in mathematics initial teacher training and its impact on developing technological pedagogical content knowledge (TPCK) are drawn.

Basic statistics with Microsoft Excel: a review.

PubMed

Divisi, Duilio; Di Leonardo, Gabriella; Zaccagna, Gino; Crisci, Roberto

2017-06-01

The scientific world is enriched daily with new knowledge, due to new technologies and continuous discoveries. The mathematical functions explain the statistical concepts particularly those of mean, median and mode along with those of frequency and frequency distribution associated to histograms and graphical representations, determining elaborative processes on the basis of the spreadsheet operations. The aim of the study is to highlight the mathematical basis of statistical models that regulate the operation of spreadsheets in Microsoft Excel.

Basic statistics with Microsoft Excel: a review

PubMed Central

Di Leonardo, Gabriella; Zaccagna, Gino; Crisci, Roberto

2017-01-01

The scientific world is enriched daily with new knowledge, due to new technologies and continuous discoveries. The mathematical functions explain the statistical concepts particularly those of mean, median and mode along with those of frequency and frequency distribution associated to histograms and graphical representations, determining elaborative processes on the basis of the spreadsheet operations. The aim of the study is to highlight the mathematical basis of statistical models that regulate the operation of spreadsheets in Microsoft Excel. PMID:28740690

Astrophysical Flows

NASA Astrophysics Data System (ADS)

Pringle, James E.; King, Andrew

2003-07-01

Almost all conventional matter in the Universe is fluid, and fluid dynamics plays a crucial role in astrophysics. This new graduate textbook provides a basic understanding of the fluid dynamical processes relevant to astrophysics. The mathematics used to describe these processes is simplified to bring out the underlying physics. The authors cover many topics, including wave propagation, shocks, spherical flows, stellar oscillations, the instabilities caused by effects such as magnetic fields, thermal driving, gravity, shear flows, and the basic concepts of compressible fluid dynamics and magnetohydrodynamics. The authors are Directors of the UK Astrophysical Fluids Facility (UKAFF) at the University of Leicester, and editors of the Cambridge Astrophysics Series. This book has been developed from a course in astrophysical fluid dynamics taught at the University of Cambridge. It is suitable for graduate students in astrophysics, physics and applied mathematics, and requires only a basic familiarity with fluid dynamics.• Provides coverage of the fundamental fluid dynamical processes an astrophysical theorist needs to know • Introduces new mathematical theory and techniques in a straightforward manner • Includes end-of-chapter problems to illustrate the course and introduce additional ideas

Demonstrating Proof by Contrapositive and Contradiction through Physical Analogs.

ERIC Educational Resources Information Center

Kaiser, Mark J.

1993-01-01

Presents examples where mathematical and physical reasoning complement each other in interpreting and analyzing some basic science concepts using proof by contradiction and contrapositive. Examples involve the rotation of the moon, the stability of electrons and protons, the electron's orbit about the nucleus, and the earth's liquid core. (MDH)

The Dreaded "Work" Problems Revisited: Connections through Problem Solving from Basic Fractions to Calculus

ERIC Educational Resources Information Center

Shore, Felice S.; Pascal, Matthew

2008-01-01

This article describes several distinct approaches taken by preservice elementary teachers to solving a classic rate problem. Their approaches incorporate a variety of mathematical concepts, ranging from proportions to infinite series, and illustrate the power of all five NCTM Process Standards. (Contains 8 figures.)

A Simple Mechanical Model for the Isotropic Harmonic Oscillator

ERIC Educational Resources Information Center

Nita, Gelu M.

2010-01-01

A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)

Changing to the Metric System.

ERIC Educational Resources Information Center

Chambers, Donald L.; Dowling, Kenneth W.

This report examines educational aspects of the conversion to the metric system of measurement in the United States. Statements of positions on metrication and basic mathematical skills are given from various groups. Base units, symbols, prefixes, and style of the metric system are outlined. Guidelines for teaching metric concepts are given,…

Using High-Probability Instructional Sequences and Explicit Instruction to Teach Multiplication Facts

ERIC Educational Resources Information Center

Leach, Debra

2016-01-01

Students with learning disabilities often struggle with math fact fluency and require specialized interventions to recall basic facts. Deficits in math fact fluency can result in later difficulties when learning higher-level mathematical computation, concepts, and problem solving. The response-to-intervention (RTI) and…

NLSE: Parameter-Based Inversion Algorithm

NASA Astrophysics Data System (ADS)

Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Aldrin, John C.; Knopp, Jeremy S.

Chapter 11 introduced us to the notion of an inverse problem and gave us some examples of the value of this idea to the solution of realistic industrial problems. The basic inversion algorithm described in Chap. 11 was based upon the Gauss-Newton theory of nonlinear least-squares estimation and is called NLSE in this book. In this chapter we will develop the mathematical background of this theory more fully, because this algorithm will be the foundation of inverse methods and their applications during the remainder of this book. We hope, thereby, to introduce the reader to the application of sophisticated mathematical concepts to engineering practice without introducing excessive mathematical sophistication.

On the use of history of mathematics: an introduction to Galileo's study of free fall motion

NASA Astrophysics Data System (ADS)

Ponce Campuzano, Juan Carlos; Matthews, Kelly E.; Adams, Peter

2018-05-01

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year university students through Galileo's experiments designed to investigate the motion of falling bodies, and his geometrical explanation of his results, via simple dynamic geometric applets designed with GeoGebra. Our goal was to enhance the students' development of mathematical thinking. Through a scholarship of teaching and learning study design, we captured data from students before, during and after the activity. Findings suggest that the historical development presented to the students helped to show the growth and evolution of the ideas and made visible authentic ways of thinking mathematically. Importantly, the activity prompted students to question and rethink what they knew about speed and acceleration, and also to appreciate the novel concepts of instantaneous speed and acceleration at which Galileo arrived.

Uses of Mathematics Textbooks for Grade (4-8) as per Basic Concepts and Questions Levels in TIMSS Test: A Study Conducted in Kingdom of Saudi Arabia Schools

ERIC Educational Resources Information Center

Al Tamimi, Abdul Rehman

2018-01-01

This study tried to explore the degree of representation of math textbooks for grades (4-8) in the Kingdom of Saudi Arabia concerning the key concepts, shape, and levels of questions used in the TIMSS test. The study population of this study includes both students and teachers from fourth grade to eighth grade. The goal of this study was…

A Modularized Tablet-Based Approach to Preparation for Remedial Mathematics

ERIC Educational Resources Information Center

Parker, K. Andrew

2016-01-01

Basic arithmetic forms the foundation of the math courses that students will face in their undergraduate careers. It is therefore crucial that students have a solid understanding of these fundamental concepts. At an open-access university offering both two-year and four-year degrees, incoming freshmen who were identified as lacking in basic…

Aeronautics: An Educator's Guide with Activities in Science, Mathematics, and Technology Education.

ERIC Educational Resources Information Center

Anderson, Charles; Biggs, Pat; Brown, Deborah; Culivan, Steve; Ellis, Sue; Gerard, James; Hardwick, Ellen; Poff, Norm; Rosenberg, Carla; Shearer, Deborah; Tripp, Octavia; Ernst, Ron

This educator's guide explains basic aeronautical concepts and provides a background in the history of aviation within the context of flight environment (atmosphere, airports, and navigation). The activities in this guide are designed to be uncomplicated and fun. They were developed by NASA Aerospace Education Services Program specialists who have…

Polynomial Calculus: Rethinking the Role of Calculus in High Schools

ERIC Educational Resources Information Center

Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell

2016-01-01

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

Affective Responses of Community College Students to Self-Selected Criteria of Success.

ERIC Educational Resources Information Center

Easton, John Q.

A study was conducted at the City Colleges of Chicago to investigate how individual expectations and self-selected criteria for success correlate with academic self-concept and course achievement. At the beginning and end of the fall semester, students enrolled in six basic mathematics classes completed questionnaires containing the Michigan State…

Toward Using Games to Teach Fundamental Computer Science Concepts

ERIC Educational Resources Information Center

Edgington, Jeffrey Michael

2010-01-01

Video and computer games have become an important area of study in the field of education. Games have been designed to teach mathematics, physics, raise social awareness, teach history and geography, and train soldiers in the military. Recent work has created computer games for teaching computer programming and understanding basic algorithms. …

Genetic algorithms

NASA Technical Reports Server (NTRS)

Wang, Lui; Bayer, Steven E.

1991-01-01

Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology.

Currency Arbitrage Detection Using a Binary Integer Programming Model

ERIC Educational Resources Information Center

Soon, Wanmei; Ye, Heng-Qing

2011-01-01

In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this…

Teaching about Hazardous and Toxic Materials. Teaching Activities in Environmental Education Series.

ERIC Educational Resources Information Center

Disinger, John F.; Lisowski, Marylin

Designed to assist practitioners of both formal and non-formal settings, this 18th volume of the ERIC Clearinghouse for Science, Mathematics, and Environmental Education's Teaching Activities in Environmental Education series specifically focuses on the theme of hazardous and toxic materials. Initially, basic environmental concepts that deal with…

Geometry in the Adult Education Classroom.

ERIC Educational Resources Information Center

Markus, Nancy

2001-01-01

For many adults, geometry is a mathematics topic that immediately makes sense to them and gives them confidence in their ability to learn, while other adult learners identify geometry with failure. Most adults, however, do recognize the need for measurement, and many have a basic understanding of measurement concepts, although they may need to…

Multiple-solution problems in a statistics classroom: an example

NASA Astrophysics Data System (ADS)

Chu, Chi Wing; Chan, Kevin L. T.; Chan, Wai-Sum; Kwong, Koon-Shing

2017-11-01

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students' understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact probability mass distribution for the sum of face values. Four different ways of solving the problem are discussed. The solutions span various basic concepts in different mathematical disciplines (sample space in probability theory, the probability generating function in statistics, integer partition in basic combinatorics and individual risk model in actuarial science) and thus promotes upper undergraduate students' awareness of knowledge connections between their courses. All solutions of the example are implemented using the R statistical software package.

Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation.

PubMed

Getto, Philipp; Marciniak-Czochra, Anna

2015-01-01

Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.

Understanding immunology via engineering design: the role of mathematical prototyping.

PubMed

Klinke, David J; Wang, Qing

2012-01-01

A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and "fitness for use," can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans.

Ross, macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens.

PubMed

Smith, David L; Battle, Katherine E; Hay, Simon I; Barker, Christopher M; Scott, Thomas W; McKenzie, F Ellis

2012-01-01

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various "Ross-Macdonald" mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955-1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention.

Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens

PubMed Central

Smith, David L.; Battle, Katherine E.; Hay, Simon I.; Barker, Christopher M.; Scott, Thomas W.; McKenzie, F. Ellis

2012-01-01

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various “Ross-Macdonald” mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955–1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention. PMID:22496640

Numerosity as a topological invariant.

PubMed

Kluth, Tobias; Zetzsche, Christoph

2016-01-01

The ability to quickly recognize the number of objects in our environment is a fundamental cognitive function. However, it is far from clear which computations and which actual neural processing mechanisms are used to provide us with such a skill. Here we try to provide a detailed and comprehensive analysis of this issue, which comprises both the basic mathematical foundations and the peculiarities imposed by the structure of the visual system and by the neural computations provided by the visual cortex. We suggest that numerosity should be considered as a mathematical invariant. Making use of concepts from mathematical topology--like connectedness, Betti numbers, and the Gauss-Bonnet theorem--we derive the basic computations suited for the computation of this invariant. We show that the computation of numerosity is possible in a neurophysiologically plausible fashion using only computational elements which are known to exist in the visual cortex. We further show that a fundamental feature of numerosity perception, its Weber property, arises naturally, assuming noise in the basic neural operations. The model is tested on an extended data set (made publicly available). It is hoped that our results can provide a general framework for future research on the invariance properties of the numerosity system.

Inverting seismic data for rock physical properties; Mathematical background and application

DOE Office of Scientific and Technical Information (OSTI.GOV)

Farfour, Mohammed; Yoon, Wang Jung; Kim, Jinmo

2016-06-08

The basic concept behind seismic inversion is that mathematical assumptions can be established to relate seismic to geological formation properties that caused their seismic responses. In this presentation we address some widely used seismic inversion method in hydrocarbon reservoirs identification and characterization. A successful use of the inversion in real example from gas sand reservoir in Boonsville field, Noth Central Texas is presented. Seismic data was not unambiguous indicator of reservoir facies distribution. The use of the inversion led to remove the ambiguity and reveal clear information about the target.

On laminar and turbulent friction

NASA Technical Reports Server (NTRS)

Von Karman, TH

1946-01-01

Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author)

ACCESS 1: Approximation Concepts Code for Efficient Structural Synthesis program documentation and user's guide

NASA Technical Reports Server (NTRS)

Miura, H.; Schmit, L. A., Jr.

1976-01-01

The program documentation and user's guide for the ACCESS-1 computer program is presented. ACCESS-1 is a research oriented program which implements a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and general mathematical programming algorithms are applied in the design optimization procedure. Implementation of the computer program, preparation of input data and basic program structure are described, and three illustrative examples are given.

What is the purpose of emission computed tomography in nuclear medicine

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phelps, M.E.

1977-01-01

ECT is a mathematical and physical concept, an instrument, a radionuclide tracer technique, a research procedure and it is certainly both an old (Kuhl began his work in the late fifties) and a new concept. It also has great and unique potential as a diagnostic technique. It is interesting that the basic principles of medical CT were exemplified and developed in Nuclear Medicine by Kuhl and coworkers and the concept of ''physiologic or function tomography'' provides a technique to advance the original charter of Nuclear Medicine in the use of radionuclides for the measure of metabolism and physiologic function.

The Development of Embodied Representations of Numerical Understanding through Gameplay

ERIC Educational Resources Information Center

Clark, Colin Travis

2012-01-01

Young children must develop basic concepts of numeracy--one being that numbers have magnitudes that increase linearly--before they are able to succeed in mathematics. Children from low-income families have been found to be at a greater disadvantage in the development of numeracy, but this disadvantage can be overcome through the use of a simple…

Academic Music: Music Instruction to Engage Third-Grade Students in Learning Basic Fraction Concepts

ERIC Educational Resources Information Center

Courey, Susan Joan; Balogh, Endre; Siker, Jody Rebecca; Paik, Jae

2012-01-01

This study examined the effects of an academic music intervention on conceptual understanding of music notation, fraction symbols, fraction size, and equivalency of third graders from a multicultural, mixed socio-economic public school setting. Students (N = 67) were assigned by class to their general education mathematics program or to receive…

Techniques of Differentiation and Integration, Mathematics (Experimental): 5297.27.

ERIC Educational Resources Information Center

Forrester, Gary B.

This guidebook on minimum course content was designed for students who have mastered the skills and concepts of analytic geometry. It is a short course in the basic techniques of calculus recommended for the student who has need of these skills in other courses such as beginning physics, economics or statistics. The course does not intend to teach…

From Fearing STEM to Playing with It: The Natural Integration of STEM into the Preschool Classroom

ERIC Educational Resources Information Center

Torres-Crespo, Marisel N.; Kraatz, Emily; Pallansch, Lindsey

2014-01-01

The article describes the process of developing and implementing a STEM Summer Camp that allowed Preschoolers to experiment and investigate with materials while learning basic concepts of science, technology, engineering, and mathematics (STEM) through play as part of the educational process. The participants were presented with problems that they…

Instructional Strategies for Online Introductory College Physics Based on Learning Styles

ERIC Educational Resources Information Center

Ekwue, Eleazer U.

2013-01-01

The practical nature of physics and its reliance on mathematical presentations and problem solving pose a challenge toward presentation of the course in an online environment for effective learning experience. Most first-time introductory college physics students fail to grasp the basic concepts of the course and the problem solving skills if the…

PROGRAPH Diagrams--A New Old System for Teaching Functional Modelling

ERIC Educational Resources Information Center

Siller, Hans-Stefan

2009-01-01

This paper shows the basic concept of Functional Modelling in mathematics education which has become more and more important in recent years. Hence it is necessary to think about suitable graphical methods to explain the fundamental idea of a function and its influence on values and other functions. PROGRAPH diagrams are a potentially good way to…

Gravity Thickening. Sludge Treatment and Disposal Course #166. Instructor's Guide [and] Student Workbook.

ERIC Educational Resources Information Center

Klopping, Paul H.

The basic operation of the gravity thickener is described in this lesson, focusing on the theory of operation, components found in a typical thickener, and the parameters which must be understood in optimizing the opeation of the thickener. Attention is given to mathematics concepts which are used in controlling hydraulic loading, detention time,…

Toward using games to teach fundamental computer science concepts

NASA Astrophysics Data System (ADS)

Edgington, Jeffrey Michael

Video and computer games have become an important area of study in the field of education. Games have been designed to teach mathematics, physics, raise social awareness, teach history and geography, and train soldiers in the military. Recent work has created computer games for teaching computer programming and understanding basic algorithms. We present an investigation where computer games are used to teach two fundamental computer science concepts: boolean expressions and recursion. The games are intended to teach the concepts and not how to implement them in a programming language. For this investigation, two computer games were created. One is designed to teach basic boolean expressions and operators and the other to teach fundamental concepts of recursion. We describe the design and implementation of both games. We evaluate the effectiveness of these games using before and after surveys. The surveys were designed to ascertain basic understanding, attitudes and beliefs regarding the concepts. The boolean game was evaluated with local high school students and students in a college level introductory computer science course. The recursion game was evaluated with students in a college level introductory computer science course. We present the analysis of the collected survey information for both games. This analysis shows a significant positive change in student attitude towards recursion and modest gains in student learning outcomes for both topics.

Understanding synergy.

PubMed

Geary, Nori

2013-02-01

Analysis of the interactive effects of combinations of hormones or other manipulations with qualitatively similar individual effects is an important topic in basic and clinical endocrinology as well as other branches of basic and clinical research related to integrative physiology. Functional, as opposed to mechanistic, analyses of interactions rely on the concept of synergy, which can be defined qualitatively as a cooperative action or quantitatively as a supra-additive effect according to some metric for the addition of different dose-effect curves. Unfortunately, dose-effect curve addition is far from straightforward; rather, it requires the development of an axiomatic mathematical theory. I review the mathematical soundness, face validity, and utility of the most frequently used approaches to supra-additive synergy. These criteria highlight serious problems in the two most common synergy approaches, response additivity and Loewe additivity, which is the basis of the isobole and related response surface approaches. I conclude that there is no adequate, generally applicable, supra-additive synergy metric appropriate for endocrinology or any other field of basic and clinical integrative physiology. I recommend that these metrics be abandoned in favor of the simpler definition of synergy as a cooperative, i.e., nonantagonistic, effect. This simple definition avoids mathematical difficulties, is easily applicable, meets regulatory requirements for combination therapy development, and suffices to advance phenomenological basic research to mechanistic studies of interactions and clinical combination therapy research.

Finding an information concept suited for a universal theory of information.

PubMed

Brier, Søren

2015-12-01

The view argued in this article is that if we want to define a universal concept of information covering subjective experiential and meaningful cognition - as well as intersubjective meaningful communication in nature, technology, society and life worlds - then the main problem is to decide, which epistemological, ontological and philosophy of science framework the concept of information should be based on and integrated in. All the ontological attempts to create objective concepts of information result in concepts that cannot encompass meaning and experience of embodied living and social systems. There is no conclusive evidence that the core of reality across nature, culture, life and mind is purely either mathematical, logical or of a computational nature. Therefore the core of the information concept should not only be based only on pure logical or mathematical rationality. We need to include interpretation, signification and meaning construction in our transdisciplinary framework for information as a basic aspect of reality alongside the physical, chemical and molecular biological. Dretske defines information as the content of new, true, meaningful, and understandable knowledge. According to this widely held definition information in a transdisciplinary theory cannot be 'objective', but has to be relativized in relation to the receiver's knowledge, as also proposed by Floridi. It is difficult to produce a quantitative statement independently of a qualitative analysis based on some sort of relation to the human condition as a semiotic animal. I therefore alternatively suggest to build information theories based on semiotics from the basic relations of embodied living systems meaningful cognition and communication. I agree with Peircean biosemiotics that all information must be part of real relational sign-processes manifesting as tokens. Copyright © 2015. Published by Elsevier Ltd.

Basic Phage Mathematics.

PubMed

Abedon, Stephen T; Katsaounis, Tena I

2018-01-01

Basic mathematical descriptions are useful in phage ecology, applied phage ecology such as in the course of phage therapy, and also toward keeping track of expected phage-bacterial interactions as seen during laboratory manipulation of phages. The most basic mathematical descriptor of phages is their titer, that is, their concentration within stocks, experimental vessels, or other environments. Various phenomena can serve to modify phage titers, and indeed phage titers can vary as a function of how they are measured. An important aspect of how changes in titers can occur results from phage interactions with bacteria. These changes tend to vary in degree as a function of bacterial densities within environments, and particularly densities of those bacteria that are susceptible to or at least adsorbable by a given phage type. Using simple mathematical models one can describe phage-bacterial interactions that give rise particularly to phage adsorption events. With elaboration one can consider changes in both phage and bacterial densities as a function of both time and these interactions. In addition, phages along with their impact on bacteria can be considered as spatially constrained processes. In this chapter we consider the simpler of these concepts, providing in particular detailed verbal explanations toward facile mathematical insight. The primary goal is to stimulate a more informed use and manipulation of phages and phage populations within the laboratory as well as toward more effective phage application outside of the laboratory, such as during phage therapy. More generally, numerous issues and approaches to the quantification of phages are considered along with the quantification of individual, ecological, and applied properties of phages.

Antibiotics in Animal Products

NASA Astrophysics Data System (ADS)

Falcão, Amílcar C.

The administration of antibiotics to animals to prevent or treat diseases led us to be concerned about the impact of these antibiotics on human health. In fact, animal products could be a potential vehicle to transfer drugs to humans. Using appropri ated mathematical and statistical models, one can predict the kinetic profile of drugs and their metabolites and, consequently, develop preventive procedures regarding drug transmission (i.e., determination of appropriate withdrawal periods). Nevertheless, in the present chapter the mathematical and statistical concepts for data interpretation are strictly given to allow understanding of some basic pharma-cokinetic principles and to illustrate the determination of withdrawal periods

How Does the Representational Status of To-Be-Counted Objects Affect Children's Understanding of Cardinality?

ERIC Educational Resources Information Center

Petersen, Lori A.

2013-01-01

When counting, the final word used to tag the final item in a set represents the cardinality, or total number, of the set. Understanding of this concept serves as a foundation for children's basic mathematical skills, such as arithmetic. However, little is known about how variations in the early learning environment affect children's understanding…

Group Solutions, Too! More Cooperative Logic Activities for Grades K-4. Teacher's Guide. LHS GEMS.

ERIC Educational Resources Information Center

Goodman, Jan M.; Kopp, Jaine

There is evidence that structured cooperative logic is an effective way to introduce or reinforce mathematics concepts, explore thinking processes basic to both math and science, and develop the important social skills of cooperative problem-solving. This book contains a number of cooperative logic activities for grades K-4 in order to improve…

First Graders' Responses to School-Taught Mathematics as a Function of Their Spontaneous Conceptions of Basic Algebraic Relationships.

ERIC Educational Resources Information Center

Kaplan, Rochelle Goldberg

The rationale of this study is based on the premise that the outcomes of children's learning are specifically shaped by the interaction of their individual cognitive structures with the presentations of curricular content in the classroom. Therefore, since the interpretive tools that children apply to instructional content may vary substantially,…

Understanding Immunology via Engineering Design: The Role of Mathematical Prototyping

PubMed Central

Klinke, David J.; Wang, Qing

2012-01-01

A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and “fitness for use,” can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans. PMID:22973412

The mathematics textbook at tertiary level as curriculum material - exploring the teacher's decision-making process

NASA Astrophysics Data System (ADS)

Randahl, Mira

2016-08-01

This paper reports on a study about how the mathematics textbook was perceived and used by the teacher in the context of a calculus part of a basic mathematics course for first-year engineering students. The focus was on the teacher's choices and the use of definitions, examples and exercises in a sequence of lectures introducing the derivative concept. Data were collected during observations of lectures and an interview, and informal talks with the teacher. The introduction and the treatment of the derivative as proposed by the teacher during the lectures were analysed in relation to the results of the content text analysis of the textbook. The teacher's decisions were explored through the lens of intended learning goals for engineering students taking the mathematics course. The results showed that the sequence of concepts and the formal introduction of the derivative as proposed by the textbook were closely followed during the lectures. The examples and tasks offered to the students focused strongly on procedural knowledge. Although the textbook proposes both examples and exercises that promote conceptual knowledge, these opportunities were not fully utilized during the observed lectures. Possible reasons for the teacher's choices and decisions are discussed.

The conceptual basis of mathematics in cardiology: (II). Calculus and differential equations.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-04-01

This is the second in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

The conceptual basis of mathematics in cardiology III: linear systems theory and integral transforms.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-05-01

This is the third in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas.This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

The conceptual basis of mathematics in cardiology IV: statistics and model fitting.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-06-01

This is the fourth in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-02-01

This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

Description and Application of a Mathematical Method for the Analysis of Harmony

PubMed Central

Zuo, Qiting; Jin, Runfang; Ma, Junxia

2015-01-01

Harmony issues are widespread in human society and nature. To analyze these issues, harmony theory has been proposed as the main theoretical approach for the study of interpersonal relationships and relationships between humans and nature. Therefore, it is of great importance to study harmony theory. After briefly introducing the basic concepts of harmony theory, this paper expounds the five elements that are essential for the quantitative description of harmony issues in water resources management: harmony participant, harmony objective, harmony regulation, harmony factor, and harmony action. A basic mathematical equation for the harmony degree, that is, a quantitative expression of harmony issues, is introduced in the paper: HD = ai − bj, where a is the uniform degree, b is the difference degree, i is the harmony coefficient, and j is the disharmony coefficient. This paper also discusses harmony assessment and harmony regulation and introduces some application examples. PMID:26167535

Mathematics education and learning disabilities in Spain.

PubMed

Casas, Ana Miranda; Castellar, Rosa García

2004-01-01

In the first part of this article, we describe the basic objectives of the math curriculum in Spain as well as the basic contents, teacher resources, and obstacles perceived in mathematics instruction. Second, we briefly describe the concept of learning disabilities (LD) as they are currently defined in Spain. As stated in the recent educational reform, a student with LD is any student with special educational needs. The emphasis is placed on the educational resources that these students need in order to achieve the curricular objectives that correspond to their age group or grade. Third, we comment specifically on the educational services model and the evaluation and instructional procedures for students with math learning disabilities. Finally, we describe some lines of research that have appeared in the last few years in Spain that have led to the development of new evaluation and intervention procedures for students with LD in computation and problem solving.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ketterer, S.P.

This manual is designed as a comprehensive hands-on instructional manual for learning the T{sub E}X* computer typesetting program in a classroom environment. Each section presents a new concept in careful detail, concluding with an exercise (T{sub E}Xercise) to reinforce the learning of the concept. The manual introduces the novice T{sub E}X user to the program's basic command structure, along with the concepts of grouping, producing accents, making font changes, and generating mathematical symbols. The T{sub E}Xercises guide the new user in generating text containing footnotes, multilevel lists, and hanging indentations, as well as in magnifying text for viewgraphs. Once themore » basic text generation is defined, the more advanced topics of formatting math equations and tables are explained. A full range of math capabilities is presented --- beginning with simple one-line equations, progressing through complex numbered and aligned equations, and concluding with matrices. The sections on table generation present the basic concepts in T{sub E}X's table-formatting program and then build on them. The new user first learns to construct simple tables, and with careful explanations and guidance, learns to add one new table enhancement at a time. By the conclusion of these sections, the user can construct tables with horizontal and vertical rules and with column entries that are paragraphs. 1 ref.« less

Multidimensional Generalized Functions in Aeroacoustics and Fluid Mechanics. Part 1; Basic Concepts and Operations

NASA Technical Reports Server (NTRS)

Farassat, Fereidoun; Myers, Michael K.

2011-01-01

This paper is the first part of a three part tutorial on multidimensional generalized functions (GFs) and their applications in aeroacoustics and fluid mechanics. The subject is highly fascinating and essential in many areas of science and, in particular, wave propagation problems. In this tutorial, we strive to present rigorously and clearly the basic concepts and the tools that are needed to use GFs in applications effectively and with ease. We give many examples to help the readers in understanding the mathematical ideas presented here. The first part of the tutorial is on the basic concepts of GFs. Here we define GFs, their properties and some common operations on them. We define the important concept of generalized differentiation and then give some interesting elementary and advanced examples on Green's functions and wave propagation problems. Here, the analytic power of GFs in applications is demonstrated with ease and elegance. Part 2 of this tutorial is on the diverse applications of generalized derivatives (GDs). Part 3 is on generalized Fourier transformations and some more advanced topics. One goal of writing this tutorial is to convince readers that, because of their powerful operational properties, GFs are absolutely essential and useful in engineering and physics, particularly in aeroacoustics and fluid mechanics.

Multivariate assessment of event-related potentials with the t-CWT method.

PubMed

Bostanov, Vladimir

2015-11-05

Event-related brain potentials (ERPs) are usually assessed with univariate statistical tests although they are essentially multivariate objects. Brain-computer interface applications are a notable exception to this practice, because they are based on multivariate classification of single-trial ERPs. Multivariate ERP assessment can be facilitated by feature extraction methods. One such method is t-CWT, a mathematical-statistical algorithm based on the continuous wavelet transform (CWT) and Student's t-test. This article begins with a geometric primer on some basic concepts of multivariate statistics as applied to ERP assessment in general and to the t-CWT method in particular. Further, it presents for the first time a detailed, step-by-step, formal mathematical description of the t-CWT algorithm. A new multivariate outlier rejection procedure based on principal component analysis in the frequency domain is presented as an important pre-processing step. The MATLAB and GNU Octave implementation of t-CWT is also made publicly available for the first time as free and open source code. The method is demonstrated on some example ERP data obtained in a passive oddball paradigm. Finally, some conceptually novel applications of the multivariate approach in general and of the t-CWT method in particular are suggested and discussed. Hopefully, the publication of both the t-CWT source code and its underlying mathematical algorithm along with a didactic geometric introduction to some basic concepts of multivariate statistics would make t-CWT more accessible to both users and developers in the field of neuroscience research.

Currency arbitrage detection using a binary integer programming model

NASA Astrophysics Data System (ADS)

Soon, Wanmei; Ye, Heng-Qing

2011-04-01

In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this work, students can learn to link several types of basic optimization models, namely linear programming, integer programming and network models, and apply the well-known sensitivity analysis procedure to accommodate realistic changes in the exchange rates. Beginning with a BIP model, we discuss how it can be reduced to an equivalent but considerably simpler model, where an efficient algorithm can be applied to find the arbitrages and incorporate the sensitivity analysis procedure. A simple comparison is then made with a different arbitrage detection model. This exercise helps students learn to apply basic Operations Research concepts to a practical real-life example, and provides insights into the processes involved in Operations Research model formulations.

The Impact of Challenging Geometry and Measurement Units on the Achievement of Grade 2 Students

ERIC Educational Resources Information Center

Gavin, M. Katherine; Casa, Tutita M.; Adelson, Jill L.; Firmender, Janine M.

2013-01-01

The primary goal of Project M[superscript 2] was to develop and field-test challenging geometry and measurement units for all K-2 students. This article reports on the achievement results for students in Grade 2 at 12 urban and suburban sites in 4 states using the Iowa Tests of Basic Skills (ITBS) mathematics concepts subtest and an open-response…

Math Remediation for the College Bound: How Teachers Can Close the Gap, from the Basics through Algebra

ERIC Educational Resources Information Center

Khatri, Daryao

2011-01-01

Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. This book fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some of the social sciences. This…

Some basic mathematical methods of diffusion theory. [emphasis on atmospheric applications

NASA Technical Reports Server (NTRS)

Giere, A. C.

1977-01-01

An introductory treatment of the fundamentals of diffusion theory is presented, starting with molecular diffusion and leading up to the statistical methods of turbulent diffusion. A multilayer diffusion model, designed to permit concentration and dosage calculations downwind of toxic clouds from rocket vehicles, is described. The concepts and equations of diffusion are developed on an elementary level, with emphasis on atmospheric applications.

A caveat concerning center of resistance

PubMed Central

Nägerl, Hans; Kubein-Meesenburg, Dietmar

2013-01-01

The center of resistance is a concept in theoretical orthodontics used to describe tooth movement under loads. It is commonly used to qualitatively predict tooth movement without recourse to complex equations or simulations. We start with a survey of the historical origin of the technical term. After this, the periodontal ligament is idealized as a linear elastic suspension. The mathematical formalism of vector and tensor calculus will clarify our reasoning. We show that a point such as the center of resistance basically only exists in two dimensions or in very special symmetric spatial configurations. In three dimensions, a simple counterexample of a suspension without a center of resistance is given. A second more tooth-like example illustrates the magnitude of the effects in question in dentistry. In conclusion, the center of resistance should be replaced by a newer and wider mathematical concept, the “center of elasticity,” together with a limiting parameter, the “radius of resistance.” PMID:24019849

Study on the tumor-induced angiogenesis using mathematical models.

PubMed

Suzuki, Takashi; Minerva, Dhisa; Nishiyama, Koichi; Koshikawa, Naohiko; Chaplain, Mark Andrew Joseph

2018-01-01

We studied angiogenesis using mathematical models describing the dynamics of tip cells. We reviewed the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examined the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. We then constructed two types of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as transient probability, particle velocity, and Boolean variables. © 2017 The Authors. Cancer Science published by John Wiley & Sons Australia, Ltd on behalf of Japanese Cancer Association.

Workbook, Basic Mathematics and Wastewater Processing Calculations.

ERIC Educational Resources Information Center

New York State Dept. of Environmental Conservation, Albany.

This workbook serves as a self-learning guide to basic mathematics and treatment plant calculations and also as a reference and source book for the mathematics of sewage treatment and processing. In addition to basic mathematics, the workbook discusses processing and process control, laboratory calculations and efficiency calculations necessary in…

Dual methods and approximation concepts in structural synthesis

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins.

On the concept of individual in ecology and evolution.

PubMed

Metz, J A J

2013-03-01

Part of the art of theory building is to construct effective basic concepts, with a large reach and yet powerful as tools for getting at conclusions. The most basic concept of population biology is that of individual. An appropriately reengineered form of this concept has become the basis for the theories of structured populations and adaptive dynamics. By appropriately delimiting individuals, followed by defining their states as well as their environment, it become possible to construct the general population equations that were introduced and studied by Odo Diekmann and his collaborators. In this essay I argue for taking the properties that led to these successes as the defining characteristics of the concept of individual, delegating the properties classically invoked by philosophers to the secondary role of possible empirical indicators for the presence of those characteristics. The essay starts with putting in place as rule for effective concept engineering that one should go for relations that can be used as basis for deductive structure building rather than for perceived ontological essence. By analysing how we want to use it in the mathematical arguments I then build up a concept of individual, first for use in population dynamical considerations and then for use in evolutionary ones. These two concepts do not coincide, and neither do they on all occasions agree with common intuition-based usage.

Self-reports of mathematics self-concept and educational outcomes: the roles of ego-dimensions and self-consciousness.

PubMed

Martin, A J; Debus, R L

1998-12-01

There is a need for research to (a) explore more fully the academic outcomes that follow from under-/over-rating of self-concept and (b) identify factors that predict the nature of self-reports of self-concept as well as under- and over-rating of this self-concept. The study examines the link between students' self-appraisals of both mathematics self-concept and under-/over-rating of this self-concept and educational outcomes in mathematics such as achievement and motivation (future plans for mathematics). Ego-dimensions (ego-orientation and competence-valuation) and public self-consciousness were examined as two factors that might contribute to predicting these self-appraisals. Findings are drawn from a sample of 382 male and female high school students ranging in age from 14 to 16 years. Students responded to a questionnaire (at Time 1) that assessed self-concept, motivation orientation, competence-valuation, self-consciousness, and mathematics motivation. Teachers rated each student using a brief mathematics self-concept scale. Higher mathematics self-concept and over-rating of this self-concept were predictive of higher levels of mathematics motivation and later mathematics achievement (Time 2). Findings also indicate that ego-orientation and competence-valuation are positively associated with mathematics self-concept and over-rating, whilst public self-consciousness negatively predicts mathematics self-concept and is also associated with a tendency to under-rate oneself in this domain.

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

A review of the basic concepts of dense gas dispersion with special regard to modelling of heat transfer

NASA Astrophysics Data System (ADS)

Tasker, M. N.

1984-01-01

Dense gas dispersion is the study of the spreading and dilution of a gas that has a density greater than that of ambient air. Models to predict the dispersion of such dense gases as chlorine, sulfur dioxide, liquefied natural gas, and liquid propane are necessary to prevent a catastrophe in environmental and/or human terms. A basic physical picture of dense gas dispersion is provided. Mathematical and wind tunnel models of dense gas flow are presented and discussed, including the constraints and disadvantages of modelling techniques. Special emphasis is given to heat transfer during dense gas dispersion.

Designing Geometry 2.0 learning environments: a preliminary study with primary school students

NASA Astrophysics Data System (ADS)

Joglar Prieto, Nuria; María Sordo Juanena, José; Star, Jon R.

2014-04-01

The information and communication technologies of Web 2.0 are arriving in our schools, allowing the design and implementation of new learning environments with great educational potential. This article proposes a pedagogical model based on a new geometry technology-integrated learning environment, called Geometry 2.0, which was tested with 39 sixth grade students from a public school in Madrid (Spain). The main goals of the study presented here were to describe an optimal role for the mathematics teacher within Geometry 2.0, and to analyse how dynamic mathematics and communication might affect young students' learning of basic figural concepts in a real setting. The analyses offered in this article illustrate how our Geometry 2.0 model facilitates deeply mathematical tasks which encourage students' exploration, cooperation and communication, improving their learning while fostering geometrical meanings.

What's Working: Program Factors Influencing California Community College Basic Skills Mathematics Students' Advancement to Transfer Level

ERIC Educational Resources Information Center

Fiero, Diane M.

2013-01-01

Purpose: The purpose of this study was to determine which basic skills program factors were exhibited by successful basic skills programs that helped students advance to transfer-level mathematics. This study specifically examined California community college basic skills programs that assist students who place in mathematics courses 2 levels…

Have Basic Mathematical Skills Grown Obsolete in the Computer Age: Assessing Basic Mathematical Skills and Forecasting Performance in a Business Statistics Course

ERIC Educational Resources Information Center

Noser, Thomas C.; Tanner, John R.; Shah, Situl

2008-01-01

The purpose of this study was to measure the comprehension of basic mathematical skills of students enrolled in statistics classes at a large regional university, and to determine if the scores earned on a basic math skills test are useful in forecasting student performance in these statistics classes, and to determine if students' basic math…

The Remarkable Number "1"

NASA Astrophysics Data System (ADS)

Allen, G. Donald

2014-09-01

In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God made the integers; all else is the work of man," has spawned a lively modern philosophical discussion, and this discussion begins by trying to get a philosophical handle on "1." This approach remains under heavy discussion, and is more-or-less unresolved (Frege in Die Grundlagen der Arithmetik (English: The foundations of arithmetic). Polhman, 1884). In this note, we consider the many facets of "one" in it many guises and applications. Nonetheless, "one" has multiple meanings, from the very practical to the abstract, from mathematics to science to basically everything. We examine here a mere slice of mathematical history with a focus on the most basic and applicable concept therein. It troubles many, particularly students, even today.

Design and Development of Basic Physical Layer WiMAX Network Simulation Models

DTIC Science & Technology

2009-01-01

Wide Web . The third software version was developed during the period of 22 August to 4 November, 2008. The software version developed during the...researched on the Web . The mathematics of some fundamental concepts such as Fourier transforms, convolutional coding techniques were also reviewed...Mathworks Matlab users’ website. A simulation model was found, entitled Estudio y Simulacion de la capa Jisica de la norma 802.16 ( Sistema WiMAX) developed

Theoretical foundations of spatially-variant mathematical morphology part ii: gray-level images.

PubMed

Bouaynaya, Nidhal; Schonfeld, Dan

2008-05-01

In this paper, we develop a spatially-variant (SV) mathematical morphology theory for gray-level signals and images in the Euclidean space. The proposed theory preserves the geometrical concept of the structuring function, which provides the foundation of classical morphology and is essential in signal and image processing applications. We define the basic SV gray-level morphological operators (i.e., SV gray-level erosion, dilation, opening, and closing) and investigate their properties. We demonstrate the ubiquity of SV gray-level morphological systems by deriving a kernel representation for a large class of systems, called V-systems, in terms of the basic SV graylevel morphological operators. A V-system is defined to be a gray-level operator, which is invariant under gray-level (vertical) translations. Particular attention is focused on the class of SV flat gray-level operators. The kernel representation for increasing V-systems is a generalization of Maragos' kernel representation for increasing and translation-invariant function-processing systems. A representation of V-systems in terms of their kernel elements is established for increasing and upper-semi-continuous V-systems. This representation unifies a large class of spatially-variant linear and non-linear systems under the same mathematical framework. Finally, simulation results show the potential power of the general theory of gray-level spatially-variant mathematical morphology in several image analysis and computer vision applications.

An Exploratory Study of Taiwanese Mathematics Teachers' Conceptions of School Mathematics, School Statistics, and Their Differences

ERIC Educational Resources Information Center

Yang, Kai-Lin

2014-01-01

This study used phenomenography, a qualitative method, to investigate Taiwanese mathematics teachers' conceptions of school mathematics, school statistics, and their differences. To collect data, we interviewed five mathematics teachers by open questions. They also responded to statements drawn on mathematical/statistical conceptions and…

Self-concept mediates the relation between achievement and emotions in mathematics.

PubMed

Van der Beek, Jojanneke P J; Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Leseman, Paul P M

2017-09-01

Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. The aims were (1) to investigate the mediating role of mathematical self-concept in the relation between mathematics achievement and the achievement emotions of enjoyment and anxiety in a comprehensive model, and (2) to test possible differences in this mediating role between low-, average-, and high-achieving students. Participants were ninth-grade students (n = 1,014) from eight secondary schools in the Netherlands. Through an online survey including mathematical problems, students were asked to indicate their levels of mathematics enjoyment, anxiety, and self-concept. Structural equation modelling was used to test the mediating role of self-concept in the relation between mathematics achievement and emotions. Multigroup analyses were performed to compare these relations across the three achievement groups. Results confirmed full mediation of the relation between mathematics achievement and emotions by mathematical self-concept. Furthermore, we found higher self-concepts, more enjoyment and less math anxiety in high-achieving students compared to their average and low-achieving peers. No differences across these achievement groups were found in the relations in the mediational model. Mathematical self-concept plays a pivotal role in students' appraisal of mathematics. Mathematics achievement is only one factor explaining students' self-concept. Likely also classroom instruction and teachers' feedback strategies help to shape students' self-concept. © 2017 The British Psychological Society.

An excerpt from an eye-tracking comparative study between Poland and Japan with the use of Force Concept Inventory

NASA Astrophysics Data System (ADS)

Rosiek, Roman; Sajka, Mirosława; Ohno, Eizo; Shimojo, Atsushi; Iwata, Michiru; Wcisło, Dariusz

2017-01-01

The paper presents the initial results of a comparative Polish-Japanese study. The research was conducted at the Department of Mathematics, Physics and Technical Science at the Pedagogical University of Cracow and at the University of Hokkaido. The participants of the study were university students of humanistic courses. The research concerns the comparison of the respondents' knowledge and understanding of the concept of force in mechanics and their ways of solving problems in the field of a basic mechanics course. A special theoretical tool was used. It was the standardized, international test diagnosing the understanding of the concept of force - the so-called "Force Concept Inventory" (FCI), in its official Polish and Japanese translations. The eye-tracking method was combined with structured interviews and discussions with all the respondents.

Foundations in Science and Mathematics Program for Middle School and High School Students

NASA Astrophysics Data System (ADS)

Desai, Karna Mahadev; Yang, Jing; Hemann, Jason

2016-01-01

The Foundations in Science and Mathematics (FSM) is a graduate student led summer program designed to help middle school and high school students strengthen their knowledge and skills in mathematics and science. FSM provides two-week-long courses over a broad spectrum of disciplines including astronomy, biology, chemistry, computer programming, geology, mathematics, and physics. Students can chose two types of courses: (1) courses that help students learn the fundamental concepts in basic sciences and mathematics (e.g., "Precalculus"); and (2) knowledge courses that might be excluded from formal schooling (e.g., "Introduction to Universe"). FSM has served over 500 students in the Bloomington, IN, community over six years by acquiring funding from Indiana University and the Indiana Space Grant Consortium. FSM offers graduate students the opportunity to obtain first hand experience through independent teaching and curriculum design as well as leadership experience.We present the design of the program, review the achievements, and explore the challenges we face. We are open to collaboration with similar educational outreach programs. For more information, please visit http://www.indiana.edu/~fsm/ .

A brief history of the most remarkable numbers e, i and γ in mathematical sciences with applications

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2015-08-01

This paper deals with a brief history of the most remarkable Euler numbers e, i and γ in mathematical sciences. Included are many properties of the constants e, i and γ and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special attention is given to the growth and decay phenomena in many real-world problems including stability and instability of their solutions. Some specific and modern applications of logarithms, complex numbers and complex exponential functions to electrical circuits and mechanical systems are presented with examples. Included are the use of complex numbers and complex functions in the description and analysis of chaos and fractals with the aid of modern computer technology. In addition, the phasor method is described with examples of applications in engineering science. The major focus of this paper is to provide basic information through historical approach to mathematics teaching and learning of the fundamental knowledge and skills required for students and teachers at all levels so that they can understand the concepts of mathematics, and mathematics education in science and technology.

Statistics for wildlifers: how much and what kind?

USGS Publications Warehouse

Johnson, D.H.; Shaffer, T.L.; Newton, W.E.

2001-01-01

Quantitative methods are playing increasingly important roles in wildlife ecology and, ultimately, management. This change poses a challenge for wildlife practitioners and students who are not well-educated in mathematics and statistics. Here we give our opinions on what wildlife biologists should know about statistics, while recognizing that not everyone is inclined mathematically. For those who are, we recommend that they take mathematics coursework at least through calculus and linear algebra. They should take statistics courses that are focused conceptually , stressing the Why rather than the How of doing statistics. For less mathematically oriented wildlifers, introductory classes in statistical techniques will furnish some useful background in basic methods but may provide little appreciation of when the methods are appropriate. These wildlifers will have to rely much more on advice from statisticians. Far more important than knowing how to analyze data is an understanding of how to obtain and recognize good data. Regardless of the statistical education they receive, all wildlife biologists should appreciate the importance of controls, replication, and randomization in studies they conduct. Understanding these concepts requires little mathematical sophistication, but is critical to advancing the science of wildlife ecology.

Preservice Elementary Mathematics Teachers' Level of Relating Mathematical Concepts in Daily Life Contexts

ERIC Educational Resources Information Center

Akkus, Oylum

2008-01-01

The purpose of this study was to investigate preservice elementary mathematics teachers' ability of relating mathematical concepts and daily life context. Two research questions were set; what is the preservice elementary mathematics teachers' level of relating mathematical concepts and daily life context regarding to their education year and…

Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

NASA Astrophysics Data System (ADS)

Misu, La; Ketut Budayasa, I.; Lukito, Agung

2018-03-01

This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

Exploring international gender differences in mathematics self-concept

PubMed Central

Goldman, Amy D.; Penner, Andrew M.

2013-01-01

This study provides an international perspective on mathematics by examnnng mathematics self-concept, achievement, and the desire to enter a career involving mathematics among eighth graders in 49 countries. Using data from the Trends in International Mathematics and Science Study, this study shows that self-concept in mathematics is more closely related to the desire to enter a career using mathematics than achievement is. Further, while gender differences in mathematics self-concept are smaller in more egalitarian countries, both girls and boys have lower mathematics self-concepts and less interest in mathematics careers in these countries. These findings reveal a policy paradox: policies aimed at training the next generation of STEM professionals often highlight the need to close the gender gap, but countries with smaller gender gaps have fewer boys and girls interested in mathematics-intensive careers. We conclude by highlighting the importance of disentangling instrumental and expressive aspects of gender inequality in STEM fields. PMID:27840545

Assessing Cognitive Learning of Analytical Problem Solving

NASA Astrophysics Data System (ADS)

Billionniere, Elodie V.

Introductory programming courses, also known as CS1, have a specific set of expected outcomes related to the learning of the most basic and essential computational concepts in computer science (CS). However, two of the most often heard complaints in such courses are that (1) they are divorced from the reality of application and (2) they make the learning of the basic concepts tedious. The concepts introduced in CS1 courses are highly abstract and not easily comprehensible. In general, the difficulty is intrinsic to the field of computing, often described as "too mathematical or too abstract." This dissertation presents a small-scale mixed method study conducted during the fall 2009 semester of CS1 courses at Arizona State University. This study explored and assessed students' comprehension of three core computational concepts---abstraction, arrays of objects, and inheritance---in both algorithm design and problem solving. Through this investigation students' profiles were categorized based on their scores and based on their mistakes categorized into instances of five computational thinking concepts: abstraction, algorithm, scalability, linguistics, and reasoning. It was shown that even though the notion of computational thinking is not explicit in the curriculum, participants possessed and/or developed this skill through the learning and application of the CS1 core concepts. Furthermore, problem-solving experiences had a direct impact on participants' knowledge skills, explanation skills, and confidence. Implications for teaching CS1 and for future research are also considered.

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

PubMed Central

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930

Special Course on Fundamentals of Fighter Aircraft Design

DTIC Science & Technology

1987-10-01

mounted centrally on a cylindrical fuselage of circular cross-section. Here the fuselage interference is shown by a calculation with an exact...M. and Schiff, L.B., "Aerodynamic Mathematical Modeling - Basic Concepts", AGARD-LS-114, 1981, Lecture 1. 30. Malcolm, G.N., "Rotary and Magnus ...thin cylindrical Intake 1.5.3. Real Intake equivalence 1.5.4. Lip thickness and auxiliary intake design 1.6. AIR INTAKE RADAR CROSS SECTION (R.C.S

Order-of-magnitude physics of neutron stars. Estimating their properties from first principles

NASA Astrophysics Data System (ADS)

Reisenegger, Andreas; Zepeda, Felipe S.

2016-03-01

We use basic physics and simple mathematics accessible to advanced undergraduate students to estimate the main properties of neutron stars. We set the stage and introduce relevant concepts by discussing the properties of "everyday" matter on Earth, degenerate Fermi gases, white dwarfs, and scaling relations of stellar properties with polytropic equations of state. Then, we discuss various physical ingredients relevant for neutron stars and how they can be combined in order to obtain a couple of different simple estimates of their maximum mass, beyond which they would collapse, turning into black holes. Finally, we use the basic structural parameters of neutron stars to briefly discuss their rotational and electromagnetic properties.

Universal gestational age effects on cognitive and basic mathematic processing: 2 cohorts in 2 countries.

PubMed

Wolke, Dieter; Strauss, Vicky Yu-Chun; Johnson, Samantha; Gilmore, Camilla; Marlow, Neil; Jaekel, Julia

2015-06-01

To determine whether general cognitive ability, basic mathematic processing, and mathematic attainment are universally affected by gestation at birth, as well as whether mathematic attainment is more strongly associated with cohort-specific factors such as schooling than basic cognitive and mathematical abilities. The Bavarian Longitudinal Study (BLS, 1289 children, 27-41 weeks gestational age [GA]) was used to estimate effects of GA on IQ, basic mathematic processing, and mathematic attainment. These estimations were used to predict IQ, mathematic processing, and mathematic attainment in the EPICure Study (171 children <26 weeks GA). For children born <34 weeks GA, each lower week decreased IQ and mathematic attainment scores by 2.34 (95% CI: -2.99, -1.70) and 2.76 (95% CI: -3.40, -2.11) points, respectively. There were no differences among children born 34-41 weeks GA. Similarly, for children born <36 weeks GA, mathematic processing scores decreased by 1.77 (95% CI: -2.20, -1.34) points with each lower GA week. The prediction function generated using BLS data accurately predicted the effect of GA on IQ and mathematic processing among EPICure children. However, these children had better attainment than predicted by BLS. Prematurity has adverse effects on basic mathematic processing following birth at all gestations <36 weeks and on IQ and mathematic attainment <34 weeks GA. The ability to predict IQ and mathematic processing scores from one cohort to another among children cared for in different eras and countries suggests that universal neurodevelopmental factors may explain the effects of gestation at birth. In contrast, mathematic attainment may be improved by schooling. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Universal Gestational Age Effects on Cognitive and Basic Mathematic Processing: 2 Cohorts in 2 Countries

PubMed Central

Wolke, Dieter; Strauss, Vicky Yu-Chun; Johnson, Samantha; Gilmore, Camilla; Marlow, Neil; Jaekel, Julia

2015-01-01

Objective To determine whether general cognitive ability, basic mathematic processing, and mathematic attainment are universally affected by gestation at birth, as well as whether mathematic attainment is more strongly associated with cohort-specific factors such as schooling than basic cognitive and mathematical abilities. Study design The Bavarian Longitudinal Study (BLS, 1289 children, 27-41 weeks gestational age [GA]) was used to estimate effects of GA on IQ, basic mathematic processing, and mathematic attainment. These estimations were used to predict IQ, mathematic processing, and mathematic attainment in the EPICure Study (171 children <26 weeks GA). Results For children born <34 weeks GA, each lower week decreased IQ and mathematic attainment scores by 2.34 (95% CI: −2.99, −1.70) and 2.76 (95% CI: −3.40, −2.11) points, respectively. There were no differences among children born 34-41 weeks GA. Similarly, for children born <36 weeks GA, mathematic processing scores decreased by 1.77 (95% CI: −2.20, −1.34) points with each lower GA week. The prediction function generated using BLS data accurately predicted the effect of GA on IQ and mathematic processing among EPICure children. However, these children had better attainment than predicted by BLS. Conclusions Prematurity has adverse effects on basic mathematic processing following birth at all gestations <36 weeks and on IQ and mathematic attainment <34 weeks GA. The ability to predict IQ and mathematic processing scores from one cohort to another among children cared for in different eras and countries suggests that universal neurodevelopmental factors may explain the effects of gestation at birth. In contrast, mathematic attainment may be improved by schooling. PMID:25842966

Improving Mastery of Basic Mathematics Facts in Elementary School through Various Learning Strategies.

ERIC Educational Resources Information Center

Haught, Laurie; Kunce, Christine; Pratt, Phyllis; Werneske, Roberta; Zemel, Susan

This report describes the intervention programs used to improve student proficiency in learning, recalling, and retaining basic mathematics facts. The targeted population consisted of first, second, third, and fifth grades in four suburban midwestern schools. The problems of recalling basic mathematics facts is documented through teacher surveys,…

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

ERIC Educational Resources Information Center

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…

Concept mapping learning strategy to enhance students' mathematical connection ability

NASA Astrophysics Data System (ADS)

Hafiz, M.; Kadir, Fatra, Maifalinda

2017-05-01

The concept mapping learning strategy in teaching and learning mathematics has been investigated by numerous researchers. However, there are still less researchers who have scrutinized about the roles of map concept which is connected to the mathematical connection ability. Being well understood on map concept, it may help students to have ability to correlate one concept to other concept in order that the student can solve mathematical problems faced. The objective of this research was to describe the student's mathematical connection ability and to analyze the effect of using concept mapping learning strategy to the students' mathematical connection ability. This research was conducted at senior high school in Jakarta. The method used a quasi-experimental with randomized control group design with the total number was 72 students as the sample. Data obtained through using test in the post-test after giving the treatment. The results of the research are: 1) Students' mathematical connection ability has reached the good enough level category; 2) Students' mathematical connection ability who had taught with concept mapping learning strategy is higher than who had taught with conventional learning strategy. Based on the results above, it can be concluded that concept mapping learning strategycould enhance the students' mathematical connection ability, especially in trigonometry.

Experimentation of cooperative learning model Numbered Heads Together (NHT) type by concept maps and Teams Games Tournament (TGT) by concept maps in terms of students logical mathematics intellegences

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

Relationships of Mathematics Anxiety, Mathematics Self-Efficacy and Mathematics Performance of Adult Basic Education Students

ERIC Educational Resources Information Center

Watts, Beverly Kinsey

2011-01-01

Competent mathematical skills are needed in the workplace as well as in the college setting. Adults in Adult Basic Education classes and programs generally perform below high school level competency, but very few studies have been performed investigating the predictors of mathematical success for adults. The current study contributes to the…

The Solar-Terrestrial Environment

NASA Astrophysics Data System (ADS)

Hargreaves, John Keith

1995-05-01

The book begins with three introductory chapters that provide some basic physics and explain the principles of physical investigation. The principal material contained in the main part of the book covers the neutral and ionized upper atmosphere, the magnetosphere, and structures, dynamics, disturbances, and irregularities. The concluding chapter deals with technological applications. The account is introductory, at a level suitable for readers with a basic background in engineering or physics. The intent is to present basic concepts, and for that reason, the mathematical treatment is not complex. SI units are given throughout, with helpful notes on cgs units where these are likely to be encountered in the research literature. This book is suitable for advanced undergraduate and graduate students who are taking introductory courses on upper atmospheric, ionospheric, or magnetospheric physics. This is a successor to The Upper Atmosphere and Solar-Terrestrial Relations, published in 1979.

Public Conceptions of Algorithms and Representations in the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Nanna, Robert J.

2016-01-01

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

The Prevalent Rate of Problem-Solving Approach in Teaching Mathematics in Ghanaian Basic Schools

ERIC Educational Resources Information Center

Nyala, Joseph; Assuah, Charles; Ayebo, Abraham; Tse, Newel

2016-01-01

Stakeholders of mathematics education decry the rate at which students' performance are falling below expectation; they call for a shift to practical methods of teaching the subject in Ghanaian basic schools. The study explores the extent to which Ghanaian basic school mathematics teachers use problem-solving approach in their lessons. The…

Interpreting Mathematics Scores on the New Jersey College Basic Skills Placement Test.

ERIC Educational Resources Information Center

Dass, Jane; Pine, Charles

The New Jersey College Basic Skills Placement Test (NJCBSPT) is designed to measure certain basic language and mathematics skills of students entering New Jersey colleges. The primary purpose of the two mathematics sections is to determine whether students are prepared to begin certain college-level work without a handicap in computation or…

The Effects of Computer Games on the Achievement of Basic Mathematical Skills

ERIC Educational Resources Information Center

Sayan, Hamiyet

2015-01-01

This study aims to analyze the relationship between playing computer games and learning basic mathematics skills. It shows the role computer games play in the learning and achievement of basic mathematical skills by students. Nowadays it is clear that individuals, especially young persons are very fond of computer and computer games. Since…

Mathematics anxiety affects counting but not subitizing during visual enumeration.

PubMed

Maloney, Erin A; Risko, Evan F; Ansari, Daniel; Fugelsang, Jonathan

2010-02-01

Individuals with mathematics anxiety have been found to differ from their non-anxious peers on measures of higher-level mathematical processes, but not simple arithmetic. The current paper examines differences between mathematics anxious and non-mathematics anxious individuals in more basic numerical processing using a visual enumeration task. This task allows for the assessment of two systems of basic number processing: subitizing and counting. Mathematics anxious individuals, relative to non-mathematics anxious individuals, showed a deficit in the counting but not in the subitizing range. Furthermore, working memory was found to mediate this group difference. These findings demonstrate that the problems associated with mathematics anxiety exist at a level more basic than would be predicted from the extant literature. Copyright 2009 Elsevier B.V. All rights reserved.

Basic numerical competences in large-scale assessment data: Structure and long-term relevance.

PubMed

Hirsch, Stefa; Lambert, Katharina; Coppens, Karien; Moeller, Korbinian

2018-03-01

Basic numerical competences are seen as building blocks for later numerical and mathematical achievement. The current study aimed at investigating the structure of early numeracy reflected by different basic numerical competences in kindergarten and its predictive value for mathematical achievement 6 years later using data from large-scale assessment. This allowed analyses based on considerably large sample sizes (N > 1700). A confirmatory factor analysis indicated that a model differentiating five basic numerical competences at the end of kindergarten fitted the data better than a one-factor model of early numeracy representing a comprehensive number sense. In addition, these basic numerical competences were observed to reliably predict performance in a curricular mathematics test in Grade 6 even after controlling for influences of general cognitive ability. Thus, our results indicated a differentiated view on early numeracy considering basic numerical competences in kindergarten reflected in large-scale assessment data. Consideration of different basic numerical competences allows for evaluating their specific predictive value for later mathematical achievement but also mathematical learning difficulties. Copyright © 2017 Elsevier Inc. All rights reserved.

Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

PubMed

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-09-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Gesture Recognition for Educational Games: Magic Touch Math

NASA Astrophysics Data System (ADS)

Kye, Neo Wen; Mustapha, Aida; Azah Samsudin, Noor

2017-08-01

Children nowadays are having problem learning and understanding basic mathematical operations because they are not interested in studying or learning mathematics. This project proposes an educational game called Magic Touch Math that focuses on basic mathematical operations targeted to children between the age of three to five years old using gesture recognition to interact with the game. Magic Touch Math was developed in accordance to the Game Development Life Cycle (GDLC) methodology. The prototype developed has helped children to learn basic mathematical operations via intuitive gestures. It is hoped that the application is able to get the children motivated and interested in mathematics.

Develop real-time dosimetry concepts and instrumentation for long term missions

NASA Technical Reports Server (NTRS)

Braby, L. A.

1982-01-01

The development of a rugged portable instrument to evaluate dose and dose equivalent is described. A tissue-equivalent proportional counter simulating a 2 micrometer spherical tissue volume was operated satisfactorily for over a year. The basic elements of the electronic system were designed and tested. And finally, the most suitable mathematical technique for evaluating dose equivalent with a portable instrument was selected. Design and fabrication of a portable prototype, based on the previously tested circuits, is underway.

An Analysis of the New 9-Year Basic Education Mathematics Curriculum in Nigeria

ERIC Educational Resources Information Center

Awofala, Adeneye O. A.

2012-01-01

The intention of this paper is to describe and reflect on the changes in the new 9-year basic education mathematics curriculum in Nigeria. The paper is divided into four major themes: history of curriculum development in mathematics education at the basic education level in Nigeria, the motivations for the revision of the primary and junior…

Improving the basic skills of teaching mathematics through learning with search-solve-create-share strategy

NASA Astrophysics Data System (ADS)

Rahayu, D. V.; Kusumah, Y. S.; Darhim

2018-05-01

This study examined to see the improvement of prospective teachers’ basic skills of teaching mathematics through search-solve-create-share learning strategy based on overall and Mathematical Prior Knowledge (MPK) and interaction of both. Quasi experiments with the design of this experimental-non-equivalent control group design involved 67 students at the mathematics program of STKIP Garut. The instrument used in this study included pre-test and post-test. The result of this study showed that: (1) The improvement and achievement of the basic skills of teaching mathematics of the prospective teachers who get the learning of search-solve-create-share strategy is better than the improvement and achievement of the prospective teachers who get the conventional learning as a whole and based on MPK; (2) There is no interaction between the learning used and MPK on improving and achieving basic skills of teaching mathematics.

Time-of-flight mass spectrometry: Introduction to the basics.

PubMed

Boesl, Ulrich

2017-01-01

The intention of this tutorial is to introduce into the basic concepts of time-of-flight mass spectrometry, beginning with the most simple single-stage ion source with linear field-free drift region and continuing with two-stage ion sources combined with field-free drift regions and ion reflectors-the so-called reflectrons. Basic formulas are presented and discussed with the focus on understanding the physical relations of geometric and electric parameters, initial distribution of ionic parameters, ion flight times, and ion flight time incertitude. This tutorial is aimed to help the applicant to identify sources of flight time broadening which limit good mass resolution and sources of ion losses which limit sensitivity; it is aimed to stimulate creativity for new experimental approaches by discussing a choice of instrumental options and to encourage those who toy with the idea to build an own time-of-flight mass spectrometer. Large parts of mathematics are shifted into a separate chapter in order not to overburden the text with too many mathematical deviations. Rather, thumb-rule formulas are supplied for first estimations of geometry and potentials when designing a home-built instrument, planning experiments, or searching for sources of flight time broadening. © 2016 Wiley Periodicals, Inc. Mass Spec Rev 36:86-109, 2017. © 2016 Wiley Periodicals, Inc.

Improvement of Word Problem Solving and Basic Mathematics Competencies in Students with Attention Deficit/Hyperactivity Disorder and Mathematical Learning Difficulties

ERIC Educational Resources Information Center

González-Castro, Paloma; Cueli, Marisol; Areces, Débora; Rodríguez, Celestino; Sideridis, Georgios

2016-01-01

Problem solving represents a salient deficit in students with mathematical learning difficulties (MLD) primarily caused by difficulties with informal and formal mathematical competencies. This study proposes a computerized intervention tool, the integrated dynamic representation (IDR), for enhancing the early learning of basic mathematical…

Computer Activities for College Algebra and Precalculus.

ERIC Educational Resources Information Center

White, Jacci Wozniak; Norwich, Vicki Howard

Mathematics software can be a great aid in understanding difficult mathematics concepts at all levels. This paper presents nine exercises on calculus concepts by using different software used in mathematics education. Each exercise includes instruction on how to use software in order to highlight a specific concept in mathematics. This paper also…

Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

Operational health physics training

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1992-06-01

The initial four sections treat basic information concerning atomic structure and other useful physical quantities, natural radioactivity, the properties of {alpha}, {beta}, {gamma}, x rays and neutrons, and the concepts and units of radiation dosimetry (including SI units). Section 5 deals with biological effects and the risks associated with radiation exposure. Background radiation and man-made sources are discussed next. The basic recommendations of the ICRP concerning dose limitations: justification, optimization (ALARA concepts and applications) and dose limits are covered in Section seven. Section eight is an expanded version of shielding, and the internal dosimetry discussion has been extensively revised tomore » reflect the concepts contained in the MIRD methodology and ICRP 30. The remaining sections discuss the operational health physics approach to monitoring radiation. Individual sections include radiation detection principles, instrument operation and counting statistics, health physics instruments and personnel monitoring devices. The last five sections deal with the nature of, operation principles of, health physics aspects of, and monitoring approaches to air sampling, reactors, nuclear safety, gloveboxes and hot cells, accelerators and x ray sources. Decontamination, waste disposal and transportation of radionuclides are added topics. Several appendices containing constants, symbols, selected mathematical topics, and the Chart of the Nuclides, and an index have been included.« less

Conceptual Foundations of Systems Biology Explaining Complex Cardiac Diseases.

PubMed

Louridas, George E; Lourida, Katerina G

2017-02-21

Systems biology is an important concept that connects molecular biology and genomics with computing science, mathematics and engineering. An endeavor is made in this paper to associate basic conceptual ideas of systems biology with clinical medicine. Complex cardiac diseases are clinical phenotypes generated by integration of genetic, molecular and environmental factors. Basic concepts of systems biology like network construction, modular thinking, biological constraints (downward biological direction) and emergence (upward biological direction) could be applied to clinical medicine. Especially, in the field of cardiology, these concepts can be used to explain complex clinical cardiac phenotypes like chronic heart failure and coronary artery disease. Cardiac diseases are biological complex entities which like other biological phenomena can be explained by a systems biology approach. The above powerful biological tools of systems biology can explain robustness growth and stability during disease process from modulation to phenotype. The purpose of the present review paper is to implement systems biology strategy and incorporate some conceptual issues raised by this approach into the clinical field of complex cardiac diseases. Cardiac disease process and progression can be addressed by the holistic realistic approach of systems biology in order to define in better terms earlier diagnosis and more effective therapy.

Integrating technology education concepts into China's educational system

NASA Astrophysics Data System (ADS)

Yang, Faxian

The problem of this study was to develop a strategy for integrating technology education concepts within the Chinese mathematics and science curricula. The researcher used a case study as the basic methodology. It included three methods for collecting data: literature review, field study in junior and senior secondary schools in America and China, and interviews with experienced educators who were familiar with the status of technology education programs in the selected countries. The data came from the following areas: Japan, Taiwan, the United Kingdom, China, and five states in the United States: Illinois, Iowa, Maryland, Massachusetts, and New York. The researcher summarized each state and country's educational data, identified the advantages and disadvantages of their current technology education program, and identified the major concepts within each program. The process determined that identified concepts would be readily acceptable into the current Chinese educational system. Modernization of, industry, agriculture, science and technology, and defense have been recent objectives of the Chinese government. Therefore, Chinese understanding of technology, or technology education, became important for the country. However, traditional thought and culture curb the implementation of technology education within China's current education system. The proposed solution was to integrate technology education concepts into China's mathematics and science curricula. The purpose of the integration was to put new thoughts and methods into the current educational structure. It was concluded that the proposed model and interventions would allow Chinese educators to carry out the integration into China's education system.

20 CFR 901.12 - Eligibility for enrollment.

Code of Federal Regulations, 2014 CFR

2014-04-01

...) Basic actuarial knowledge. The applicant shall demonstrate knowledge of basic actuarial mathematics and... mathematics and methodology including compound interest, principles of life contingencies, commutation... concentration was actuarial mathematics, or (ii) Which included at least as many semester hours or quarter hours...

20 CFR 901.12 - Eligibility for enrollment.

Code of Federal Regulations, 2012 CFR

2012-04-01

...) Basic actuarial knowledge. The applicant shall demonstrate knowledge of basic actuarial mathematics and... mathematics and methodology including compound interest, principles of life contingencies, commutation... concentration was actuarial mathematics, or (ii) Which included at least as many semester hours or quarter hours...

20 CFR 901.12 - Eligibility for enrollment.

Code of Federal Regulations, 2013 CFR

2013-04-01

...) Basic actuarial knowledge. The applicant shall demonstrate knowledge of basic actuarial mathematics and... mathematics and methodology including compound interest, principles of life contingencies, commutation... concentration was actuarial mathematics, or (ii) Which included at least as many semester hours or quarter hours...

Basic statistics (the fundamental concepts).

PubMed

Lim, Eric

2014-12-01

An appreciation and understanding of statistics is import to all practising clinicians, not simply researchers. This is because mathematics is the fundamental basis to which we base clinical decisions, usually with reference to the benefit in relation to risk. Unless a clinician has a basic understanding of statistics, he or she will never be in a position to question healthcare management decisions that have been handed down from generation to generation, will not be able to conduct research effectively nor evaluate the validity of published evidence (usually making an assumption that most published work is either all good or all bad). This article provides a brief introduction to basic statistical methods and illustrates its use in common clinical scenarios. In addition, pitfalls of incorrect usage have been highlighted. However, it is not meant to be a substitute for formal training or consultation with a qualified and experienced medical statistician prior to starting any research project.

Concept Maps Provide a Window onto Preservice Elementary Teachers' Knowledge in the Teaching and Learning of Mathematics

ERIC Educational Resources Information Center

Chichekian, Tanya; Shore, Bruce M.

2013-01-01

This collaborative concept-mapping exercise was conducted in a second-year mathematics methods course. Teachers' visual representations of their mathematical content and pedagogical knowledge provided insight into their understanding of how students learn mathematics. We collected 28 preservice student teachers' concept maps and analyzed them by…

Game Multimedia in Numeracy Learning for Elementary School Students

NASA Astrophysics Data System (ADS)

Rohendi, D.; Sumarna, N.; Sutarno, H.

2017-03-01

Numeracy is one of the basic skills for elementary students to understand further concepts of mathematics. However teaching numeracy is still using recitation that can overload student’s memory and make them reluctant to learn mathematics, so an innovative way by using multimedia to attract student interest in numeracy is needed. Therefore, the purpose of this study are: 1) to develop numeracy learning multimedia for elementary school students; and 2) to find out whether the implementation of numeracy learning multimedia can improve the students numeracy skills, and how is the response of elementary school students by using multimedia in learning numeracy? The results showed that multimedia can improve students’ numeracy skill which is quit medium and the student response by using multimedia in numeracy learning are good.

Students' Conceptions of a Mathematical Definition

ERIC Educational Resources Information Center

Zaslavsky, Orit; Shir, Karni

2005-01-01

This article deals with 12th-grade students' conceptions of a mathematical definition. Their conceptions of a definition were revealed through individual and group activities in which they were asked to consider a number of possible definitions of four mathematical concepts: two geometric and two analytic. Data consisted of written responses to…

Student understanding of pH: "i don't know what the log actually is, i only know where the button is on my calculator".

PubMed

Watters, Dianne J; Watters, James J

2006-07-01

In foundation biochemistry and biological chemistry courses, a major problem area that has been identified is students' lack of understanding of pH, acids, bases, and buffers and their inability to apply their knowledge in solving acid/base problems. The aim of this study was to explore students' conceptions of pH and their ability to solve problems associated with the behavior of biological acids to understand the source of student difficulties. The responses given by most students are characteristic of an atomistic approach in which they pay no attention to the structure of the problem and concentrate only on juggling the elements together until they get a solution. Many students reported difficulty in understanding what the question was asking and were unable to interpret a simple graph showing the pH activity profile of an enzyme. The most startling finding was the lack of basic understanding of logarithms and the inability of all except one student to perform a simple calculation on logs without a calculator. This deficiency in high school mathematical skills severely hampered their understanding of pH. This study has highlighted a widespread deficiency in basic mathematical skills among first year undergraduates and a fragmented understanding of acids and bases. Implications for the way in which the concepts of pH and buffers are taught are discussed. Copyright © 2006 International Union of Biochemistry and Molecular Biology, Inc.

Construction of the mathematical concept of pseudo thinking students

NASA Astrophysics Data System (ADS)

Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.

2018-05-01

Thinking process is a process that begins with the acceptance of information, information processing and information calling in memory with structural changes that include concepts or knowledges. The concept or knowledge is individually constructed by each individual. While, students construct a mathematical concept, students may experience pseudo thinking. Pseudo thinking is a thinking process that results in an answer to a problem or construction to a concept “that is not true”. Pseudo thinking can be classified into two forms there are true pseudo and false pseudo. The construction of mathematical concepts in students of pseudo thinking should be immediately known because the error will have an impact on the next construction of mathematical concepts and to correct the errors it requires knowledge of the source of the error. Therefore, in this article will be discussed thinking process in constructing of mathematical concepts in students who experience pseudo thinking.

Six to Ten Digits Multiplication Fun Learning Using Puppet Prototype

NASA Astrophysics Data System (ADS)

Islamiah Rosli, D.'oria; Ali, Azita; Peng, Lim Soo; Sujardi, Imam; Usodo, Budi; Adie Perdana, Fengky

2017-01-01

Logic and technical subjects require students to understand basic knowledge in mathematic. For instance, addition, minus, division and multiplication operations need to be mastered by students due to mathematic complexity as the learning mathematic grows higher. Weak foundation in mathematic also contribute to high failure rate in mathematic subjects in schools. In fact, students in primary schools are struggling to learn mathematic because they need to memorize formulas, multiplication or division operations. To date, this study will develop a puppet prototyping for learning mathematic for six to ten digits multiplication. Ten participants involved in the process of developing the prototype in this study. Students involved in the study were those from the intermediate class students whilst teachers were selected based on their vast knowledge and experiences and have more than five years of experience in teaching mathematic. Close participatory analysis will be used in the prototyping process as to fulfil the requirements of the students and teachers whom will use the puppet in learning six to ten digit multiplication in mathematic. Findings showed that, the students had a great time and fun learning experience in learning multiplication and they able to understand the concept of multiplication using puppet. Colour and materials of the puppet also help to attract student attention during learning. Additionally, students able to visualized and able to calculate accurate multiplication value and the puppet help them to recall in multiplying and adding the digits accordingly.

Using "Flatland 2: Sphereland" to Help Teach Motion and Multiple Dimensions

NASA Astrophysics Data System (ADS)

Caplan, Seth; Johnson, Dano; Vondracek, Mark

2015-01-01

The 1884 book Flatland: A Romance of Many Dimensions,1 written by Edwin Abbott, has captured the interest of numerous generations, and has also been used in schools to help students learn and think about the concept of dimension in a creative, fun way. In 2007, a film was released called "Flatland: The Movie,"2 and over one million students have watched it worldwide, primarily in mathematics classes. Since then, a sequel to the "Flatland" movie was released in 2012, entitled "Flatland 2: Sphereland."3 A primary goal of this sequel is to expand the use of the movie beyond mathematics classes and into physics classes because a central premise to "Sphereland" is the notion of warped space. This latest movie provides an engaging and interesting visual way for students to think about both dimension and motion through warped space. In addition, basic motion concepts such as speed and acceleration can be studied by students in introductory physics classes, for instance, by using frame-by-frame analysis of various scenes in the movie.

Undergraduate Students' Perceptions of the Mathematics Courses Included in the Primary School Teacher Education Program

ERIC Educational Resources Information Center

Serin, Mehmet Koray; Incikabi, Semahat

2017-01-01

Mathematics educators have reported on many issues regarding students' mathematical education, particularly students who received mathematics education at different departments such as engineering, science or primary school, including their difficulties with mathematical concepts, their understanding of and preferences for mathematical concepts.…

Analysis of Prospective Mathematics Teachers’ Basic Teaching Skills (a Study of Mathematics Education Departement Students’ Field Experience Program at STKIP Garut)

NASA Astrophysics Data System (ADS)

Rahayu, D. V.

2017-02-01

This study was intended to figure out basic teaching skills of Mathematics Department Students of STKIP Garut at Field Experience Program in academic year 2014/2015. This study was qualitative research with analysis descriptive technique. Instrument used in this study was observation sheet to measure basic teaching mathematics skills. The result showed that ability of content mastery and explaining skill were in average category. Questioning skill, conducting variations skill and conducting assessment skill were in good category. Managing classroom skill and giving motivation skill were in poor category. Based on the result, it can be concluded that the students’ basic teaching skills weren’t optimal. It is recommended for the collegians to get lesson with appropriate strategy so that they can optimize their basic teaching skills.

Improving students’ understanding of mathematical concept using maple

NASA Astrophysics Data System (ADS)

Ningsih, Y. L.; Paradesa, R.

2018-01-01

This study aimed to improve students’ understanding of mathematical concept ability through implementation of using Maple in learning and expository learning. This study used a quasi-experimental research with pretest-posttest control group design. The sample on this study was 61 students in the second semester of Mathematics Education of Universitas PGRI Palembang, South Sumatera in academic year 2016/2017. The sample was divided into two classes, one class as the experiment class who using Maple in learning and the other class as a control class who received expository learning. Data were collective through the test of mathematical initial ability and mathematical concept understanding ability. Data were analyzed by t-test and two ways ANOVA. The results of this study showed (1) the improvement of students’ mathematical concept understanding ability who using Maple in learning is better than those who using expository learning; (2) there is no interaction between learning model and students’ mathematical initial ability toward the improvement of students’ understanding of mathematical concept ability.

The Recruitment of Shifting and Inhibition in On-line Science and Mathematics Tasks.

PubMed

Vosniadou, Stella; Pnevmatikos, Dimitrios; Makris, Nikos; Lepenioti, Despina; Eikospentaki, Kalliopi; Chountala, Anna; Kyrianakis, Giorgos

2018-06-13

Prior research has investigated the recruitment of inhibition in the use of science/mathematics concepts in tasks that require the rejection of a conflicting, nonscientific initial concept. The present research examines if inhibition is the only EF skill recruited in such tasks and investigates whether shifting is also involved. It also investigates whether inhibition and/or shifting are recruited in tasks in which the use of science/mathematics concepts does not require the rejection of an initial concept, or which require only the use of initial concepts. One hundred and thirty-three third- and fifth-grade children participated in two inhibition and shifting tasks and two science and mathematics conceptual understanding and conceptual change (CU&C) tasks. All the tasks were on-line, and performance was measured in accuracy and RTs. The CU&C tasks involved the use of initial concepts and of science/mathematics concepts which required conceptual changes for their initial formation. Only in one of the tasks the use of the science/mathematics concepts required the concurrent rejection of an initial concept. The results confirmed that in this task inhibition was recruited and also showed that the speed of shifting was a significant predictor of performance. Shifting was a significant predictor of performance in all the tasks, regardless of whether they involved science/mathematics or initial concepts. It is argued that shifting is likely to be recruited in complex tasks that require multiple comparisons of stimuli and the entertainment of different perspectives. Inhibition seems to be a more selective cognitive skill likely to be recruited when the use of science/mathematics concepts requires the rejection of a conflicting initial concept. © 2018 Cognitive Science Society, Inc.

Prospective Mathematics Teachers' Ability to Identify Mistakes Related to Angle Concept of Sixth Grade Students

ERIC Educational Resources Information Center

Arslan, Cigdem; Erbay, Hatice Nur; Guner, Pinar

2017-01-01

In the present study we try to highlight prospective mathematics teachers' ability to identify mistakes of sixth grade students related to angle concept. And also we examined prospective mathematics teachers' knowledge of angle concept. Study was carried out with 30 sixth-grade students and 38 prospective mathematics teachers. Sixth grade students…

Mathematics Objectives and Measurement Specifications 1986-1990. Exit Level. Texas Educational Assessment of Minimum Skills (TEAMS).

ERIC Educational Resources Information Center

Texas Education Agency, Austin. Div. of Educational Assessment.

This document lists the objectives for the Texas educational assessment program in mathematics. Eighteen objectives for exit level mathematics are listed, by category: number concepts (4); computation (3); applied computation (5); statistical concepts (3); geometric concepts (2); and algebraic concepts (1). Then general specifications are listed…

Mathematical modeling of infectious disease dynamics

PubMed Central

Siettos, Constantinos I.; Russo, Lucia

2013-01-01

Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814

Programming an interim report on the SETL project. Part I: generalities. Part II: the SETL language and examples of its use

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schwartz, J T

1975-06-01

A summary of work during the past several years on SETL, a new programming language drawing its dictions and basic concepts from the mathematical theory of sets, is presented. The work was started with the idea that a programming language modeled after an appropriate version of the formal language of mathematics might allow a programming style with some of the succinctness of mathematics, and that this might ultimately enable one to express and experiment with more complex algorithms than are now within reach. Part I discusses the general approach followed in the work. Part II focuses directly on the detailsmore » of the SETL language as it is now defined. It describes the facilities of SETL, includes short libraries of miscellaneous and of code optimization algorithms illustrating the use of SETL, and gives a detailed description of the manner in which the set-theoretic primitives provided by SETL are currently implemented. (RWR)« less

A knowledge-based system for controlling automobile traffic

NASA Technical Reports Server (NTRS)

Maravas, Alexander; Stengel, Robert F.

1994-01-01

Transportation network capacity variations arising from accidents, roadway maintenance activity, and special events as well as fluctuations in commuters' travel demands complicate traffic management. Artificial intelligence concepts and expert systems can be useful in framing policies for incident detection, congestion anticipation, and optimal traffic management. This paper examines the applicability of intelligent route guidance and control as decision aids for traffic management. Basic requirements for managing traffic are reviewed, concepts for studying traffic flow are introduced, and mathematical models for modeling traffic flow are examined. Measures for quantifying transportation network performance levels are chosen, and surveillance and control strategies are evaluated. It can be concluded that automated decision support holds great promise for aiding the efficient flow of automobile traffic over limited-access roadways, bridges, and tunnels.

Effects of using multi-vide ruler kit in the acquisition of numeracy skills among PROTIM students

NASA Astrophysics Data System (ADS)

Arumugan, Hemalatha A./P.; Obeng, Sharifah Nasriah Wan; Talib, Corrienna Abdul; Bunyamin, Muhammad Abdul Hadi; Ali, Marlina; Ibrahim, Norhasniza; Zawadzki, Rainer

2017-08-01

One effective way to teach arithmetic more interestingly and make it easier to learn is through the use of instructional materials. These can help students master certain mathematical skills, particularly multiplication and division, often considered difficult amongst primary school pupils. Nevertheless, the insufficiency of appropriate instructional materials causes difficulty in understanding how to use the proper technique or apply the concept, especially in multiplication. With this in mind, this study investigated whether the innovative and creative instructional material designed to assist and enhance numeracy skills, namely the Multi-vide Ruler kit, could increase students' ability in solving multiplication and division questions and whether it affected their interest in solving numeracy problems. Participants in this study included ten PROTIM (Program Tiga M [Three M Program] - membaca [reading], menulis [writing] dan mengira [calculate]) students, 9-10 years old, who had difficulties in reading, writing and arithmetic. In order to get appropriate support for qualitative research, a pre and post-test containing ten basic mathematical operations, was implemented together with the Multi-vide Ruler Kit. The findings of the qualitative case study, with the pre and post-tests, showed significant differences in their achievement and interest in two-digit multiplication and division operations. The results suggest that this approach could improve PROTIM student's ability to solve basic mathematical operations. What was most encouraging was the increase in students' interest in solving numeracy problems.

Exponentiation: A New Basic?

ERIC Educational Resources Information Center

Davis, Brent

2015-01-01

For centuries, the basic operations of school mathematics have been identified as addition, subtraction, multiplication, and division. Notably, these operations are "basic," not because they are foundational to mathematics knowledge, but because they were vital to a newly industrialized and market-driven economy several hundred years…

Role of Visualization in Mathematical Abstraction: The Case of Congruence Concept

ERIC Educational Resources Information Center

Yilmaz, Rezan; Argun, Ziya

2018-01-01

Mathematical abstraction is an important process in mathematical thinking. Also, visualization is a strong tool for searching mathematical problems, giving meaning to mathematical concepts and the relationships between them. In this paper, we aim to investigate the role of visualizations in mathematical abstraction through a case study on five…

Development of Mathematical Skills Developing Game Software.

PubMed

Hajdics, Gyula; Guzsvinecz, Tibor; Szucs, Veronika; Sik Lanyi, Cecilia

2017-01-01

Using basic mathematical operations is not easy for everyone. The AndMaths game for Android devices was developed to help elementary school students to learn these basic mathematical skills in the number ranges of twenties, fifties, hundreds and thousands. The user can freely select the number ranges.

On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling

NASA Astrophysics Data System (ADS)

Falcke, Martin; Moein, Mahsa; TilÅ«naitÄ--, Agne; Thul, Rüdiger; Skupin, Alexander

2018-04-01

The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems and is the basis of the predictive power of theoretical physics. While physicists have confidence in this correspondence, it is less recognized in cellular biophysics. On the one hand, the complex organization of cellular dynamics involving a plethora of interacting molecules and the basic observation of cell variability seem to question its possibility. The practical difficulties of deriving the equations describing cellular behaviour from first principles support these doubts. On the other hand, ignoring such a correspondence would severely limit the possibility of predictive quantitative theory in biophysics. Additionally, the existence of functional modules (like pathways) across cell types suggests also the existence of mathematical structures with comparable universality. Only a few cellular systems have been sufficiently investigated in a variety of cell types to follow up these basic questions. IP3 induced Ca2+signalling is one of them, and the mathematical structure corresponding to it is subject of ongoing discussion. We review the system's general properties observed in a variety of cell types. They are captured by a reaction diffusion system. We discuss the phase space structure of its local dynamics. The spiking regime corresponds to noisy excitability. Models focussing on different aspects can be derived starting from this phase space structure. We discuss how the initial assumptions on the set of stochastic variables and phase space structure shape the predictions of parameter dependencies of the mathematical models resulting from the derivation.

First- and Second-Generation Immigrant Adolescents' Multidimensional Mathematics and Science Self-Concepts and Their Achievement in Mathematics and Science

ERIC Educational Resources Information Center

Areepattamannil, Shaljan

2012-01-01

This study, drawing on data from the Trends in International Mathematics and Science Study 2007, examined the predictive effects of multiple dimensions of mathematics and science self-concept--positive affect toward mathematics and science and self-perceived competence in mathematics and science--on mathematics and science achievement among 1,752…

Mathematics Content Coverage and Student Learning in Kindergarten

PubMed Central

Engel, Mimi; Claessens, Amy; Watts, Tyler; Farkas, George

2017-01-01

Analyzing data from two nationally representative kindergarten cohorts, we examine the mathematics content teachers cover in kindergarten. We expand upon prior research, finding that kindergarten teachers report emphasizing basic mathematics content. Although teachers reported increased coverage of advanced content between the 1998–99 and 2010–11 school years, they continued to place more emphasis on basic content. We find that time on advanced content is positively associated with student learning, whereas time on basic content has a negative association with learning. We argue that increased exposure to more advanced mathematics content could benefit the vast majority of kindergartners. PMID:29353913

Investigating adaptive reasoning and strategic competence: Difference male and female

NASA Astrophysics Data System (ADS)

Syukriani, Andi; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

The series of adaptive reasoning and strategic competencies represent the five components of mathematical proficiency to describe the students' mathematics learning success. Gender contribute to the problem-solving process. This qualitative research approach investigated the adaptive reasoning and strategic competence aspects of a male student and a female student when they solved mathematical problem. They were in the eleventh grade of high school in Makassar. Both also had similar mathematics ability and were in the highest category. The researcher as the main instrument used secondary instrument to obtain the appropriate subject and to investigate the aspects of adaptive reasoning and strategic competence. Test of mathematical ability was used to locate the subjects with similar mathematical ability. The unstructured guideline interview was used to investigate aspects of adaptive reasoning and strategic competence when the subject completed the task of mathematical problem. The task of mathematical problem involves several concepts as the right solution, such as the circle concept, triangle concept, trigonometry concept, and Pythagoras concept. The results showed that male and female subjects differed in applying a strategy to understand, formulate and represent the problem situation. Furthermore, both also differed in explaining the strategy used and the relationship between concepts and problem situations.

Cognitive correlates of performance in advanced mathematics.

PubMed

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-03-01

Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.

Introducing Seismic Tomography with Computational Modeling

NASA Astrophysics Data System (ADS)

Neves, R.; Neves, M. L.; Teodoro, V.

2011-12-01

Learning seismic tomography principles and techniques involves advanced physical and computational knowledge. In depth learning of such computational skills is a difficult cognitive process that requires a strong background in physics, mathematics and computer programming. The corresponding learning environments and pedagogic methodologies should then involve sets of computational modelling activities with computer software systems which allow students the possibility to improve their mathematical or programming knowledge and simultaneously focus on the learning of seismic wave propagation and inverse theory. To reduce the level of cognitive opacity associated with mathematical or programming knowledge, several computer modelling systems have already been developed (Neves & Teodoro, 2010). Among such systems, Modellus is particularly well suited to achieve this goal because it is a domain general environment for explorative and expressive modelling with the following main advantages: 1) an easy and intuitive creation of mathematical models using just standard mathematical notation; 2) the simultaneous exploration of images, tables, graphs and object animations; 3) the attribution of mathematical properties expressed in the models to animated objects; and finally 4) the computation and display of mathematical quantities obtained from the analysis of images and graphs. Here we describe virtual simulations and educational exercises which enable students an easy grasp of the fundamental of seismic tomography. The simulations make the lecture more interactive and allow students the possibility to overcome their lack of advanced mathematical or programming knowledge and focus on the learning of seismological concepts and processes taking advantage of basic scientific computation methods and tools.

Clar theory and resonance energy

NASA Astrophysics Data System (ADS)

Gutman, Ivan; Gojak, Sabina; Furtula, Boris

2005-09-01

A mathematical model, referred here as the Zhang-Zhang polynomial ζ( x), that embraces all the main concepts encountered in the Clar aromatic sextet theory of benzenoid hydrocarbons, was recently put forward by Zhang and Zhang. We now show that ζ( x) is related to resonance energy, and that ln ζ( x) and RE are best correlated when x ≈ 1. This indicates that ζ(1) could be viewed as a (novel) structure-descriptor, playing a role analogous to the Kekulé structure count in Kekulé-structure-based theories. Some basic properties of ζ(1) are established.

Geometry and physics of pseudodifferential operators on manifolds

NASA Astrophysics Data System (ADS)

Esposito, Giampiero; Napolitano, George M.

2016-09-01

A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: existence theorem for the function that generalizes the phase; analogue of Taylor's theorem; torsion and curvature terms in the symbolic calculus; the two kinds of derivative acting on smooth sections of the cotangent bundle of the Riemannian manifold; the concept of symbol as an equivalence class. Physical motivations and applications are then outlined, with emphasis on Green functions of quantum field theory and Parker's evaluation of Hawking radiation.

Connecting coherent structures and strange attractors

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1990-01-01

A concept of turbulence derived from nonlinear dynamical systems theory suggests that turbulent solutions to the Navier-Stokes equations are restricted to strange attractors, and, by implication, that turbulent phenomenology must find some expression or source in the structure of these mathematical objects. Examples and discussions are presented to link coherent structures to some of the commonly known characteristics of strange attractors. Basic to this link is a geometric interpretation of conditional sampling techniques employed to educe coherent structures that offers an explanation for their appearance in measurements as well as their size.

Construction and reconstruction concept in mathematics instruction

NASA Astrophysics Data System (ADS)

Mumu, Jeinne; Charitas Indra Prahmana, Rully; Tanujaya, Benidiktus

2017-12-01

The purpose of this paper is to describe two learning activities undertaken by lecturers, so that students can understand a mathematical concept. The mathematical concept studied in this research is the Vector Space in Linear Algebra instruction. Classroom Action Research used as a research method with pre-service mathematics teacher at University of Papua as the research subject. Student participants are divided into two parallel classes, 24 students in regular class, and remedial class consist of 18 students. Both approaches, construct and reconstruction concept, are implemented on both classes. The result shows that concept construction can only be done in regular class while in remedial class, learning with concept construction approach is not able to increase students' understanding on the concept taught. Understanding the concept of a student in a remedial class can only be carried out using the concept reconstruction approach.

Abstraction in Mathematics and Mathematics Learning

ERIC Educational Resources Information Center

Mitchelmore, Michael; White, Paul

2004-01-01

It is claimed that, since mathematics is essentially a self-contained system, mathematical objects may best be described as "abstract-apart." On the other hand, fundamental mathematical ideas are closely related to the real world and their learning involves empirical concepts. These concepts may be called "abstract-general" because they embody…

Teachers' Conceptions of Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather

2013-01-01

The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

A Network Analysis of Concept Maps of Triangle Concepts

ERIC Educational Resources Information Center

Haiyue, Jin; Khoon Yoong, Wong

2010-01-01

Mathematics educators and mathematics standards of curriculum have emphasised the importance of constructing the interconnectedness among mathematic concepts ("conceptual understanding") instead of only the ability to carry out standard procedures in an isolated fashion. Researchers have attempted to assess the knowledge networks in…

Teaching Mathematics: Challenging the Sacred Cow of Mathematical Certainty.

ERIC Educational Resources Information Center

Borba, Marcelo C.

1992-01-01

Challenges the concept of mathematical certainty and questions whether it is a useful concept for elementary and secondary mathematics curriculum. Encourages teachers to bring this issue into the classroom and ask students to think about it critically. (HB)

Adiabatic invariants in stellar dynamics. 1: Basic concepts

NASA Technical Reports Server (NTRS)

Weinberg, Martin D.

1994-01-01

The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results that precisely define the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause significant evolution stellar dynamical systems even if its time scale is longer than any internal orbital time scale. This additional 'heating' may have serious implications for the evolution of star clusters and dwarf galaxies which are subject to long-term environmental forces. The mathematical developments leading to these results are reviewed, and the conditions for applicability to and further implications for stellar systems are discussed. Companion papers present a computational method for a general time-dependent disturbance and detailed example.

Relationship between mathematical abstraction in learning parallel coordinates concept and performance in learning analytic geometry of pre-service mathematics teachers: an investigation

NASA Astrophysics Data System (ADS)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2018-05-01

As one of the non-conventional mathematics concepts, Parallel Coordinates is potential to be learned by pre-service mathematics teachers in order to give them experiences in constructing richer schemes and doing abstraction process. Unfortunately, the study related to this issue is still limited. This study wants to answer a research question “to what extent the abstraction process of pre-service mathematics teachers in learning concept of Parallel Coordinates could indicate their performance in learning Analytic Geometry”. This is a case study that part of a larger study in examining mathematical abstraction of pre-service mathematics teachers in learning non-conventional mathematics concept. Descriptive statistics method is used in this study to analyze the scores from three different tests: Cartesian Coordinate, Parallel Coordinates, and Analytic Geometry. The participants in this study consist of 45 pre-service mathematics teachers. The result shows that there is a linear association between the score on Cartesian Coordinate and Parallel Coordinates. There also found that the higher levels of the abstraction process in learning Parallel Coordinates are linearly associated with higher student achievement in Analytic Geometry. The result of this study shows that the concept of Parallel Coordinates has a significant role for pre-service mathematics teachers in learning Analytic Geometry.

38 CFR 21.3344 - Special assistance for the educationally disadvantaged.

Code of Federal Regulations, 2014 CFR

2014-07-01

... language skills and mathematics skills may be made by: (i) A VA counseling psychologist or vocational...) (f) Basic skills. Basic English language courses or mathematics courses will be authorized when it is..., speaking, or essential mathematics. (Authority: 38 U.S.C. 3533) [61 FR 26112, May 24, 1996, as amended at...

38 CFR 21.3344 - Special assistance for the educationally disadvantaged.

Code of Federal Regulations, 2011 CFR

2011-07-01

... language skills and mathematics skills may be made by: (i) A VA counseling psychologist or vocational...) (f) Basic skills. Basic English language courses or mathematics courses will be authorized when it is..., speaking, or essential mathematics. (Authority: 38 U.S.C. 3533) [61 FR 26112, May 24, 1996, as amended at...

38 CFR 21.3344 - Special assistance for the educationally disadvantaged.

Code of Federal Regulations, 2012 CFR

2012-07-01

... language skills and mathematics skills may be made by: (i) A VA counseling psychologist or vocational...) (f) Basic skills. Basic English language courses or mathematics courses will be authorized when it is..., speaking, or essential mathematics. (Authority: 38 U.S.C. 3533) [61 FR 26112, May 24, 1996, as amended at...

20 CFR 901.13 - Eligibility for enrollment of individuals applying for enrollment on or after January 1, 1976.

Code of Federal Regulations, 2011 CFR

2011-04-01

... actuarial mathematics and methodology by one of the following: (1) Joint Board basic examination. Successful... basic actuarial mathematics and methodology including compound interest, principles of life... major area of concentration was actuarial mathematics, or (ii) Which included at least as many semester...

38 CFR 21.3344 - Special assistance for the educationally disadvantaged.

Code of Federal Regulations, 2013 CFR

2013-07-01

... language skills and mathematics skills may be made by: (i) A VA counseling psychologist or vocational...) (f) Basic skills. Basic English language courses or mathematics courses will be authorized when it is..., speaking, or essential mathematics. (Authority: 38 U.S.C. 3533) [61 FR 26112, May 24, 1996, as amended at...

Trends in Basic Mathematical Competencies of Beginning Undergraduates in Ireland, 2003-2013

ERIC Educational Resources Information Center

Treacy, Páraic; Faulkner, Fiona

2015-01-01

Deficiencies in beginning undergraduate students' basic mathematical skills has been an issue of concern in higher education, particularly in the past 15 years. This issue has been tracked and analysed in a number of universities in Ireland and internationally through student scores recorded in mathematics diagnostic tests. Students beginning…

Mathematics: A Practical View. Volume I, Teacher Edition. Applied Basic Curriculum Series.

ERIC Educational Resources Information Center

Evaluation, Dissemination and Assessment Center, Dallas.

The activities in this volume of practical mathematics are intended for the intermediate grades. The manual contains three components which can be structured in different combinations according to different student needs. Built around a review of selected objectives in the mathematics basic curriculum, the material is intended to stimulate…

Didactics and History of Mathematics: Knowledge and Self-Knowledge

ERIC Educational Resources Information Center

Fried, Michael N.

2007-01-01

The basic assumption of this paper is that mathematics and history of mathematics are both forms of knowledge and, therefore, represent different ways of knowing. This was also the basic assumption of Fried (2001) who maintained that these ways of knowing imply different conceptual and methodological commitments, which, in turn, lead to a conflict…

1970-71 Basic Mathematics Improvement Component. Final Report.

ERIC Educational Resources Information Center

Rodosky, Robert

The Basic Mathematics Improvement Component, funded under Title I of the 1965 Elementary Secondary Education Act, served nearly 800 pupils in grades four through nine in 20 high priority inner-city schools. The philosophy behind the program was that high achievement in mathematics correlates highly with the high achievement in other areas, and a…

Massachusetts Adult Basic Education Curriculum Framework for Mathematics and Numeracy

ERIC Educational Resources Information Center

Massachusetts Department of Education, 2005

2005-01-01

Over the past number of years, several initiatives have set the stage for writing the Massachusetts ABE (Adult Basic Education) Curriculum Frameworks for Mathematics and Numeracy. This current version of the "Massachusetts ABE Mathematics Curriculum Frameworks" is a second revision of that first framework, but it is heavily influenced by…

Genetics and Mathematics: Evidence from Prader-Willi Syndrome

ERIC Educational Resources Information Center

Semenza, Carlo; Pignatti, Riccardo; Bertella, Laura; Ceriani, Francesca; Mori, Ileana; Molinari, Enrico; Giardino, Daniela; Malvestiti, Francesca; Grugni, Graziano

2008-01-01

Mathematical abilities were tested in people with Prader-Willi syndrome (PWS), using a series of basic mathematical tasks for which normative data are available. The difference between the deletion and the disomy variants of this condition was explored. While a wide phenotypic variation was found, some basic findings emerge clearly. As expected…

38 CFR 21.3344 - Special assistance for the educationally disadvantaged.

Code of Federal Regulations, 2010 CFR

2010-07-01

... language skills and mathematics skills may be made by: (i) A VA counseling psychologist or vocational...) (f) Basic skills. Basic English language courses or mathematics courses will be authorized when it is..., speaking, or essential mathematics. (Authority: 38 U.S.C. 3533) [61 FR 26112, May 24, 1996, as amended at...

Teaching a High-Level Contextualized Mathematics Curriculum to Adult Basic Learners

ERIC Educational Resources Information Center

Showalter, Daniel A.; Wollett, Chelsie; Reynolds, Sharon

2014-01-01

This paper reports on the implementation of a high level contextualized mathematics curriculum by 12 adult basic instructors in a midwestern state. The 10-week pilot curriculum embedded high level mathematics in contexts that were familiar to adult learners. Instructors' weekly online posts were coded, and the following themes emerged: (a)…

Mathematics Teacher Candidates' Metaphors about the Concept of "Mathematics"

ERIC Educational Resources Information Center

Erdogan, Ahmet; Yazlik, Derya Ozlem; Erdik, Cengiz

2014-01-01

The main purpose of this study was to research mathematics teacher candidates' perceptions about the concept of "mathematics" through the use of metaphors. The research is conducted during 2012-2013 academic year, on a group of 111 mathematics teacher candidates at the Education Faculty of a University in Turkey. To collect the research…

ICT and Constructivist Strategies Instruction for Science and Mathematics Education

ERIC Educational Resources Information Center

Kong, Ng Wai; Lai, Kong Sow

2005-01-01

Concept learning in science and mathematics had often times been taught based on assumptions of alternative concepts or even in some instances based on misconceptions. Some educational researchers favour a constructivist approach in teaching science and mathematics. The constructivist literature existing makes use of alternative conceptions as…

Pupils' View of Mathematics: Initial Report for an International Comparison Project. Research Report 152.

ERIC Educational Resources Information Center

Pehkonen, Erkki

This report describes the theoretical background of an international comparison project on pupils' mathematical beliefs and outlines its realization. The first chapter briefly discusses problems with the underlying concepts of "belief" and "conception." The central concept, view of mathematics, is introduced in the second…

Preservice Mathematics Teachers' Conceptions of and Approaches to Learning: A Phenomenographic Study

ERIC Educational Resources Information Center

Erdogan, Ahmet

2012-01-01

Knowing the preservice mathematics teachers' conceptions of learning is one of the key factors of taking significant educational measures regarding the future. The purpose of this study was to investigate preservice mathematics teachers' conceptions of and approaches to learning. The phenomenographic qualitative research method was used to…

Circles, Materiality and Movement

ERIC Educational Resources Information Center

Chorney, Sean

2017-01-01

This paper approaches the concept of the circle through the framework of mathematics-as-becoming. This paper focuses specifically on how a concept can be thought of as a process, and on the implications that this might have for mathematics learning. Contrary to long-standing assumptions about mathematical concepts as ideal, inert, Platonic forms,…

Preservice Mathematics Teachers' Experiences about Function and Equation Concepts

ERIC Educational Resources Information Center

Dede, Yuksel; Soybas, Danyal

2011-01-01

The purpose of this study is to determine the experience of mathematics preservice teachers related to function and equation concepts and the relations between them. Determining preservice mathematics teachers' understanding of function and equation concepts has great importance since it directly affects their future teaching careers. Data were…

On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2016-03-01

Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.

Rotation covariant image processing for biomedical applications.

PubMed

Skibbe, Henrik; Reisert, Marco

2013-01-01

With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences.

University students' perspectives on diagnostic testing in mathematics

NASA Astrophysics Data System (ADS)

fhloinn, Eabhnat Ní; Macan Bhaird, Ciarán; Nolan, Brien

2014-01-01

Many universities issue mathematical diagnostic tests to incoming first-year students, covering a range of the basic concepts with which they should be comfortable from secondary school. As far as many lecturers are concerned, the purpose of this test is to determine the students' mathematical knowledge on entry. It should also provide an early indication of which students are likely to need additional help, and hopefully encourage such students to avail of extra support mechanisms at an early stage. However, it is not clear that students recognize these intentions and there is a fear that students who score poorly in the test will have their confidence further damaged in relation to mathematics and will be reluctant to seek help. To this end, a questionnaire was developed to explore students' perspectives on diagnostic testing. Analysis of responses received to the questionnaire provided an interesting insight into students' perspectives including the optimum time to conduct such a test, their views on the aims of diagnostic testing, whether they feel that testing is a good idea, and their attitudes to the support systems put in place to help those who scored poorly in the test.

On the learning difficulty of visual and auditory modal concepts: Evidence for a single processing system.

PubMed

Vigo, Ronaldo; Doan, Karina-Mikayla C; Doan, Charles A; Pinegar, Shannon

2018-02-01

The logic operators (e.g., "and," "or," "if, then") play a fundamental role in concept formation, syntactic construction, semantic expression, and deductive reasoning. In spite of this very general and basic role, there are relatively few studies in the literature that focus on their conceptual nature. In the current investigation, we examine, for the first time, the learning difficulty experienced by observers in classifying members belonging to these primitive "modal concepts" instantiated with sets of acoustic and visual stimuli. We report results from two categorization experiments that suggest the acquisition of acoustic and visual modal concepts is achieved by the same general cognitive mechanism. Additionally, we attempt to account for these results with two models of concept learning difficulty: the generalized invariance structure theory model (Vigo in Cognition 129(1):138-162, 2013, Mathematical principles of human conceptual behavior, Routledge, New York, 2014) and the generalized context model (Nosofsky in J Exp Psychol Learn Mem Cogn 10(1):104-114, 1984, J Exp Psychol 115(1):39-57, 1986).

Contemplating Symbolic Literacy of First Year Mathematics Students

ERIC Educational Resources Information Center

Bardini, Caroline; Pierce, Robyn; Vincent, Jill

2015-01-01

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

The Mathematics--Children's-Literature Connection.

ERIC Educational Resources Information Center

Gailey, Stavroula K.

1993-01-01

Describes three types of children's books for use in developing mathematical concepts. Discusses the characteristics of a good mathematical concept book, methods of incorporating reading into the mathematics class, and three examples of children's books. Includes a bibliography of 159 children's trade books selected for integration into…

Mathematics, Music, and Movement: Exploring Concepts and Connections.

ERIC Educational Resources Information Center

Shilling, Wynne A.

2002-01-01

Explores connections between mathematics, music, and movement in early childhood curriculum. Presents music activities in which mathematical concepts are embedded; focuses on activities providing experiences with time-based relationships and rhythmic patterns. Asserts that integrating movement and mathematics into music activities provides a way…

The big-fish-little-pond effect on mathematics self-concept: Evidence from the United Arab Emirates.

PubMed

Areepattamannil, Shaljan; Khine, Myint Swe; Al Nuaimi, Samira

2017-08-01

This study examined the big-fish-little-pond effect (BFLPE; Marsh, 1987) on mathematics self-concept of 7404 adolescents (female = 3767 [51%], male = 3637 [49%]; M age  = 15.85 years, SD = 0.28) from 456 schools in the United Arab Emirates, one of the Arab states of the Persian Gulf. The results of multilevel regression analyses indicated good support for the BFLPE's theoretical predictions: the effect of individual student mathematics achievement on individual student mathematics self-concept was positive and statistically significant, whereas the effect of school-average mathematics achievement on individual student mathematics self-concept was negative and statistically significant. Moreover, the interaction between school-average mathematics achievement and individual student mathematics achievement was small and non-significant. Implications of the findings for policy and practice are briefly discussed. Copyright © 2017 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

New Materialist Ontologies in Mathematics Education: The Body in/of Mathematics

ERIC Educational Resources Information Center

de Freitas, Elizabeth; Sinclair, Nathalie

2013-01-01

In this paper we study the mathematical body as an assemblage of human and non-human mathematical concepts. We argue that learners' bodies are always in the process of becoming assemblages of diverse and dynamic materialities. Following the work of the historian of science Karen Barad, we argue that mathematical concepts must be considered dynamic…

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Teaching the Mathematics of Radioactive Dating.

ERIC Educational Resources Information Center

Shea, James H.

2001-01-01

Describes a method used to teach the concept of radiometric dating using mathematical equations. Explores the lack of information in textbooks on how to solve radiometric dating problems using mathematical concepts. (SAH)

Shortage of Mathematics Teachers in Thai Basic Education Level

ERIC Educational Resources Information Center

Puncreobutr, Vichian; Rattanatumma, Tawachai

2016-01-01

The objective of this study was to identify the reasons for shortage of Mathematics teachers at Thai Basic Education level. This research is both quantitative and qualitative in nature. For the purpose of study, survey was conducted with senior high school students, in order to find out their willingness to pursue mathematics in Bachelor of…

A Hybrid Model of Mathematics Support for Science Students Emphasizing Basic Skills and Discipline Relevance

ERIC Educational Resources Information Center

Jackson, Deborah C.; Johnson, Elizabeth D.

2013-01-01

The problem of students entering university lacking basic mathematical skills is a critical issue in the Australian higher-education sector and relevant globally. The Maths Skills programme at La Trobe University has been developed to address under preparation in the first-year science cohort in the absence of an institutional mathematics support…

Effects of Digital-Based Math Fluency Interventions on Learners with Math Difficulties: A Review of the Literature

ERIC Educational Resources Information Center

Cozad, Lauren E.; Riccomini, Paul J.

2016-01-01

Mathematical proficiency serves as a foundation for student success in the classroom and real world. One component of mathematical proficiency is fluency with basic facts. Frequently, students with mathematics difficulties struggle to become proficient and fluent in the four basic operations. Interventions are available to help develop and promote…

A Mediation Model to Explain the Role of Mathematics Skills and Probabilistic Reasoning on Statistics Achievement

ERIC Educational Resources Information Center

Primi, Caterina; Donati, Maria Anna; Chiesi, Francesca

2016-01-01

Among the wide range of factors related to the acquisition of statistical knowledge, competence in basic mathematics, including basic probability, has received much attention. In this study, a mediation model was estimated to derive the total, direct, and indirect effects of mathematical competence on statistics achievement taking into account…

Investigation of Primary Mathematics Student Teachers' Concept Images: Cylinder and Cone

ERIC Educational Resources Information Center

Ertekin, Erhan; Yazici, Ersen; Delice, Ali

2014-01-01

The aim of the present study is to determine the influence of concept definitions of cylinder and cone on primary mathematics student teachers' construction of relevant concept images. The study had a relational survey design and the participants were 238 primary mathematics student teachers. Statistical analyses implied the following: mathematics…

Students' Mathematical Work on Absolute Value: Focusing on Conceptions, Errors and Obstacles

ERIC Educational Resources Information Center

Elia, Iliada; Özel, Serkan; Gagatsis, Athanasios; Panaoura, Areti; Özel, Zeynep Ebrar Yetkiner

2016-01-01

This study investigates students' conceptions of absolute value (AV), their performance in various items on AV, their errors in these items and the relationships between students' conceptions and their performance and errors. The Mathematical Working Space (MWS) is used as a framework for studying students' mathematical work on AV and the…

Analysis of Undergraduate Students’ Mathematical Understanding Ability of the Limit of Function Based on APOS Theory Perspective

NASA Astrophysics Data System (ADS)

Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

2017-09-01

The aim of this study was to know the level of undergraduate students’ mathematical understanding ability based on APOS theory perspective. The APOS theory provides an evaluation framework to describe the level of students’ understanding and mental structure about their conception to a mathematics concept. The levels of understanding in APOS theory are action, process, object, and schema conception. The subjects were 59 students of mathematics education whom had attended a class of the limit of function at a university in Palembang. The method was qualitative descriptive with 4 test items. The result showed that most of students were still at the level of action conception. They could calculate and use procedure precisely to the mathematics objects that was given, but could not reach the higher conception yet.

Enhancing Students' Understanding of Algebra Concepts through Cooperative Computer Instruction

ERIC Educational Resources Information Center

Gambari, Amos Isiaka; Shittu, Ahmed Tajudeen; Taiwo, Oladipupo Abimbola

2016-01-01

Values are the personal convictions which one finds important. Three different aspects which are associated with mathematics education differently are identified, namely, values through mathematics education, values of mathematics education, and values for mathematics. These are paired with Bishop's (1996) conceptions of general educational,…

Undergraduate Students' Conceptions of Mathematics: An International Study

ERIC Educational Resources Information Center

Petocz, Peter; Reid, Anna; Wood, Leigh N.; Smith, Geoff H.; Mather, Glyn; Harding, Ansie; Engelbrecht, Johann; Houston, Ken; Hillel, Joel; Perrett, Gillian

2007-01-01

In this paper, we report on an international study of undergraduate mathematics students; conceptions of mathematics. Almost 1,200 students in five countries completed a short survey including three open-ended questions asking about their views of mathematics and its role in their future studies and planned professions. Responses were analysed…

The Teaching of Mathematics in Secondary Schools as a Tool for Self-Reliance and Re-Branding Process in Nigeria

ERIC Educational Resources Information Center

Jonah, Tali D.; Caleb, Mbwas .L.; Stephen, Abe A.

2012-01-01

Mathematics teaching is an interaction between the teacher and the learners that leads to acquisition of desirable mathematical knowledge, ideas and skills necessary for applicability in our everyday life. This paper therefore looks at the concept of self-reliance, the concept of mathematics teaching, problems and prospects of mathematics teaching…

Teaching and assessment of mathematical principles for software correctness using a reasoning concept inventory

NASA Astrophysics Data System (ADS)

Drachova-Strang, Svetlana V.

As computing becomes ubiquitous, software correctness has a fundamental role in ensuring the safety and security of the systems we build. To design and develop software correctly according to their formal contracts, CS students, the future software practitioners, need to learn a critical set of skills that are necessary and sufficient for reasoning about software correctness. This dissertation presents a systematic approach to both introducing these reasoning skills into the curriculum, and assessing how well the students have learned them. Specifically, it introduces a comprehensive Reasoning Concept Inventory (RCI) that captures the fine details of basic reasoning skills that are ideally learned across the undergraduate curriculum to reason about software correctness, to develop high quality software, and to understand why software works as specified. The RCI forms the basis for developing learning outcomes that help educators to assess the adequacy of current techniques and pinpoint necessary improvements. This dissertation contains results from experimentation and assessment over the past few years in multiple CS courses. The results show that the finer principles of mathematical reasoning of software correctness can be taught effectively and continuously improved with the help of the RCI using suitable teaching practices, and supporting methods and tools.

How Far a Star. A Supplement in Space Oriented Concepts for Science and Mathematics Curricula for Intermediate Grades.

ERIC Educational Resources Information Center

Maben, Jerrold William

Space science-oriented concepts and suggested activities are presented for intermediate grade teachers of science and mathematics in a book designed to help bring applications of space-oriented mathematics into the classroom. Concepts and activities are considered in these areas: methods of keeping time (historically); measurement as related to…

Engineering Students' Conceptions of the Derivative and Some Implications for Their Mathematical Education

ERIC Educational Resources Information Center

Bingolbali, E.; Monaghan, J.; Roper, T.

2007-01-01

This paper explores Mechanical Engineering students' conceptions of and preferences for conceptions of the derivative, and their views on mathematics. Data comes from pre-, post- and delayed post-tests, a preference test, interviews with students and an analysis of calculus courses. Data from Mathematics students is used to make comparisons with…

Can Interactive Visualization Tools Engage and Support Pre-University Students in Exploring Non-Trivial Mathematical Concepts?

ERIC Educational Resources Information Center

Liang, Hai-Ning; Sedig, Kamran

2010-01-01

Many students find it difficult to engage with mathematical concepts. As a relatively new class of learning tools, visualization tools may be able to promote higher levels of engagement with mathematical concepts. Often, development of new tools may outpace empirical evaluations of the effectiveness of these tools, especially in educational…

Understanding of Prospective Mathematics Teachers of the Concept of Diagonal

ERIC Educational Resources Information Center

Ayvaz, Ülkü; Gündüz, Nazan; Bozkus, Figen

2017-01-01

This study aims to investigate the concept images of prospective mathematics teachers about the concept of diagonal. With this aim, case study method was used in the study. The participants of the study were consisted of 7 prospective teachers educating at the Department of Mathematics Education. Criterion sampling method was used to select the…

Using the Tower of Hanoi Puzzle to Infuse Your Mathematics Classroom with Computer Science Concepts

ERIC Educational Resources Information Center

Marzocchi, Alison S.

2016-01-01

This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…

Incorporating Learning Motivation and Self-Concept in Mathematical Communicative Ability

ERIC Educational Resources Information Center

Rajagukguk, Waminton

2016-01-01

This research is trying to determine of the mathematical concepts, instead by integrating the learning motivation (X[subscript 1]) and self-concept (X[subscript 2]) can contribute to the mathematical communicative ability (Y). The test instruments showed the following results: (1) simple regressive equation Y on X[subscript 1] was Y = 32.891 +…

Universal Basic Education and the Provision of Quality Mathematics in Southern Africa

ERIC Educational Resources Information Center

Kazima, Mercy

2014-01-01

In this paper, I discuss Universal Basic Education (UBE) in relation to the teaching and learning of mathematics in Southern Africa. I present the status of UBE for all countries in the region and then use 3 selected examples: Botswana, Malawi, and Zambia, to illustrate the provision of mathematics in the general framework of UBE in the countries.…

Making Basic Math Skills Work for You in Marketing. Student Manual and Laboratory Guide.

ERIC Educational Resources Information Center

Klewer, Edwin D.

This student manual and workbook is the second part of a mathematics series for use with high school students. The manual is to be used to apply the mathematics skills that students have learned in a first part called "Developing Basic Math Skills for Marketing." The manual presents conceptual instruction in mathematics in a competency based…

Two Dilemmas in Communicating Mathematics in Adult Basic Courses: "How To Support Pre-Knowledge of Adult Learners" and "How To Support Democratic Classroom Decisions."

ERIC Educational Resources Information Center

Lindenskov, Lena; Hansen, Eigil Peter

This study explores how adults' perspectives, intentions, blockages, resistance, and fascinations are reconstructed during a mathematics course in adult basic education. These aspects are discussed as important building blocks for developing theory in adult educational research. Adult mathematics education was compared in different institutional…

Categorizing and Promoting Reversibility of Mathematical Concepts

ERIC Educational Resources Information Center

Simon, Martin A.; Kara, Melike; Placa, Nicora; Sandir, Hakan

2016-01-01

Reversibility of concepts, a key aspect of mathematical development, is often problematic for learners. In this theoretical paper, we present a typology we have developed for categorizing the different reverse concepts that can be related to a particular initial concept and explicate the relationship among these different reverse concepts. We…

Prospective elementary teachers' conceptions of multidigit number: exemplifying a replication framework for mathematics education

NASA Astrophysics Data System (ADS)

Jacobson, Erik; Simpson, Amber

2018-04-01

Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser's (Educational Studies in Mathematics 75:241-251, 2010) study of prospective elementary teachers' conceptions of multidigit number and examined the main claim that most elementary pre-service teachers think about digits incorrectly at least some of the time. Results indicated no statistically significant difference in the distribution of conceptions between the original and replication samples and, moreover, no statistically significant differences in the distribution of sub-conceptions among prospective teachers with the most common conception. These results suggest confidence is warranted both in the generality of the main claim and in the utility of the conceptions framework for describing prospective elementary teachers' conceptions of multidigit number. The report further contributes a framework for replication of mathematics education research adapted from the field of psychology.

Substantiation of basic scheme of grain cleaning machine for preparation of agricultural crops seeds

NASA Astrophysics Data System (ADS)

Giyevskiy, A. M.; Orobinsky, V. I.; Tarasenko, A. P.; Chernyshov, A. V.; Kurilov, D. O.

2018-03-01

The article presents data on the feasibility of the concept of a high-efficiency seed cleaner with the consistent use of the air flow in aspiration and the multi-tier placement of the sorting grids in grating mills. As a result of modeling, the directions for further improvement of air-screen seed cleaning machines have been identified: an increase in the proportion of sorting grids in the mills up to 70 ... 80% and an increase in the speed of the air flow in the channel of the pre-filter cleaning up to 8.0 m / s. Experiments have established the competence of using mathematical modeling of airflow in the pneumatic system with the use of a finite-volume method for solving hydrodynamic equations for substantiating the basic parameters of the pneumatic system.

Scientific cousins: the relationship between Charles Darwin and Francis Galton.

PubMed

Fancher, Raymond E

2009-01-01

This article traces the personal as well as the intellectual and scientific relationship between Charles Darwin and his younger half-cousin Francis Galton. Although they had been on friendly terms as young men, and Darwin had in some ways been a role model for Galton, the two did not share major scientific interests until after the publication of Darwin's On the Origin of Species in 1859. That work precipitated a religious and philosophical crisis in Galton, which he gradually resolved after conceiving and developing the basic ideas of "hereditary genius" and eugenics. More mathematically inclined than Darwin, he subsequently contributed to the Darwinian evolutionary discussion, and to the future science of psychology, by proposing the basic concept of the nature-nurture dichotomy, the conceptual and statistical foundations for behavior genetics, and the idea for intelligence testing. 2009 APA, all rights reserved

Mathematics Teachers' Response to the Reform Agenda: Results of the 1993 National Survey of Science and Mathematics Education.

ERIC Educational Resources Information Center

Weiss, Iris R.

The NCTM Standards call for the introduction of challenging mathematics content for all students beginning in the early grades. If teachers are to guide students in their exploration of mathematics concepts, they must themselves have a firm grasp of powerful mathematics concepts. This paper uses data from the 1993 National Survey of Science and…

Aeronautics. An Educator's Guide with Activities in Science, Mathematics, and Technology Education: What Pilot, Astronaut, or Aeronautical Engineer didn't Start out with a Toy Glider?

NASA Technical Reports Server (NTRS)

Biggs, Pat (Editor); Huetter, Ted (Editor)

1998-01-01

Welcome to the exciting world of aeronautics. The term aeronautics originated in France, and was derived from the Greek words for "air" and "to sail." It is the study of flight and the operation of aircraft. This educator guide explains basic aeronautical concepts, provides a background in the history of aviation, and sets them within the context of the flight environment (atmosphere, airports, and navigation). The activities in this guide are designed to be uncomplicated and fun. They have been developed by NASA Aerospace Education Services Program specialists, who have successfully used them in countless workshops and student programs around the United States. The activities encourage students to explore the nature of flight, and experience some real-life applications of mathematics, science, and technology. The subject of flight has a wonderful power to inspire learning.

How Syntactic Reasoners Can Develop Understanding, Evaluate Conjectures, and Generate Counterexamples in Advanced Mathematics

ERIC Educational Resources Information Center

Weber, Keith

2009-01-01

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…

Questions To Ask and Issues To Consider While Supervising Elementary Mathematics Student Teachers.

ERIC Educational Resources Information Center

Philip, Randolph A.

2000-01-01

Presents four questions to consider when supervising elementary mathematics teachers, who come with many preconceptions about teaching and learning mathematics: What mathematical concepts, procedures, or algorithms are you teaching? Are the concepts and procedures part of a unit? What types of questions do you pose? and What understanding of…

Mathematics Teacher-Candidates' Performance in Solving Problems with Different Representation Styles: The Trigonometry Example

ERIC Educational Resources Information Center

Dündar, Sefa

2015-01-01

Using multiple representations of a problem can reveal the relationship between complex concepts by expressing the same mathematical condition differently and can contribute to the meaningful learning of mathematical concepts. The purpose of this study is to assess the performances of mathematics teacher-candidates on trigonometry problems…

Semiotic-conceptual analysis: a proposal

NASA Astrophysics Data System (ADS)

Priss, Uta

2017-07-01

This paper provides the basic definitions of Semiotic-conceptual analysis (SCA), which is a mathematical modelling of signs as elements of a triadic relation. FCA concept lattices are constructed for each of the three sign components. It is demonstrated how core linguistic and semiotic notions (such as synonymy and icon) can be represented with SCA. While the usefulness of SCA has already been demonstrated in a number of applications and several propositions are proven in this paper, there are still many open questions as to what to do next with SCA. Therefore, this paper is meant as a proposal and encouragement for further development.

Influence of Self-Concept, Study Habit and Gender on Attitude and Achievement of Secondary School Students in Mathematics

ERIC Educational Resources Information Center

Kamoru, Usman; Ramon, Olosunde Gbolagade

2017-01-01

This study examined the relationship between self-concept, attitude of the students towards mathematics, and math achievement. Also, this study investigated the influence of study habits on achievement; study habits on attitude of students to mathematics. The influence of gender and self-concept and study habit group on achievement and attitude…

A Teacher's Conception of Definition and Use of Examples When Doing and Teaching Mathematics

ERIC Educational Resources Information Center

Johnson, Heather Lynn; Blume, Glendon W.; Shimizu, Jeanne K.; Graysay, Duane; Konnova, Svetlana

2014-01-01

To contribute to an understanding of the nature of teachers' mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher's conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical…

Using a Technology-Supported Approach to Preservice Teachers' Multirepresentational Fluency: Unifying Mathematical Concepts and Their Representations

ERIC Educational Resources Information Center

McGee, Daniel; Moore-Russo, Deborah

2015-01-01

A test project at the University of Puerto Rico in Mayagüez used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers. For this study, this fluency was defined as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to…

Evaluating High School Students' Conceptions of the Relationship between Mathematics and Physics: Development of a Questionnaire

ERIC Educational Resources Information Center

Kapucu, S.; Öçal, M. F.; Simsek, M.

2016-01-01

The purposes of this study were (1) to develop a questionnaire measuring high school students' conceptions of the relationship between mathematics and physics, (2) and to determine the students' conceptions of the relationship between mathematics and physics. A total of 718 high school students (343 male, 375 female) participated in this study.…

Identification and Assessment of Taiwanese Children's Conceptions of Learning Mathematics

ERIC Educational Resources Information Center

Chiu, Mei-Shiu

2012-01-01

The aim of the present study was to identify children's conceptions of learning mathematics and to assess the identified conceptions. Children's conceptions are identified by interviewing 73 grade 5 students in Taiwan. The interviews are analyzed using qualitative data analysis methods, which results in a structure of 5 major conceptions, each…

Motivational, Parental, and Cultural Influences on Achievement and Persistence in Basic Skills Mathematics at the Community College

ERIC Educational Resources Information Center

Nordstrom, Donna E.

2012-01-01

The purpose of this study was to address the gap in the current literature on community college students in basic math courses by examining motivational, parental and cultural factors as predictors of achievement and persistence of students enrolled in basic skills mathematics courses at a community college. More specifically, this study…

Matematicas en la vida actual. Volumen II, edicion para el maestro. (Mathematics: A Practical View. Volume II, Teacher Edition). Applied Basic Curriculum Series.

ERIC Educational Resources Information Center

Evaluation, Dissemination and Assessment Center, Dallas.

This Spanish language teacher's edition of a practical mathematics text for the intermediate grades contains three components which can be structured in different combinations according to different student needs. Built around a review of selected objectives in the mathematics basic curriculum, the material is intended to stimulate interest in…

Matematicas en la vida actual. Volumen I, edicion para el maestro. (Mathematics: A Practical View. Volume I, Teacher Edition). Applied Basic Curriculum Series.

ERIC Educational Resources Information Center

Evaluation, Dissemination and Assessment Center, Dallas.

This Spanish language teacher's edition of a practical mathematics text for the intermediate grades contains three components which can be structured in different combinations according to different student needs. Built around a review of selected objectives in the mathematics basic curriculum, the material is intended to stimulate interest in…

Matematicas en la vida actual. Volumen III, edicion para el maestro. (Mathematics: A Practical View. Volume III, Teacher Edition). Applied Basic Curriculum Series.

ERIC Educational Resources Information Center

Evaluation, Dissemination and Assessment Center, Dallas.

This Spanish language teacher's edition of a practical mathematics text for the intermediate grades contains three components which can be structured in different combinations according to different student needs. Built around a review of selected objectives in the mathematics basic curriculum, the material is intended to stimulate interest in…

A trend study of self-concept and mathematics achievement in a cross-cultural context

NASA Astrophysics Data System (ADS)

Wang, Jianjun

2007-12-01

The TIMSS 1995, 1999, and 2003 data have been gathered from Hong Kong before and after its sovereignty switch from the United Kingdom to China in 1997. Built on a reciprocal relation theory from the research literature, this investigation is designed to examine models of student self-concept and mathematics achievement during the political transition. Along with a perceived `brain drain' from the population migration, there was a non-monotonic change in the reciprocal relationship between self-concept and mathematics achievement. In addition, indicators of mathematics achievement and self-concept have demonstrated different linkages to the permanent emigration of Hong Kong residents with valued or desirable skills and qualifications. Interpretation of these empirical findings entails a need of enhancing cross-cultural understanding in mathematics education.

Conceptions for Relating the Evolution of Mathematical Concepts to Mathematics Learning--Epistemology, History, and Semiotics Interacting: To the Memory of Carl Menger (1902-1985)

ERIC Educational Resources Information Center

Schubring, Gert

2011-01-01

There is an over-arching consensus that the use of the history of mathematics should decidedly improve the quality of mathematics teaching. Mathematicians and mathematics educators show here a rare unanimity. One deplores, however, and in a likewise general manner, the scarcity of positive examples of such a use. This paper analyses whether there…

Mathematical Representation by Students in Building Relational Understanding on Concepts of Area and Perimeter of Rectangle

ERIC Educational Resources Information Center

Anwar, Rahmad Bustanul; Yuwono, Ipung; As'ari, Abdur Rahman; Sisworo; Dwi, Rahmawati

2016-01-01

Representation is an important aspect of learners in building a relational understanding of mathematical concepts. But the ability of a mathematical representation of students in building relational understanding is still very limited. The purpose of this research is to description of mathematical representation of students who appear in building…

The Vector Space as a Unifying Concept in School Mathematics.

ERIC Educational Resources Information Center

Riggle, Timothy Andrew

The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…

Textbook and Course Materials for 21-127 "Concepts of Mathematics"

ERIC Educational Resources Information Center

Sullivan, Brendan W.

2013-01-01

Concepts of Mathematics (21-127 at CMU) is a course designed to introduce students to the world of abstract mathematics, guiding them from more calculation-based math (that one learns in high school) to higher mathematics, which focuses more on abstract thinking, problem solving, and writing "proofs." This transition tends to be a shock:…

Il Concetto di Infinito nell'Intuizione Matematica (Concept of Infinity in Mathematical Intuition).

ERIC Educational Resources Information Center

Ferrari, E.; And Others

1995-01-01

Investigated the acquisition and maturation of the infinity concept in mathematics of students ages 13-15. Found the infinity concept is learned by students only when provided with appropriate guidance. (Author/MKR)

The NIE Conference on Basic Mathematical Skills and Learning (Euclid, Ohio, October 4-6, 1975). Volume I: Contributed Position Papers.

ERIC Educational Resources Information Center

National Inst. of Education (DHEW), Washington, DC.

In October 1975 a conference was convened in Euclid, Ohio, by the Basic Skills Group of the National Institute of Education (NIE). Thirty-three participants presented position papers addressing two major questions: (1) What are basic mathematical skills and learning? (2) What are the major problems related to children's acquisition of basic…

Thinking Process of Pseudo Construction in Mathematics Concepts

ERIC Educational Resources Information Center

Subanji; Nusantara, Toto

2016-01-01

This article aims at studying pseudo construction of student thinking in mathematical concepts, integer number operation, algebraic forms, area concepts, and triangle concepts. 391 junior high school students from four districts of East Java Province Indonesia were taken as the subjects. Data were collected by means of distributing the main…

The articulation of integration of clinical and basic sciences in concept maps: differences between experienced and resident groups.

PubMed

Vink, Sylvia; van Tartwijk, Jan; Verloop, Nico; Gosselink, Manon; Driessen, Erik; Bolk, Jan

2016-08-01

To determine the content of integrated curricula, clinical concepts and the underlying basic science concepts need to be made explicit. Preconstructed concept maps are recommended for this purpose. They are mainly constructed by experts. However, concept maps constructed by residents are hypothesized to be less complex, to reveal more tacit basic science concepts and these basic science concepts are expected to be used for the organization of the maps. These hypotheses are derived from studies about knowledge development of individuals. However, integrated curricula require a high degree of cooperation between clinicians and basic scientists. This study examined whether there are consistent variations regarding the articulation of integration when groups of experienced clinicians and basic scientists and groups of residents and basic scientists-in-training construct concept maps. Seven groups of three clinicians and basic scientists on experienced level and seven such groups on resident level constructed concept maps illuminating clinical problems. They were guided by instructions that focused them on articulation of integration. The concept maps were analysed by features that described integration. Descriptive statistics showed consistent variations between the two expertise levels. The concept maps of the resident groups exceeded those of the experienced groups in articulated integration. First, they used significantly more links between clinical and basic science concepts. Second, these links connected basic science concepts with a greater variety of clinical concepts than the experienced groups. Third, although residents did not use significantly more basic science concepts, they used them significantly more frequent to organize the clinical concepts. The conclusion was drawn that not all hypotheses could be confirmed and that the resident concept maps were more elaborate than expected. This article discusses the implications for the role that residents and basic scientists-in-training might play in the construction of preconstructed concept maps and the development of integrated curricula.

Number theoretical foundations in cryptography

NASA Astrophysics Data System (ADS)

Atan, Kamel Ariffin Mohd

2017-08-01

In recent times the hazards in relationships among entities in different establishments worldwide have generated exciting developments in cryptography. Central to this is the theory of numbers. This area of mathematics provides very rich source of fundamental materials for constructing secret codes. Some number theoretical concepts that have been very actively used in designing crypto systems will be highlighted in this presentation. This paper will begin with introduction to basic number theoretical concepts which for many years have been thought to have no practical applications. This will include several theoretical assertions that were discovered much earlier in the historical development of number theory. This will be followed by discussion on the "hidden" properties of these assertions that were later exploited by designers of cryptosystems in their quest for developing secret codes. This paper also highlights some earlier and existing cryptosystems and the role played by number theoretical concepts in their constructions. The role played by cryptanalysts in detecting weaknesses in the systems developed by cryptographers concludes this presentation.

[Mathematics in the Out Doors].

ERIC Educational Resources Information Center

Barcomb, Francois; And Others

Designed for the instruction of emotionally handicapped children and youth, this guide presents mathematical concepts and activities which may be utilized in outdoor education. Three authors provide three individualized resource guides on mathematics; Guide 1 deals with the concepts of measurement, time, estimation, geometry, counting, and…

Remembering the hindu festivities mathematically by the balinese using integer operations and least common multiple

NASA Astrophysics Data System (ADS)

Budi Darmayasa, Jero; Wahyudin; Mulyana, Tatang; Subali Noto, Muchamad

2018-04-01

Ethnomathematicsis considered as a new study in mathematic education. As a study, numerous regions in this world starts to explore through ethnomathematics, including Indonesia. As the intersection between mathematics and mathematical modelling and culture, ethnomathematics exists in various society’s cultural elements, including in the Balinese Hindus’ festivities. To find the mathematical concept used in determining the festivity days, the researcher(s) conducted ethnographic research in Bali Mula society in Kintamani District, Bali. Participation observation, in-depth interview, and literature and documentation were used in collecting the data. As the result, the researcher(s) revealed that the mathematical concept used is integer operations, least common multiple, mixed fraction, and number sequences. Since it contains mathematical concept used in junior high, thus ethnomathematics of “4-hindu’s festivities” may be used as context in mathematics learning. By using ethnomathematics as the context, the researcher(s) expect that it will help teachers in motivation their students to learn mathematics.

Mutual relationship between mathematics and astronomy in the ancient Greece

NASA Astrophysics Data System (ADS)

Obradovic, S.

2006-05-01

In the paper we consider the foundations of mathematics in the ancient Greece as a deductive system, especially the Euclidean geometry. We investigate the concepts of continuum and discreteness in mathematics and nature. A special attention is given to the mathematics applied to the foundation of the Pythagorean concept of the universe and adoption of Aristotle's and Ptolemy's worldviews.

Implicit Theories, Expectancies, and Values Predict Mathematics Motivation and Behavior across High School and College.

PubMed

Priess-Groben, Heather A; Hyde, Janet Shibley

2017-06-01

Mathematics motivation declines for many adolescents, which limits future educational and career options. The present study sought to identify predictors of this decline by examining whether implicit theories assessed in ninth grade (incremental/entity) predicted course-taking behaviors and utility value in college. The study integrated implicit theory with variables from expectancy-value theory to examine potential moderators and mediators of the association of implicit theories with college mathematics outcomes. Implicit theories and expectancy-value variables were assessed in 165 American high school students (47 % female; 92 % White), who were then followed into their college years, at which time mathematics courses taken, course-taking intentions, and utility value were assessed. Implicit theories predicted course-taking intentions and utility value, but only self-concept of ability predicted courses taken, course-taking intentions, and utility value after controlling for prior mathematics achievement and baseline values. Expectancy for success in mathematics mediated associations between self-concept of ability and college outcomes. This research identifies self-concept of ability as a stronger predictor than implicit theories of mathematics motivation and behavior across several years: math self-concept is critical to sustained engagement in mathematics.

Bridging History of the Concept of Function with Learning of Mathematics: Students' Meta-Discursive Rules, Concept Formation and Historical Awareness

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Petersen, Pernille Hviid

2014-01-01

In this paper we present a matrix-organised implementation of an experimental course in the history of the concept of a function. The course was implemented in a Danish high school. One of the aims was to bridge history of mathematics with the teaching and learning of mathematics. The course was designed using the theoretical frameworks of a…

The Development of Learning Devices Based Guided Discovery Model to Improve Understanding Concept and Critical Thinking Mathematically Ability of Students at Islamic Junior High School of Medan

ERIC Educational Resources Information Center

Yuliani, Kiki; Saragih, Sahat

2015-01-01

The purpose of this research was to: 1) development of learning devices based guided discovery model in improving of understanding concept and critical thinking mathematically ability of students at Islamic Junior High School; 2) describe improvement understanding concept and critical thinking mathematically ability of students at MTs by using…

Comparison of risk assessment procedures used in OCRA and ULRA methods

PubMed Central

Roman-Liu, Danuta; Groborz, Anna; Tokarski, Tomasz

2013-01-01

The aim of this study was to analyse the convergence of two methods by comparing exposure and the assessed risk of developing musculoskeletal disorders at 18 repetitive task workstations. The already established occupational repetitive actions (OCRA) and the recently developed upper limb risk assessment (ULRA) produce correlated results (R = 0.84, p = 0.0001). A discussion of the factors that influence the values of the OCRA index and ULRA's repetitive task indicator shows that both similarities and differences in the results produced by the two methods can arise from the concepts that underlie them. The assessment procedure and mathematical calculations that the basic parameters are subjected to are crucial to the results of risk assessment. The way the basic parameters are defined influences the assessment of exposure and risk assessment to a lesser degree. The analysis also proved that not always do great differences in load indicator values result in differences in risk zones. Practitioner Summary: We focused on comparing methods that, even though based on different concepts, serve the same purpose. The results proved that different methods with different assumptions can produce similar assessment of upper limb load; sharp criteria in risk assessment are not the best solution. PMID:24041375

Rotation Covariant Image Processing for Biomedical Applications

PubMed Central

Reisert, Marco

2013-01-01

With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences. PMID:23710255

10 CFR Appendix B to Part 73 - General Criteria for Security Personnel

Code of Federal Regulations, 2012 CFR

2012-01-01

... or pass an equivalent performance examination designed to measure basic job-related mathematical... equivalent performance examination designed to measure basic mathematical, language, and reasoning skills... administered by a licensed physician. The examination shall be designed to measure the individual's physical...

Drawing Space: Mathematicians' Kinetic Conceptions of Eigenvectors

ERIC Educational Resources Information Center

Sinclair, Nathalie; Gol Tabaghi, Shiva

2010-01-01

This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of…

Designing Online Playgrounds for Learning Mathematics

ERIC Educational Resources Information Center

Johnson, Heather Lynn; Hornbein, Peter; Bryson, Dana

2016-01-01

Fully online courses can provide teachers fresh opportunities to expand their mathematical conceptions and infuse technology into their classroom teaching. In this article, the authors share the experience of two classroom teachers (Hornbein and Bryson) who participated in a fully online mathematics education course--Expanding Conceptions of…

Electromagnetic Concepts in Mathematical Representation of Physics.

ERIC Educational Resources Information Center

Albe, Virginie; Venturini, Patrice; Lascours, Jean

2001-01-01

Addresses the use of mathematics when studying the physics of electromagnetism. Focuses on common electromagnetic concepts and their associated mathematical representation and arithmetical tools. Concludes that most students do not understand the significant aspects of physical situations and have difficulty using relationships and models specific…

A language based on analogy to communicate cultural concepts in SETI

NASA Astrophysics Data System (ADS)

Musso, Paolo

2011-02-01

The present paper is a synthesis of three presentation given by myself at the Toulouse IAC 2001 ( Analogy as a tool to communicate abstract concepts in SETI), the Bremen IAC 2003 ( From maths to culture: towards an effective message), and the Vancouver IAC 2004 ( Philosophical and religious implications of extraterrestrial intelligent life). Its aim is to find a way to make our cultural concepts understandable to hypothetical extraterrestrials (ETs) in a SETI communication. First of all, I expose the reasons why I think that analogy could be a good tool for this purpose. Then, I try to show that this is possible only in the context of an integrated language, using both abstract symbols and pictures, also sketching two practical examples about some basic concepts of our moral and religious tradition. Further studies are required to determine whether this method could be extended to the higher-level abstract concepts in the other fields of our culture. Finally, I discuss the possible role of mathematics, logic and natural science in the construction of an analogy-based language for interstellar messages with a cultural content and a possible way of managing this matter from a social point of view.

Volumic visual perception: principally novel concept

NASA Astrophysics Data System (ADS)

Petrov, Valery

1996-01-01

The general concept of volumic view (VV) as a universal property of space is introduced. VV exists in every point of the universe where electromagnetic (EM) waves can reach and a point or a quasi-point receiver (detector) of EM waves can be placed. Classification of receivers is given for the first time. They are classified into three main categories: biological, man-made non-biological, and mathematically specified hypothetical receivers. The principally novel concept of volumic perception is introduced. It differs chiefly from the traditional concept which traces back to Euclid and pre-Euclidean times and much later to Leonardo da Vinci and Giovanni Battista della Porta's discoveries and practical stereoscopy as introduced by C. Wheatstone. The basic idea of novel concept is that humans and animals acquire volumic visual data flows in series rather than in parallel. In this case the brain is free from extremely sophisticated real time parallel processing of two volumic visual data flows in order to combine them. Such procedure seems hardly probable even for humans who are unable to combine two primitive static stereoscopic images in one quicker than in a few seconds. Some people are unable to perform this procedure at all.

Increasing Communication in Geometry by Using a Personal Math Concept Chart

ERIC Educational Resources Information Center

Friedman, Rhonda; Kazerouni, Gety; Lax, Stacey; Weisdorf, Elli

2011-01-01

The action research team developed a "Personal Math Concept Chart". This chart required students to describe the mathematical concepts that they were studying in the Geometry strand of Mathematics using their own images and words. In this study, students were encouraged to express their own understanding of geometric concepts in order to…

Mathematical Knowledge for Teaching the Function Concept and Student Learning Outcomes

ERIC Educational Resources Information Center

Hatisaru, Vesife; Erbas, Ayhan Kursat

2017-01-01

The purpose of this study was to examine the potential interrelationships between teachers' mathematical knowledge for teaching (MKT) the function concept and their students' learning outcomes of this concept. Data were collected from two teachers teaching in a vocational high school and their students through a function concept test for teachers…

Ten Essential Concepts for Remediation in Mathematics.

ERIC Educational Resources Information Center

Roseman, Louis

1985-01-01

Ten crucial mathematical concepts with which errors are made are listed, with methods used to teach them to high school students. The concepts concern order, place values, inverse operations, multiplication and division, remainders, identity elements, fractions, conversions, decimal points, and percentages. (MNS)

Contextual approach using VBA learning media to improve students’ mathematical displacement and disposition ability

NASA Astrophysics Data System (ADS)

Chotimah, Siti; Bernard, M.; Wulandari, S. M.

2018-01-01

The main problems of the research were the lack of reasoning ability and mathematical disposition of students to the learning of mathematics in high school students in Cimahi - West Java. The lack of mathematical reasoning ability in students was caused by the process of learning. The teachers did not train the students to do the problems of reasoning ability. The students still depended on each other. Sometimes, one of patience teacher was still guiding his students. In addition, the basic ability aspects of students also affected the ability the mathematics skill. Furthermore, the learning process with contextual approach aided by VBA Learning Media (Visual Basic Application for Excel) gave the positive influence to the students’ mathematical disposition. The students are directly involved in learning process. The population of the study was all of the high school students in Cimahi. The samples were the students of SMA Negeri 4 Cimahi class XIA and XIB. There were both of tested and non-tested instruments. The test instrument was a description test of mathematical reasoning ability. The non-test instruments were questionnaire-scale attitudes about students’ mathematical dispositions. This instrument was used to obtain data about students’ mathematical reasoning and disposition of mathematics learning with contextual approach supported by VBA (Visual Basic Application for Excel) and by conventional learning. The data processed in this study was from the post-test score. These scores appeared from both of the experimental class group and the control class group. Then, performing data was processed by using SPSS 22 and Microsoft Excel. The data was analyzed using t-test statistic. The final result of this study concluded the achievement and improvement of reasoning ability and mathematical disposition of students whose learning with contextual approach supported by learning media of VBA (Visual Basic Application for Excel) was better than students who got conventional learning.

Which Preschool Mathematics Competencies Are Most Predictive of Fifth Grade Achievement?

PubMed

Nguyen, Tutrang; Watts, Tyler W; Duncan, Greg J; Clements, Douglas H; Sarama, Julie S; Wolfe, Christopher; Spitler, Mary Elaine

In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children's emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement.

Psychology and Didactics of Mathematics in France--An Overview.

ERIC Educational Resources Information Center

Vergnaud, Gerard

1983-01-01

Examples are given of the variety of mathematical concepts and problems being studied by psychologically oriented researchers in France. Work on decimals, circles, natural numbers, decimal and real numbers, and didactic transposition are included. Comments on designing research on mathematics concept formation conclude the article. (MNS)

The Important Things about Writing in Secondary Mathematics Classes

ERIC Educational Resources Information Center

Jao, Limin; Hall, Jennifer

2018-01-01

In this article, the authors present a writing activity that allowed pre-service teachers to be creative in the mathematics classroom. Inspired by "The Important Book" by Margaret Wise Brown, students explored secondary-level mathematics concepts, discussing various attributes/characteristics of each concept through their written…

Developing Basic Mathematics Skills through the Use of African-American Children's Literature.

ERIC Educational Resources Information Center

Stewart, Loraine Moses

1997-01-01

Discusses several books, such as "Feast for 10" and "One Smiling Grandma," which are effective in reinforcing basic mathematical skills. States that counting books ("Feast for 10," for example) are useful for elementary curriculum enhancement as well as fun to read. (PA)

Mathematical Abstraction: Constructing Concept of Parallel Coordinates

NASA Astrophysics Data System (ADS)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2017-09-01

Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.

A hybrid model of mathematics support for science students emphasizing basic skills and discipline relevance

NASA Astrophysics Data System (ADS)

Jackson, Deborah C.; Johnson, Elizabeth D.

2013-09-01

The problem of students entering university lacking basic mathematical skills is a critical issue in the Australian higher-education sector and relevant globally. The Maths Skills programme at La Trobe University has been developed to address under preparation in the first-year science cohort in the absence of an institutional mathematics support centre. The programme was delivered through first-year science and statistics subjects with large enrolments and focused on basic mathematical skills relevant to each science discipline. The programme offered a new approach to the traditional mathematical support centre or class. It was designed through close collaboration between science subject coordinators and the project leader, a mathematician, and includes resources relevant to science and mathematics questions written in context. Evaluation of the programme showed it improved the confidence of the participating students who found it helpful and relevant. The programme was delivered through three learning modes to allow students to select activities most suitable for them, which was appreciated by students. Mathematics skills appeared to increase following completion of the programme and student participation in the programme correlated positively and highly with academic grades in their relevant science subjects. This programme offers an alternative model for mathematics support tailored to science disciplines.

Staircase and fractional part functions

NASA Astrophysics Data System (ADS)

Amram, Meirav; Dagan, Miriam; Ioshpe, Michael; Satianov, Pavel

2016-10-01

The staircase and fractional part functions are basic examples of real functions. They can be applied in several parts of mathematics, such as analysis, number theory, formulas for primes, and so on; in computer programming, the floor and ceiling functions are provided by a significant number of programming languages - they have some basic uses in various programming tasks. In this paper, we view the staircase and fractional part functions as a classical example of non-continuous real functions. We introduce some of their basic properties, present some interesting constructions concerning them, and explore some intriguing interpretations of such functions. Throughout the paper, we use these functions in order to explain basic concepts in a first calculus course, such as domain of definition, discontinuity, and oddness of functions. We also explain in detail how, after researching the properties of such functions, one can draw their graph; this is a crucial part in the process of understanding their nature. In the paper, we present some subjects that the first-year student in the exact sciences may not encounter. We try to clarify those subjects and show that such ideas are important in the understanding of non-continuous functions, as a part of studying analysis in general.

A Multiple Intelligence Pedagogical Approach in Fifth Grade Mathematics: A Mixed Method Study

ERIC Educational Resources Information Center

Davis, Claudine Davillier

2012-01-01

The need for mathematics intervention has increased tremendously over the years, particularly after the No Child Left Behind Act of 2001.Students who lack basic mathematics skills and students who experience mathematics difficulties greatly benefit from mathematics interventions. This study examined mathematics intervention through the use of the…

A brain-based account of “basic-level” concepts

PubMed Central

Bauer, Andrew James; Just, Marcel Adam

2017-01-01

This study provides a brain-based account of how object concepts at an intermediate (basic) level of specificity are represented, offering an enriched view of what it means for a concept to be a basic-level concept, a research topic pioneered by Rosch and others (Rosch et al., 1976). Applying machine learning techniques to fMRI data, it was possible to determine the semantic content encoded in the neural representations of object concepts at basic and subordinate levels of abstraction. The representation of basic-level concepts (e.g. bird) was spatially broad, encompassing sensorimotor brain areas that encode concrete object properties, and also language and heteromodal integrative areas that encode abstract semantic content. The representation of subordinate-level concepts (robin) was less widely distributed, concentrated in perceptual areas that underlie concrete content. Furthermore, basic-level concepts were representative of their subordinates in that they were neurally similar to their typical but not atypical subordinates (bird was neurally similar to robin but not woodpecker). The findings provide a brain-based account of the advantages that basic-level concepts enjoy in everyday life over subordinate-level concepts: the basic level is a broad topographical representation that encompasses both concrete and abstract semantic content, reflecting the multifaceted yet intuitive meaning of basic-level concepts. PMID:28826947

A brain-based account of "basic-level" concepts.

PubMed

Bauer, Andrew James; Just, Marcel Adam

2017-11-01

This study provides a brain-based account of how object concepts at an intermediate (basic) level of specificity are represented, offering an enriched view of what it means for a concept to be a basic-level concept, a research topic pioneered by Rosch and others (Rosch et al., 1976). Applying machine learning techniques to fMRI data, it was possible to determine the semantic content encoded in the neural representations of object concepts at basic and subordinate levels of abstraction. The representation of basic-level concepts (e.g. bird) was spatially broad, encompassing sensorimotor brain areas that encode concrete object properties, and also language and heteromodal integrative areas that encode abstract semantic content. The representation of subordinate-level concepts (robin) was less widely distributed, concentrated in perceptual areas that underlie concrete content. Furthermore, basic-level concepts were representative of their subordinates in that they were neurally similar to their typical but not atypical subordinates (bird was neurally similar to robin but not woodpecker). The findings provide a brain-based account of the advantages that basic-level concepts enjoy in everyday life over subordinate-level concepts: the basic level is a broad topographical representation that encompasses both concrete and abstract semantic content, reflecting the multifaceted yet intuitive meaning of basic-level concepts. Copyright © 2017 Elsevier Inc. All rights reserved.

Trends in basic mathematical competencies of beginning undergraduates in Ireland, 2003-2013

NASA Astrophysics Data System (ADS)

Treacy, Páraic; Faulkner, Fiona

2015-11-01

Deficiencies in beginning undergraduate students' basic mathematical skills has been an issue of concern in higher education, particularly in the past 15 years. This issue has been tracked and analysed in a number of universities in Ireland and internationally through student scores recorded in mathematics diagnostic tests. Students beginning their science-based and technology-based undergraduate courses in the University of Limerick have had their basic mathematics skills tested without any prior warning through a 40 question diagnostic test during their initial service mathematics lecture since 1998. Data gathered through this diagnostic test have been recorded in a database kept at the university and explored to track trends in mathematical competency of these beginning undergraduates. This paper details findings surrounding an analysis of the database between 2003 and 2013, outlining changes in mathematical competencies of these beginning undergraduates in an attempt to determine reasons for such changes. The analysis found that the proportion of students tested through this diagnostic test that are predicted to be at risk of failing their service mathematics end-of-semester examinations has increased significantly between 2003 and 2013. Furthermore, when students' performance in secondary level mathematics was controlled, it was determined that the performance of beginning undergraduates in 2013 was statistically significantly below that of the performance of the beginning undergraduates recorded 10 years previously.

Helping Students with Mathematics Difficulties Understand Ratios and Proportions

ERIC Educational Resources Information Center

Dougherty, Barbara; Bryant, Diane Pedrotty; Bryant, Brian R.; Shin, Mikyung

2016-01-01

Ratios and proportions are foundational to student understanding across multiple topics in mathematics and science. In mathematics, they are central to developing concepts and skills related to slope, constant rate of change, and similar figures, which are all fundamental to algebraic concepts and skills. This article examines the importance of…

Students' Conceptions of Mathematics Bridging Courses

ERIC Educational Resources Information Center

Gordon, Sue; Nicholas, Jackie

2013-01-01

In this study we investigate the conceptions of mathematics bridging courses held by students enrolled in these courses at a major Australian university. We report on the participants' responses to email-interview questions about the mathematics bridging courses to describe a two-dimensional outcome space of variations in awareness about the…

Preservice Mathematics Teachers' Personal Figural Concepts and Classifications about Quadrilaterals

ERIC Educational Resources Information Center

Erdogan, Emel Ozdemir; Dur, Zeliha

2014-01-01

The aim of this study was to determine preservice mathematics teachers' personal figural concepts and hierarchical classifications about quadrilaterals and to investigate the relationships between them. The participants were 57 preservice primary mathematics teachers in their senior year at a state university in Turkey. The preservice mathematics…

Concept Map as an Assessment Tool in Secondary School Mathematics: An Analysis of Teachers' Perspectives

ERIC Educational Resources Information Center

Mutodi, Paul; Chigonga, Benard

2016-01-01

This paper reports on teachers' views on concept mapping: its applicability; reliability; advantages and; difficulties. A close-ended questionnaire was administered to 50 purposefully selected secondary school mathematics teachers from Sekhukhune District, Limpopo, South Africa. The findings indicate that mathematics teachers generally perceive…

Secondary School Teachers' Conceptions and Their Teaching Practices Using Graphing Calculators

ERIC Educational Resources Information Center

Lee, Jane A.; McDougall, Douglas E.

2010-01-01

This article investigates secondary school teachers' conceptions of mathematics and their teaching practices in the use of graphing calculators in their mathematics classrooms. Case studies on three teacher participants were developed using quantitative and qualitative data that consisted of self-assessments on beliefs in mathematics,…

A study of the continuum of integration of mathematics content with science concepts at the middle school level in West Virginia

NASA Astrophysics Data System (ADS)

Meisel, Edna Marie

The purpose of this study was to examine the practices and perceptions of regular education seventh grade middle school mathematics teachers in West Virginia concerning the integration of mathematics objectives with science concepts. In addition, this study also emphasized the use of integrated curriculum continuum models to study mathematics teachers' practices and perceptions for teaching mathematics objectives in connection with science concepts. It was argued that the integrated curriculum continuum model can be used to help educators begin to form a common definition of integrated curriculum. The population was described as the regular education seventh grade middle school mathematics teachers in West Virginia. The entire population (N = 173) was used as the participants in this study. Data was collected using an integrated curriculum practices and perceptions survey constructed by the researcher. This was a descriptive study that incorporated the Chi Square statistic to show trends in teacher practices and perceptions. Also, an ex post facto design, that incorporated the Mann-Whitney U statistic, was used to compare practices and perceptions between teachers grouped according to factors that influence teaching practices and perceptions. These factors included teaching certificate endorsement and teacher professional preparation. Results showed that the regular education seventh grade middle school mathematics teachers of West Virginia are teaching mathematics objectives mainly at a discipline-based level with no formal attempt for integration with science concepts. However, these teachers perceived that many of the mathematics objectives should be taught at varying levels of integration with science concepts. It was also shown that teachers who experienced professional preparation courses that emphasized integrated curriculum courses did teach many of the mathematics objectives at higher levels of integration with science than those teachers who did not experience integrated curriculum courses.

Mathematics for Drafting.

ERIC Educational Resources Information Center

Clary, Joseph R.; Nery, Karen P.

This set of three modules was designed for use primarily to help teach and reinforce the basic mathematics skills in drafting classes. The modules are based on the needs of drafting students in beginning courses as determined by a survey of teachers across North Carolina. Each module consists of basic information and examples and problem sheets…

Basic Applied Mathematics Part 1.

ERIC Educational Resources Information Center

New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.

This guide, published by the New York City Board of Education, presents 62 lesson plans in basic mathematics for tenth grade students. Lesson plans and performance objectives focus on the following areas: (1) fundamental operations with signed numbers; (2) linear, weight and temperature measurements; (3) fractions, decimals and percents; (4)…

S.M.P. SEQUENTIAL MATHEMATICS PROGRAM.

ERIC Educational Resources Information Center

CICIARELLI, V; LEONARD, JOSEPH

A SEQUENTIAL MATHEMATICS PROGRAM BEGINNING WITH THE BASIC FUNDAMENTALS ON THE FOURTH GRADE LEVEL IS PRESENTED. INCLUDED ARE AN UNDERSTANDING OF OUR NUMBER SYSTEM, AND THE BASIC OPERATIONS OF WORKING WITH WHOLE NUMBERS--ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION. COMMON FRACTIONS ARE TAUGHT IN THE FIFTH, SIXTH, AND SEVENTH GRADES. A…

Mathematics Placement at Cottey College.

ERIC Educational Resources Information Center

Callahan, Susan

In response to the large numbers of students who were failing or dropping out of basic algebra and calculus classes, Cottey College, in Missouri, developed a math placement program in 1982 using Basic Algebra (BA) and Calculus Readiness (CR) tests from the Mathematical Association of America's Placement Testing Program. Cut off scores for the…

Performance in Basic Mathematics of Indigenous Students

ERIC Educational Resources Information Center

Sicat, Lolita V.; David, Ma. Elena D.

2016-01-01

This analytical study analyzed the performance in Basic Mathematics of the indigenous students, the Aeta students (Grade 6) of Sta. Juliana Elementary School, Capas, Tarlac, and the APC students of Malaybalay City, Bukidnon. Results were compared with regular students in rural, urban, private, and public schools to analyze indigenous students'…

Dynamic Boolean Mathematics

ERIC Educational Resources Information Center

Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen

2016-01-01

Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…

The Interplay between Spoken Language and Informal Definitions of Statistical Concepts

ERIC Educational Resources Information Center

Lavy, Ilana; Mashiach-Eizenberg, Michal

2009-01-01

Various terms are used to describe mathematical concepts, in general, and statistical concepts, in particular. Regarding statistical concepts in the Hebrew language, some of these terms have the same meaning both in their everyday use and in mathematics, such as Mode; some of them have a different meaning, such as Expected value and Life…

Exploring the Opinions about the Concepts of "Formula" and "Rule" in Mathematics

ERIC Educational Resources Information Center

Altintas, Esra; Ilgün, Sükrü

2017-01-01

The purpose of this study is to draw attention to the concepts of "formula" and "rule" in mathematics, thereby revealing the views of pre-service teachers relating to these concepts by exploring their knowledge in, and their capacity to exemplify these concepts. The study is important in that it would reveal how pre-service…

The Relationship among Self-Concept, Self-Efficacy, and Performance in Mathematics during Secondary School.

ERIC Educational Resources Information Center

Pietsch, James; Walker, Richard; Chapman, Elaine

2003-01-01

Examines the relationship among self-concept, self-efficacy, and performance in mathematics among 416 high school students. Confirmatory factor analyses supported the existence of two self-concept components--a competency component and an affective component. Self-efficacy items and the competency items of self-concept also loaded on a single…

The astronomy education through interactive materials

NASA Astrophysics Data System (ADS)

de Macedo, Josué Antunes; Voelzke, Marcos Rincon

2014-11-01

This study presents results of a survey conducted at the Federal Institution of Education, Science and Technology in the North of Minas Gerais (IFNMG), and aimed to investigate the potentialities of the use of interactive materials in the teaching of astronomy. An advanced training course with involved learning activities about basic concepts of astronomy was offered to thirty-two Licenciate students in Physics, Mathematics and Biological Sciences, using three pedagogical moments. Among other aspects, the viability of the use of resources was noticed, involving digital technologies and interactive materials on teaching of astronomy, which may contribute to the broadening of methodological options for future teachers and meet their training needs

Computer simulation of the heavy-duty turbo-compounded diesel cycle for studies of engine efficiency and performance

NASA Technical Reports Server (NTRS)

Assanis, D. N.; Ekchian, J. A.; Heywood, J. B.; Replogle, K. K.

1984-01-01

Reductions in heat loss at appropriate points in the diesel engine which result in substantially increased exhaust enthalpy were shown. The concepts for this increased enthalpy are the turbocharged, turbocompounded diesel engine cycle. A computer simulation of the heavy duty turbocharged turbo-compounded diesel engine system was undertaken. This allows the definition of the tradeoffs which are associated with the introduction of ceramic materials in various parts of the total engine system, and the study of system optimization. The basic assumptions and the mathematical relationships used in the simulation of the model engine are described.

Importance of disentanglement and entanglement during DNA replication and segregation. Comment on: "Disentangling DNA molecules" by Alexander Vologodskii

NASA Astrophysics Data System (ADS)

Bates, David; Pettitt, B. Montgomery; Buck, Gregory R.; Zechiedrich, Lynn

2016-09-01

In the Vologodskii review[19], the accompanying comments, and many other publications, there has been considerable effort to analyze the actions of type II topoisomerases, especially with regard to ;topological simplification; [4]. Whereas these efforts could be characterized as a battle of the models, with each research team arguing for their version of how it might work, each specific kinetic concept adds important considerations to the fundamental question of how these enzymes function. The basic tenet, however, of what is called the ;hooked juxtaposition model [1],; is not a modeling aspect, but is simply a geometric mathematical fact.

Solar stills for agricultural purposes

NASA Technical Reports Server (NTRS)

Selcuk, M. K.; Tran, V. V.

1975-01-01

Basic concepts of using desalinated water for agricultural purposes are outlined. A mathematical model describing heat and mass transfer in a system combining a solar still with a greenhouse, its solution, and test results of a small-scale unit built at the Middle East Technical University, Ankara, Turkey, are discussed. The unit was employed to demonstrate the technical feasibility of the system. Further development and modifications are necessary for larger-scale operations. The basis of an optimization study which is underway at the Brace Research Institute of McGill University in Montreal, Canada, aimed at finding the best combination of design and operation parameters is also presented.

The cognitive apprenticeship theory for the teaching of mathematics in an online 3D virtual environment

NASA Astrophysics Data System (ADS)

Bouta, Hara; Paraskeva, Fotini

2013-03-01

Research spanning two decades shows that there is a continuing development of 3D virtual worlds and investment in such environments for educational purposes. Research stresses the need for these environments to be well-designed and for suitable pedagogies to be implemented in the teaching practice in order for these worlds to be fully effective. To this end, we propose a pedagogical framework based on the cognitive apprenticeship for deriving principles and guidelines to inform the design, development and use of a 3D virtual environment. This study examines how the use of a 3D virtual world facilitates the teaching of mathematics in primary education by combining design principles and guidelines based on the Cognitive Apprenticeship Theory and the teaching methods that this theory introduces. We focus specifically on 5th and 6th grade students' engagement (behavioral, affective and cognitive) while learning fractional concepts over a period of two class sessions. Quantitative and qualitative analyses indicate considerable improvement in the engagement of the students who participated in the experiment. This paper presents the findings regarding students' cognitive engagement in the process of comprehending basic fractional concepts - notoriously hard for students to master. The findings are encouraging and suggestions are made for further research.

Building Knowledge Structures by Testing Helps Children with Mathematical Learning Difficulty

ERIC Educational Resources Information Center

Zhang, Yiyun; Zhou, Xinlin

2016-01-01

Mathematical learning difficulty (MLD) is prevalent in the development of mathematical abilities. Previous interventions for children with MLD have focused on number sense or basic mathematical skills. This study investigated whether mathematical performance of fifth grade children with MLD could be improved by developing knowledge structures by…

Secondary Schools Curriculum Guide, Mathematics, Grades 10-12. Revised.

ERIC Educational Resources Information Center

Cranston School Dept., RI.

Behavioral objectives for grades 10 through 12 are specified for plane geometry, algebra, general mathematics, computer mathematics, slide rule mathematics, basic college mathematics, trigonometry, analytic geometry, calculus and probability. Most sections present material in terms of portions of a school year. At least one major objective is…

Objectifying the adjacent and opposite angles: a cultural historical analysis

NASA Astrophysics Data System (ADS)

Daher, Wajeeh; Musallam, Nadera

2018-02-01

The angle topic is central to the development of geometric knowledge. Two of the basic concepts associated with this topic are the adjacent and opposite angles. It is the goal of the present study to analyze, based on the cultural historical semiotics framework, how high-achieving seventh grade students objectify the adjacent and opposite angles' concepts. We videoed the learning of a group of three high-achieving students who used technology, specifically GeoGebra, to explore geometric relations related to the adjacent and opposite angles' concepts. To analyze students' objectification of these concepts, we used the categories of objectification of knowledge (attention and awareness) and the categories of generalization (factual, contextual and symbolic), developed by Radford. The research results indicate that teacher's and students' verbal and visual signs, together with the software dynamic tools, mediated the students' objectification of the adjacent and opposite angles' concepts. Specifically, eye and gestures perceiving were part of the semiosis cycles in which the participating students were engaged and which related to the mathematical signs that signified the adjacent and the opposite angles. Moreover, the teacher's suggestions/requests/questions included/suggested semiotic signs/tools, including verbal signs that helped the students pay attention, be aware of and objectify the adjacent and opposite angles' concepts.

Understanding Mathematic Concept in Relation and Function Method through Active Learning Type Group to Group Distributed LKS

NASA Astrophysics Data System (ADS)

Kudri, F.; Rahmi, R.; Haryono, Y.

2018-04-01

This research is motivated by the lack of understanding of mathematical concepts students and teachers have not familiarize students discussed in groups. This researchaims to determine whether an understanding of mathematical concepts junior class VIII SMPN 2 in Ranah Batahan Kabupaten Pasaman Barat by applying active learning strategy group to group types with LKS better than conventional learning. The type of research is experimental the design of randomized trials on the subject. The population in the study were all students VIII SMPN 2 Ranah Batahan Kabupaten Pasaman Barat in year 2012/2013 which consists of our class room experiment to determine the grade and control class with do nerandomly, so that classes VIII1 elected as a experiment class and class VIII4 as a control class. The instruments used in the test empirically understanding mathematical concepts are shaped by the essay with rt=0,82 greater than rt=0,468 means reliable tests used. The data analysis technique used is the test with the help of MINITAB. Based on the results of the data analisis known that both of the sample are normal and homogenity in real rate α = 0,05, so the hypothesis of this research is received. So, it can be concluded students’ understanding mathematical concept applied the active Group to Group learning strategy with LKS is better than the students’ understanding mathematical concept with Conventional Learning.

Physical Concepts and Mathematical Symbols

NASA Astrophysics Data System (ADS)

Grelland, Hans Herlof

2007-12-01

According to traditional empiricist philosophy of science, concepts and meaning grow out of sense experience, and the mathematical structure of a physical theory is nothing but a formalisation of a given meaning-content. This view seems to work well in classical mechanics. But it breaks down in quantum physics, where we have a self-supported mathematical structure which resists any conceptual or pictorial interpretation in the traditional sense. Thus, traditional empiricism is flawed. Quantum physics teaches us that mathematics is a language in itself which extends beyond ordinary language. To understand the meaning of this extended language, we have to explore how new concepts and intuitions grow out of mathematics, not the other way around. The symbolic structure is prior to its meaning. This point of view is called linguistic empiricism, to stress that the connection with experience is still crucial. As cases, I compare the concept of stiffness in classical mechanics and the concept of electron density in quantum mechanics. The last case demonstrates that the wave function has a richer interpretation than the probabilistic one concerning measurement of position.

Research on the selection of innovation compound using Possibility Construction Space Theory and fuzzy pattern recognition

NASA Astrophysics Data System (ADS)

Xie, Songhua; Li, Dehua; Nie, Hui

2009-10-01

There are a large number of fuzzy concepts and fuzzy phenomena in traditional Chinese medicine, which have led to great difficulties for study of traditional Chinese medicine. In this paper, the mathematical methods are used to quantify fuzzy concepts of drugs and prescription. We put forward the process of innovation formulations and selection method in Chinese medicine based on the Possibility Construction Space Theory (PCST) and fuzzy pattern recognition. Experimental results show that the method of selecting medicines from a number of characteristics of traditional Chinese medicine is consistent with the basic theory of traditional Chinese medicine. The results also reflect the integrated effects of the innovation compound. Through the use of the innovation formulations system, we expect to provide software tools for developing new traditional Chinese medicine and to inspire traditional Chinese medicine researchers to develop novel drugs.

Fluid Mechanics

NASA Astrophysics Data System (ADS)

Pnueli, David; Gutfinger, Chaim

1997-01-01

This text is intended for the study of fluid mechanics at an intermediate level. The presentation starts with basic concepts, in order to form a sound conceptual structure that can support engineering applications and encourage further learning. The presentation is exact, incorporating both the mathematics involved and the physics needed to understand the various phenomena in fluid mechanics. Where a didactical choice must be made between the two, the physics prevails. Throughout the book the authors have tried to reach a balance between exact presentation, intuitive grasp of new ideas, and creative applications of concepts. This approach is reflected in the examples presented in the text and in the exercises given at the end of each chapter. Subjects treated are hydrostatics, viscous flow, similitude and order of magnitude, creeping flow, potential flow, boundary layer flow, turbulent flow, compressible flow, and non-Newtonian flows. This book is ideal for advanced undergraduate students in mechanical, chemical, aerospace, and civil engineering. Solutions manual available.

Conceptual developments of non-equilibrium statistical mechanics in the early days of Japan

NASA Astrophysics Data System (ADS)

Ichiyanagi, Masakazu

1995-11-01

This paper reviews the research in nonequilibrium statistical mechanics made in Japan in the period between 1930 and 1960. Nearly thirty years have passed since the discovery of the exact formula for the electrical conductivity. With the rise of the linear response theory, the methods and results of which are quickly grasped by anyone, its rationale was pushed aside and even at the stage where the formulation was still incomplete some authors hurried to make physical applications. Such an attitude robbed it of most of its interest for the average physicist, who would approach an understanding of some basic concept, not through abstract and logical analysis but by simply increasing his technical experiences with the concept. The purpose of this review is to rescue the linear response theory from being labeled a mathematical tool and to show that it has considerable physical content. Many key papers, originally written in Japanese, are reproduced.

The Shapes of Tomorrow.

ERIC Educational Resources Information Center

Vermont Univ., Burlington.

This book, written by classroom teachers, introduces the application of secondary school mathematics to space exploration, and is intended to unify science and mathematics. In early chapters geometric concepts are used with general concepts of space and rough approximations of space measurements. Later, these concepts are refined to include the…

Does an Ability to Pattern Indicate That Our Thinking Is Mathematical?

ERIC Educational Resources Information Center

McCluskey, Catherine; Mitchelmore, Michael; Mulligan, Joanne

2013-01-01

Research affirms that pattern and structure underlie the development of a broad range of mathematical concepts. However, the concept of pattern also occurs in other fields. This theoretical paper explores pattern recognition, a neurological construct based on the world of Goldberg (2005), and pattern as defined in the field of mathematics to…

Students' Quality of Mathematical Discussion and Their Self-Determination in Mathematics

ERIC Educational Resources Information Center

Kosko, Karl W.; Wilkins, Jesse L. M.

2012-01-01

Mathematical discussion allows for students to reflect upon math concepts and understand such concepts at a deeper level. This process of reflection requires a certain amount of internalization on the part of the student. This internalization is facilitated by meeting the needs of autonomy, competence, and relatedness as advocated by…

Insurance and Mathematics: Developing Democratic Citizenship through Interdisciplinary Approaches to Contemporary Issues

ERIC Educational Resources Information Center

Misco, Thomas; Lee, Lena; Malone, Kevin; Goley, G. Steven; Seabolt, Phaedra

2012-01-01

Insurance is an interesting interdisciplinary topic that can offer generative meaning and relevance for students. By adapting real life examples and authentic simulations, mathematical concepts can be applied to insurance-related social studies issues and content. This article explores ways to teach insurance and related mathematical concepts to…

Mathematics Undergraduate Student Teachers' Conceptions of Guided Inductive and Deductive Teaching Approaches

ERIC Educational Resources Information Center

Ndemo, Zakaria; Zindi, Fred; Mtetwa, David

2017-01-01

This contribution aimed at developing an understanding of student teachers' conceptions of guided discovery teaching approaches. A cross-sectional survey design involving eleven secondary mathematics teachers who had enrolled for an in-service mathematics education degree was used to address the research question: What are undergraduate student…

Turkish High School Teachers' Conceptions of Creativity in Mathematics

ERIC Educational Resources Information Center

Aktas, Meral Cansiz

2016-01-01

The aim of this research is to explore Turkish high school teachers' conceptions of creativity in mathematics. The research was carried out using qualitative research methods. The sample consisted of seven mathematics teachers, and semi-structured interviews were used as a data collection tool. Analysis of the responses indicated that mathematics…

Self-Concept Mediates the Relation between Achievement and Emotions in Mathematics

ERIC Educational Resources Information Center

Van der Beek, Jojanneke P. J.; Van der Ven, Sanne H. G.; Kroesbergen, Evelyn H.; Leseman, Paul P. M.

2017-01-01

Background: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. Aims: The aims were (1) to investigate the…

A Mixed Methods Analysis of Students' Understanding of Slope and Derivative Concepts and Students' Mathematical Dispositions

ERIC Educational Resources Information Center

Patel, Rita Manubhai

2013-01-01

This dissertation examined understanding of slope and derivative concepts and mathematical dispositions of first-semester college calculus students, who are recent high school graduates, transitioning to university mathematics. The present investigation extends existing research in the following ways. First, based on this investigation, the…

Shadows constructing a relationship between light and color pigments by physical and mathematical perspectives

NASA Astrophysics Data System (ADS)

Yurumezoglu, Kemal; Karabey, Burak; Yigit Koyunkaya, Melike

2017-03-01

Full shadows, partial shadows and multilayer shadows are explained based on the phenomenon of the linear dispersion of light. This paper focuses on progressing the understanding of shadows from physical and mathematical perspectives. A significant relationship between light and color pigments is demonstrated with the help of the concept of sets. This integration of physical and mathematical reasoning not only manages an operational approach to the concept of shadows, it also outputs a model that can be used in science, technology, engineering and mathematics (STEM) curricula by providing a concrete and physical example for abstract concept of the empty set.

Mathematical modeling and simulation in animal health. Part I: Moving beyond pharmacokinetics.

PubMed

Riviere, J E; Gabrielsson, J; Fink, M; Mochel, J

2016-06-01

The application of mathematical modeling to problems in animal health has a rich history in the form of pharmacokinetic modeling applied to problems in veterinary medicine. Advances in modeling and simulation beyond pharmacokinetics have the potential to streamline and speed-up drug research and development programs. To foster these goals, a series of manuscripts will be published with the following goals: (i) expand the application of modeling and simulation to issues in veterinary pharmacology; (ii) bridge the gap between the level of modeling and simulation practiced in human and veterinary pharmacology; (iii) explore how modeling and simulation concepts can be used to improve our understanding of common issues not readily addressed in human pharmacology (e.g. breed differences, tissue residue depletion, vast weight ranges among adults within a single species, interspecies differences, small animal species research where data collection is limited to sparse sampling, availability of different sampling matrices); and (iv) describe how quantitative pharmacology approaches could help understanding key pharmacokinetic and pharmacodynamic characteristics of a drug candidate, with the goal of providing explicit, reproducible, and predictive evidence for optimizing drug development plans, enabling critical decision making, and eventually bringing safe and effective medicines to patients. This study introduces these concepts and introduces new approaches to modeling and simulation as well as clearly articulate basic assumptions and good practices. The driving force behind these activities is to create predictive models that are based on solid physiological and pharmacological principles as well as adhering to the limitations that are fundamental to applying mathematical and statistical models to biological systems. © 2015 John Wiley & Sons Ltd.

A Multiphase Flow in the Antroduodenal Portion of the Gastrointestinal Tract: A Mathematical Model

PubMed Central

Trusov, P. V.

2016-01-01

A group of authors has developed a multilevel mathematical model that focuses on functional disorders in a human body associated with various chemical, physical, social, and other factors. At this point, the researchers have come up with structure, basic definitions and concepts of a mathematical model at the “macrolevel” that allow describing processes in a human body as a whole. Currently we are working at the “mesolevel” of organs and systems. Due to complexity of the tasks, this paper deals with only one meso-fragment of a digestive system model. It describes some aspects related to modeling multiphase flow in the antroduodenal portion of the gastrointestinal tract. Biochemical reactions, dissolution of food particles, and motor, secretory, and absorbing functions of the tract are taken into consideration. The paper outlines some results concerning influence of secretory function disorders on food dissolution rate and tract contents acidity. The effect which food density has on inflow of food masses from a stomach to a bowel is analyzed. We assume that the future development of the model will include digestive enzymes and related reactions of lipolysis, proteolysis, and carbohydrates breakdown. PMID:27413393

An Investigation of the Relative Effectiveness of the Basic Mathematics Review Program at Essex Community College.

ERIC Educational Resources Information Center

Bloomberg, Jerome

Basic Mathematics Review (BMR) is a remedial non-credit course at Essex Community College (Maryland) being taught on an individualized basis. Following diagnostic testing and placement, instruction utilizes programmed materials, tutors, and self-tests. Evaluation of the new individualized BMR and comparison with the traditional remedial course…

User's Manual for the Basic Math Mastery Tests.

ERIC Educational Resources Information Center

Weiss, David J.; Trombley, Robert J.

This user manual introduces and explains the Basic Math Mastery Tests (BMMT), a collection of 10 tests of specific mathematics skills. The tests were designed to assess mastery of specific skills required for successful performance in vocational education or in occupations requiring mathematics skills. All 10 tests are administered and scored by…

Basic Mathematics Machine Calculator Course.

ERIC Educational Resources Information Center

Windsor Public Schools, CT.

This series of four text-workbooks was designed for tenth grade mathematics students who have exhibited lack of problem-solving skills. Electric desk calculators are to be used with the text. In the first five chapters of the series, students learn how to use the machine while reviewing basic operations with whole numbers, decimals, fractions, and…

Effects of Two Interventions on Solving Basic Fact Problems by Second Graders with Mathematics Learning Disabilities

ERIC Educational Resources Information Center

Dennis, Minyi Shih; Sorrells, Audrey McCray; Falcomata, Terry S.

2016-01-01

This study used a multiple probe across participants design, replicated across two interventions and counterbalanced across participant groups to examine the effects of number sense intervention and extensive practice intervention on strategy transformation when students with mathematics learning disabilities (MLD) solved basic fact problems. In…

The enhancement of mathematical analogical reasoning ability of university students through concept attainment model

NASA Astrophysics Data System (ADS)

Angraini, L. M.; Kusumah, Y. S.; Dahlan, J. A.

2018-05-01

This study aims to see the enhancement of mathematical analogical reasoning ability of the university students through concept attainment model learning based on overall and Prior Mathematical Knowledge (PMK) and interaction of both. Quasi experiments with the design of this experimental-controlled equivalent group involved 54 of second semester students at the one of State Islamic University. The instrument used is pretest-postest. Kolmogorov-Smirnov test, Levene test, t test, two-way ANOVA test were used to analyse the data. The result of this study includes: (1) The enhancement of the mathematical analogical reasoning ability of the students who gets the learning of concept attainment model is better than the enhancement of the mathematical analogical reasoning ability of the students who gets the conventional learning as a whole and based on PMK; (2) There is no interaction between the learning that is used and PMK on enhancing mathematical analogical reasoning ability.

Opening the World of Mathematics: The Daily Math Discussion

ERIC Educational Resources Information Center

Donoahue, Zoe

2016-01-01

During the author's everyday math discussions with her class, young children talk about mathematical ideas, theories, and concepts within a predictable structure. These discussions include many concepts from--and beyond--the first-grade math curriculum, and their depth and complexity build throughout the school year. Concepts and skills include…

Explicating the Concept of Contrapositive Equivalence

ERIC Educational Resources Information Center

Dawkins, Paul Christian; Hub, Alec

2017-01-01

This paper sets forth a concept (Simon, 2017) of contrapositive equivalence and explores some related phenomena of learning through a case study of Hugo's learning in a teaching experiment guiding the reinvention of mathematical logic. Our proposed concept of contrapositive equivalence rests upon set-based meanings for mathematical categories and…

Profile of mathematical reasoning ability of 8th grade students seen from communicational ability, basic skills, connection, and logical thinking

NASA Astrophysics Data System (ADS)

Sumarsih; Budiyono; Indriati, D.

2018-04-01

This research aims to understand the students’ weaknesses in mathematical reasoning ability in junior secondary school. A set of multiple choice tests were used to measure this ability involve components mathematical communication, basic skills, connection, and logical thinking. A total of 259 respondents were determined by stratified cluster random sampling. Data were analyzed using one-way Anova test with Fobs = 109.5760 and F = 3.0000. The results show that students’ ability from schools with high National Exam in mathematics category was the best and followed by medium and low category. Mathematical connection is the most difficult component performed by students. In addition, most students also have difficulty in expressing ideas and developing logical arguments.

Essential concepts and underlying theories from physics, chemistry, and mathematics for "biochemistry and molecular biology" majors.

PubMed

Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis

2013-01-01

Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology. © 2013 by The International Union of Biochemistry and Molecular Biology.

Computer Mathematical Tools: Practical Experience of Learning to Use Them

ERIC Educational Resources Information Center

Semenikhina, Elena; Drushlyak, Marina

2014-01-01

The article contains general information about the use of specialized mathematics software in the preparation of math teachers. The authors indicate the reasons to study the mathematics software. In particular, they analyze the possibility of presenting basic mathematical courses using mathematical computer tools from both a teacher and a student,…

What Software to Use in the Teaching of Mathematical Subjects?

ERIC Educational Resources Information Center

Berežný, Štefan

2015-01-01

We can consider two basic views, when using mathematical software in the teaching of mathematical subjects. First: How to learn to use specific software for the specific tasks, e. g., software Statistica for the subjects of Applied statistics, probability and mathematical statistics, or financial mathematics. Second: How to learn to use the…

Pre-Service Secondary Mathematics Teachers Making Sense of Definitions of Functions

ERIC Educational Resources Information Center

Chesler, Joshua

2012-01-01

Definitions play an essential role in mathematics. As such, mathematics teachers and students need to flexibly and productively interact with mathematical definitions in the classroom. However, there has been little research about mathematics teachers' understanding of definitions. At an even more basic level, there is little clarity about what…

The Effect of Concept Attainment Model on Mathematically Critical Thinking Ability of The University Students

NASA Astrophysics Data System (ADS)

Angraini, L. M.; Kartasasmita, B.; Dasari, D.

2017-02-01

This study examined the university students’ mathematically critical thinking ability through Concept Attainment Model learning. The Kolmogorov-Smirnov test, Levene test, t test, ANOVA one and two ways were used to analyse the data. The results of this study showed that (1) there is no difference grade on the student’s mathematical critical thinking ability between experimental group and conventional group as a whole, (2) there is no difference on the students’ mathematical critical thinking ability of experimental classes based on their mathematical early ability (3) there is no interaction between the learning that is used with the students’ mathematical early ability on the students’ mathematical critical thinking ability.

Preservice Agricultural Education Teachers' Mathematics Ability

ERIC Educational Resources Information Center

Stripling, Christopher T.; Roberts, T. Grady

2012-01-01

The purpose of this study was to examine the mathematics ability of the nation's preservice agricultural education teachers. Based on the results of this study, preservice teachers were not proficient in solving agricultural mathematics problems, and agricultural teacher education programs require basic and intermediate mathematics as their…

Which Preschool Mathematics Competencies Are Most Predictive of Fifth Grade Achievement?

PubMed Central

Nguyen, Tutrang; Watts, Tyler W.; Duncan, Greg J.; Clements, Douglas H.; Sarama, Julie S.; Wolfe, Christopher; Spitler, Mary Elaine

2016-01-01

In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children’s emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement. PMID:27057084

An Investigation of K-8 Preservice Teachers' Concept Images and Mathematical Definitions of Polygons

ERIC Educational Resources Information Center

Ward, Robin A.

2004-01-01

In this paper, the author presents a study which explored K-8 preservice teachers' concept images and mathematical definitions of polygons. This study was carried out in which K-8 teacher candidates enrolled in an elementary mathematics content course were asked to sort, identify, and provide definitions of such shapes including triangles,…

The Mental Representation of Integers: An Abstract-to-Concrete Shift in the Understanding of Mathematical Concepts

ERIC Educational Resources Information Center

Varma, Sashank; Schwartz, Daniel L.

2011-01-01

Mathematics has a level of structure that transcends untutored intuition. What is the cognitive representation of abstract mathematical concepts that makes them meaningful? We consider this question in the context of the integers, which extend the natural numbers with zero and negative numbers. Participants made greater and lesser judgments of…

Biomedical Mathematics, Unit I: Measurement, Linear Functions and Dimensional Algebra. Student Text. Revised Version, 1975.

ERIC Educational Resources Information Center

Biomedical Interdisciplinary Curriculum Project, Berkeley, CA.

This text presents lessons relating specific mathematical concepts to the ideas, skills, and tasks pertinent to the health care field. Among other concepts covered are linear functions, vectors, trigonometry, and statistics. Many of the lessons use data acquired during science experiments as the basis for exercises in mathematics. Lessons present…

A Conceptual Analysis of the Knowledge of Prospective Mathematics Teachers about Degree and Radian

ERIC Educational Resources Information Center

Tuna, Abdulkadir

2013-01-01

This study examined the knowledge levels of prospective mathematics teachers about the concepts of degree and radian, which are among the angle measuring units that constitute the basis of trigonometry, and the relationships between those concepts. The study group consisted of 93 prospective mathematics teachers attending a state university in…

Prototype Images in Mathematics Education: The Case of The Graphical Representation of The Definite Integral

ERIC Educational Resources Information Center

Jones, Steven R.

2018-01-01

Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits…

Critical Reviews in Mathematics Education. Materialien und Studien, Band 9.

ERIC Educational Resources Information Center

Bielefeld Univ. (West Germany). Inst. for Didactics in Mathematics.

Four papers are presented which view research in mathematics education from different perspectives. The titles are: (1) Review of Recent Research Related to the Concepts of Fractions and of Ratio; (2) Some Trends in Research and the Acquisition and Use of Space and Geometry Concepts; (3) A Portrayal of Traditional Teachers of Mathematics in…

The Development of Mathematical Self-Concept during College: Unique Benefits for Women in Math-Intensive Majors? ASHE Annual Meeting Paper.

ERIC Educational Resources Information Center

Sax, Linda J.

While previous research has outlined factors that can be used to predict academic self-concept among college students, much of this research pays little attention to how self-concept develops differently for unique subgroups of students. This paper examines the development of mathematical self-concept during college for four groups of students who…

Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

Introducing geometry concept based on history of Islamic geometry

NASA Astrophysics Data System (ADS)

Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

2018-01-01

Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

Family Matters: An Approach to the Theatre and to Theatre Research.

ERIC Educational Resources Information Center

Addington, David W.

The relational concepts developed in mathematics and psychology are used in this paper to explicate the needs and responsibilities of dramatic acting and theatre research. A parallel is constructed between the emergence of the mathematical concept of function, the awakening of psychology to the concept of relationship (especially regarding family…

Prospective Mathematics Teachers' Understanding of the Base Concept

ERIC Educational Resources Information Center

Horzum, Tugba; Ertekin, Erhan

2018-01-01

The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers (PMTs) have about the base concept (BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn…

The Connection Competencies of Pre-Service Mathematics Teachers about Geometric Concepts to Daily-Life

ERIC Educational Resources Information Center

Pirasa, Nimet

2016-01-01

However, geometry is the area with the most concrete possibility of mathematical topics which contains more abstract concepts, students experience difficulties while understanding. Therefore, the connection of issues with daily life to concrete the subjects and the ability of connecting geometric concepts with daily life of the teachers and…

Understanding Mathematics and Logic Using BASIC Computer Games.

ERIC Educational Resources Information Center

Ahl, David H.

This combination teacher's guide and student workbook serves as a companion volume to 101 BASIC Computer Games (EM 011 681). It presents ideas, exercises and supplemental projects which will aid the teaching and learning of a wide variety of academic subjects in grades 7 through 12, although the emphasis is upon mathematics and logic. In addition,…

Freddie Fish. A Primary Environmental Study of Basic Numerals, Sets, Ordinals and Shapes.

ERIC Educational Resources Information Center

Kraynak, Ola

This teacher's guide and study guide are an environmental approach to mathematics education in the primary grades. The mathematical studies of the numerals 0-10, ordinals, number sets, and basic shapes - diamond, circle, square, rectangle, and triangle - are developed through the story of Freddie Fish and his search for clean water. The…

Debates on the Basic Education Curriculum Reform and Teachers' Challenges in China: The Case of Mathematics

ERIC Educational Resources Information Center

Li, Qiong; Ni, Yu-jing

2012-01-01

Focusing on the case of mathematics, this paper reviews debates on China's new Basic Education Curriculum Reform program, including the status of knowledge within the reformed curriculum, the arrangement of the curriculum system, and the push toward real-life applicability and hands-on participation. It discusses the related challenges that…

From Research to Practice: Basic Mathematics Skills and Success in Introductory Statistics

ERIC Educational Resources Information Center

Lunsford, M. Leigh; Poplin, Phillip

2011-01-01

Based on previous research of Johnson and Kuennen (2006), we conducted a study to determine factors that would possibly predict student success in an introductory statistics course. Our results were similar to Johnson and Kuennen in that we found students' basic mathematical skills, as measured on a test created by Johnson and Kuennen, were a…

The Mathematics Attitude Inventory: Instrument and User's Manual.

ERIC Educational Resources Information Center

Sandman, Richard S.

1980-01-01

The Mathematics Attitude Inventory, designed to measure the attitudes toward mathematics of secondary students, and its accompanying user's manual, are described. The six scales measure perception of mathematics teachers, value of mathematics, self-concept in mathematics, and anxiety toward, enjoyment of, and motivation in mathematics. (MK)

The stabilizing role of the Sabbath in pre-monarchic Israel: a mathematical model.

PubMed

Livni, Joseph; Stone, Lewi

2015-03-01

The three monotheistic cultures have many common institutions and some of them germinated in pre-monarchic Israel. Reasonably, the essential institutions were in place at that starting point; this work explores the possibility that the Sabbath is one of these institutions. Our mathematical examination points to the potential cultural, civic, and social role of the weekly Sabbath, that is, the Sabbath institution, in controlling deviation from social norms. It begins with an analogy between spread of transgression (defined as lack of conformity with social norms) and of biological infection. Borrowing well-known mathematical methods, we derive solution sets of social equilibrium and study their social stability. The work shows how a weekly Sabbath could in theory enhance social resilience in comparison with a similar assembly with a more natural and longer period, say between New Moon and Full Moon. The examination reveals that an efficient Sabbath institution has the potential to ensure a stable organization and suppress occasional appearances of transgression from cultural norms and boundaries. The work suggests the existence of a sharp threshold governed by the "Basic Sabbath Number ש0"-a critical observance of the Sabbath, or large enough ש0, is required to ensure suppression of transgression. Subsequently, the model is used to explore an interesting question: how old is the Sabbath? The work is interdisciplinary, combining anthropological concepts with mathematical analysis and with archaeological parallels in regards to the findings.

Spatial/Spectral Identification of Endmembers from AVIRIS Data using Mathematical Morphology

NASA Technical Reports Server (NTRS)

Plaza, Antonio; Martinez, Pablo; Gualtieri, J. Anthony; Perez, Rosa M.

2001-01-01

During the last several years, a number of airborne and satellite hyperspectral sensors have been developed or improved for remote sensing applications. Imaging spectrometry allows the detection of materials, objects and regions in a particular scene with a high degree of accuracy. Hyperspectral data typically consist of hundreds of thousands of spectra, so the analysis of this information is a key issue. Mathematical morphology theory is a widely used nonlinear technique for image analysis and pattern recognition. Although it is especially well suited to segment binary or grayscale images with irregular and complex shapes, its application in the classification/segmentation of multispectral or hyperspectral images has been quite rare. In this paper, we discuss a new completely automated methodology to find endmembers in the hyperspectral data cube using mathematical morphology. The extension of classic morphology to the hyperspectral domain allows us to integrate spectral and spatial information in the analysis process. In Section 3, some basic concepts about mathematical morphology and the technical details of our algorithm are provided. In Section 4, the accuracy of the proposed method is tested by its application to real hyperspectral data obtained from the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) imaging spectrometer. Some details about these data and reference results, obtained by well-known endmember extraction techniques, are provided in Section 2. Finally, in Section 5 we expose the main conclusions at which we have arrived.

Effects of a Mathematics Fluency Program on Mathematics Performance of Students with Challenging Behaviors

ERIC Educational Resources Information Center

Whitney, Todd; Hirn, Regina G.; Lingo, Amy S.

2016-01-01

In the present study, we examined the effects of a fluency-building mathematics program called Great Leaps Math on fluency of basic addition mathematics facts zero to nine and word problem solving using a multiple probe design across participants. Three elementary students with challenging behaviors and mathematics difficulty participated in the…

Some environmental and attitudinal characteristics as predictors of mathematical creativity

NASA Astrophysics Data System (ADS)

Kanhai, Abhishek; Singh, Bhoodev

2017-04-01

There are many things which can be made more useful and interesting through the application of creativity. Self-concept in mathematics and some school environmental factors such as resource adequacy, teachers' support to the students, teachers' classroom control, creative stimulation by the teachers, etc. were selected in the study. The sample of the study comprised 770 seventh grade students. Pearson correlation, multiple correlation, regression equation and multiple discriminant function analyses of variance were used to analyse the data. The result of the study showed that the relationship between mathematical creativity and each attitudinal and environmental characteristic was found to be positive and significant. Index of forecasting efficiency reveals that mathematical creativity may be best predicted by self-concept in mathematics. Environmental factors, resource adequacy and creative stimulation by the teachers' are found to be the most important factors for predicting mathematical creativity, while social-intellectual involvement among students and educational administration of the schools are to be suppressive factors. The multiple correlation between mathematical creativity and attitudinal and school environmental characteristic suggests that the combined contribution of these variables plays a significant role in the development of mathematical creativity. Mahalanobis analysis indicates that self-concept in mathematics and total school environment were found to be contributing significantly to the development of mathematical creativity.

Mathematical Concepts and Proofs from Nicole Oresme: Using the History of Calculus to Teach Mathematics

ERIC Educational Resources Information Center

Babb, Jeff

2005-01-01

This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323-1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite series. The historical importance and pedagogical value of his work will be considered in the context of an undergraduate course on…

Implications of Overlapping Difficulties in Mathematics and Reading on Self-Concept and Academic Achievement

ERIC Educational Resources Information Center

Holopainen, Leena; Taipale, Airi; Savolainen, Hannu

2017-01-01

In this study, the relationship between adolescents' difficulty in mathematics and reading and the influence on academic self-concept and school grades was examined. The participants (N = 585; 299 girls, 286 boys) were one age group of ninth-graders whose mathematics and reading skills were assessed at the end of comprehensive school at age…

Pokémon Battles as a Context for Mathematical Modeling

ERIC Educational Resources Information Center

McGuffey, William

2017-01-01

In this article I explore some of the underlying mathematics of Poke´mon battles and describe ways that teachers at the secondary level could explore concepts of mathematical game theory in this context. I discuss various ways of representing and analyzing a Poke´mon battle using game theory and conclude with an example of applying concepts of…

Saussurian Linguistics Revisited: Can It Inform Our Interpretation of Mathematical Activity?.

ERIC Educational Resources Information Center

McNamara, O.

1995-01-01

Examines the basic notions of Ferdinand de Saussure and proposes that language is fundamental to the process of learning mathematics. Investigates possible mathematical perspectives upon Saussure's ideas and explores the contribution his work can offer to enhance and enrich the interpretive framework through which mathematical activity is observed…

A Guide to Curriculum Planning in Mathematics. Bulletin No. 6284.

ERIC Educational Resources Information Center

Chambers, Donald L.; And Others

This guide was written under the basic assumptions that the mathematics curriculum must continuously change and that mathematics is most effectively learned through a spiral approach. Further, it is assumed that the audience will be members of district mathematics curriculum committees. Instructional objectives have been organized to reveal the…

Mathematics for Electronics.

ERIC Educational Resources Information Center

Clary, Joseph R.; Nery, Karen P.

This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…

Where Have All the Mathematics Teachers Gone?

ERIC Educational Resources Information Center

Clever, George

Three basic causes for the general decline in mathematics achievement among high school graduates nationally are poor motivation to learn math, poor math curriculum, and poor or no mathematics instruction. Many Native Americans drop mathematics because of lack of challenging courses or interesting teachers in their high schools. Since American…

Quantum mechanical wavefunction: visualization at undergraduate level

NASA Astrophysics Data System (ADS)

Chhabra, Mahima; Das, Ritwick

2017-01-01

Quantum mechanics (QM) forms the most crucial ingredient of modern-era physical science curricula at undergraduate level. The abstract ideas involved in QM related concepts pose a challenge towards appropriate visualization as a consequence of their counter-intuitive nature and lack of experiment-assisted visualization tools. At the heart of the quantum mechanical formulation lies the concept of ‘wavefunction’, which forms the basis for understanding the behavior of physical systems. At undergraduate level, the concept of ‘wavefunction’ is introduced in an abstract framework using mathematical tools and therefore opens up an enormous scope for alternative conceptions and erroneous visualization. The present work is an attempt towards exploring the visualization models constructed by undergraduate students for appreciating the concept of ‘wavefunction’. We present a qualitative analysis of the data obtained from administering a questionnaire containing four visualization based questions on the topic of ‘wavefunction’ to a group of ten undergraduate-level students at an institute in India which excels in teaching and research of basic sciences. Based on the written responses, all ten students were interviewed in detail to unravel the exact areas of difficulty in visualization of ‘wavefunction’. The outcome of present study not only reveals the gray areas in students’ conceptualization, but also provides a plausible route to address the issues at the pedagogical level within the classroom.

Design of a control configured tanker aircraft

NASA Technical Reports Server (NTRS)

Walker, S. A.

1976-01-01

The benefits that accrue from using control configured vehicle (CCV) concepts were examined along with the techniques for applying these concepts to an advanced tanker aircraft design. Reduced static stability (RSS) and flutter mode control (FMC) were the two primary CCV concepts used in the design. The CCV tanker was designed to the same mission requirements specified for a conventional tanker design. A seven degree of freedom mathematical model of the flexible aircraft was derived and used to synthesize a lateral stability augmentation system (SAS), a longitudinal control augmentation system (CAS), and a FMC system. Fatigue life and cost analyses followed the control system synthesis, after which a comparative evaluation of the CCV and conventional tankers was made. This comparison indicated that the CCV weight and cost were lower but that, for this design iteration, the CCV fatigue life was shorter. Also, the CCV crew station acceleration was lower, but the acceleration at the boom operator station was higher relative to the corresponding conventional tanker. Comparison of the design processes used in the CCV and conventional design studies revealed that they were basically the same.

Damage-mitigating control of aerospace systems for high performance and extended life

NASA Technical Reports Server (NTRS)

Ray, Asok; Wu, Min-Kuang; Carpino, Marc; Lorenzo, Carl F.; Merrill, Walter C.

1992-01-01

The concept of damage-mitigating control is to minimize fatigue (as well as creep and corrosion) damage of critical components of mechanical structures while simultaneously maximizing the system dynamic performance. Given a dynamic model of the plant and the specifications for performance and stability robustness, the task is to synthesize a control law that would meet the system requirements and, at the same time, satisfy the constraints that are imposed by the material and structural properties of the critical components. The authors present the concept of damage-mitigating control systems design with the following objectives: (1) to achieve high performance with a prolonged life span; and (2) to systematically update the controller as the new technology of advanced materials evolves. The major challenge is to extract the information from the material properties and then utilize this information in a mathematical form so that it can be directly applied to robust control synthesis for mechanical systems. The basic concept of damage-mitigating control is illustrated using a relatively simplified model of a space shuttle main engine.

The impact of mathematical models of teaching materials on square and rectangle concepts to improve students' mathematical connection ability and mathematical disposition in middle school

NASA Astrophysics Data System (ADS)

Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

2017-05-01

The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.

Statistical Content in Middle Grades Mathematics Textbooks

ERIC Educational Resources Information Center

Pickle, Maria Consuelo Capiral

2012-01-01

This study analyzed the treatment and scope of statistical concepts in four, widely-used, contemporary, middle grades mathematics textbook series: "Glencoe Math Connects," "Prentice Hall Mathematics," "Connected Mathematics Project," and "University of Chicago School Mathematics Project." There were three…

Applying Computerized Concept Maps in Guiding Pupils to Reason and Solve Mathematical Problems: The Design Rationale and Effect

ERIC Educational Resources Information Center

Chen, I-Ching; Hu, Shueh-Cheng

2013-01-01

The capability of solving fundamental mathematical problems is essential to elementary school students; however instruction based on ordinary narration usually perplexes students. Concept mapping is well known for its effectiveness on assimilating and organizing knowledge, which is essential to meaningful learning. A variety of concept map-based…

A Study of the Effects of Verbalization on Concept Formation in Mathematics.

ERIC Educational Resources Information Center

Albig, David L.

The purpose of the study was to investigate the hypothesis that requiring a student to verbalize a newly discovered mathematical concept interferes with his ability to use that concept. Five semi-programmed lessons (dealing with function machines, exponents, marker games, geometry, and One Pile Nim) were prepared and taught to a random selection…

Angle Concept: A High School and Tertiary Longitudinal Perspective to Minimize Obstacles

ERIC Educational Resources Information Center

Barabash, Marita

2017-01-01

The concept of angle emerges in numerous forms as the learning of mathematics and its applications advances through the high school and tertiary curriculum. Many difficulties and misconceptions in the usage of this multifaceted concept might be avoided or at least minimized should the lecturers in different areas of pure and applied mathematics be…

Interdisciplinary Mathematics-Physics Approaches to Teaching the Concept of Angle in Elementary School

ERIC Educational Resources Information Center

Munier, Valerie; Merle, Helene

2009-01-01

The present study takes an interdisciplinary mathematics-physics approach to the acquisition of the concept of angle by children in Grades 3-5. This paper first presents the theoretical framework we developed, then we analyse the concept of angle and the difficulties pupils have with it. Finally, we report three experimental physics-based teaching…

Destrezas de Matematica: Curriculo Basico. Guia para el Maestro (Mathematics Skills: Basic Curriculum. Teacher's Guide).

ERIC Educational Resources Information Center

Puerto Rico State Dept. of Education, Hato Rey. Office of Special Education.

The fundamental importance of basic mathematics to daily life is emphasized in this teacher's guide for special education teachers in Puerto Rico. While it is necessary for the teacher to determine the needs and abilities of each student and adapt the curriculum accordingly, this guide presents, in Spanish, a set of lesson plans, each with an…

Developing Basic Mathematical Skills of Pre-School Children by Using Plasticized Clay

ERIC Educational Resources Information Center

Chumark, Charung; Puncreobutr, Vichian

2016-01-01

The main objective of this research was to study the development of basic mathematical skills in preschool children by using plasticized clay. A pre-test and post-test design was adopted for the study to compare the difference before and after the art activity. The experimental group of 15 preschool children of 3-4 years old, attending…

Job-Related Basic Math Skills: An Analysis of Employees and Employers/Supervisors' Perception of Needed Math Skills for Office Occupations.

ERIC Educational Resources Information Center

Redmann, Donna H.

Phase I of a study was conducted to identify the basic mathematics competencies needed for job success in office occupations (14 job clusters). It also sought to determine the differences between employees' and employer/supervisors' perceptions of the degree of importance of mathematics skills for office occupations. Following a review of…

Four (Algorithms) in One (Bag): An Integrative Framework of Knowledge for Teaching the Standard Algorithms of the Basic Arithmetic Operations

ERIC Educational Resources Information Center

Raveh, Ira; Koichu, Boris; Peled, Irit; Zaslavsky, Orit

2016-01-01

In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic…

Do Different Types of School Mathematics Development Depend on Different Constellations of Numerical versus General Cognitive Abilities?

ERIC Educational Resources Information Center

Fuchs, Lynn S.; Geary, David C.; Compton, Donald L.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Bryant, Joan D.; Schatschneider, Christopher

2010-01-01

The purpose of this study was to examine the interplay between basic numerical cognition and domain-general abilities (such as working memory) in explaining school mathematics learning. First graders (N = 280; mean age = 5.77 years) were assessed on 2 types of basic numerical cognition, 8 domain-general abilities, procedural calculations, and word…

Fundamentals handbook of electrical and computer engineering. Volume 1 Circuits fields and electronics

NASA Astrophysics Data System (ADS)

Chang, S. S. L.

State of the art technology in circuits, fields, and electronics is discussed. The principles and applications of these technologies to industry, digital processing, microwave semiconductors, and computer-aided design are explained. Important concepts and methodologies in mathematics and physics are reviewed, and basic engineering sciences and associated design methods are dealt with, including: circuit theory and the design of magnetic circuits and active filter synthesis; digital signal processing, including FIR and IIR digital filter design; transmission lines, electromagnetic wave propagation and surface acoustic wave devices. Also considered are: electronics technologies, including power electronics, microwave semiconductors, GaAs devices, and magnetic bubble memories; digital circuits and logic design.

A brief introduction to probability.

PubMed

Di Paola, Gioacchino; Bertani, Alessandro; De Monte, Lavinia; Tuzzolino, Fabio

2018-02-01

The theory of probability has been debated for centuries: back in 1600, French mathematics used the rules of probability to place and win bets. Subsequently, the knowledge of probability has significantly evolved and is now an essential tool for statistics. In this paper, the basic theoretical principles of probability will be reviewed, with the aim of facilitating the comprehension of statistical inference. After a brief general introduction on probability, we will review the concept of the "probability distribution" that is a function providing the probabilities of occurrence of different possible outcomes of a categorical or continuous variable. Specific attention will be focused on normal distribution that is the most relevant distribution applied to statistical analysis.

The astronomy education through interactive materials

NASA Astrophysics Data System (ADS)

Voelzke, Marcos Rincon; Macedo, Josue

This study presents results of a survey conducted at the Federal Institution of Education, Science and Technology in the North of Minas Gerais (IFNMG), and aimed to investigate the potentialities of the use of interactive materials in the teaching of astronomy. An advanced training course with involved learning activities about basic concepts of astronomy was offered to thirty-two Licenciate students in Physics, Mathematics and Biological Sciences, using the mixed methodology, combined with the three pedagogical moments. Among other aspects, the viability of the use of resources was noticed, involving digital technologies and interactive materials on teaching of astronomy, which may contribute to the broadening of methodological options for future teachers and meet their training needs.

Astronomy education through interactive materials

NASA Astrophysics Data System (ADS)

Voelzke, Marcos Rincon; Antunes de Macêdo, Josué

2015-08-01

This study presents results of a survey conducted at the Federal Institution of Education, Science and Technology in the North of Minas Gerais (IFNMG), and aimed to investigate the potentialities of the use of interactive materials in the teaching of astronomy. An advanced training course with involved learning activities about basic concepts of astronomy was offered to thirty-two Licenciate students in Physics, Mathematics and Biological Sciences, using the mixed methodology, combined with the three pedagogical moments. Among other aspects, the viability of the use of resources was noticed, involving digital technologies and interactive materials on teaching of astronomy, which may contribute to the broadening of methodological options for future teachers and meet their training needs.

Research on the potential use of interactive materials on astronomy education

NASA Astrophysics Data System (ADS)

Voelzke, Marcos Rincon; Macedo, Josue

2016-07-01

This study presents results of a survey conducted at the Federal Institution of Education, Science and Technology in the North of Minas Gerais (IFNMG), and aimed to investigate the potentialities of the use of interactive materials in the teaching of astronomy. An advanced training course with involved learning activities about basic concepts of astronomy was offered to thirty-two Licenciate students in Physics, Mathematics and Biological Sciences, using the mixed methodology, combined with the three pedagogical moments. Among other aspects, the viability of the use of resources was noticed, involving digital technologies and interactive materials on teaching of astronomy, which may contribute to the broadening of methodological options for future teachers and meet their training needs.

Rosalind Franklin's X-ray photo of DNA as an undergraduate optical diffraction experiment

NASA Astrophysics Data System (ADS)

Thompson, J.; Braun, G.; Tierney, D.; Wessels, L.; Schmitzer, H.; Rossa, B.; Wagner, H. P.; Dultz, W.

2018-02-01

Rosalind Franklin's X-ray diffraction patterns of DNA molecules rendered the important clue that DNA has the structure of a double helix. The most famous X-ray photograph, Photo 51, is still printed in most Biology textbooks. We suggest two optical experiments for undergraduates that make this historic achievement comprehensible for students by using macromodels of DNA and visible light to recreate a diffraction pattern similar to Photo 51. In these macromodels, we replace the double helix both mathematically and experimentally with its two-dimensional (flat) projection and explain why this is permissible. Basic optical concepts are used to infer certain well-known characteristics of DNA from the diffraction pattern.

Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law

NASA Astrophysics Data System (ADS)

Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Yamato, Ichiro

2013-07-01

There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.

Issues in Developing a Normative Descriptive Model for Dyadic Decision Making

NASA Technical Reports Server (NTRS)

Serfaty, D.; Kleinman, D. L.

1984-01-01

Most research in modelling human information processing and decision making has been devoted to the case of the single human operator. In the present effort, concepts from the fields of organizational behavior, engineering psychology, team theory and mathematical modelling are merged in an attempt to consider first the case of two cooperating decisionmakers (the Dyad) in a multi-task environment. Rooted in the well-known Dynamic Decision Model (DDM), the normative descriptive approach brings basic cognitive and psychophysical characteristics inherent to human behavior into a team theoretic analytic framework. An experimental paradigm, involving teams in dynamic decision making tasks, is designed to produce the data with which to build the theoretical model.

Geospatial Education: Working with the NASA Airborne Science Program

NASA Astrophysics Data System (ADS)

Lockwood, C. M.; Handley, L.; Handley, N.

2010-12-01

WETMAAP (Wetland Education Through Maps and Aerial Photography) , a program of CNL World, supports the NASA Strategic Goals and Objectives for Education by providing classroom teachers and formal and informal educators with professional development. WETMAAP promotes science by inquiry through the use of a building-block process, comparative analysis, and analytical observations. Through the WETMAAP workshops and website, educators receive the concepts necessary to provide students with a basic understanding of maps, aerial photography, and satellite and airborne imagery that focus on the study of wetlands and wetland change. The program targets educators, Grades 5 - 12, in earth science, environmental science, biology, geography, and mathematics, and emphasizes a comprehensive curriculum approach.

Health: The No-Man's-Land Between Physics and Biology.

PubMed

Mansfield, Peter J

2015-10-01

Health as a positive attribute is poorly understood because understanding requires concepts from physics, of which physicians and other life scientists have a very poor grasp. This paper reviews the physics that bears on biology, in particular complex quaternions and scalar fields, relates these to the morphogenetic fields proposed by biologists, and defines health as an attribute of living action within these fields. The distinction of quality, as juxtaposed with quantity, proves essential. Its basic properties are set out, but a science and mathematics of quality are awaited. The implications of this model are discussed, particularly as proper health enhancement could set a natural limit to demand for, and therefore the cost of, medical services.

A survey of basic reproductive ratios in vector-borne disease transmission modeling

NASA Astrophysics Data System (ADS)

Soewono, E.; Aldila, D.

2015-03-01

Vector-borne diseases are commonly known in tropical and subtropical countries. These diseases have contributed to more than 10% of world infectious disease cases. Among the vectors responsible for transmitting the diseases are mosquitoes, ticks, fleas, flies, bugs and worms. Several of the diseases are known to contribute to the increasing threat to human health such as malaria, dengue, filariasis, chikungunya, west nile fever, yellow fever, encephalistis, and anthrax. It is necessary to understand the real process of infection, factors which contribute to the complication of the transmission in order to come up with a good and sound mathematical model. Although it is not easy to simulate the real transmission process of the infection, we could say that almost all models have been developed from the already long known Host-Vector model. It constitutes the main transmission processes i.e. birth, death, infection and recovery. From this simple model, the basic concepts of Disease Free and Endemic Equilibria and Basic Reproductive Ratio can be well explained and understood. Theoretical, modeling, control and treatment aspects of disease transmission problems have then been developed for various related diseases. General construction as well as specific forms of basic reproductive ratios for vector-borne diseases are discusses here.

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

Mathematics is always invisible, Professor Dowling

NASA Astrophysics Data System (ADS)

Cable, John

2015-09-01

This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.

Implications of Informal Education Experiences for Mathematics Teachers' Ability to Make Connections beyond Formal Classroom

ERIC Educational Resources Information Center

Popovic, Gorjana; Lederman, Judith S.

2015-01-01

The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real-world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and…

Has Progress in Mathematics Slowed Down?

ERIC Educational Resources Information Center

Halmos, Paul R.

1990-01-01

Reported is whether and how mathematics has changed during the 75 years of the Mathematical Association of America's (MAA) existence. The progress of mathematics is organized into 9 concepts, 2 explosions, and 11 developments. (KR)

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

The Language of Mathematics: Learning to Read Mathematics for Understanding and Success

ERIC Educational Resources Information Center

Im, Yang Ok

2013-01-01

The intention of this project was to explore the effect of utilizing basic reading skills to promote student growth in mathematical literacy among middle school students. Mathematics was approached as a linquistical language and teachers utilized decoding skills as the treatment. This study used a nonequivalent control group quasi-experimental…

Visual Representations in Mathematics Teaching: An Experiment with Students

ERIC Educational Resources Information Center

Debrenti, Edith

2015-01-01

General problem-solving skills are of central importance in school mathematics achievement. Word problems play an important role not just in mathematical education, but in general education as well. Meaningful learning and understanding are basic aspects of all kinds of learning and it is even more important in the case of learning mathematics. In…

Emotion Work and Affective Stance in the Mathematics Classroom: The Case of IRE Sequences in Finnish Classroom Interaction

ERIC Educational Resources Information Center

Tainio, Liisa; Laine, Anu

2015-01-01

Although according to the Finnish curriculum the learning environment in mathematics lessons should promote supportive interaction, Finnish pupils' attitudes toward and self-beliefs regarding mathematics deteriorate during basic education. This article investigates emotion work in teacher-student interaction in Finnish mathematics classrooms; the…

Measuring the Effectiveness of a Mathematics Support Service: An Email Survey

ERIC Educational Resources Information Center

Gillard, Jonathan; Robathan, Kirsty; Wilson, Robert

2011-01-01

Over the last decade the "mathematics problem" (students lacking basic mathematical skills on entry into higher education), and proposed solutions of this problem have been widely debated. One method to help combat this issue has been the introduction of mathematics support centres across higher education institutions. This article describes the…

A Conceptual Metaphor Framework for the Teaching of Mathematics

ERIC Educational Resources Information Center

Danesi, Marcel

2007-01-01

Word problems in mathematics seem to constantly pose learning difficulties for all kinds of students. Recent work in math education (for example, [Lakoff, G. & Nunez, R. E. (2000). "Where mathematics comes from: How the embodied mind brings mathematics into being." New York: Basic Books]) suggests that the difficulties stem from an…

Learning Mathematics in English at Basic Schools in Ghana: A Benefit or Hindrance?

ERIC Educational Resources Information Center

Fredua-Kwarteng, Eric; Ahia, Francis

2015-01-01

Facilitating effective mathematics learning and higher mathematics achievement have long been recognized as a key to the scientific and technological advancement of the African continent. While the central role that language proficiency plays in mathematics teaching and learning has received an overwhelming research attention in the literature…

Conceptualisations of infinity by primary pre-service teachers

NASA Astrophysics Data System (ADS)

Date-Huxtable, Elizabeth; Cavanagh, Michael; Coady, Carmel; Easey, Michael

2018-05-01

As part of the Opening Real Science: Authentic Mathematics and Science Education for Australia project, an online mathematics learning module embedding conceptual thinking about infinity in science-based contexts, was designed and trialled with a cohort of 22 pre-service teachers during 1 week of intensive study. This research addressed the question: "How do pre-service teachers conceptualise infinity mathematically?" Participants argued the existence of infinity in a summative reflective task, using mathematical and empirical arguments that were coded according to five themes: definition, examples, application, philosophy and teaching; and 17 codes. Participants' reflections were differentiated as to whether infinity was referred to as an abstract (A) or a real (R) concept or whether both (B) codes were used. Principal component analysis of the reflections, using frequency of codings, revealed that A and R codes occurred at different frequencies in three groups of reflections. Distinct methods of argument were associated with each group of reflections: mathematical numerical examples and empirical measurement comparisons characterised arguments for infinity as an abstract concept, geometric and empirical dynamic examples and belief statements characterised arguments for infinity as a real concept and empirical measurement and mathematical examples and belief statements characterised arguments for infinity as both an abstract and a real concept. An implication of the results is that connections between mathematical and empirical applications of infinity may assist pre-service teachers to contrast finite with infinite models of the world.

The availability and accessibility of basic concept vocabulary in AAC software: a preliminary study.

PubMed

McCarthy, Jillian H; Schwarz, Ilsa; Ashworth, Morgan

2017-09-01

Core vocabulary lists obtained through the analyses of children's utterances include a variety of basic concept words. Supporting young children who use augmentative and alternative communication (AAC) to develop their understanding and use of basic concepts is an area of practice that has important ramifications for successful communication in a classroom environment. This study examined the availability of basic concept words across eight frequently used, commercially available AAC language systems, iPad© applications, and symbol libraries used to create communication boards. The accessibility of basic concept words was subsequently examined using two AAC language page sets and two iPad applications. Results reveal that the availability of basic concept words represented within the different AAC language programs, iPad applications, and symbol libraries varied but was limited across programs. However, there is no significant difference in the accessibility of basic concept words across the language program page sets or iPad applications, generally because all of them require sophisticated motor and cognitive plans for access. These results suggest that educators who teach or program vocabulary in AAC systems need to be mindful of the importance of basic concept words in classroom settings and, when possible, enhance the availability and accessibility of these words to users of AAC.

Special relativity from observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2015-09-01

When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

The Physics of Vibration

NASA Astrophysics Data System (ADS)

Pippard, A. B.

1989-11-01

The study of vibration in physical systems is an important part of almost all fields in physics and engineering. This work, originally published in two volumes, examines the classical aspects in Part I and the quantum oscillator in Part II. The classical linear vibrator is treated first and the underlying unity of all linear oscillations in electrical, mechanical and acoustic systems is emphasized. Following this the book turns to the treatment of nonlinear vibrations, a field with which engineers and physicists are generally less familiar. In Part II the emphasis turns to quantum systems, that is those systems which can only be adequately described by quantum mechanics. The treatment concentrates on vibrations in atoms and molecules and their interaction with electromagnetic radiation. The similarities of classical and quantum methods are stressed and the limits of the classical treatment are examined. Throughout the book, each phenomenon discussed is illustrated with many examples and theory and experiment are compared. Although the reader may find that the physics discussed is demanding and the concepts are subtle in places, all mathematics used is familiar to both engineers and experimental scientists. Although not a textbook this is a useful introduction to the more advanced mathematical treatment of vibrations as it bridges the gap between the basic principles and more specialized concepts. It will be of great interest to advanced undergraduates and postgraduates as well as applied mathematicians, physicists and engineers in university and industry.

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students' mathematical performance

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-12-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students' mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students' simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students' formulation and combination of equations. Several reasons may explain this difference, including the students' different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

Saturation behavior: a general relationship described by a simple second-order differential equation.

PubMed

Kepner, Gordon R

2010-04-13

The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical constants governing the behavior of these phenomena led to an alternative perspective on saturation behavior kinetics. Their essential commonality was revealed by this analysis, based on the second-order differential equation.

The solar-terrestrial environment. An introduction to geospace - the science of the terrestrial upper atmosphere, ionosphere and magnetosphere.

NASA Astrophysics Data System (ADS)

Hargreaves, J. K.

This textbook is a successor to "The upper atmosphere and solar-terrestrial relations" first published in 1979. It describes physical conditions in the upper atmosphere and magnetosphere of the Earth. This geospace environment begins 70 kilometres above the surface of the Earth and extends in near space to many times the Earth's radius. It is the region of near-Earth environment where the Space Shuttle flies, the aurora is generated, and the outer atmosphere meets particles streaming out of the sun. The account is introductory. The intent is to present basic concepts, and for that reason the mathematical treatment is not complex. There are three introductory chapters that give basic physics and explain the principles of physical investigation. The principal material contained in the main part of the book covers the neutral and ionized upper atmosphere, the magetosphere, and structures, dynamics, disturbances and irregularities. The concluding chapter deals with technological applications.

History of Mathematics: Illuminating Understanding of School Mathematics Concepts for Prospective Mathematics Teachers

ERIC Educational Resources Information Center

Clark, Kathleen Michelle

2012-01-01

The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…

The Role of Mediators in the Development of Longitudinal Mathematics Achievement Associations

PubMed Central

Watts, Tyler W.; Duncan, Greg J.; Chen, Meichu; Claessens, Amy; Davis-Kean, Pamela E.; Duckworth, Kathryn; Engel, Mimi; Siegler, Robert; Susperreguy, Maria Ines

2016-01-01

Despite research demonstrating a strong association between early and later mathematics achievement, few studies have investigated mediators of this association. Using longitudinal data (n=1362), we tested the extent to which mathematics self-concepts, school placement, executive functioning, and proficiency in fractions and division account for the association between mathematics achievement in first grade and at age 15. As hypothesized, a strong longitudinal association between first grade and adolescent mathematics achievement was present (β= .36) even after controlling for a host of background characteristics, including cognitive skills and reading ability. The mediators accounted for 39% of this association, with mathematics self-concept, gifted and talented placement, and knowledge of fractions and division, serving as significant mediators. PMID:26332124

Preservice Mathematics Teachers' Metaphorical Perceptions towards Proof and Proving

ERIC Educational Resources Information Center

Ersen, Zeynep Bahar

2016-01-01

Since mathematical proof and proving are in the center of mathematics; preservice mathematics teachers' perceptions against these concepts have a great importance. Therefore, the study aimed to determine preservice mathematics teachers' perceptions towards proof and proving through metaphors. The participants consisted of 192 preservice…

Forms of Understanding in Mathematical Problem Solving.

DTIC Science & Technology

1982-08-01

mathematical concepts, but more recent studies (e.g., Gelman & Gallistel , 1978) indicate that significant understanding of those concepts should be...Beranek, & Newman, 1980. Gelman, R., & Gallistel , C. R. The child’s understanding of number. Cambridge, Mass.: Harvard University Press, 1978. 43 Greeno

Peirce's Philosophy of Mathematical Education: Fostering Reasoning Abilities for Mathematical Inquiry

ERIC Educational Resources Information Center

Campos, Daniel G.

2010-01-01

I articulate Charles S. Peirce's philosophy of mathematical education as related to his conception of mathematics, the nature of its method of inquiry, and especially, the reasoning abilities required for mathematical inquiry. The main thesis is that Peirce's philosophy of mathematical education primarily aims at fostering the development of the…

A Comparative Study of the FET Phase Mathematical Literacy and Mathematics Curriculum

ERIC Educational Resources Information Center

Mhakure, Duncan; Mokoena, Mamolahluwa Amelia

2011-01-01

This article is based on a study that compared the FET (further education and training) phase mathematics literacy curriculum and mathematics curriculum. The study looked into how the conceptualization of a mathematical literacy curriculum enhanced the acquisition of mathematical concepts among the learners. In order to carry out this comparison…

Mathematics and Water in the Garden: Weaving Mathematics into the Students' Lived Environment

ERIC Educational Resources Information Center

Clarkson, Philip

2010-01-01

In an earlier issue of "Australian Primary Mathematics Classroom," Sparrow discussed the concept of real-world mathematics and the use of mathematics to explore problems in real-life situations. Environmental issues have provided a context that some teachers have used for teaching mathematics. An example of a particular environmental…

A Descriptive Study Examining the Impact of Digital Writing Environments on Communication and Mathematical Reasoning for Students with Learning Disabilities

ERIC Educational Resources Information Center

Huscroft-D'Angelo, Jacqueline; Higgins, Kristina N.; Crawford, Lindy L.

2014-01-01

Proficiency in mathematics, including mathematical reasoning skills, requires students to communicate their mathematical thinking. Mathematical reasoning involves making sense of mathematical concepts in a logical way to form conclusions or judgments, and is often underdeveloped in students with learning disabilities. Technology-based environments…

The Effect of the Success in Teaching Geometry of Basic Level Education Mathematics

ERIC Educational Resources Information Center

Yavuz, Ayse; Aydin, Bünyamin; Avci, Musa

2016-01-01

The purpose of this study was to investigate primary and secondary mathematics teachers' candidates' effect of the success in geometry education. The sample of the study consists of students first and last class preservice primary mathematics teachers which are enrolled program education at department of mathematics and students first and last…

Mathematics for the Technical Student: The Use of the Computer in the Systems Approach to Instruction.

ERIC Educational Resources Information Center

Capps, Joan P.

An instructional method using flow-chart symbols to make mathematical abstractions more concrete was implemented for a year in a technical mathematics course. Students received instruction in computer applications and programming in the BASIC language in order to increase motivation and firm the mathematical skills and problem-solving approaches…

Making a Case for Exact Language as an Aspect of Rigour in Initial Teacher Education Mathematics Programmes

ERIC Educational Resources Information Center

van Jaarsveld, Pieter

2016-01-01

Pre-service secondary mathematics teachers have a poor command of the exact language of mathematics as evidenced in assignments, micro-lessons and practicums. The unrelenting notorious annual South African National Senior Certificate outcomes in mathematics and the recognition by the Department of Basic Education (DBE) that the correct use of…

Exploring Mathematics Teachers' Pedagogical Content Knowledge in the Context of Knowledge of Students

ERIC Educational Resources Information Center

Aksu, Zeki; Kul, Ümit

2016-01-01

Functions are one of the basic topics taught in mathematics curriculum at Secondary school level requiring knowledge from the students' past, and uniting mathematical topics. Mathematics teachers have both their own learning experience of functions, as well as their own teaching experience, leading to the question of what level of student…

Promoting Access to Common Core Mathematics for Students with Severe Disabilities through Mathematical Problem Solving

ERIC Educational Resources Information Center

Spooner, Fred; Saunders, Alicia; Root, Jenny; Brosh, Chelsi

2017-01-01

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…

The Role of Prior Mathematical Experience in Predicting Mathematics Performance in Higher Education

ERIC Educational Resources Information Center

Faulkner, Fiona; Hannigan, Ailish; Fitzmaurice, Olivia

2014-01-01

Evidence of deficiencies in basic mathematical skills of beginning undergraduates has been documented worldwide. Many different theories have been set out as to why these declines in mathematical competency levels have occurred over time. One such theory is the widening access to higher education which has resulted in a less mathematically…

Future Directions for The Math You Need, When You Need It: Adaptation and Implementation of Online Student-Centered Tutorials that Remediate Introductory Geoscience-Related Mathematical Skills

NASA Astrophysics Data System (ADS)

Wenner, J. M.; Burn, H.; Baer, E. M.

2009-12-01

Requiring introductory geoscience students to apply mathematical concepts and solve quantitative problems can be an arduous task because these courses tend to attract students with diverse levels of mathematical preparedness. Perhaps more significantly, geoscience instructors grapple with quantitative content because of the difficulties students have transferring their prior mathematical learning to common geological problems. As a result, instructors can choose to eliminate the mathematics, spend valuable class time teaching basic mathematical skills or let students flounder in the hope that they will learn on their own. None of these choices are ideal. Instead, research suggests that introductory geoscience courses are opportune places to increase students’ quantitative abilities but that students need effective support at their own skill level. To provide such support, we developed The Math You Need, When You Need It (TMYN): a set of online geoscience context-rich tutorials that students complete just before they encounter a mathematical or numerical skill in their introductory course. The tutorials are modular; each mathematical topic has a set of pages that students work through toward a final assessment. The 11 modules currently available, including unit conversions, graphing, calculating density, and rearranging equations, touch on quantitative topics that cross a number of geologic contexts. TMYN modules are designed to be stand-alone and flexible - faculty members can choose modules appropriate for their courses and implement them at any time throughout the term. The flexible and adaptable nature of TMYN enables faculty to provide a supportive learning environment that remediates math for those who need it without taking significant classroom time. Since spring 2008, seven instructors at Highline Community College and University of Wisconsin Oshkosh successfully implemented TMYN in six geoscience courses with diverse student audiences. Evaluation of pilot implementations suggests that the flexibility of TYMN is one of its strengths. Specifically, faculty members responded positively to the ability to choose relevant topics and provide students with competence in pertinent mathematical concepts; students liked the supportive, contextual environment and the ability to work at their own pace. And, despite the fact that each implementation varied in the number and type of modules used, the timing of module use, grading stakes, and course size, pre/post test results consistently showed improvement in student skills associated with a given module, suggesting that all implementations were successful. Post-module surveys likewise revealed that both instructors and students found the experience valuable. We present the wide variety of successful implementations with an eye toward exploring future directions for the project, including soliciting new and diverse ways in which other institutions and instructors might adapt and apply TMYN to their own courses.

Badminton--Teaching Concepts.

ERIC Educational Resources Information Center

Gibbs, Marilyn J.

1988-01-01

Teaching four basic badminton concepts along with the usual basic skill shots allows players to develop game strategy awareness as well as mechanical skills. These four basic concepts are: (1) ready position, (2) flight trajectory, (3) early shuttle contact, and (4) camouflage. (IAH)

Bioinspired nanovalves with selective permeability and pH sensitivity

NASA Astrophysics Data System (ADS)

Zheng, Z.; Huang, X.; Schenderlein, M.; Moehwald, H.; Xu, G.-K.; Shchukin, D. G.

2015-01-01

Biological systems with controlled permeability and release functionality, which are among the successful examples of living beings to survive in evolution, have attracted intensive investigation and have been mimicked due to their broad spectrum of applications. We present in this work, for the first time, an example of nuclear pore complexes (NPCs)-inspired controlled release system that exhibits on-demand release of angstrom-sized molecules. We do so in a cost-effective way by stabilizing porous cobalt basic carbonates as nanovalves and realizing pH-sensitive release of entrapped subnano cargo. The proof-of-concept work also consists of the establishment of two mathematical models to explain the selective permeability of the nanovalves. Finally, gram-sized (or larger) quantities of the bio-inspired controlled release system can be synthesized through a scaling-up strategy, which opens up opportunities for controlled release of functional molecules in wider practical applications.Biological systems with controlled permeability and release functionality, which are among the successful examples of living beings to survive in evolution, have attracted intensive investigation and have been mimicked due to their broad spectrum of applications. We present in this work, for the first time, an example of nuclear pore complexes (NPCs)-inspired controlled release system that exhibits on-demand release of angstrom-sized molecules. We do so in a cost-effective way by stabilizing porous cobalt basic carbonates as nanovalves and realizing pH-sensitive release of entrapped subnano cargo. The proof-of-concept work also consists of the establishment of two mathematical models to explain the selective permeability of the nanovalves. Finally, gram-sized (or larger) quantities of the bio-inspired controlled release system can be synthesized through a scaling-up strategy, which opens up opportunities for controlled release of functional molecules in wider practical applications. Electronic supplementary information (ESI) available. See DOI: 10.1039/c4nr06378c

The System of Coordinates as an Obstacle in Understanding the Concept of Dimension

ERIC Educational Resources Information Center

Skordoulis, Constantine; Vitsas, Theodore; Dafermos, Vassilis; Koleza, Eugenia

2009-01-01

The concept of dimension, one of the most fundamental ideas in mathematics, is firmly rooted in the basis of the school geometry in such a way that mathematics teachers rarely feel the need to mention anything about it. However, the concept of dimension is far from being fully understood by students, even at the college level. In this paper, we…

Why Johnny Struggles When Familiar Concepts Are Taken to a New Mathematical Domain: Towards a Polysemous Approach

ERIC Educational Resources Information Center

Kontorovich, Igor'

2018-01-01

This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

towards a theory-based multi-dimensional framework for assessment in mathematics: The "SEA" framework

NASA Astrophysics Data System (ADS)

Anku, Sitsofe E.

1997-09-01

Using the reform documents of the National Council of Teachers of Mathematics (NCTM) (NCTM, 1989, 1991, 1995), a theory-based multi-dimensional assessment framework (the "SEA" framework) which should help expand the scope of assessment in mathematics is proposed. This framework uses a context based on mathematical reasoning and has components that comprise mathematical concepts, mathematical procedures, mathematical communication, mathematical problem solving, and mathematical disposition.

Pre-K Mathematics. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2007

2007-01-01

"Pre-K Mathematics" is a supplemental curriculum designed to develop informal mathematical knowledge and skills in preschool children. Mathematical content is organized into seven units. Specific mathematical concepts and skills from each unit are taught in the classroom through teacher-guided, small-group activities with concrete…

Literacy in Language and Mathematics: More in Common Than You Think

ERIC Educational Resources Information Center

Thompson, Denisse R.; Rubenstein, Rheta N.

2014-01-01

This paper shares perspectives on literacy in mathematics, particularly highlighting commonalities with literacy in language arts. We discuss levels of language development appropriate for the mathematics classroom, issues related to mathematical definitions, implied meanings in many mathematics concepts, and the importance of justification. We…

Finding Meaning in Mathematical Mnemonics

ERIC Educational Resources Information Center

Miller, Geoffrey; Obara, Samuel

2017-01-01

A mathematical mnemonic is a visual cue or verbal strategy that is used to aid initial memorisation and recall of a mathematical concept or procedure. Used wisely, mathematical mnemonics can benefit students' performance and understanding. Explorations into how mathematical mnemonics work can also offer students opportunities to engage in proof…

Using the Tower of Hanoi puzzle to infuse your mathematics classroom with computer science concepts

NASA Astrophysics Data System (ADS)

Marzocchi, Alison S.

2016-07-01

This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi puzzle. These concepts include, but are not limited to, conditionals, iteration, and recursion. Lessons, such as the one proposed in this article, are easily implementable in mathematics classrooms and extracurricular programmes as they are good candidates for 'drop in' lessons that do not need to fit into any particular place in the typical curriculum sequence. As an example for readers, the author describes how she used the puzzle in her own Number Sense and Logic course during the federally funded Upward Bound Math/Science summer programme for college-intending low-income high school students. The article explains each computer science term with real-life and mathematical examples, applies each term to the Tower of Hanoi puzzle solution, and describes how students connected the terms to their own solutions of the puzzle. It is timely and important to expose mathematics students to computer science concepts. Given the rate at which technology is currently advancing, and our increased dependence on technology in our daily lives, it has become more important than ever for children to be exposed to computer science. Yet, despite the importance of exposing today's children to computer science, many children are not given adequate opportunity to learn computer science in schools. In the United States, for example, most students finish high school without ever taking a computing course. Mathematics lessons, such as the one described in this article, can help to make computer science more accessible to students who may have otherwise had little opportunity to be introduced to these increasingly important concepts.