Role Playing Based on Multicultural for Understanding Fraction in Primary School

NASA Astrophysics Data System (ADS)

Aryanto, S.; Budiarti, T.; Rahmatullah, R.; Utami, S. R.; Jupri, A.

2017-09-01

Multicultural serve as a reference in the development of innovative mathematical learning materials and is expected to be a solution in improving the ability of students in understanding the fraction matter based on social and mathematical approach, so this study aims to determine the improvement of students’ understanding in fraction matter through role playing by integrating multicultural concepts as development learning content. Classroom Action Research conducted on 34 students in elementary school class proves that students’ understanding in fraction matter shows improvement in cycle II as much as 67% of students are able to apply the concept or formula exactly when compared with the result of cycles I of 33%. This research is expected to be the reference of teachers in developing innovative mathematical learning, let alone explicitly, this concept not only emphasizes the cognitive abilities of students, but implicitly can develop their social skills in mathematical perspective.

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 Concept Maps to Show "Connections" in Measurement: An Example from the Australian Curriculum

ERIC Educational Resources Information Center

Marshman, Margaret

2014-01-01

Within the "Australian Curriculum: Mathematics" the Understanding proficiency strand states, "Students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and…

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…

The Role of Reasoning in the Australian Curriculum: Mathematics

ERIC Educational Resources Information Center

McCluskey, Catherine; Mulligan, Joanne; Mitchelmore, Mike

2016-01-01

The mathematical proficiencies in the "Australian Curriculum: Mathematics" of understanding, problem solving, reasoning, and fluency are intended to be entwined actions that work together to build generalised understandings of mathematical concepts. A content analysis identifying the incidence of key proficiency terms (KPTs) embedded in…

DOE Fundamentals Handbook: Mathematics, Volume 1

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

Not Available

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclearmore » facility operations.« less

DOE Fundamentals Handbook: Mathematics, Volume 2

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

Not Available

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclearmore » facility operations.« less

Life on the Number Line: Routes to Understanding Fraction Magnitude for Students With Difficulties Learning Mathematics.

PubMed

Gersten, Russell; Schumacher, Robin F; Jordan, Nancy C

Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number lines broaden the concept of fractions for students who are tied to the more general part-whole representations of area models. We also discuss how number lines, compared to other representations, are a superior and more mathematically correct way to explain fraction concepts.

Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis

ERIC Educational Resources Information Center

Gilmore, Camilla K.; Papadatou-Pastou, Marietta

2009-01-01

Some theories from cognitive psychology and mathematics education suggest that children's understanding of mathematical concepts develops together with their knowledge of mathematical procedures. However, previous research into children's understanding of the inverse relationship between addition and subtraction suggests that there are individual…

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…

Implementation of cooperative learning model type STAD with RME approach to understanding of mathematical concept student state junior high school in Pekanbaru

NASA Astrophysics Data System (ADS)

Nurhayati, Dian Mita; Hartono

2017-05-01

This study aims to determine whether there is a difference in the ability of understanding the concept of mathematics between students who use cooperative learning model Student Teams Achievement Division type with Realistic Mathematic Education approach and students who use regular learning in seventh grade SMPN 35 Pekanbaru. This study was quasi experiments with Posttest-only Control Design. The populations in this research were all the seventh grade students in one of state junior high school in Pekanbaru. The samples were a class that is used as the experimental class and one other as the control class. The process of sampling is using purposive sampling technique. Retrieval of data in this study using the documentation, observation sheets, and test. The test use t-test formula to determine whether there is a difference in student's understanding of mathematical concepts. Before the t-test, should be used to test the homogeneity and normality. Based in the analysis of these data with t0 = 2.9 there is a difference in student's understanding of mathematical concepts between experimental and control class. Percentage of students experimental class with score more than 65 was 76.9% and 56.4% of students control class. Thus be concluded, the ability of understanding mathematical concepts students who use the cooperative learning model type STAD with RME approach better than students using the regular learning. So that cooperative learning model type STAD with RME approach is well used in learning process.

The Role of Mathematical Knowledge in Children's Understanding of Geographical Concepts.

ERIC Educational Resources Information Center

Kaplan, Rochelle G.

This study examines the relationship between children's procedural and conceptual understanding of mathematics and their accuracy in reporting and interpreting geography text material containing mathematical information. It was hypothesized that (1) children's misconceptions or lack of experience with particular mathematical content areas would be…

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 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…

The Use of Applets for Developing Understanding in Mathematics: A Case Study Using Maplets for Calculus with Continuity Concepts

ERIC Educational Resources Information Center

Patenaude, Raymond E.

2013-01-01

The Common Core State Standards for Mathematics (CCSSM) are founded on a long history of mathematics education research emphasizing the importance of teaching mathematics for understanding. The CCSSM along with the National Council of Teachers of Mathematics (NCTM) recommend the use of technology in the teaching of mathematics. New mobile…

Mathematics education graduate students' understanding of trigonometric ratios

NASA Astrophysics Data System (ADS)

Yiǧit Koyunkaya, Melike

2016-10-01

This study describes mathematics education graduate students' understanding of relationships between sine and cosine of two base angles in a right triangle. To explore students' understanding of these relationships, an elaboration of Skemp's views of instrumental and relational understanding using Tall and Vinner's concept image and concept definition was developed. Nine students volunteered to complete three paper and pencil tasks designed to elicit evidence of understanding and three students among these nine students volunteered for semi-structured interviews. As a result of fine-grained analysis of the students' responses to the tasks, the evidence of concept image and concept definition as well as instrumental and relational understanding of trigonometric ratios was found. The unit circle and a right triangle were identified as students' concept images, and the mnemonic was determined as their concept definition for trigonometry, specifically for trigonometric ratios. It is also suggested that students had instrumental understanding of trigonometric ratios while they were less flexible to act on trigonometric ratio tasks and had limited relational understanding. Additionally, the results indicate that graduate students' understanding of the concept of angle mediated their understanding of trigonometry, specifically trigonometric ratios.

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…

The Money Context

ERIC Educational Resources Information Center

Tabach, Michal; Friedlander, Alex

2009-01-01

One of the basic disagreements in mathematics education concerns the roles that rules and procedures, on the one hand, and concepts and principles, on the other hand, should play in students' learning of mathematics. The use of procedures and an understanding of concepts are considered to be two separate aspects of mathematical activity.…

Language matters in demonstrations of understanding in early years mathematics assessment

NASA Astrophysics Data System (ADS)

Mushin, Ilana; Gardner, Rod; Munro, Jennifer M.

2013-09-01

In classrooms tests, students are regularly required to demonstrate their understanding of mathematical concepts. When children encounter problems in demonstrating such understanding, it is often not clear whether this is because of the language of the teachers' questions and instructions or a genuine non-understanding of the concept itself. This paper uses Conversation Analysis to investigate the role that language plays in Year 1 oral maths assessment in an Australian Indigenous community school. This approach allows us to monitor the very subtle communicative gestures, verbal and non-verbal, that contribute to the trajectory of a particular test task. Here we are able to bring to light a range of ways in which language may interfere with demonstrations of understanding of mathematical concepts. These include particular mathematical words (e.g., size, shape, same), as well as problems with what is being asked in an instruction. We argue that while all children must learn new mathematical language in their early years of schooling, the challenge for the students we have recorded may be compounded by the language differences between the Indigenous variety of language they speak in the community, and the Standard Australian English of the classroom and teachers.

Pre-Service Mathematics Teachers' Understanding of Quadrilaterals and the Internal Relationships between Quadrilaterals: The Case of Parallelograms

ERIC Educational Resources Information Center

Kozakli Ulger, Tugce; Tapan Broutin, Menekse Seden

2017-01-01

This study attempts to reveal pre-service teachers' conceptions, definitions, and understanding of quadrilaterals and their internal relationships in terms of personal and formal figural concepts via case of the parallelograms. To collect data, an open-ended question was addressed to 27 pre-service mathematics teachers, and clinical interviews…

The Incoming Statistical Knowledge of Undergraduate Majors in a Department of Mathematics and Statistics

ERIC Educational Resources Information Center

Cook, Samuel A.; Fukawa-Connelly, Timothy

2016-01-01

Studies have shown that at the end of an introductory statistics course, students struggle with building block concepts, such as mean and standard deviation, and rely on procedural understandings of the concepts. This study aims to investigate the understandings entering freshman of a department of mathematics and statistics (including mathematics…

Old Habits Die Hard: An Uphill Struggle against Rules without Reason in Mathematics Teacher Education

ERIC Educational Resources Information Center

O'Meara, Niamh; Fitzmaurice, Olivia; Johnson, Patrick

2017-01-01

Mathematics teacher educators in the University of Limerick became aware of a lack of conceptual understanding of key mathematics concepts of prospective secondary mathematics teachers through observation on teaching placement and in pedagogy lectures. A pilot study to enhance the conceptual understanding of prospective teachers was carried out…

Orthogonal Reflections on Computer Microworlds, Constructivism, Play and Mathematical Understanding.

ERIC Educational Resources Information Center

Kieren, Thomas E.

1994-01-01

Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…

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.

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.

The analysis of the mathematics concept comprehension of senior high school student on dynamic fluid material

NASA Astrophysics Data System (ADS)

Kristian, P. L. Y.; Cari, C.; Sunarno, W.

2018-04-01

This study purposes to describe and analyse the students' concept understanding of dynamic fluid. The subjects of this research are 10 students of senior high school. The data collected finished the essay test that consists of 5 questions have been adapted to the indicators of learning. The data of this research is analysed using descriptive-qualitative approach by referring of the student's argumentations about their answer from the questions that given. The results showed that students still have incorrect understanding the concept of dynamic fluids, especially on the Bernoulli’s principle and its application. Based on the results of this research, the teachers should emphasize the concept understanding of the students therefore the students don not only understand the physics concept in mathematical form.

Manipulative Apps to Support Students with Disabilities in Mathematics

ERIC Educational Resources Information Center

Bouck, Emily C.; Working, Christopher; Bone, Erin

2018-01-01

Understanding mathematical concepts is important for all students, although often challenging for many students with disabilities. Historically, educators have used concrete manipulatives to support and build conceptual understanding. Mobile devices provide a valuable option to support students with disabilities in mathematics through app-based…

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…

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…

Is Small, Small Enough? Students' Understanding the Need for the Definition of the Derivative as a Limit

ERIC Educational Resources Information Center

Kidron, Ivy

2015-01-01

The research relates to undergraduate students' understanding of mathematical concepts that relate to the conceptualisation of the continuous such as the notion of limit. The cognitive difficulties that accompany the learning of these concepts at the different stages of the mathematics education are well reported in the literature. I analyse the…

Exploring Effects of High School Students' Mathematical Processing Skills and Conceptual Understanding of Chemical Concepts on Algorithmic Problem Solving

ERIC Educational Resources Information Center

Gultepe, Nejla; Yalcin Celik, Ayse; Kilic, Ziya

2013-01-01

The purpose of the study was to examine the effects of students' conceptual understanding of chemical concepts and mathematical processing skills on algorithmic problem-solving skills. The sample (N = 554) included grades 9, 10, and 11 students in Turkey. Data were collected using the instrument "MPC Test" and with interviews. The MPC…

The Use of Concept Maps to Assess Preservice Teacher Understanding: A Formative Approach in Mathematics Education

ERIC Educational Resources Information Center

Brakoniecki, Aaron; Shah, Fahmil

2017-01-01

The research reported in this article explored the methods by which concept maps served as formative assessment by capturing changes in the ways preservice mathematics teachers represented their understanding of algebra. The participants were enrolled in a course on high school algebra for teachers and created the maps on the first and last day of…

Mathematics for the New Millennium

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2004-01-01

Courses below calculus need to be refocused to emphasise conceptual understanding and realistic applications via mathematical modelling rather than an overarching focus on developing algebraic skills that may be needed for calculus. Without understanding the concepts, students will not be able to transfer the mathematics to new situations or to…

Mathematics Education Graduate Students' Understanding of Trigonometric Ratios

ERIC Educational Resources Information Center

Yigit Koyunkaya, Melike

2016-01-01

This study describes mathematics education graduate students' understanding of relationships between sine and cosine of two base angles in a right triangle. To explore students' understanding of these relationships, an elaboration of Skemp's views of instrumental and relational understanding using Tall and Vinner's concept image and concept…

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…

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…

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…

Students' Conceptions of Function Transformation in a Dynamic Mathematical Environment

ERIC Educational Resources Information Center

Daher, Wajeeh; Anabousy, Ahlam

2015-01-01

The study of function transformations helps students understand the function concept which is a basic and main concept in mathematics, but this study is problematic to school students as well as college students, especially when transformations are performed on non-basic functions. The current research tried to facilitate grade 9 students'…

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…

Content Knowledge, Attitudes, and Self-Efficacy in the Mathematics New York City Teaching Fellows (NYCTF) Program

ERIC Educational Resources Information Center

Evans, Brian R.

2011-01-01

The purpose of this study was to understand the mathematical content knowledge new teachers have both before and after taking a mathematics methods course in the NYCTF program. Further, the purpose was to understand the attitudes toward mathematics and concepts of self-efficacy that Teaching Fellows had over the course of the semester. The sample…

Teachers' Explanations of a Key Developmental Understanding of Multiplicative Reasoning

ERIC Educational Resources Information Center

Rhee, Katherine L.

2012-01-01

This qualitative research study explores teachers' understandings of multiplicative reasoning as a key developmental understanding (KDU). A KDU entails knowingly applying the same mathematical concepts within different contexts. A KDU supports an individual to build a connected understanding of mathematics as opposed to only understanding…

What is rate? Does context or representation matter?

NASA Astrophysics Data System (ADS)

Herbert, Sandra; Pierce, Robyn

2011-12-01

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students' conceptions of rate, focussing on the influence of representation and context on their expression of their understanding of rate. This analysis shows that different representations of functions provide varying levels of rate-related information for individual students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context. Rate is an important, but commonly misunderstood, mathematical concept with many everyday applications (Swedosh, Dowsey, Caruso, Flynn, & Tynan, 2007). It is a complicated concept comprising many interwoven ideas such as the ratio of two numeric, measurable quantities but in a context where both quantities are changing. In mathematics classes, this is commonly expressed as change in the dependent variable resulting from a unit change in the independent variable, and variously described as constant or variable rate; average or instantaneous rate. In addition, rate may be seen as a purely abstract mathematical notion or embedded in the understanding of real-world applications. This paper explores the research question: Are students' expressions of their conceptions of rate affected by either context or mathematical representation? This question was part of a larger study (Herbert, 2010) conducted with Grade 10 students from the Australian state of Victoria.

Key Understandings in School Mathematics: 1

ERIC Educational Resources Information Center

Watson, Anne

2010-01-01

This article is the first in a series which draws on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation." The Nuffield report is soundly based on research about how children learn some of the concepts involved in mathematics. In this series of articles the author takes key…

Using Prediction to Promote Mathematical Understanding and Reasoning

ERIC Educational Resources Information Center

Kasmer, Lisa; Kim, Ok-Kyeong

2011-01-01

Research has shown that prediction has the potential to promote the teaching and learning of mathematics because it can be used to enhance students' thinking and reasoning at all grade levels in various topics. This article addresses the effectiveness of using prediction on students' understanding and reasoning of mathematical concepts in a middle…

Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It?

ERIC Educational Resources Information Center

Pirie, Susan; Kieren, Thomas

1994-01-01

Proposes a model for the growth of mathematical understanding based on the consideration of understanding as a whole, dynamic, leveled but nonlinear process. Illustrates the model using the concept of fractions. How to map the growth of understanding is explained in detail. (Contains 26 references.) (MKR)

Find the Dimensions: Students Solving a Tiling Problem

ERIC Educational Resources Information Center

Obara, Samuel

2018-01-01

Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

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…

Stress, deformation, conservation, and rheology: a survey of key concepts in continuum mechanics

USGS Publications Warehouse

Major, J.J.

2013-01-01

This chapter provides a brief survey of key concepts in continuum mechanics. It focuses on the fundamental physical concepts that underlie derivations of the mathematical formulations of stress, strain, hydraulic head, pore-fluid pressure, and conservation equations. It then shows how stresses are linked to strain and rates of distortion through some special cases of idealized material behaviors. The goal is to equip the reader with a physical understanding of key mathematical formulations that anchor continuum mechanics in order to better understand theoretical studies published in geomorphology.

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.

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…

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.

Asynchronous Discourse in a Web-Assisted Mathematics Education Course

ERIC Educational Resources Information Center

Li, Zhongxiao

2009-01-01

Fall term of 2006, a web-assisted undergraduate mathematics course was taught at the University of Idaho: Math 235 Mathematics for Elementary Teachers I. The course goals were: To foster a deep understanding of critical mathematical content; and to promote the development of mathematical communication and collaboration concepts, skills, and…

Secondary-Level Student Teachers' Conceptions of Mathematical Proof

ERIC Educational Resources Information Center

Varghese, Thomas

2009-01-01

Recent reforms in mathematics education have led to an increased emphasis on proof and reasoning in mathematics curricula. The National Council of Teachers of Mathematics highlights the important role that teachers' knowledge and beliefs play in shaping students' understanding of mathematics, their confidence in and outlook on mathematics…

Pushing the Limit: A Class Project

ERIC Educational Resources Information Center

Odafe, Victor U.

2012-01-01

Instructors are constantly struggling to help students understand mathematical concepts as well as the relevance of mathematics to the real world. In calculus, students possess misconceptions of the limit concept. "Pushing the Limit" refers to a semester-long calculus class project that required students to read about, interview calculus…

Building Mathematics Discourse in Students

ERIC Educational Resources Information Center

Gresham, Gina; Shannon, Tracy

2017-01-01

Mathematics discourse is a teaching approach that encourages student discussion and reveals an understanding of concepts as students engage in mathematical reasoning and debate (Cobb 2006). Grabowski and Ke (2007) posit that students have significantly higher achievement and positive attitudes toward mathematics after participating in gaming…

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.

Exploring positioning as an analytical tool for understanding becoming mathematics teachers' identities

NASA Astrophysics Data System (ADS)

Skog, Kicki; Andersson, Annica

2015-03-01

The aim of this article is to explore how a sociopolitical analysis can contribute to a deeper understanding of critical aspects for becoming primary mathematics teachers' identities during teacher education. The question we ask is the following: How may power relations in university settings affect becoming mathematics teachers' subject positioning? We elaborate on the elusive and interrelated concepts of identity, positioning and power, seen as dynamic and changeable. As these concepts represent three interconnected parts of research analysis in an on-going larger project data from different sources will be used in this illustration. In this paper, we clarify the theoretical stance, ground the concepts historically and strive to connect them to research analysis. In this way, we show that power relations and subject positioning in social settings are critical aspects and need to be taken seriously into account if we aim at understanding becoming teachers' identities.

Comparison of university students' understanding of graphs in different contexts

NASA Astrophysics Data System (ADS)

Planinic, Maja; Ivanjek, Lana; Susac, Ana; Milin-Sipus, Zeljka

2013-12-01

This study investigates university students’ understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was administered to 385 first year students at University of Zagreb who were either prospective physics or mathematics teachers or prospective physicists or mathematicians. Rasch analysis of data was conducted and linear measures for item difficulties were obtained. Average difficulties of items in three domains (mathematics, physics, and other contexts) and over two concepts (graph slope, area under the graph) were computed and compared. Analysis suggests that the variation of average difficulty among the three domains is much smaller for the concept of graph slope than for the concept of area under the graph. Most of the slope items are very close in difficulty, suggesting that students who have developed sufficient understanding of graph slope in mathematics are generally able to transfer it almost equally successfully to other contexts. A large difference was found between the difficulty of the concept of area under the graph in physics and other contexts on one side and mathematics on the other side. Comparison of average difficulty of the three domains suggests that mathematics without context is the easiest domain for students. Adding either physics or other context to mathematical items generally seems to increase item difficulty. No significant difference was found between the average item difficulty in physics and contexts other than physics, suggesting that physics (kinematics) remains a difficult context for most students despite the received instruction on kinematics in high school.

Predicting Phenotypes from Genetic Crosses: A Mathematical Concept to Help Struggling Biology Students

ERIC Educational Resources Information Center

Baurhoo, Neerusha; Darwish, Shireef

2012-01-01

Predicting phenotypic outcomes from genetic crosses is often very difficult for biology students, especially those with learning disabilities. With our mathematical concept, struggling students in inclusive biology classrooms are now better equipped to solve genetic problems and predict phenotypes, because of improved understanding of dominance…

The Distributive Property in Grade 3?

ERIC Educational Resources Information Center

Benson, Christine C.; Wall, Jennifer J.; Malm, Cheryl

2013-01-01

The Common Core State Standards for Mathematics (CCSSM) call for an in depth, integrated look at elementary school mathematical concepts. Some topics have been realigned to support an integration of topics leading to conceptual understanding. For example, the third-grade standards call for relating the concept of area (geometry) to multiplication…

Advanced Mathematical Thinking and Students' Mathematical Learning: Reflection from Students' Problem-Solving in Mathematics Classroom

ERIC Educational Resources Information Center

Sangpom, Wasukree; Suthisung, Nisara; Kongthip, Yanin; Inprasitha, Maitree

2016-01-01

Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…

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.

Proportional Reasoning: An Essential Component of Scientific Understanding

ERIC Educational Resources Information Center

Hilton, Annette; Hilton, Geoff

2016-01-01

In many scientific contexts, students need to be able to use mathematical knowledge in order to engage in scientific reasoning and problem-solving, and their understanding of scientific concepts relies heavily on their ability to understand and use mathematics in often new or unfamiliar contexts. Not only do science students need high levels of…

Students' Understanding of Mathematical Expressions in Physical Chemistry Contexts: An Analysis Using Sherin's Symbolic Forms

ERIC Educational Resources Information Center

Becker, Nicole; Towns, Marcy

2012-01-01

Undergraduate physical chemistry courses require students to be proficient in calculus in order to develop an understanding of thermodynamics concepts. Here we present the findings of a study that examines student understanding of mathematical expressions, including partial derivative expressions, in two undergraduate physical chemistry courses.…

Understanding Number Sequences Leads to Understanding Mathematics Concepts

ERIC Educational Resources Information Center

Pasnak, Robert; Schmerold, Katrina Lea; Robinson, Melissa Fetterer; Gadzichowski, K. Marinka; Bock, Allison M.; O'Brien, Sarah Eva; Kidd, Julie K.; Gallington, Deb A.

2016-01-01

Ninety-six first grade students in an urban school system were tested in October and May on reading, mathematics, and their understanding of sequences of letters and numbers. A time lag analysis was subsequently conducted. In such analyses, cross-correlations between the first measurement of one variable and the second measurement of another are…

A structural equation modeling analysis of students' understanding in basic mathematics

NASA Astrophysics Data System (ADS)

Oktavia, Rini; Arif, Salmawaty; Ferdhiana, Ridha; Yuni, Syarifah Meurah; Ihsan, Mahyus

2017-11-01

This research, in general, aims to identify incoming students' understanding and misconceptions of several basic concepts in mathematics. The participants of this study are the 2015 incoming students of Faculty of Mathematics and Natural Science of Syiah Kuala University, Indonesia. Using an instrument that were developed based on some anecdotal and empirical evidences on students' misconceptions, a survey involving 325 participants was administered and several quantitative and qualitative analysis of the survey data were conducted. In this article, we discuss the confirmatory factor analysis using Structural Equation Modeling (SEM) on factors that determine the new students' overall understanding of basic mathematics. The results showed that students' understanding on algebra, arithmetic, and geometry were significant predictors for their overall understanding of basic mathematics. This result supported that arithmetic and algebra are not the only predictors of students' understanding of basic mathematics.

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…

Preparing Mathematics Teachers for Elementary High-Poverty Schools: Perceptions and Suggestions from Preservice Teachers

ERIC Educational Resources Information Center

McKinney, Sueanne E.; Berry, Robert Q., III; Jackson, Joan M.

2007-01-01

The National Council of Teachers of Mathematics articulates an ambitious vision of a high-quality mathematics program. Achieving this vision requires competent and knowledgeable teachers who can support all students in learning mathematics concepts with understanding. Effective mathematics teachers are especially needed for high-poverty schools…

Johann Christoph Sturm's universal mathematics and metaphysics (German Title: Universalmathematik und Metaphysik bei Johann Christoph Sturm)

NASA Astrophysics Data System (ADS)

Leinsle, Ulrich G.

In order to understand Sturm's concept of a universal mathematics as a replacement or complement of metaphysics, one first has to examine the evolution of the idea of a mathesis universalis up to Sturm, and his concept of metaphysics. According to the understanding of those times, natural theology belongs to metaphysics. The last section is concerned with Sturm's statements on the existence of God and his assessments for a physico-theology.

Mathematics Mastery: Secondary Evaluation Report

ERIC Educational Resources Information Center

Jerrim, John; Austerberry, Helen; Crisan, Cosette; Ingold, Anne; Morgan, Candia; Pratt, Dave; Smith, Cathy; Wiggins, Meg

2015-01-01

The Mathematics Mastery programme is a whole-school approach to teaching mathematics that aims to raise attainment for all pupils and close the attainment gap between pupils from low income families and their peers. The programme aims to deepen pupils' conceptual understanding of key mathematical concepts. This clustered Randomised Controlled…

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.

Developing Second Grade Teachers' Pedagogical Content Knowledge of Place Value

ERIC Educational Resources Information Center

Kulhanek, Stefani Michelle

2013-01-01

An understanding of whole number place value is a critical component of second-grade mathematics. This understanding of place value provides the foundational concept for operations with whole numbers. The ability to understand the concept of place value and transfer that understanding to teaching addition and subtraction are often problems…

Funny Face Contest: A Formative Assessment

ERIC Educational Resources Information Center

Colen, Yong S.

2010-01-01

Many American students begin their high school mathematics study with the algebra 1-geometry-algebra 2 sequence. After algebra 2, then, students with average or below-average mathematical ability face a dilemma in choosing their next mathematics course. For students to succeed in higher mathematics, understanding the concept of functions is…

The Mathematics and Mathematical Thinking of Seamstresses.

ERIC Educational Resources Information Center

Hancock, Sabrina J. C.

This study documents the mathematics practiced by four women in the context of sewing. The study describes the mathematics recognized in the skills, thinking and strategies used by the seamstresses. Through their work, the seamstresses exhibited an understanding of the concepts of angles, direction, parallel, reflection, symmetry, proportion,…

Teaching Gifted Children Mathematics in Grades Four Through Six.

ERIC Educational Resources Information Center

Gensley, Juliana T.

Intended for teachers of gifted students in grades 4-6, the guide emphasizes the need for specialized instruction in mathematics, suggests methods for teaching mathematical facts and concepts, describes approaches and materials to develop students' understanding of mathematical principles, and explores ways to build skills and creativity. Stressed…

Method and Effectiveness of an Individualized Exercise of Fundamental Mathematics.

ERIC Educational Resources Information Center

Yoshioka, Takayoshi; Nishizawa, Hitoshi; Tsukamoto Takehiko

2001-01-01

Describes a method used to provide mathematics students in Japanese colleges of engineering with supplementary exercises to aid their learning. Outlines the online operation of individualized exercises that help the students to understand mathematical methods used to solve problems and also mathematical ideas or concepts upon which methods are…

Acting Is Learning: Focus on the Construction of Mathematical Concepts

ERIC Educational Resources Information Center

Arzarello, Ferdinando; Robutti, Ornella; Bazzini, Luciana

2005-01-01

The purpose of this paper is to focus on the nature of the thinking processes supporting pupils' construction and understanding of mathematical concepts. We assume that interaction with reality plays a crucial role in learning. In particular, human perception and action and, more generally, interaction with artefacts, are very important for…

Lagrange Multipliers, Adjoint Equations, the Pontryagin Maximum Principle and Heuristic Proofs

ERIC Educational Resources Information Center

Ollerton, Richard L.

2013-01-01

Deeper understanding of important mathematical concepts by students may be promoted through the (initial) use of heuristic proofs, especially when the concepts are also related back to previously encountered mathematical ideas or tools. The approach is illustrated by use of the Pontryagin maximum principle which is then illuminated by reference to…

Learning about "Half": Critical Aspects and Pedagogical Strategies in Designed Preschool Activities

ERIC Educational Resources Information Center

Björklund, Camilla

2018-01-01

This is an empirical inquiry concerning children's concept development and early mathematics teaching. The intention is to broaden the understanding of preschool children's perceptions of the concept "half" (as 1 of 2 equal parts of a whole), in designed mathematics teaching settings. Three teachers working with 4-5-year-old children…

Motion sensors in mathematics teaching: learning tools for understanding general math concepts?

NASA Astrophysics Data System (ADS)

Urban-Woldron, Hildegard

2015-05-01

Incorporating technology tools into the mathematics classroom adds a new dimension to the teaching of mathematics concepts and establishes a whole new approach to mathematics learning. In particular, gathering data in a hands-on and real-time method helps classrooms coming alive. The focus of this paper is on bringing forward important mathematics concepts such as functions and rate of change with the motion detector. Findings from the author's studies suggest that the motion detector can be introduced from a very early age and used to enliven classes at any level. Using real-world data to present the main functions invites an experimental approach to mathematics and encourages students to engage actively in their learning. By emphasizing learning experiences with computer-based motion detectors and aiming to involve students in mathematical representations of real-world phenomena, six learning activities, which were developed in previous research studies, will be presented. Students use motion sensors to collect physical data that are graphed in real time and then manipulate and analyse them. Because data are presented in an immediately understandable graphical form, students are allowed to take an active role in their learning by constructing mathematical knowledge from observation of the physical world. By utilizing a predict-observe-explain format, students learn about slope, determining slope and distance vs. time graphs through motion-filled activities. Furthermore, exploring the meaning of slope, viewed as the rate of change, students acquire competencies for reading, understanding and interpreting kinematics graphs involving a multitude of mathematical representations. Consequently, the students are empowered to efficiently move among tabular, graphical and symbolic representation to analyse patterns and discover the relationships between different representations of motion. In fact, there is a need for further research to explore how mathematics teachers can integrate motion sensors into their classrooms.

Using Integer Manipulatives: Representational Determinism

ERIC Educational Resources Information Center

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

2016-01-01

Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…

A Tale of Three Teachers

ERIC Educational Resources Information Center

Chapman, Sue; Leonard, Allison; Burciaga, Sandra; Jernigan, Theresa

2013-01-01

The improvement of mathematics teaching and learning is a complicated undertaking. It relies on teacher understanding of math curriculum in addition to awareness of how children acquire mathematics concepts. It also depends on teachers' abilities to translate these understandings into learning tasks and instructional routines, as well as the…

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…

Learning Mathematics in High School Courses beyond Mathematics: Combating the Need for Post-Secondary Remediation in Mathematics

ERIC Educational Resources Information Center

Young, R. Brent; Hodge, Angie; Edwards, M. Craig; Leising, James G.

2012-01-01

The purpose of this study was to empirically test the posit that students who participated in a contextualized, mathematics-enhanced high school agricultural power and technology (APT) curriculum and aligned instructional approach would develop a deeper and more sustained understanding of selected mathematics concepts than those students who…

An Analysis of Pre-Service Mathematics Teachers' Performance in Modelling Tasks in Terms of Spatial Visualisation Ability

ERIC Educational Resources Information Center

Tasova, Halil Ibrahim; Delice, Ali

2012-01-01

Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…

Examining Students' Generalizations of the Tangent Concept: A Theoretical Perspective

ERIC Educational Resources Information Center

Çekmez, Erdem; Baki, Adnan

2016-01-01

The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

College Students' Understanding of the Domain and Range of Functions on Graphs

ERIC Educational Resources Information Center

Cho, Young Doo

2013-01-01

The mathematical concept of function has been revisited and further developed with regularity since its introduction in ancient Babylonia (Kleiner, 1989). The difficulty of the concept of a function contributes to complications when students learn of functions and their graphs (Leinhardt, Zaslavsky, & Stein, 1990). To understand the concept of…

Slope, Rate of Change, and Steepness: Do Students Understand These Concepts?

ERIC Educational Resources Information Center

Teuscher, Dawn; Reys, Robert E.

2010-01-01

How do mathematics teachers introduce the concepts of slope, rate of change, and steepness in their classrooms? Do students understand these concepts as interchangeable or regard them as three different ideas? In this article, the authors report the results of a study of high school Advanced Placement (AP) Calculus students who displayed…

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.

Community College Developmental Education Students' Understanding of Foundational Fraction Concepts

ERIC Educational Resources Information Center

Alexander, Cathleen Marie

2013-01-01

Mathematics, in general, and algebra courses, in particular, have been categorized as "gatekeepers" for higher education, better jobs, and even citizenship. For many low-income and working adults, community college is the institution where they choose to develop their mathematics understanding so they can pursue their dreams.…

Investigating Students' Mathematical Difficulties with Quadratic Equations

ERIC Educational Resources Information Center

O'Connor, Bronwyn Reid; Norton, Stephen

2016-01-01

This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

A Surprisingly Radical Problem

ERIC Educational Resources Information Center

Ledford, Sarah D.; Garner, Mary L.; Teachey, Angela L.

2012-01-01

Sometimes, in the teaching and learning of mathematics, open-ended problems posed by teachers or students can lead to a fuller understanding of mathematical concepts--a depth of understanding that no one could have anticipated. Interesting solutions and ideas emerged unexpectedly when the authors asked prospective and in-service teachers an "old"…

Mathematics in Early Childhood: Research-Based Rationale and Practical Strategies

ERIC Educational Resources Information Center

Linder, Sandra M.; Powers-Costello, Beth; Stegelin, Dolores A.

2011-01-01

Mathematics education is a critical part of the curriculum for students worldwide. The foundation for understanding mathematical concepts related to number sense begins early in life, and early childhood classrooms can provide the seeds for mathematical skills that will be needed later in life. In this article, the authors make a case for…

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…

Adding Math to Biology.

ERIC Educational Resources Information Center

Texley, Juliana

2001-01-01

Describes a teaching method in which students learn about evolutionary biology through the use of mathematics. Uses the concept of biostatistics, the mathematical analysis of the variation in nature, to understand evolution. (SAH)

Student Strategies Suggesting Emergence of Mental Structures Supporting Logical and Abstract Thinking: Multiplicative Reasoning

ERIC Educational Resources Information Center

Carrier, Jim

2014-01-01

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

What Form of Mathematics Are Assessments Assessing? The Case of Multiplication and Division in Fourth Grade NAEP Items

ERIC Educational Resources Information Center

Kosko Karl W.; Singh, Rashmi

2018-01-01

Multiplicative reasoning is a key concept in elementary school mathematics. Item statistics reported by the National Assessment of Educational Progress (NAEP) assessment provide the best current indicator for how well elementary students across the U.S. understand this, and other concepts. However, beyond expert reviews and statistical analysis,…

The Vital Role of Basic Mathematics in Teaching and Learning the Mole Concept

ERIC Educational Resources Information Center

Mehrotra, Alka; Koul, Anjni

2016-01-01

This article focuses on the importance of activity-based teaching in understanding the mole concept and the vital role of basic mathematical operations. It describes needs-based training for teachers in a professional development programme in India. Analysis of test results before and after the training indicates that teachers improved their…

Local Instruction Theory on Division in Mathematics GASING: The Case of Rural Area's Student in Indonesia

ERIC Educational Resources Information Center

Prahmana, Rully Charitas Indra; Suwasti, Petra

2014-01-01

Several studies on learning mathematics for rural area's student indicate that students have difficulty in understanding the concept of division operation. Students are more likely to be introduced by the use of the formula without involving the concept itself and learning division separate the concrete situation of learning process. This…

Functions and Relations: Some Applications from Database Management for the Teaching of Classroom Mathematics.

ERIC Educational Resources Information Center

Hauge, Sharon K.

While functions and relations are important concepts in the teaching of mathematics, research suggests that many students lack an understanding and appreciation of these concepts. The present paper discusses an approach for teaching functions and relations that draws on the use of illustrations from database management. This approach has the…

Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

Adapting Math Instruction to Support Prospective Elementary Teachers

ERIC Educational Resources Information Center

LeSage, Ann

2012-01-01

Purpose: Elementary teachers' understanding of mathematics is a significant contributor to student success with mathematics. Consequently, teacher educators are frequently charged with the responsibility of supporting the development of prospective elementary teachers' mathematics content knowledge as they re-learn concepts in ways they are…

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…

Relational Understanding of the Derivative Concept through Mathematical Modeling: A Case Study

ERIC Educational Resources Information Center

Sahin, Zulal; Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat

2015-01-01

The purpose of this study was to investigate three second-year graduate students' awareness and understanding of the relationships among the "big ideas" that underlie the concept of derivative through modeling tasks and Skemp's distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up,…

Units Matter

ERIC Educational Resources Information Center

I, Ji Yeong; Dougherty, Barbara J.; Berkaliev, Zaur

2015-01-01

Young children spend a much greater amount of time on practicing multiplication facts compared to understanding the concept of multiplication. When students have long-term, foundational concepts rather than a series of fragmented algorithms or facts, they are more likely to understand and generalize the mathematics. Using generalized models that…

Using Problem Solving to Assess Young Children's Mathematics Knowledge

ERIC Educational Resources Information Center

Charlesworth, Rosalind; Leali, Shirley A.

2012-01-01

Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…

Initial Understandings of Fraction Concepts Evidenced by Students with Mathematics Learning Disabilities and Difficulties: A Framework

ERIC Educational Resources Information Center

Hunt, Jessica H.; Welch-Ptak, Jasmine J.; Silva, Juanita M.

2016-01-01

Documenting how students with learning disabilities (LD) initially conceive of fractional quantities, and how their understandings may align with or differ from students with mathematics difficulties, is necessary to guide development of assessments and interventions that attach to unique ways of thinking or inherent difficulties these students…

Rate of Change: AP Calculus Students' Understandings and Misconceptions after Completing Different Curricular Paths

ERIC Educational Resources Information Center

Teuscher, Dawn; Reys, Robert E.

2012-01-01

This study examined Advanced Placement Calculus students' mathematical understanding of rate of change, after studying four years of college preparatory (integrated or single-subject) mathematics. Students completed the Precalculus Concept Assessment (PCA) and two open-ended tasks with questions about rates of change. After adjusting for prior…

The Importance of Equal Sign Understanding in the Middle Grades

ERIC Educational Resources Information Center

Knuth, Eric J.; Alibali, Martha W.; Hattikudur, Shanta; McNeil, Nicole M.; Stephens, Ana C.

2008-01-01

The equal sign is perhaps the most prevalent symbol in school mathematics, and developing an understanding of it has typically been considered mathematically straightforward. In fact, after its initial introduction during students' early elementary school education, little, if any instructional time is explicitly spent on the concept in the later…

Students' Perceptions and Development of Conceptual Understanding Regarding Trigonometry and Trigonometric Function

ERIC Educational Resources Information Center

Cetin, Omer Faruk

2015-01-01

This study aims to analyse university level mathematics education students' perceptions on conceptual understanding of trigonometry and trigonometric functions and their content development of these concepts. A case study was conducted with 90 freshman students of Elementary Mathematics Department. The data were gathered via a scale; they included…

A Literature Review: The Effect of Implementing Technology in a High School Mathematics Classroom

ERIC Educational Resources Information Center

Murphy, Daniel

2016-01-01

This study is a literature review to investigate the effects of implementing technology into a high school mathematics classroom. Mathematics has a hierarchical structure in learning and it is essential that students get a firm understanding of mathematics early in education. Some students that miss beginning concepts may continue to struggle with…

Preliminary Evaluation Report on the Los Angeles City Schools SB 28 Demonstration Program in Mathematics. CSE Working Paper No. 1.

ERIC Educational Resources Information Center

Gordon, C. Wayne

The objectives of the Los Angeles Model Mathematics Project (LAMMP) are stated by the administration as improvement of mathematical skills and understanding of mathematical concepts; improvement of the pupils' self-image; identification of specific assets and limitations relating to the learning process; development and use of special…

Preliminary Evaluation Report on the Los Angeles City Schools, SB 28 Demonstration Program in Mathematics.

ERIC Educational Resources Information Center

Gordon, C. Wayne

The purpose of this preliminary report is to describe and evaluate the Los Angeles Model Mathematics Project (LAMMP). The objectives of this project include the improvement of mathematical skills and understanding of mathematical concepts, the improvement of students' self-image, the development of instructional materials and the assessment of…

Development of Energy Concepts in Introductory Physics Courses.

ERIC Educational Resources Information Center

Arons, Arnold B.

1999-01-01

Believes that a student's understanding of energy concepts can be enhanced by introducing and using the concept of internal energy by articulating the first law of thermodynamics in a simple, phenomenological form without mathematical encumbrances. (Author/CCM)

Facilitating Student Understanding of Buffering by an Integration of Mathematics and Chemical Concepts

ERIC Educational Resources Information Center

Curtright, Robert; Emry, Randall; Heaton, Ruth M.; Markwell, John

2004-01-01

We describe a simple undergraduate exercise involving the titration of a weak acid by a strong base using a pH meter and a micropipette. Students then use their data and carry out graphical analyses with a spreadsheet. The analyses involve using mathematical concepts such as first-derivative and semi-log plots and provide an opportunity for…

Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving

ERIC Educational Resources Information Center

Ben-Hur, Meir

2006-01-01

Fact-filled textbooks that stress memorization and drilling are not very good for teaching students how to think mathematically and solve problems. But this is a book that comes to the rescue with an instructional approach that helps students in every grade level truly understand math concepts so they can apply them on high-stakes assessments,…

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…

Investigating middle school students’ difficulties in mathematical literacy problems level 1 and 2

NASA Astrophysics Data System (ADS)

Setiawati, S.; Herman, T.; Jupri, A.

2017-11-01

The background of this study is the lack of mathematical literacy skills of students. The proficiency of students’ mathematical literacy skills based on the results of the PISA 2015 study shows that Indonesian students at the proficiency level 1. This fact gave rise to this study which aims to investigate middle school students’ difficulties in mathematical literacy problems level 1 and 2. Qualitative research was used in this study. An individual written test on mathematical literacy problems was administered, followed by interviews. The subjects of the study were 61 students grade VII in Bandung and 26 of them were interviewed afterward. Data analysis revealed that students’ error in performing arithmetic most frequently observed. Other observed difficulties concerned understanding about algebra concept, applying arithmetic operation in algebraic expressions, and interpreting symbols to represent the unknown. In solving mathematical literacy problems, students use their prior knowledge, although sometimes not relevant to the questions. Based on the results, we suggest that mathematics learning in contextual learning and which invites students to participate in the processes of understanding the concepts.

QR-STEM: Energy and Environment as a Context for Improving QR and STEM Understandings of 6-12 Grade Teachers II. The Quantitative Reasoning

NASA Astrophysics Data System (ADS)

Mayes, R.; Lyford, M. E.; Myers, J. D.

2009-12-01

The Quantitative Reasoning in STEM (QR STEM) project is a state level Mathematics and Science Partnership Project (MSP) with a focus on the mathematics and statistics that underlies the understanding of complex global scientific issues. This session is a companion session to the QR STEM: The Science presentation. The focus of this session is the quantitative reasoning aspects of the project. As students move from understandings that range from local to global in perspective on issues of energy and environment, there is a significant increase in the need for mathematical and statistical conceptual understanding. These understandings must be accessible to the students within the scientific context, requiring the special understandings that are endemic within quantitative reasoning. The QR STEM project brings together interdisciplinary teams of higher education faculty and middle/high school teachers to explore complex problems in energy and environment. The disciplines include life sciences, physics, chemistry, earth science, statistics, and mathematics. These interdisciplinary teams develop open ended performance tasks to implement in the classroom, based on scientific concepts that underpin energy and environment. Quantitative reasoning is broken down into three components: Quantitative Literacy, Quantitative Interpretation, and Quantitative Modeling. Quantitative Literacy is composed of arithmetic concepts such as proportional reasoning, numeracy, and descriptive statistics. Quantitative Interpretation includes algebraic and geometric concepts that underlie the ability to interpret a model of natural phenomena which is provided for the student. This model may be a table, graph, or equation from which the student is to make predictions or identify trends, or from which they would use statistics to explore correlations or patterns in data. Quantitative modeling is the ability to develop the model from data, including the ability to test hypothesis using statistical procedures. We use the term model very broadly, so it includes visual models such as box models, as well as best fit equation models and hypothesis testing. One of the powerful outcomes of the project is the conversation which takes place between science teachers and mathematics teachers. First they realize that though they are teaching concepts that cross their disciplines, the barrier of scientific language within their subjects restricts students from applying the concepts across subjects. Second the mathematics teachers discover the context of science as a means of providing real world situations that engage students in the utility of mathematics as a tool for solving problems. Third the science teachers discover the barrier to understanding science that is presented by poor quantitative reasoning ability. Finally the students are engaged in exploring energy and environment in a manner which exposes the importance of seeing a problem from multiple interdisciplinary perspectives. The outcome is a democratic citizen capable of making informed decisions, and perhaps a future scientist.

Historical Objections against the Number Line

ERIC Educational Resources Information Center

Heeffer, Albrecht

2011-01-01

Historical studies on the development of mathematical concepts will help mathematics teachers to relate their students' difficulties in understanding to conceptual problems in the history of mathematics. We argue that one popular tool for teaching about numbers, the number line, may not be fit for early teaching of operations involving negative…

The Effect of Eliciting Repair of Mathematics Explanations of Students with Learning Disabilities

ERIC Educational Resources Information Center

Liu, Jia; Xin, Yan Ping

2017-01-01

Mathematical reasoning is important in conceptual understanding and problem solving. In current reform-based, discourse-oriented mathematics classrooms, students with learning disabilities (LD) encounter challenges articulating or explaining their reasoning processes. Enlightened by the concept of conversational repair borrowed from the field of…

Can Group Discussions and Individualized Assignments Help More Students Succeed in Developmental Mathematics?

ERIC Educational Resources Information Center

Jaafar, Reem

2015-01-01

Students taking developmental mathematics courses resist attempting word problems when they are presented to them. Although word problems can help students contextualize learning, develop better understanding of the concepts and apply world knowledge, they constitute an impediment to students' progress in developmental mathematics courses. A…

Representations in Problem Solving: A Case Study with Optimization Problems

ERIC Educational Resources Information Center

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

2009-01-01

Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

Sunny Side Up in Mathematics.

ERIC Educational Resources Information Center

LaHart, David, Ed.

Energy is a problem affecting all individuals. To help today's students understand the problem and become realistic decision-makers, materials have been developed by the Sunny Side Up (in Mathematics) program to introduce energy concepts into the mathematics curriculum. Objectives of the program are to: (1) provide highly effective practice in…

Virtual Manipulatives: Tools for Teaching Mathematics to Students with Learning Disabilities

ERIC Educational Resources Information Center

Shin, Mikyung; Bryant, Diane P.; Bryant, Brian R.; McKenna, John W.; Hou, Fangjuan; Ok, Min Wook

2017-01-01

Many students with learning disabilities demonstrate difficulty in developing a conceptual understanding of mathematical topics. Researchers recommend using visual models to support student learning of the concepts and skills necessary to complete abstract and symbolic mathematical problems. Virtual manipulatives (i.e., interactive visual models)…

Beyond the Write Answer: Mathematical Connections

ERIC Educational Resources Information Center

Haltiwanger, Leigh; Simpson, Amber M.

2013-01-01

As math teachers, the authors often encountered students who could ace a test but not explain their reasoning. This phenomenon was disturbing to them, and they fought for years to help students both understand mathematical concepts and develop meaning for them. Since their primary goal was to develop mathematically literate students, their…

A Cognitive Theory Driven New Orientation of Indonesian Lessons

ERIC Educational Resources Information Center

Nowinska, Edyta

2014-01-01

The main focus of this design research was on students' mathematical thinking and skills and on their understanding of mathematical concepts and methods. The mathematical content our project starts with is the introduction of integers. For this content new learning environments have been developed, implemented and evaluated. An important question…

Scott Foresman-Addison Wesley Elementary Mathematics. What Works Clearinghouse Intervention Report. Updated

ERIC Educational Resources Information Center

What Works Clearinghouse, 2013

2013-01-01

"Scott Foresman-Addison Wesley Elementary Mathematics" is a core mathematics curriculum for students in prekindergarten through grade 6. The program aims to improve students' understanding of key math concepts through problem-solving instruction, hands-on activities, and math problems that involve reading and writing. The curriculum…

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.

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.

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.

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…

Teaching Statistics in Middle School Mathematics Classrooms: Making Links with Mathematics but Avoiding Statistical Reasoning

ERIC Educational Resources Information Center

Savard, Annie; Manuel, Dominic

2015-01-01

Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school…

The Application of Contextual Approach in Learning Mathematics to Improve Students Motivation at SMPN 1 Kupang

ERIC Educational Resources Information Center

Ekowati, Ch. Krisnandari; Darwis, Muhammad; Upa, H. M. D. Pua; Tahmir, Suradi

2015-01-01

This research is an action research which aims to implement contextual teaching and learning (CTL) approach to learn mathematics, focus on the integration subjects. The approach utilizes the use of mathematics manipulative so that students can understand a mathematical concept to construct their own. The method which used in this research are…

Examining the Relationship between Secondary Mathematics Teachers' Self-Efficacy, Attitudes, and Use of Technology to Support Communication and Mathematics Literacy

ERIC Educational Resources Information Center

Letwinsky, Karim Medico

2017-01-01

The rich language surrounding mathematical concepts often is reduced in many classrooms to a narrow process of memorizing isolated procedures with little context. This approach has proven to be detrimental to students' ability to understand mathematics at deeper levels and remain engaged with this content. The current generation of students values…

Students' Conceptual Understanding of a Function and Its Derivative in an Experimental Calculus Course

ERIC Educational Resources Information Center

Habre, Samer; Abboud, May

2006-01-01

Calculus has been witnessing fundamental changes in its curriculum, with an increased emphasis on visualization. This mode for representing mathematical concepts is gaining more strength due to the advances in computer technology and the development of dynamical mathematical software. This paper focuses on the understanding of the function and its…

Unpacking Understanding: The (Re)search for the Holy Grail of Mathematics Education

ERIC Educational Resources Information Center

Llewellyn, Anna

2012-01-01

In this article, I deconstruct the concept of understanding in mathematics education, examining how it is spoken into being and what work it does for primary school student teachers. I use poststructural analysis to unpack interviews with a student teacher, Jane, drawn from a larger longitudinal study. I show how she negotiates tensions between…

Transitions between School and Work: Some New Understandings and Questions about Adult Mathematics.

ERIC Educational Resources Information Center

Beach, King

There is dissonance between the lives of adult students in rural Nepal in a subsistence-level agrarian community and their participation in school. The concept of "transfer" has several shortcomings from the standpoint of understanding relations between mathematical reasoning in the classroom and in the workplace. It is more helpful to…

A Chinese young adult non-scientist's epistemologies and her understandings of the concept of speed

NASA Astrophysics Data System (ADS)

Cao, Ying; Brizuela, Barbara M.

2015-08-01

Past research has investigated students' epistemologies while they were taking courses that required an integrated understanding of mathematical and scientific concepts. However, past studies have not investigated students who are not currently enrolled in such classes. Additionally, past studies have primarily focused on individuals who are native English speakers from Western cultures. In this paper, we aim to investigate whether Hammer and his colleagues' claims concerning learners' epistemologies could be extended to individuals who lack advanced mathematics and science training, have had different cultural and learning experiences, and have grown up speaking and learning in another language. To this end, we interviewed a participant with these characteristics about her understandings of the concept of speed. Our findings show that previous theoretical frameworks can be used to explain the epistemologies of the individual examined in this study. The case suggests that these theories may be relevant regardless of the learner's mathematics and science background, language, educational experience, and cultural background. In the future, more cases should be examined with learners from different academic backgrounds and cultures to further support this finding.

Lacking a Formal Concept of Limit: Advanced Non-Mathematics Students' Personal Concept Definitions

ERIC Educational Resources Information Center

Beynon, Kenneth A.; Zollman, Alan

2015-01-01

This mixed-methods study examines the conceptual understanding of limit among 22 undergraduate engineering students from two different sections of the same introductory differential equations course. The participants' concepts of limit (concept images and personal concept definitions) were examined using written tasks followed by one-on-one…

We?re Poppin' For Math

ERIC Educational Resources Information Center

Levert, Brenda

2004-01-01

Each year, students in my seventh- and eighth-grade math classes plan and organize a schoolwide popcorn sale. This activity brings to life mathematical concepts learned in the classroom. By transferring textbook mathematics to a real-world situation, my students learn to value the mathematics being studied and are able to understand how it can…

How Young Children View Mathematical Representations: A Study Using Eye-Tracking Technology

ERIC Educational Resources Information Center

Bolden, David; Barmby, Patrick; Raine, Stephanie; Gardner, Matthew

2015-01-01

Background: It has been shown that mathematical representations can aid children's understanding of mathematical concepts but that children can sometimes have difficulty in interpreting them correctly. New advances in eye-tracking technology can help in this respect because it allows data to be gathered concerning children's focus of attention and…

Identifying Mathematics Content and Integrating It into Science Instruction

ERIC Educational Resources Information Center

Schwols, Amitra; Miller, Kirsten Brush

2012-01-01

Science teachers know that the mathematics concepts taught in the Common Core are critical for students' understanding of science. But what can a teacher do when his/her students lack the necessary mathematics skills to master science content? There may be other reasons besides students not paying attention in their math courses. Maybe the…

Scott Foresman-Addison Wesley Elementary Mathematics. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2010

2010-01-01

"Scott Foresman-Addison Wesley Elementary Mathematics" is a core curriculum for students at all ability levels in prekindergarten through grade 6. The program supports students' understanding of key math concepts and skills and covers a range of mathematical content across grades. The What Works Clearinghouse (WWC) reviewed 12 studies on…

Using Spreadsheets to Teach Aspects of Biology Involving Mathematical Models

ERIC Educational Resources Information Center

Carlton, Kevin; Nicholls, Mike; Ponsonby, David

2004-01-01

Some aspects of biology, for example the Hardy-Weinberg simulation of population genetics or modelling heat flow in lizards, have an undeniable mathematical basis. Students can find the level of mathematical skill required to deal with such concepts to be an insurmountable hurdle to understanding. If not used effectively, spreadsheet models…

Making It Count: Strategies for Improving Mathematics Instruction for Students in Short-Term Facilities. Strategy Guide

ERIC Educational Resources Information Center

Leone, Peter; Wilson, Michael; Mulcahy, Candace

2010-01-01

This guide is designed to support the development of mathematics proficiency for youth in short-term juvenile correctional facilities. Mathematics proficiency includes mastery and fluency in foundational numeracy; an understanding of complex, grade-appropriate concepts and procedures; and application of those competencies to solve relevant,…

Improving Primary Students' Mathematical Literacy through Problem Based Learning and Direct Instruction

ERIC Educational Resources Information Center

Firdaus, Fery Muhamad; Wahyudin; Herman, Tatang

2017-01-01

This research was done on primary school students who are able to understand mathematical concepts, but unable to apply them in solving real life problems. Therefore, this study aims to improve primary school students' mathematical literacy through problem-based learning and direct instruction. In addition, the research was conducted to determine…

Procedural Explanations in Mathematics Writing: A Framework for Understanding College Students' Effective Communication Practices

ERIC Educational Resources Information Center

Kline, Susan L.; Ishii, Drew K.

2008-01-01

This study analyzes the procedural explanations written by remedial college mathematics students. Relevant literatures suggest that six communication activities might be key in effective procedural explanations in mathematics writing: (a) orienting the learner, (b) providing kernels or definitions of concepts and procedures, (c) using exemplars or…

Developing and Piloting the Planning for Facilitating Mathematical Processes and Strategies for Preschool Learners

ERIC Educational Resources Information Center

Botha, M.; Maree, J. G.; de Witt, M. W.

2005-01-01

From an early age young children actively engage informally in acquiring fundamental concepts and process skills that form a basis for mathematical understanding. Quite logically, questions will arise during planning when young children first encounter a more formal learning environment: what strategy should one use to develop mathematical …

Inquiry-Based Argumentation in Primary Mathematics: Reflecting on Evidence

ERIC Educational Resources Information Center

Fielding-Wells, Jill

2013-01-01

Argumentation in mathematics teaching has potential to move students beyond tacit understanding of mathematical concepts and procedures towards articulation and justification of their ideas; a practice in which evidence is central. Design-based research was used to examine the nature of evidence used by a class of primary students through levels…

A Fruitful Activity for Finding the Greatest Common Factor

ERIC Educational Resources Information Center

Bell, Carol J.; Leisner, Heather J.; Shelley, Kristina

2011-01-01

Posing mathematics problems in different ways will raise students' level of cognitive demand because it will push them to think more deeply about mathematics. By engaging students in a task that requires them to determine their own solution strategies, students will gain a deeper understanding of the mathematical concept explored through the task.…

Differential forms for scientists and engineers

NASA Astrophysics Data System (ADS)

Blair Perot, J.; Zusi, Christopher J.

2014-01-01

This paper is a review of a number of mathematical concepts from differential geometry and exterior calculus that are finding increasing application in the numerical solution of partial differential equations. The objective of the paper is to introduce the scientist/ engineer to some of these ideas via a number of concrete examples in 2, 3, and 4 dimensions. The goal is not to explain these ideas with mathematical precision but to present concrete examples and enable a physical intuition of these concepts for those who are not mathematicians. The objective of this paper is to provide enough context so that scientist/engineers can interpret, implement, and understand other works which use these elegant mathematical concepts.

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…

Epistemological Obstacles on the Topic of Ratio and Proportion among Junior High School Students

NASA Astrophysics Data System (ADS)

Wahyuningrum, A. S.; Suryadi, D.; Turmudi

2017-09-01

This study intends to investigate how students’ understanding of ratio and proportion concept indicates epistemological obstacles. It was part of Didactical Design Research which was conducted to 72 students of 8th grade who ever learned about ratio and proportion. Data were collected through the students’ answers and interview in solving ratio and proportion problems. The results show that students’ conception, the ways of applying other mathematical concepts, the ways of using the rules, and variety of contexts are factors influencing epistemological obstacles in teaching and learning of ratio and proportion. These conditions can affect the students’ understanding o f related mathematics topics. Based on analysis of the results, this study is expected to overcome or minimize the epistemological obstacles.

Science and Mathematics in Astronomy

NASA Technical Reports Server (NTRS)

Woolack, Edward

2009-01-01

A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.

A Study of Parent-Child Numeracy Interaction in Families of English Language Learners

ERIC Educational Resources Information Center

Stiles, Terri F.

2010-01-01

Current research has focused on early numeracy in the preschool setting, but few studies have addressed the relationship between elementary school children's understanding of mathematical concepts and parent-child interactions during math play or work. As a result, the researcher sought to understand the extent to which math concepts were…

An Exce-L-ent Algorithm for Factors and Multiples

ERIC Educational Resources Information Center

Lee, Jae Ki; Choi, Kyong Mi; McAninch, Melissa

2012-01-01

Research has proved that American students, as well as some adults, struggle with understanding fraction concepts and operations (Behr et al. 1992; NCES 2011). Having a solid understanding of this topic is important because fraction concepts are a foundation for many areas in secondary school mathematics, such as rate of change, rational…

Supporting Middle Grades Mathematics Teachers and Students: A Curricular Activity System Used in an Urban School District

ERIC Educational Resources Information Center

Roy, George J.; Fueyo, Vivian; Vahey, Philip

2017-01-01

The exploration of proportional relationships is foundational to the mathematics studied in the middle grades and beyond. Research has shown that an early emphasis on procedures often leaves students with a shallow understanding of the important underlying mathematical concepts of proportional relationships. One approach that addresses the needs…

Using the Construct of the Didactic Contract to Understand Student Transition into University Mathematics Education

ERIC Educational Resources Information Center

Pepin, Birgit

2014-01-01

In this article the concept of the Didactic Contract is used to investigate student "transition" from upper secondary into university mathematics education. The findings are anchored in data from the TransMaths project, more particularly the case of an ethnic minority student's journey from his school to a university mathematics course…

Effectiveness of ST Math in College Remedial Mathematics Students Learning of Fraction Concepts

ERIC Educational Resources Information Center

Ito, Taro

2017-01-01

This study examined the extent to which the iPad app, Spatial Temporal Mathematics (ST Math), diminished college remedial mathematics students' natural number bias and deepened their fraction conceptual understanding. In this quasi-experimental study one class played the ST Math fraction games for 8 weeks, and they were compared to a control class…

The Number Line as a Representation of Decimal Numbers: A Research with Sixth Grade Students

ERIC Educational Resources Information Center

Michaelidou, Niki; Gagatsis, Athanasios; Pitta-Pantazi, Demetra

2004-01-01

One of the aims of mathematics instruction is to achieve the understanding of mathematical concepts through the development of rich and well organized cognitive representations (Goldin, 1998; NCTM, 2000; DeWindt-King, & Goldin, 2003). In this study the term representation is interpreted as the tool used for representing mathematical ideas such…

How to Enlarge the Scope of the Curriculum Integration of Mathematics and Science (CIMAS): A Delphi Study

ERIC Educational Resources Information Center

Kim, Minkee; Aktan, Tugba

2014-01-01

Studies have not yet consented whether integrating mathematics into science would enhance students' learning or confuse their understanding of abstract mathematical concepts. In spite of the social need for solving social-scientific problems with multiple facets, there has not been a holistic integration model of the disciplines. Hence, this study…

Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 4

ERIC Educational Resources Information Center

Boaler, Jo; Munson, Jen; Williams, Cathy

2017-01-01

The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the fourth-grade level through visualization, play, and…

Teacher Classroom Practices and Mathematics Performance in South African Schools: A Reflection on TIMSS 2011

ERIC Educational Resources Information Center

Arends, Fabian; Winnaar, Lolita; Mosimege, Mogege

2017-01-01

Teachers play an important role in the provision of quality education. The variety of classroom practices they use in interacting with learners play a critical role in the understanding of mathematical concepts and overall performance in Mathematics. Following the work done by Hattie (2009, 2012) in relation to classroom practices this study…

What's the Word for... ? Is There a Word for... ? How Understanding Mi'kmaw Language Can Help Support Mi'kmaw Learners in Mathematics

ERIC Educational Resources Information Center

Borden, Lisa Lunney

2013-01-01

As part of a larger project focused on decolonising mathematics education for Aboriginal students in Atlantic Canada, this article reports on the role of the Mi'kmaw language in mathematics teaching. By exploring how mathematical concepts are talked about (or not talked about) in the Mi'kmaw language, teachers and researchers can gain insight into…

Conceptions of Function Composition in College Precalculus Students

ERIC Educational Resources Information Center

Bowling, Stacey

2014-01-01

Past research has shown that students have difficulty developing a robust conception of function. However, little prior research has been performed dealing with student knowledge of function composition, a potentially powerful mathematical concept. This dissertation reports the results of an investigation into student understanding and use of…

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)

Undergraduate students' initial conceptions of factorials

NASA Astrophysics Data System (ADS)

Lockwood, Elise; Erickson, Sarah

2017-05-01

Counting problems offer rich opportunities for students to engage in mathematical thinking, but they can be difficult for students to solve. In this paper, we present a study that examines student thinking about one concept within counting, factorials, which are a key aspect of many combinatorial ideas. In an effort to better understand students' conceptions of factorials, we conducted interviews with 20 undergraduate students. We present a key distinction between computational versus combinatorial conceptions, and we explore three aspects of data that shed light on students' conceptions (their initial characterizations, their definitions of 0!, and their responses to Likert-response questions). We present implications this may have for mathematics educators both within and separate from combinatorics.

The Development of an Assessment Tool: Student Knowledge of the Concept of Place Value

ERIC Educational Resources Information Center

Major, Karen

2012-01-01

The importance of student understanding of the concept of place value cannot be underestimated. Place value is a "gate keeper" in developing mathematical understanding. The purpose of this study was to examine and develop a teacher-made test of place value knowledge. The questions were developed using the progressions from the Number…

Preservice Elementary Teachers Use Drawings and Make Sets of Materials to Explain Multiplication and Division by Fractions

ERIC Educational Resources Information Center

Rule, Audrey C., Ed.; Hallagan, Jean E., Ed.

2006-01-01

Background: Multiplication and division by fractions are among the most troublesome concepts in the elementary mathematics curriculum. Recent studies have shown that preservice elementary teachers in the United States do not have deep understandings of these concepts. Effective ways to improve preservice teachers' conceptual understanding of these…

Student Competence in Understanding the Matter Concept and Its Implications for Science Curriculum Standards

ERIC Educational Resources Information Center

Liu, Xiufeng

2006-01-01

Using the US national sample from the 1995 Third International Mathematics and Science Study (TIMSS), this study examined students' competence levels in understanding the matter concept at grades 3, 4, 7, 8 and high school graduation, and compared them to the expectations in the US national science education standards. It was found that…

Prospective Elementary Teachers' Conceptions of Unitizing with Whole Numbers and Fractions

ERIC Educational Resources Information Center

Tobias, Jennifer M.; Roy, George J.; Safi, Farshid

2015-01-01

This article examines prospective elementary teachers' conceptions of unitizing with whole numbers and fraction concepts and operations throughout a semester-long mathematics content course. Student work samples and classroom conversations are used to illustrate the types of unitizing understandings that prospective teachers bring to teacher…

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…

Using Mental Imagery Processes for Teaching and Research in Mathematics and Computer Science

ERIC Educational Resources Information Center

Arnoux, Pierre; Finkel, Alain

2010-01-01

The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

The Integration of Mathematics in Middle School Science: Student and Teacher Impacts Related to Science Achievement and Attitudes towards Integration

ERIC Educational Resources Information Center

McHugh, Luisa

2016-01-01

Contemporary research has suggested that in order for students to compete globally in the 21st century workplace, pedagogy must shift to include the integration of science and mathematics, where teachers effectively incorporate the two disciplines seamlessly. Mathematics facilitates a deeper understanding of science concepts and has been linked to…

Analysis of Student Understanding of Science Concepts Including Mathematical Representations: Ph Values and the Relative Differences of pH Values

ERIC Educational Resources Information Center

Park, Eun-Jung; Choi, Kyunghee

2013-01-01

In general, mathematical representations such as formulae, numbers, and graphs are the inseparable components in science used to better describe or explain scientific phenomena or knowledge. Regardless of their necessity and benefit, science seems to be difficult for some students, as a result of the mathematical representations and problem…

Intangible heritage for sustainable future: mathematics in the paddy field

NASA Astrophysics Data System (ADS)

Dewanto, Stanley P.; Kusuma, Dianne A.; Nurani Ruchjana, Budi; Setiawan Abdullah, Atje

2017-10-01

Mathematics, as the only general language, can describe all phenomena on earth. Mathematics not only helps us to understand these phenomena, but it also can sustain human activities, consequently ensure that the future development is sustainable. Indonesia, with high cultural diversity, should aware to have its understanding, skills, and philosophies developed by certain societies, with long histories of interaction with their natural surroundings, which will provide a foundation for locally appropriate sustainable development. This paper discussed the condition and situation on certain area in Cigugur, Indonesia, and what skills, knowledge, and concept can be transmitted, regarding simple mathematics (arithmetic). Some examples are provided.

A Worked Example for Creating Worked Examples

ERIC Educational Resources Information Center

McGinn, Kelly M.; Lange, Karin E.; Booth, Julie L.

2015-01-01

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

Mathematical knowledge in teaching of fraction concepts using diagrammatical approach

NASA Astrophysics Data System (ADS)

Veloo, Palanisamy Kathir; Puteh, Marzita

2017-05-01

Teachers need various types of knowledge in order to deliver various fraction concepts at elementary level. In this paper, Balls' framework (2008) or, Mathematical Knowledge for Teaching (MKT) is used as benchmark guideline. This paper investigates and explores component of MKT knowledge among eight experienced teachers of the primary school. Data was collected using paper pencil test, interview and video recording. This paper, narrowed to teacher's knowledge and their practices while teaching of various fractions concepts using diagrammatical approach in present of MKT. The data gathered from teachers were analyzed using thematic analysis techniques. The results indicated that teachers lack various components of MKT knowledge as a proposal by various researchers and assumed that teaching as procedural more than enough due to lack of deep understanding of mathematics and the various types of MKT is not required due to the present of practices in the mathematics classroom.

Using an evaluative tool to develop effective mathscasts

NASA Astrophysics Data System (ADS)

Galligan, Linda; Hobohm, Carola; Peake, Katherine

2017-09-01

This study is situated in a course designed for both on-campus and online pre-service and in-service teachers, where student-created mathscasts provide a way for university lecturers to assess students' quality of teaching, and understanding of mathematics. Teachers and pre-service teachers, in a university course with 90% online enrolment, were asked to create mathscasts to explain mathematics concepts at middle school level. This paper describes the process of developing and refining a tool for the creation and evaluation of quality student-produced mathscasts. The study then investigates the usefulness of the tool within the context of pedagogy and mathematical understanding. Despite an abundance of mathscasts already available on the web, there is merit in creating mathscasts, not only as a tool for teaching, but also as a means of learning by doing. The premise for creating student-produced mathscasts was to capture the creators' mathematical understanding and pedagogical approach to teaching a mathematical concept, which were then peer-assessed and graded. The analysis included surveys, practice mathscasts with peer- and self-reviews, and students' final assessed mathscasts. The results indicate that the use of the evaluative tool resulted in an improvement in quality of student-created mathscasts and critiques thereof. The paper concludes with a discussion on future directions of student-produced mathscasts.

Supporting Teachers' Understandings of Function through Online Professional Development

ERIC Educational Resources Information Center

Silverman, Jason

2017-01-01

This article explores one segment of an extended research and development project that was conducted to better understand the ways online teacher professional development can support teachers' development of deep and connected mathematical understandings. In particular, this article discusses teachers' understandings of the concept of…

Exploring Young Children's Understanding about the Concept of Volume through Engineering Design in a STEM Activity: A Case Study

ERIC Educational Resources Information Center

Park, Do-Yong; Park, Mi-Hwa; Bates, Alan B.

2018-01-01

This case study explores young children's understanding and application of the concept of volume through the practices of engineering design in a STEM activity. STEM stands for science, technology, engineering, and mathematics. However, engineering stands out as a challenging area to implement. In addition, most early engineering education…

Designing Professional Development around Key Principles and Formative Assessments to Improve Teachers' Knowledge to Teach Mathematics

ERIC Educational Resources Information Center

Vendlinski, Terry P.; Hemberg, Bryan; Mundy, Chris; Phelan, Julia

2009-01-01

The authors' hypothesis is that if teachers (as experts) understand and teach concepts from the position of expertise teacher quality will improve. They believe that focusing on the key ideas will deepen both teacher and student understanding and allow learners to build the concepts necessary to form solid foundations for the application 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…

Pre-College Deaf Students' Understanding of Fractional Concepts: What We Know and What We Do Not Know

ERIC Educational Resources Information Center

Mousley, Keith; Kurz, Christopher

2015-01-01

Mathematical knowledge and skills are crucial to success in academics and the workplace. The Common Core State Standards emphasizes fraction teaching and learning in elementary school. This mixed-method study explores fraction concept understanding among 14 deaf and hard of hearing participants between the ages of 8 and 16, as quantitatively…

Indicators of Multiplicative Reasoning among Fourth Grade Students

ERIC Educational Resources Information Center

Carrier, James A.

2010-01-01

Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

Intra-mathematical connections made by high school students in performing Calculus tasks

NASA Astrophysics Data System (ADS)

García-García, Javier; Dolores-Flores, Crisólogo

2018-02-01

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas, concepts, definitions, theorems, procedures, representations and meanings among themselves, with other disciplines or with real life. Task-based interviews were used to collect data and thematic analysis was used to analyze them. Through the analysis of the productions of the 25 participants, we identified 223 intra-mathematical connections. The data allowed us to establish a mathematical connections system which contributes to the understanding of higher concepts, in our case, the Fundamental Theorem of Calculus. We found mathematical connections of the types: different representations, procedural, features, reversibility and meaning as a connection.

The Integration of Mathematics in Middle School Science: Student and Teacher Impacts Related to Science Achievement and Attitudes Towards Integration

NASA Astrophysics Data System (ADS)

McHugh, Luisa

Contemporary research has suggested that in order for students to compete globally in the 21st century workplace, pedagogy must shift to include the integration of science and mathematics, where teachers effectively incorporate the two disciplines seamlessly. Mathematics facilitates a deeper understanding of science concepts and has been linked to improved student perception of the integration of science and mathematics. Although there is adequate literature to substantiate students' positive responses to integration in terms of attitudes, there has been little empirical data to support significant academic improvement when both disciplines are taught in an integrated method. This research study, conducted at several school districts on Long Island and New York City, New York, examined teachers' attitudes toward integration and students' attitudes about, and achievement on assessments in, an integrated 8th grade science classroom compared to students in a non-integrated classroom. An examination of these parameters was conducted to analyze the impact of the sizeable investment of time and resources needed to teach an integrated curriculum effectively. These resources included substantial teacher training, planning time, collaboration with colleagues, and administration of student assessments. The findings suggest that students had positive outcomes associated with experiencing an integrated science and mathematics curriculum, though these were only weakly correlated with teacher confidence in implementing the integrated model successfully. The positive outcomes included the ability of students to understand scientific concepts within a concrete mathematical framework, improved confidence in applying mathematics to scientific ideas, and increased agreement with the usefulness of mathematics in interpreting science concepts. Implications of these research findings may be of benefit to educators and policymakers looking to adapt integrated curricula in order to improve the preparation of students to learn and achieve in a global society.

Understanding Magnitudes to Understand Fractions

ERIC Educational Resources Information Center

Gabriel, Florence

2016-01-01

Fractions are known to be difficult to learn and difficult to teach, yet they are vital for students to have access to further mathematical concepts. This article uses evidence to support teachers employing teaching methods that focus on the conceptual understanding of the magnitude of fractions.

Why Is the Learning of Elementary Arithmetic Concepts Difficult? Semiotic Tools for Understanding the Nature of Mathematical Objects

ERIC Educational Resources Information Center

Godino, Juan D.; Font, Vicenc; Wilhelmi, Miguel R.; Lurduy, Orlando

2011-01-01

The semiotic approach to mathematics education introduces the notion of "semiotic system" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and…

Selected Effects of a Curriculum Integration Intervention on the Mathematics Performance of Secondary Students Enrolled in an Agricultural Power and Technology Course: An Experimental Study

ERIC Educational Resources Information Center

Parr, Brian; Edwards, M. Craig; Leising, James G.

2009-01-01

The purpose of this study was to empirically test the posit that students who participated in a contextualized, mathematics-enhanced high school agricultural power and technology (APT) curriculum and aligned instructional approach would develop a deeper and more sustained understanding of selected mathematics concepts than those students who…

An Intervention for Early Mathematical Success: Outcomes from the Hybrid Version of the Building Math Readiness Parents as Partners (MRPP) Project

ERIC Educational Resources Information Center

Kritzer, Karen L.; Pagliaro, Claudia M.

2013-01-01

The Building Math Readiness in Young Deaf/Hard-of-Hearing Children: Parents as Partners (MRPP) Project works with parents to increase the understanding of foundational mathematics concepts in their preschool deaf/hard-of-hearing (d/hh) children in preparation for formal mathematics education. A multiple-case/single-unit case study incorporating…

Student Connections of Linear Algebra Concepts: An Analysis of Concept Maps

ERIC Educational Resources Information Center

Lapp, Douglas A.; Nyman, Melvin A.; Berry, John S.

2010-01-01

This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernaud's theory of conceptual fields and Pirie and Kieren's model for the growth of mathematical understanding.…

An intervention for early mathematical success: outcomes from the hybrid version of the Building Math Readiness Parents as Partners (MRPP) project.

PubMed

Kritzer, Karen L; Pagliaro, Claudia M

2013-01-01

The Building Math Readiness in Young Deaf/Hard-of- Hearing Children: Parents as Partners (MRPP) Project works with parents to increase the understanding of foundational mathematics concepts in their preschool deaf/hard-of-hearing (d/hh) children in preparation for formal mathematics education. A multiple-case/single-unit case study incorporating descriptive statistics and grounded theory analysis was conducted on the hybrid version of the intervention. Results showed productive changes in parental behaviors indicating a possible positive effect on parent knowledge, recognition, and mediation of early matthematics concepts with their young d/hh children.

Children Learn Spurious Associations in Their Math Textbooks: Examples from Fraction Arithmetic

ERIC Educational Resources Information Center

Braithwaite, David W.; Siegler, Robert S.

2018-01-01

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

Shaking up Pre-Calculus: Incorporating Engineering into K-12 Curricula

ERIC Educational Resources Information Center

Sabo, Chelsea; Burrows, Andrea; Childers, Lois

2014-01-01

Projects highlighting Science, Technology, Engineering, and Mathematics (STEM) education in high schools have promoted student interest in engineering-related fields and enhanced student understanding of mathematics and science concepts. The Science and Technology Enhancement Program (Project STEP), funded by a NSF GK-12 grant at the University of…

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…

ELPSA as a Lesson Design Framework

ERIC Educational Resources Information Center

Lowrie, Tom; Patahuddin, Sitti Maesuri

2015-01-01

This paper offers a framework for a mathematics lesson design that is consistent with the way we learn about, and discover, most things in life. In addition, the framework provides a structure for identifying how mathematical concepts and understanding are acquired and developed. This framework is called ELPSA and represents five learning…

From Sailing Ships to Subtraction Symbols: Multiple Representations to Support Abstraction

ERIC Educational Resources Information Center

Jao, Limin

2013-01-01

Teachers are tasked with supporting students' learning of abstract mathematical concepts. Students can represent their mathematical understanding in a variety of modes, for example: manipulatives, pictures, diagrams, spoken languages, and written symbols. Although most students easily pick up rudimentary knowledge through the use of concrete…

Mathematics Pedagogical Change: Rethinking Identity and Reflective Practice

ERIC Educational Resources Information Center

Walshaw, Margaret

2010-01-01

This article deals with issues that are central to changed mathematics pedagogical practice. It engages general debates about teaching reflexivity and within that, more specific debates in relation to identity. It uses theoretical concepts derived from Lacanian psychoanalysis as a way of understanding what structures a teacher's narrative about…

Cleared for Takeoff: Paper Airplanes in Flight

ERIC Educational Resources Information Center

Reeder, Stacy L.

2012-01-01

As middle school mathematics becomes more abstract, it is imperative for teachers to introduce concepts in ways that are interesting and meaningful to students. Since her students struggled at times to stay engaged in mathematics and seemed to have difficulty developing conceptual understanding, the author looked for ways to create learning…

Focus in Grade 8: Teaching with Curriculum Focal Points

ERIC Educational Resources Information Center

Schielack, Jane

2010-01-01

This book describes and illustrates learning paths for the mathematical concepts and skills of each grade 8 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate understanding, stimulate productive discussions about…

Mathematics and the Heart: Understanding Cardiac Output

ERIC Educational Resources Information Center

Champanerkar, Jyoti

2013-01-01

This paper illustrates a biological application of the concepts of relative change and area under a curve, from mathematics. We study two biological measures "relative change in cardiac output" and "cardiac output", which are predictors of heart blockages and other related ailments. Cardiac output refers to the quantity of…

Changes in Pre-Service Teachers' Algebraic Misconceptions by Using Computer-Assisted Instruction

ERIC Educational Resources Information Center

Lin, ByCheng-Yao; Ko, Yi-Yin; Kuo, Yu-Chun

2014-01-01

In order to carry out current reforms regarding algebra and technology in elementary school mathematics successfully, pre-service elementary mathematics teachers must be equipped with adequate understandings of algebraic concepts and self-confidence in using computers for their future teaching. This paper examines the differences in preservice…

Building a Knowledge Base: Understanding Prospective Elementary Teachers' Mathematical Content Knowledge

ERIC Educational Resources Information Center

Thanheiser, Eva; Browning, Christine; Edson, Alden J.; Kastberg, Signe; Lo, Jane-Jane

2013-01-01

This survey of the literature summarizes and reflects on research findings regarding elementary preservice teachers' (PSTs') mathematics conceptions and the development thereof. Despite the current focus on teacher education, peer-reviewed journals offer a surprisingly sparse insight in these areas. The limited research that exists…

Nature's optics and our understanding of light

NASA Astrophysics Data System (ADS)

Berry, M. V.

2015-01-01

Optical phenomena visible to everyone have been central to the development of, and abundantly illustrate, important concepts in science and mathematics. The phenomena considered from this viewpoint are rainbows, sparkling reflections on water, mirages, green flashes, earthlight on the moon, glories, daylight, crystals and the squint moon. And the concepts involved include refraction, caustics (focal singularities of ray optics), wave interference, numerical experiments, mathematical asymptotics, dispersion, complex angular momentum (Regge poles), polarisation singularities, Hamilton's conical intersections of eigenvalues ('Dirac points'), geometric phases and visual illusions.

Working with Functions without Understanding: An Assessment of the Perceptions of Basotho College Mathematics Specialists on the Idea of Function

ERIC Educational Resources Information Center

Polaki, Mokaeane Victor

2005-01-01

It is a well-known fact that the idea of function plays a unifying role in the development of mathematical concepts. Yet research has shown that many students do not understand it adequately even though they have experienced a great deal of success in performing a plethora of operations on function, and on using functions to solve various types of…

[For the Introduction of a Conceptual Perspective in Mathematics: Dedekind, Noether, van der Waerden].

PubMed

Koreuber, Mechthild

2015-09-01

,,She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine - of all that is characterized by the term ‚Begriffliche Mathematik‘.“ The aim of this paper is to illuminate this "new direction", which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831-1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a "free creation of the human spirit". They thus stand for an abstract perspective of mathematics in their entirety, described as 'modern algebra' in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on "general mathematical concepts" [allgemein-mathematische Begriffe], was the success of a cultural movement whose most important protagonists included Emmy Noether (1882-1935) and her pupil Bartel L. van der Waerden (1903-1996). With the use of the term 'conceptual', a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the "working and conceptual methods" [Arbeits- und Auffassungsmethoden] of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term "conceptual world" [Begriffswelt] in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School.

Validation and structural analysis of the kinematics concept test

NASA Astrophysics Data System (ADS)

Lichtenberger, A.; Wagner, C.; Hofer, S. I.; Stern, E.; Vaterlaus, A.

2017-06-01

The kinematics concept test (KCT) is a multiple-choice test designed to evaluate students' conceptual understanding of kinematics at the high school level. The test comprises 49 multiple-choice items about velocity and acceleration, which are based on seven kinematic concepts and which make use of three different representations. In the first part of this article we describe the development and the validation process of the KCT. We applied the KCT to 338 Swiss high school students who attended traditional teaching in kinematics. We analyzed the response data to provide the psychometric properties of the test. In the second part we present the results of a structural analysis of the test. An exploratory factor analysis of 664 student answers finally uncovered the seven kinematics concepts as factors. However, the analysis revealed a hierarchical structure of concepts. At the higher level, mathematical concepts group together, and then split up into physics concepts at the lower level. Furthermore, students who seem to understand a concept in one representation have difficulties transferring the concept to similar problems in another representation. Both results have implications for teaching kinematics. First, teaching mathematical concepts beforehand might be beneficial for learning kinematics. Second, instructions have to be designed to teach students the change between different representations.

Constructing conceptual knowledge and promoting "number sense" from computer-managed practice in rounding whole numbers

NASA Astrophysics Data System (ADS)

Hativa, Nira

1993-12-01

This study sought to identify how high achievers learn and understand new concepts in arithmetic from computer-based practice which provides full solutions to examples but without verbal explanations. Four high-achieving second graders were observed in their natural school settings throughout all their computer-based practice sessions which involved the concept of rounding whole numbers, a concept which was totally new to them. Immediate post-session interviews inquired into students' strategies for solutions, errors, and their understanding of the underlying mathematical rules. The article describes the process through which the students construct their knowledge of the rounding concepts and the errors and misconceptions encountered in this process. The article identifies the cognitive abilities that promote student self-learning of the rounding concepts, their number concepts and "number sense." Differences in the ability to generalise, "mathematical memory," mindfulness of work and use of cognitive strategies are shown to account for the differences in patterns of, and gains in, learning and in maintaining knowledge among the students involved. Implications for the teaching of estimation concepts and of promoting students' "number sense," as well as for classroom use of computer-based practice are discussed.

A Strategy for Improving US Middle School Student Mathematics Word Problem Solving Performance

NASA Technical Reports Server (NTRS)

Thomas, Valerie L.

2004-01-01

U.S. middle school students have difficulty understanding and solving mathematics word problems. Their mathematics performance on the Third International Mathematics and Science Study (TIMMS) is far below their international peers, and minority students are less likely than high socioeconomic status (SES) White/Asian students to be exposed to higher-level mathematics concepts. Research literature also indicates that when students use both In-School and Out-of-School knowledge and experiences to create authentic mathematics word problems, student achievement improves. This researcher developed a Strategy for improving mathematics problem solving performance and a Professional Development Model (PDM) to effectively implement the Strategy.

It's All Connected: The Power of Proportional Reasoning to Understand Mathematics Concepts, Gr. 6-8

ERIC Educational Resources Information Center

Whitman, Carmen

2011-01-01

"It's All Connected" provides teachers of mathematics the support they need to improve their instruction. This in-demand collection of lessons for grades 6-8 explores proportionality, proportional relationships, and proportional reasoning, acknowledging that the ability to reason proportionally is crucial in the middle school mathematics…

Constructing Contracts: Making Discrete Mathematics Relevant to Beginning Programmers

ERIC Educational Resources Information Center

Gegg-Harrison, Timothy S.

2005-01-01

Although computer scientists understand the importance of discrete mathematics to the foundations of their field, computer science (CS) students do not always see the relevance. Thus, it is important to find a way to show students its relevance. The concept of program correctness is generally taught as an activity independent of the programming…

Field Dependency and Performance in Mathematics

ERIC Educational Resources Information Center

Onwumere, Onyebuchi; Reid, Norman

2014-01-01

Mathematics is an important school subject but one which often poses problems for learners. It has been found that learners do not possess the cognitive capacity to handle understanding procedures, representations, concepts, and applications at the same time. while the extent of field dependency may hold the key to one way by which the working…

Teaching and Assessing Polygons Using Technology

ERIC Educational Resources Information Center

Soucie, Tanja; Radovic, Nikol; Svedrec, Renata; Kokic, Ivana

2011-01-01

Studying geometry is an integral component of learning mathematics because it allows students to analyse and interpret the world they live in as well as equip them with tools they can apply in other areas of mathematics. Therefore, students need to develop an understanding of geometric concepts as well as gaining adequate geometry related skills.…

Obstacles to Mathematization in Physics: The Case of the Differential

ERIC Educational Resources Information Center

López-Gay, R.; Martinez Sáez, J.; Martinez Torregrosa, J.

2015-01-01

The process of the mathematization of physical situations through differential calculus requires an understanding of the justification for and the meaning of the differential in the context of physics. In this work, four different conceptions about the differential in physics are identified and assessed according to their utility for the…

The Development of a Cognitively-Diagnostic Formative Assessment of the Early Concept of Angle

ERIC Educational Resources Information Center

Khasanova, Elvira

2016-01-01

Students' development of conceptual understandings is a central goal of mathematics education (CCSS-Mathematics, 2010). Such a challenging, yet ambiguous, goal cannot be achieved without empowering teachers with the knowledge and tools critical for their ability to adequately convey the content, and assess and interpret students' performance. This…

Using Challenging Tasks for Formative Assessment on Quadratic Functions with Senior Secondary Students

ERIC Educational Resources Information Center

Wilkie, Karina J.

2016-01-01

Senior secondary mathematics students who develop conceptual understanding that moves them beyond "rules without reasons" to connections between related concepts are in a strong place to tackle the more difficult mathematics application problems. Current research is examining how the use of challenging tasks at different levels of…

Using Action Research to Develop a Course in Statistical Inference for Workplace-Based Adults

ERIC Educational Resources Information Center

Forbes, Sharleen

2014-01-01

Many adults who need an understanding of statistical concepts have limited mathematical skills. They need a teaching approach that includes as little mathematical context as possible. Iterative participatory qualitative research (action research) was used to develop a statistical literacy course for adult learners informed by teaching in…

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…

1982 Maths Investigation: Technical Report. Mt. Druitt Longitudinal Study.

ERIC Educational Resources Information Center

Houghton, Karen; Low, Brian

Aims of this phase of a longitudinal mathematics achievement investigation were to (1) detect individual and group differences in math achievement among a sample of fourth-year children, (2) monitor changes in math skills since a 1981 math investigation, and (3) identify limits of children's understanding of mathematical concepts. (The math test…

Knowing and Teaching Middle School Mathematics: A Professional Development Course for In-Service Teachers

ERIC Educational Resources Information Center

Anderson, Celia Rousseau; Hoffmeister, April M.

2007-01-01

This article describes a professional development course intended to improve the content understanding of middle school mathematics teachers. The design of the course included three professional learning strategies: problem solving, examination of student thinking, and discussion of research. The concepts studied in the course included multi-digit…

Understanding Student Use of Differentials in Physics Integration Problems

ERIC Educational Resources Information Center

Hu, Dehui; Rebello, N. Sanjay

2013-01-01

This study focuses on students' use of the mathematical concept of differentials in physics problem solving. For instance, in electrostatics, students need to set up an integral to find the electric field due to a charged bar, an activity that involves the application of mathematical differentials (e.g., "dr," "dq"). In this…

Improving the Fraction Word Problem Solving of Students with Mathematics Learning Disabilities: Interactive Computer Application

ERIC Educational Resources Information Center

Shin, Mikyung; Bryant, Diane P.

2017-01-01

Students with mathematics learning disabilities (MLD) have a weak understanding of fraction concepts and skills, which are foundations of algebra. Such students might benefit from computer-assisted instruction that utilizes evidence-based instructional components (cognitive strategies, feedback, virtual manipulatives). As a pilot study using a…

Geometry-Related Children's Literature Improves the Geometry Achievement and Attitudes of Second-Grade Students

ERIC Educational Resources Information Center

McAndrew, Erica M.; Morris, Wendy L.; Fennell, Francis

2017-01-01

Use of mathematics-related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi-experimental study of two second-grade classrooms assessed whether daily inclusion of geometry-related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the…

Maple (Computer Algebra System) in Teaching Pre-Calculus: Example of Absolute Value Function

ERIC Educational Resources Information Center

Tuluk, Güler

2014-01-01

Modules in Computer Algebra Systems (CAS) make Mathematics interesting and easy to understand. The present study focused on the implementation of the algebraic, tabular (numerical), and graphical approaches used for the construction of the concept of absolute value function in teaching mathematical content knowledge along with Maple 9. The study…

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.

Quantum and Multidimensional Explanations in a Neurobiological Context of Mind.

PubMed

Korf, Jakob

2015-08-01

This article examines the possible relevance of physical-mathematical multidimensional or quantum concepts aiming at understanding the (human) mind in a neurobiological context. Some typical features of the quantum and multidimensional concepts are briefly introduced, including entanglement, superposition, holonomic, and quantum field theories. Next, we consider neurobiological principles, such as the brain and its emerging (physical) mind, evolutionary and ontological origins, entropy, syntropy/neg-entropy, causation, and brain energy metabolism. In many biological processes, including biochemical conversions, protein folding, and sensory perception, the ubiquitous involvement of quantum mechanisms is well recognized. Quantum and multidimensional approaches might be expected to help describe and model both brain and mental processes, but an understanding of their direct involvement in mental activity, that is, without mediation by molecular processes, remains elusive. More work has to be done to bridge the gap between current neurobiological and physical-mathematical concepts with their associated quantum-mind theories. © The Author(s) 2014.

Testing Understanding and Understanding Testing.

ERIC Educational Resources Information Center

Pedersen, Jean; Ross, Peter

1985-01-01

Provides examples in which graphs are used in the statements of problems or in their solutions as a means of testing understanding of mathematical concepts. Examples (appropriate for a beginning course in calculus and analytic geometry) include slopes of lines and curves, quadratic formula, properties of the definite integral, and others. (JN)

Calculus Instructors' and Students' Discourses on the Derivative

ERIC Educational Resources Information Center

Park, Jungeun

2011-01-01

Recently, there has been an increasing interest in collegiate mathematics education, especially teaching and learning calculus (e.g., Oehrtman, Carlson, & Thompson, 2008; Speer, Smith, & Horvath, 2010). Of many calculus concepts, the derivative is known as a difficult concept for students to understand because it involves various concepts…

The Concept of Slope: Comparing Teachers' Concept Images and Instructional Content

ERIC Educational Resources Information Center

Nagle, Courtney; Moore-Russo, Deborah

2013-01-01

In the field of mathematics education, understanding teachers' content knowledge (Grossman, 1995; Hill, Sleep, Lewis, & Ball, 2007; Munby, Russell, & Martin, 2001) and studying the relationship between content knowledge and instructional decisions (Fennema & Franke, 1992; Raymond, 1997) are both crucial. Teachers need a robust…

Teaching undergraduate biomechanics with Just-in-Time Teaching.

PubMed

Riskowski, Jody L

2015-06-01

Biomechanics education is a vital component of kinesiology, sports medicine, and physical education, as well as for many biomedical engineering and bioengineering undergraduate programmes. Little research exists regarding effective teaching strategies for biomechanics. However, prior work suggests that student learning in undergraduate physics courses has been aided by using the Just-in-Time Teaching (JiTT). As physics understanding plays a role in biomechanics understanding, the purpose of study was to evaluate the use of a JiTT framework in an undergraduate biomechanics course. This two-year action-based research study evaluated three JiTT frameworks: (1) no JiTT; (2) mathematics-based JiTT; and (3) concept-based JiTT. A pre- and post-course assessment of student learning used the biomechanics concept inventory and a biomechanics concept map. A general linear model assessed differences between the course assessments by JiTT framework in order to evaluate learning and teaching effectiveness. The results indicated significantly higher learning gains and better conceptual understanding in a concept-based JiTT course, relative to a mathematics-based JiTT or no JiTT course structure. These results suggest that a course structure involving concept-based questions using a JiTT strategy may be an effective method for engaging undergraduate students and promoting learning in biomechanics courses.

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.

Development of 3-D Mechanical Models of Electric Circuits and Their Effect on Students' Understanding of Electric Potential Difference

ERIC Educational Resources Information Center

Balta, Nuri

2015-01-01

Visualizing physical concepts through models is an essential method in many sciences. While students are mostly proficient in handling mathematical aspects of problems, they frequently lack the ability to visualize and interpret abstract physical concepts in a meaningful way. In this paper, initially the electric circuits and related concepts were…

Discovering and understanding the vector field using simulation in android app

NASA Astrophysics Data System (ADS)

Budi, A.; Muliyati, D.

2018-05-01

An understanding of vector field’s concepts are fundamental parts of the electrodynamics course. In this paper, we use a simple simulation that can be used to show qualitative imaging results as a variation of the vector field. Android application packages the simulation with consideration of the efficiency of use during the lecture. In addition, this simulation also trying to cover the divergences and curl concepts from the same conditions that students have a complete understanding and can distinguish concepts that have been described only mathematically. This simulation is designed to show the relationship between the field magnitude and its potential. This application can show vector field simulations in various conditions that help to improve students’ understanding of vector field concepts and their relation to particle existence around the field vector.

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…

The Concept of Fractional Number among Hearing-Impaired Students.

ERIC Educational Resources Information Center

Titus, Janet C.

This study investigated hearing-impaired students' understanding of the mathematical concept of fractional numbers, as measured by their ability to determine the order and equivalence of fractional numbers. Twenty-one students (ages 10-16) with hearing impairments were compared with 26 students with normal hearing. The study concluded that…

Two-Year College Mathematics Instructors' Conceptions of Variation

ERIC Educational Resources Information Center

Dabos, Monica Graciela Gandhini

2011-01-01

Statistics education researchers are urging teachers of statistics to help students develop a more sophisticated understanding of variation, since variation is the core of statistics. However, little research has been done into the conceptions of variation held by instructors of statistics. This is of particular importance at the community college…

Shadows Constructing a Relationship between Light and Color Pigments by Physical and Mathematical Perspectives

ERIC Educational Resources Information Center

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

2017-01-01

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.…

BASIC MATHEMATICS I FOR THE SECONDARY SCHOOLS.

ERIC Educational Resources Information Center

MCCARTHY, CHARLES T.; AND OTHERS

THE COURSE IS GEARED TO MEET THE NEEDS OF STUDENTS ENTERING SENIOR HIGH SCHOOL WITH A MATHEMATICS ACHIEVEMENT LEVEL BELOW SIXTH GRADE. SINCE TWO PRINCIPAL CAUSES OF SERIOUS DEFICIENCIES IN ARITHMETIC ARE A LACK OF UNDERSTANDING OF THE DECIMAL SYSTEM OF NOTATION AND A LACK OF KNOWLEDGE OF THE BASIC FUNDAMENTALS OF ARITHMETIC, BASIC CONCEPTS MUST BE…

Students' Dichotomous Experiences of the Illuminating and Illusionary Nature of Pattern Recognition in Mathematics

ERIC Educational Resources Information Center

Mhlolo, Michael Kainose

2016-01-01

The concept of pattern recognition lies at the heart of numerous deliberations concerned with new mathematics curricula, because it is strongly linked to improved generalised thinking. However none of these discussions has made the deceptive nature of patterns an object of exploration and understanding. Yet there is evidence showing that pattern…

Norms for Participation in a Middle School Mathematics Classroom and Its Effect on Student Motivation

ERIC Educational Resources Information Center

Megowan-Romanowicz, M. Colleen; Middleton, James A.; Ganesh, Tirupalavanam; Joanou, Jamie

2013-01-01

In this article we examine how students engage in learning mathematical concepts in the middle grades of an urban public school in the Southwestern United States. In the context of a 3-year National Science Foundation-funded longitudinal study of the development of students' rational number understanding, we encountered differing levels of…

Interdisciplinary Working Practices: Can Creative Dance Improve Math?

ERIC Educational Resources Information Center

Leandro, Cristina Rebelo; Monteiro, Elisabete; Melo, Filipe

2018-01-01

This study is integrated in the field of Dance in Education, focusing on the instrumentalist aspect of art. We focused on creative dance as a catalyst to learn Mathematics' contents. This interdisciplinary work can enhance the learning, as far as the understanding of Mathematics' concepts is achieved through the body and revealed by expressive and…

Virtual vs. Concrete Manipulatives in Mathematics Teacher Education: Is One Type More Effective than the Other?

ERIC Educational Resources Information Center

Hunt, Annita W.; Nipper, Kelli L.; Nash, Linda E.

2011-01-01

Are virtual manipulatives as effective as concrete (hands-on) manipulatives in building conceptual understanding of number concepts and relationships in pre-service middle grades teachers? In the past, the use of concrete manipulatives in mathematics courses for Clayton State University's pre-service middle grades teachers has been effective in…

The Cognitive Roots of Scientific and Mathematical Ability and Discussant Reaction: Alternative Representations: A Key to Academic Talent?

ERIC Educational Resources Information Center

Perkins, D. N.; Simmons, Rebecca

This paper examines the cognitive structures and processes that mediate mathematical and scientific ability. Ability is divided into achieved abilities and precursor abilities. Identified concepts in the area of achieved ability include expertise, understanding, and problem-solving. Other abilities can be seen as precursors to such achieved…

What Do Croatian Pre-Service Teachers Remember from Their Calculus Course?

ERIC Educational Resources Information Center

Jukic, Ljerka; Brückler, Franka Miriam

2014-01-01

This paper reports a study on retention of core concepts in differential and integral calculus by examining the knowledge of two pre-service mathematics students. The study is conducted using a mixed method approach and the obtained data were analyzed using theory of three worlds of mathematics. The results showed that having good understanding of…

Scaffolding Mathematics Remediation for Academically At-Risk Students Following Developmental Education Reform in Florida

ERIC Educational Resources Information Center

Rebecca, Brower L.; Woods, Chenoa S.; Bertrand Jones, Tamara; Park, Toby J.; Hu, Shouping; Tandberg, David A.; Nix, Amanda; Rhaming, Sophia G.; Martindale, Sandra K.

2017-01-01

The purpose of this qualitative study is to understand how educational scaffolding may explain changing patterns of student success in mathematics in the era of developmental education (DE or remediation) reform in Florida College System (FCS) institutions. Specifically, we apply the concept of scaffolding to underprepared FCS students who are at…

Scaffolding Mathematics Remediation for Academically At-Risk Students Following Developmental Education Reform in Florida

ERIC Educational Resources Information Center

Brower, Rebecca L.; Woods, Chenoa S.; Jones, Tamara Bertrand; Park, Toby J.; Hu, Shouping; Tandberg, David A.; Nix, Amanda N.; Rahming, Sophia G.; Martindale, Sandra K.

2018-01-01

The purpose of this qualitative study is to understand how educational scaffolding may explain changing patterns of student success in mathematics in the era of developmental education (DE or remediation) reform in Florida College System (FCS) institutions. Specifically, we apply the concept of scaffolding to underprepared FCS students who are at…

A Teachable Agent Game Engaging Primary School Children to Learn Arithmetic Concepts and Reasoning

ERIC Educational Resources Information Center

Pareto, Lena

2014-01-01

In this paper we will describe a learning environment designed to foster conceptual understanding and reasoning in mathematics among younger school children. The learning environment consists of 48 2-player game variants based on a graphical model of arithmetic where the mathematical content is intrinsically interwoven with the game idea. The…

Characteristics of manipulative in mathematics laboratory

NASA Astrophysics Data System (ADS)

Istiandaru, A.; Istihapsari, V.; Prahmana, R. C. I.; Setyawan, F.; Hendroanto, A.

2017-12-01

A manipulative is a teaching aid designed such that students could understand mathematical concepts by manipulating it. This article aims to provide an insight to the characteristics of manipulatives produced in the mathematics laboratory of Universitas Ahmad Dahlan, Indonesia. A case study was conducted to observe the existing manipulatives produced during the latest three years and classified the manipulatives based on the characteristics found. There are four kinds of manipulatives: constructivism manipulative, virtual manipulative, informative manipulative, and game-based manipulative. Each kinds of manipulative has different characteristics and impact towards the mathematics learning.

Problem Posing with Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Mahendra, R.; Slamet, I.; Budiyono

2017-09-01

One of the difficulties of students in the learning of geometry is on the subject of plane that requires students to understand the abstract matter. The aim of this research is to determine the effect of Problem Posing learning model with Realistic Mathematics Education Approach in geometry learning. This quasi experimental research was conducted in one of the junior high schools in Karanganyar, Indonesia. The sample was taken using stratified cluster random sampling technique. The results of this research indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students’ conceptual understanding significantly in geometry learning especially on plane topics. It is because students on the application of Problem Posing with Realistic Mathematics Education Approach are become to be active in constructing their knowledge, proposing, and problem solving in realistic, so it easier for students to understand concepts and solve the problems. Therefore, the model of Problem Posing learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on geometry material. Furthermore, the impact can improve student achievement.

Reference Framework for Describing and Assessing Students' Understanding in First Year Calculus

ERIC Educational Resources Information Center

Kannemeyer, Larry

2005-01-01

This paper presents aspects of a study that investigates the development of an instrument, a reference framework, to analyse students' written responses to non-routine problems in a first year calculus course in order to describe the complexities of their understanding and to assess their understanding of particular mathematical concepts.…

Exploring Students' Understanding of Ordinary Differential Equations Using Computer Algebraic System (CAS)

ERIC Educational Resources Information Center

Maat, Siti Mistima; Zakaria, Effandi

2011-01-01

Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students' understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly…

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

NASA Astrophysics Data System (ADS)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

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 variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

Multiple Representations and Connections with the Sierpinski Triangle

ERIC Educational Resources Information Center

Kirwan, J. Vince; Tobias, Jennifer M.

2014-01-01

To understand multiple representations in algebra, students must be able to describe relationships through a variety of formats, such as graphs, tables, pictures, and equations. NCTM indicates that varied representations are "essential elements in supporting students' understanding of mathematical concepts and relationships" (NCTM…

Problematic topics in first-year mathematics: lecturer and student views

NASA Astrophysics Data System (ADS)

Ní Shé, Caitríona; Mac an Bhaird, Ciarán; Ní Fhloinn, Eabhnat; O'Shea, Ann

2017-07-01

In this paper we report on the outcomes of two surveys carried out in higher education institutions of Ireland; one of students attending first-year undergraduate non-specialist mathematics modules and another of their lecturers. The surveys aimed to identify the topics that these students found difficult, whether they had most difficulty with the concepts or procedures involved in the topics, and the resources they used to overcome these difficulties. In this paper we focus on the mathematical concepts and procedures that students found most difficult. While there was agreement between students and lecturers on certain problematic topics, this was not uniform across all topics, and students rated their conceptual understanding higher than their ability to do questions, in contrast to lecturers' opinions.

First-Year Non-STEM Majors' Use of Definitions to Solve Calculus Tasks: Benefits of Using Concept Image over Concept Definition?

ERIC Educational Resources Information Center

Dahl, Bettina

2017-01-01

Six US first-year university students in humanities or social science degree programmes were interviewed while solving 4 tasks on continuity and asymptotes in a required mathematics course. The focus was on how the students referred to the definitions or to the concept images when solving the tasks and if partial understandings appeared. Partial…

The profile of conceptual comprehension of pre-service teacher in the mathematical problem solving with low emotional intelligence

NASA Astrophysics Data System (ADS)

Prayitno, S. H.; Suwarsono, St.; Siswono, T. Y. E.

2018-03-01

Conceptual comprehension in this research is the ability to use the procedures that are owned by pre-service teachers to solve problems by finding the relation of the concept to another, or can be done by identifying the type of problem and associating it with a troubleshooting procedures, or connect the mathematical symbols with mathematical ideas and incorporate them into a series of logical reasoning, or by using prior knowledge that occurred directly, through its conceptual knowledge. The goal of this research is to describe the profile of conceptual comprehensin of pre-service teachers with low emotional intelligence in mathematical problems solving. Through observation and in-depth interview with the research subject the conclusion was that: pre-service teachers with low emotional intelligence pertained to the level of formal understanding in understanding the issues, relatively to the level of intuitive understanding in planning problem solving, to the level of relational understanding in implementing the relational problem solving plan, and pertained to the level of formal understanding in looking back to solve the problem.

Teachers' Understanding of Inflation: Developing a Crystalline Concept

ERIC Educational Resources Information Center

Bansilal, Sarah

2017-01-01

Inflation rates are often reported in the media and interpreted differently by various people. The purpose of the study was to explore mathematical literacy teachers' written responses to questions based on the concept of percentage increase and inflation. The participants were a group of 59 in-service South African teachers who were enrolled on a…

United States Middle School Students' Perspectives on Learning Statistics

ERIC Educational Resources Information Center

Dwyer, Jerry; Moorhouse, Kim; Colwell, Malinda J.

2009-01-01

This paper describes an intervention at the 8th grade level where university mathematics researchers presented a series of lessons on introductory concepts in probability and statistics. Pre- and post-tests, and interviews were conducted to examine whether or not students at this grade level can understand these concepts. Students showed a…

Undergraduate Students' Initial Conceptions of Factorials

ERIC Educational Resources Information Center

Lockwood, Elise; Erickson, Sarah

2017-01-01

Counting problems offer rich opportunities for students to engage in mathematical thinking, but they can be difficult for students to solve. In this paper, we present a study that examines student thinking about one concept within counting, factorials, which are a key aspect of many combinatorial ideas. In an effort to better understand students'…

Pre-Service Teachers' Mental Constructions of Concepts in Matrix Algebra

ERIC Educational Resources Information Center

Ndlovu, Zanele; Brijlall, Deonarain

2015-01-01

This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers…

Escher's Tessellations in Understanding Group Theory

ERIC Educational Resources Information Center

Konyalioglu, Serpil

2009-01-01

In this study, it is explained how to use Escher's tessellations in teaching group concept which is one of the most abstract concepts in mathematics. MC Escher's monohedral tessellations provide detailed study in an undergraduate course in abstract algebra. This study attempts to provide useful visual references for the students on learning some…

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…

Students' Progression of Understanding the Matter Concept from Elementary to High School

ERIC Educational Resources Information Center

Liu, Xiufeng; Lesniak, Kathleen M.

2005-01-01

Using the US national sample from the Third International Mathematics and Science Study (TIMSS) and the Rasch modeling method, this study identified the conceptual progression sequence of various matter concept aspects, and compared students' latent abilities against the sequence. We found that the four matter aspects, i.e. conservation, physical…

Improving Conceptual and Procedural Knowledge: The Impact of Instructional Content within a Mathematics Lesson

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Fyfe, Emily R.; Loehr, Abbey M.

2016-01-01

Background: Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding. Aims: This study evaluated the effect of instruction on a math…

Designing and Redesigning a Framework for Assessing Students' Understanding of Foundational Fractions Concepts

ERIC Educational Resources Information Center

Mendiburo, Maria; Williams, Laura; Henson, Robert; Hasselbring, Ted

2013-01-01

The fact that research has shown that fractions are among the most difficult mathematical concepts for elementary school students to master (Behr, Harel, Post, & Lesh, 1992; Bezuk & Cramer, 1989; Moss & Case, 1999) provides a compelling motivation for research and innovation focused on improving the available assessment and…

Helping students mathematical construction on square and rectangle’s area by using Sarong motive chess

NASA Astrophysics Data System (ADS)

Zuliana, Eka; Setyawan, Fariz; Veloo, Arsaythamby

2017-12-01

The aim of this study is developing the learning trajectory to construct students’ understanding of the concept of the area of square and rectangle by using Sarong Motive Chess. This research is a design research which is consists of three stages. The stages are preparing for the experiment, designing experiment, and making a retrospective analysis. The activities started by the activity of using sarong motive chess as the manipulative measurement unit. The Sarong motive chess helps students to understand the concept of area of square and rectangle. In the formal stage of cognitive level, students estimate the area of square and rectangle by determining the square unit at the surface area of sarong through many ways. The result of this study concludes that Sarong motive chess can be used for mathematics learning process. It helps the students to construct the concept of a square and rectangle’s area. This study produces learning trajectory to construct the concept of a square and rectangle’s area by using Sarong motive chess, especially for elementary school students.

Visualizing Volume to Help Students Understand the Disk Method on Calculus Integral Course

NASA Astrophysics Data System (ADS)

Tasman, F.; Ahmad, D.

2018-04-01

Many research shown that students have difficulty in understanding the concepts of integral calculus. Therefore this research is interested in designing a classroom activity integrated with design research method to assist students in understanding the integrals concept especially in calculating the volume of rotary objects using disc method. In order to support student development in understanding integral concepts, this research tries to use realistic mathematical approach by integrating geogebra software. First year university student who takes a calculus course (approximately 30 people) was chosen to implement the classroom activity that has been designed. The results of retrospective analysis show that visualizing volume of rotary objects using geogebra software can assist the student in understanding the disc method as one way of calculating the volume of a rotary object.

The Importance of Multiple Representations of Mathematical Problems: Evidence from Chinese Preservice Elementary Teachers' Analysis of a Learning Goal

ERIC Educational Resources Information Center

Kang, Rui; Liu, Di

2018-01-01

This article describes a study of how Chinese preservice teachers unpacked a learning goal pertaining to adding fractions and understanding the concepts underlying the operation. Based on work in the USA by Morris, Hiebert, and Spizter ("Journal for Research in Mathematics Education," 40(5), 491-529, 2009), 50 Chinese preservice teachers…

The Process of Thinking among Junior High School Students in Solving HOTS Question

ERIC Educational Resources Information Center

Bakry, Md Nor Bin Bakar

2015-01-01

Higher order thinking skills (HOTS) is one of the important aspect of teaching and learning mathematics. By using HOTS, student will be able to acquire a deep understand of mathematical concepts and can be applied in real life. Students ability to develop the capacity of the HOTS is closely related with thinking processes while solving mathematics…

Evidence for the Effectiveness of Inquiry-Based, Particulate-Level Instruction on Conceptions of the Particulate Nature of Matter

ERIC Educational Resources Information Center

Bridle, Chad A.; Yezierski, Ellen J.

2012-01-01

Research has shown that students in traditional college-preparatory chemistry courses become masters of mathematical equations without an understanding of the conceptual basis for the mathematical relationships. This problem is rooted not only in what curriculum is presented to students, but also in how it is experienced by the students. Ample…

Boundary Spanners as Bridges of Student and School Discourses in an Urban Science and Mathematics High School

ERIC Educational Resources Information Center

Buxton, Cory A.; Carlone, Heidi B.; Carlone, David

2005-01-01

A key to improving urban science and mathematics education is to facilitate the mutual understanding of the participants involved and then look for strategies to bridge differences. Educators need new theoretical tools to do so. In this paper the argument is made that the concept of "boundary spanner" is such a tool. Boundary spanners…

Learning within Context: Exploring Lesson Study as an Aid in Enhancing Teachers' Implementations, Conceptions, and Perceptions of the Mathematics Teaching Practices

ERIC Educational Resources Information Center

Prince, Kyle

2016-01-01

With traditional teaching methods pervasive in the U.S., it is crucial that mathematics teacher educators and professional development leaders understand what methods result in authentic changes in classroom instruction. Lesson study presents a promising approach to developing reform-oriented instruction, as it is situated within the classroom,…

Understanding Dyscalculia for Teaching

ERIC Educational Resources Information Center

Vaidya, Sheila Rao

2004-01-01

Dyscalculia, a poor understanding of the number concept and the number system, is a learning problem affecting many individuals. However, less is known about this disability than about the reading disability, dyslexia, because society accepts learning problems in mathematics as quite normal. This article provides a summary of the research on…

Aviation Technician Training I and Task Analyses: Semester II. Field Review Copy.

ERIC Educational Resources Information Center

Upchurch, Richard

This guide for aviation technician training begins with a course description, resource information, and a course outline. Tasks/competencies are categorized into 16 concept/duty areas: understanding technical symbols and abbreviations; understanding mathematical terms, symbols, and formulas; computing decimals; computing fractions; computing ratio…

Traditional Instruction of Differential Equations and Conceptual Learning

ERIC Educational Resources Information Center

Arslan, Selahattin

2010-01-01

Procedural and conceptual learning are two types of learning, related to two types of knowledge, which are often referred to in mathematics education. Procedural learning involves only memorizing operations with no understanding of underlying meanings. Conceptual learning involves understanding and interpreting concepts and the relations between…

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

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.

Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence.

PubMed

Ozaktas, Haldun M; Yüksel, Serdar; Kutay, M Alper

2002-08-01

A linear algebraic theory of partial coherence is presented that allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights but also allows us to employ the conceptual and algebraic tools of linear algebra in applications. We define several scalar measures of the degree of partial coherence of an optical field that are zero for full incoherence and unity for full coherence. The mathematical definitions are related to our physical understanding of the corresponding concepts by considering them in the context of Young's experiment.

Profile of Metacognition of Mathematics Pre-Service Teachers in Understanding the Concept of Integral Calculus with Regard Gender Differences

NASA Astrophysics Data System (ADS)

Misu, L.; Budayasa, I. K.; Lukito, A.

2018-01-01

This research is to describe metacognition profile of female and male mathematics’ pre-service teachers in understanding the concept of integral calculus. The subjects of this study are one female and 1 male mathematics’ pre-service teachers who have studied integral calculus. This research type is an explorative study with the qualitative approach. The main data collection of this research was obtained by using Interview technique. In addition, there are supporting data which is the result of the written work of research subjects (SP) in understanding the question of integral calculus. The results of this study are as follows: There is a difference in metacognition profiles between male and female mathematics’ pre-service teachers in the understanding concept of integral calculus in the interpreting category, especially the definite integral concept. While in the category of exemplifying, there is no difference in metacognition profile between male and female mathematics’ pre-service teachers either the definite integral concept and the indefinite integral concept.

Writing to Promote and Assess Conceptual Understanding in College Algebra

ERIC Educational Resources Information Center

Gay, A. Susan; Peterson, Ingrid

2014-01-01

Concept-focused quiz questions required College Algebra students to write about their understanding. The questions can be viewed in three broad categories: a focus on sense-making, a focus on describing a mathematical object such as a graph or an equation, and a focus on understanding vocabulary. Student responses from 10 classes were analyzed.…

Comparing the Effects of Representational Tools in Collaborative and Individual Inquiry Learning

ERIC Educational Resources Information Center

Kolloffel, Bas; Eysink, Tessa H. S.; de Jong, Ton

2011-01-01

Constructing a representation in which students express their domain understanding can help them improve their knowledge. Many different representational formats can be used to express one's domain understanding (e.g., concept maps, textual summaries, mathematical equations). The format can direct students' attention to specific aspects of the…

The Codevelopment of Children's Fraction Arithmetic Skill and Fraction Magnitude Understanding

ERIC Educational Resources Information Center

Bailey, Drew H.; Hansen, Nicole; Jordan, Nancy C.

2017-01-01

The importance of fraction knowledge to later mathematics achievement, along with U.S. students' poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants' (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed…

Helping Secondary School Students Develop a Conceptual Understanding of Refraction

ERIC Educational Resources Information Center

Ashmann, Scott; Anderson, Charles W.; Boeckman, Heather

2016-01-01

Using real-world examples, ray diagrams, and a cognitive apprenticeship cycle, this paper focuses on developing students' conceptual (not mathematical) understanding of refraction. Refraction can be a difficult concept for students to comprehend if they do not have well-designed opportunities to practice explaining situations where reflection and…

Graphing Calculator Mini Course

NASA Technical Reports Server (NTRS)

Karnawat, Sunil R.

1996-01-01

The "Graphing Calculator Mini Course" project provided a mathematically-intensive technologically-based summer enrichment workshop for teachers of American Indian students on the Turtle Mountain Indian Reservation. Eleven such teachers participated in the six-day workshop in summer of 1996 and three Sunday workshops in the academic year. The project aimed to improve science and mathematics education on the reservation by showing teachers effective ways to use high-end graphing calculators as teaching and learning tools in science and mathematics courses at all levels. In particular, the workshop concentrated on applying TI-82's user-friendly features to understand the various mathematical and scientific concepts.

Mathematics, anxiety, and the brain.

PubMed

Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

2017-05-24

Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

[Gaston Bachelard anagogical reverie and surrational at stake].

PubMed

Castellana, Mario

2015-01-01

The latest studies on epistemological thought of Gaston Bachelard, especially in France and Italy, they are highlighting some fundamental issues, such as creative and propulsive assigned to mathematics in the construction of physical reality. The studies of Bachelard on the quantum mechanics of the '30s, and especially on the theoretical physics of Paul Dirac, introduced a particular concept of "anagogical reverie" precisely in order to understand the increasingly abstract and creative thinking of mathematics in the various levels of physical reality. In the wake of what Federigo Enriques called "mathematical poetry", Bachelard comes to propose a real "nouménologie mathématique" which characterizes the contemporary scientific thought and which provides the basis epistemic appropriate to understand the 'rational effectiveness' of mathematics and the real meaning of their application to the real. For these reasons, Bachelard in the '30s used a new term to describe his rationalist engagement, the "surrationalisme", just to understand in depth what Enriques called the "implicit philosophy" in sciences, the "pensée des sciences", where mathematics, thanks to the "anagogical reverie", put in place continue "enjeux" of the rational.

Pre-University Students' Errors in Integration of Rational Functions and Implications for Classroom Teaching

ERIC Educational Resources Information Center

Yee, Ng Kin; Lam, Toh Tin

2008-01-01

This paper reports on students' errors in performing integration of rational functions, a topic of calculus in the pre-university mathematics classrooms. Generally the errors could be classified as those due to the students' weak algebraic concepts and their lack of understanding of the concept of integration. With the students' inability to link…

Construction of High School Students' Abstraction Levels in Understanding the Concept of Quadrilaterals

ERIC Educational Resources Information Center

Budiarto, Mega Teguh; Khabibah, Siti; Setianingsih, Rini

2017-01-01

The purpose of this study was to examine the abstraction thinking or the vertical reorganization activity of mathematical concepts of high school students while taking account of the abstraction that was constructed earlier, and the socio-cultural background. This study was qualitative in nature with task-based interviews as the method of…

Substitution and Sameness: Two Components of a Relational Conception of the Equals Sign

ERIC Educational Resources Information Center

Jones, Ian; Inglis, Matthew; Gilmore, Camilla; Dowens, Margaret

2012-01-01

A sophisticated and flexible understanding of the equals sign (=) is important for arithmetic competence and for learning further mathematics, particularly algebra. Research has identified two common conceptions held by children: the equals sign as an operator and the equals sign as signaling the same value on both sides of the equation. We argue…

Area Conceptions Sprout on Earth Day

ERIC Educational Resources Information Center

Wickstrom, Megan H.; Nelson, Julie; Chumbley, Jean

2015-01-01

With the adoption of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), many concepts related to area are covered in third grade: (1) Recognizing area as an attribute of a plane figure; (2) Understanding that a square with a side length of one is a unit square; (3) Measuring area by tiling figures and counting the squares it…

An Investigation of the Effectiveness of Computer Simulation Programs as Tutorial Tools for Teaching Population Ecology at University.

ERIC Educational Resources Information Center

Korfiatis, K.; Papatheodorou, E.; Paraskevopoulous, S.; Stamou, G. P.

1999-01-01

Describes a study of the effectiveness of computer-simulation programs in enhancing biology students' familiarity with ecological modeling and concepts. Finds that computer simulations improved student comprehension of ecological processes expressed in mathematical form, but did not allow a full understanding of ecological concepts. Contains 28…

A Cross-Cultural Investigation into the Development of Place-Value Concepts of Children in Taiwan and the United States.

ERIC Educational Resources Information Center

Yang, Ma Tzu-Lin; Cobb, Paul

1995-01-01

Compares mathematics achievement of children in Taiwan and the United States by analyzing the arithmetical learning contexts of each. Interviews with parents and teachers identify cultural beliefs about learning arithmetic; interviews with students identify level of sophistication of arithmetical concepts. Found greater understanding by Chinese…

Understanding Calculus beyond Computations: A Descriptive Study of the Parallel Meanings and Expectations of Teachers and Users of Calculus

ERIC Educational Resources Information Center

Ferguson, Leann J.

2012-01-01

Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…

Teaching Pre-Service Teachers to Make Digital Stories That Explain Complex Mathematical Concepts in a Real-World Context: The "Math-eo" Project, Creating "Cool New Tools"

ERIC Educational Resources Information Center

Walters, Lynne Masel; Green, Martha R.; Goldsby, Dianne; Walters, Timothy N.; Wang, Liangyan

2016-01-01

This mixed methods study examines whether engaging in a problem-solving project to create Math-eos (digital videos) increases pre-service teachers' understanding of the relationship between visual, auditory, and verbal representation and critical thinking in mathematics. Additionally, the study looks at what aspects of a digital problem solving…

An Examination of the Effects of Collaborative Scientific Visualization via Model-Based Reasoning on Science, Technology, Engineering, and Mathematics (STEM) Learning within an Immersive 3D World

ERIC Educational Resources Information Center

Soleimani, Ali

2013-01-01

Immersive 3D worlds can be designed to effectively engage students in peer-to-peer collaborative learning activities, supported by scientific visualization, to help with understanding complex concepts associated with learning science, technology, engineering, and mathematics (STEM). Previous research studies have shown STEM learning benefits…

How Visual Imagery Contributed to College: A Case of How Visual Imagery Contributes to a College Algebra Student's Understanding of the Concept of Function in the United States

ERIC Educational Resources Information Center

Lane, Rebekah M.

2011-01-01

This investigation utilized the qualitative case study method. Seventy-one College Algebra students were given a mathematical processing instrument. This testing device measured a student's preference for visual thinking. Two students were purposefully selected using the instrument. The visual mathematical learner (VL) was discussed in this…

Summary of Research Academic Departments, 1987-1988

DTIC Science & Technology

1988-12-01

quantify the computer nccring students and their faculty with roughly system’s ability to enhance learning of the course equivalent computers; one group...Sponsor: Naval Academy Instructional Development Advisory Committee To understand mathematics , a student must under- also to explain the central concepts... Mathematics Department. The project will attempt resources for in-class and extra instruction , to move toward these goals by preparing extra Students

Preparing Prospective Elementary Teachers To Foster Conceptually Based Mathematical Understandings: A Study Investigating Change in Prospective Teachers' Conceptions Related to Mathematics Teaching and Learning.

ERIC Educational Resources Information Center

Benken, Babette M.; Brown, Nancy

More than two decades of research and experience supports the idea that computer and calculator technologies can have an important role to play in supporting and effecting student learning (Heid, 1988; Kaput, 1992; Kutzler, 1996; Papert, 1980; Waits and Demana, 1999). The development of Classroom Communication Systems (CCSs) is providing new…

"It Doesn't Feel Like a Job to Learn": Preservice Elementary Teachers' Perceptions of Dance-Themed Mathematics Education

ERIC Educational Resources Information Center

An, Song A.; Kim, So Jung; Tillman, Daniel; Robertson, William; Juarez, Martha; Guo, Connie

2017-01-01

A series of dance activities were introduced to preservice teachers (n = 76) to help them understand how mathematics concepts could be associated with dance performance and choreography processes. A total of 468 pieces of qualitative data were collected, including 147 online discussion entries with 248 follow-up comments, and 73 individual…

How concept images affect students' interpretations of Newton's method

NASA Astrophysics Data System (ADS)

Engelke Infante, Nicole; Murphy, Kristen; Glenn, Celeste; Sealey, Vicki

2018-07-01

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus students, we determined how evoked concept images of tangent lines and roots contributed to students' interpretation and application of Newton's method. Results show that some students' concept images of root and tangent line developed throughout the interview process, and most students were able to adequately interpret the text on Newton's method. However, students with insufficient concept images of tangent line and students who were unwilling or unable to modify their concept images of tangent line after reading the text were not successful in interpreting Newton's method.

How students learn to coordinate knowledge of physical and mathematical models in cellular physiology

NASA Astrophysics Data System (ADS)

Lira, Matthew

This dissertation explores the Knowledge in Pieces (KiP) theory to account for how students learn to coordinate knowledge of mathematical and physical models in biology education. The KiP approach characterizes student knowledge as a fragmented collection of knowledge elements as opposed to stable and theory-like knowledge. This dissertation sought to use this theoretical lens to account for how students understand and learn with mathematical models and representations, such as equations. Cellular physiology provides a quantified discipline that leverages concepts from mathematics, physics, and chemistry to understand cellular functioning. Therefore, this discipline provides an exemplary context for assessing how biology students think and learn with mathematical models. In particular, the resting membrane potential provides an exemplary concept well defined by models of dynamic equilibrium borrowed from physics and chemistry. In brief, membrane potentials, or voltages, "rest" when the electrical and chemical driving forces for permeable ionic species are equal in magnitude but opposite in direction. To assess students' understandings of this concept, this dissertation employed three studies: the first study employed the cognitive clinical interview to assess student thinking in the absence and presence of equations. The second study employed an intervention to assess student learning and the affordances of an innovative assessment. The third student employed a human-computer-interaction paradigm to assess how students learn with a novel multi-representational technology. Study 1 revealed that students saw only one influence--the chemical gradient--and that students coordinated knowledge of only this gradient with the related equations. Study 2 revealed that students benefited from learning with the multi-representational technology and that the assessment detected performance gains across both calculation and explanation tasks. Last, Study 3 revealed how students shift from recognizing one influence to recognizing both the chemical and the electrical gradients as responsible for a cell's membrane potential reaching dynamic equilibrium. Together, the studies illustrate that to coordinate knowledge, students need opportunities to reflect upon relations between representations of mathematical and physical models as well as distinguish between physical quantities such as molarities for ions and transmembrane voltages.

What is the problem in problem-based learning in higher education mathematics

NASA Astrophysics Data System (ADS)

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

RSA Encryption with the TI-82.

ERIC Educational Resources Information Center

Sigmon, Neil; Yankosky, Bill

2002-01-01

Description of integrating one of the most widely used cryptosystems into a mathematics course for Liberal Arts majors. Application of this cryptosystem requires understanding of the concepts of exponentiation and modular arithmetic only. (MM)

Group Theory in Spectroscopy

ERIC Educational Resources Information Center

Mooney, A.

1973-01-01

Discusses application of group theory to the teaching of selection rules in electronic and vibrational spectroscopy. Indicates that acquaintance with such a mathematical concept is essential for high school students to understand molecular spectrum courses. (CC)

A study of competence in mathematics and mechanics in an engineering curriculum

NASA Astrophysics Data System (ADS)

Munns, Andrew

2017-11-01

Professional bodies expect engineers to show competence in both mathematics and engineering topics such as mechanics, using their abilities in both of these to solve problems. Yet within engineering programmes there is a phenomenon known as 'The Mathematics Problem', with students not demonstrating understanding of the subject. This paper will suggest that students are constructing different concept images in engineering and mathematics, based on their perception of either the use or exchange-value for the topics. Using a mixed methods approach, the paper compares 10 different types of concept image constructed by students, which suggests that familiar procedural images are preferred in mathematics. In contrast strategic and conceptual images develop for mechanics throughout the years of the programme, implying that different forms of competence are being constructed by students between the two subjects. The paper argues that this difference is attributed to the perceived use-value of mechanics in the career of the engineer, compared to the exchange-value associated with mathematics. Questions are raised about the relevance of current definitions of competence given that some routine mathematical operations previously performed by engineers are now being replaced by technology, in the new world of work.

What Does It Mean for a Student to Understand the First-Year Calculus? Perspectives of 24 Experts

ERIC Educational Resources Information Center

Sofronas, Kimberly S.; DeFranco, Thomas C.; Vinsonhaler, Charles; Gorgievski, Nicholas; Schroeder, Larissa; Hamelin, Chris

2011-01-01

This article presents the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus. A framework emerged that includes four overarching end goals for understanding of the first-year calculus: (a) mastery of the fundamental concepts and-or skills of…

Assessing the Impact of Computer Programming in Understanding Limits and Derivatives in a Secondary Mathematics Classroom

ERIC Educational Resources Information Center

de Castro, Christopher H.

2011-01-01

This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…

Students' Understanding of Loops and Nested Loops in Computer Programming: An APOS Theory Perspective

ERIC Educational Resources Information Center

Cetin, Ibrahim

2015-01-01

The purpose of this study is to explore students' understanding of loops and nested loops concepts. Sixty-three mechanical engineering students attending an introductory programming course participated in the study. APOS (Action, Process, Object, Schema) is a constructivist theory developed originally for mathematics education. This study is the…

Fraction Multiplication and Division Models: A Practitioner Reference Paper

ERIC Educational Resources Information Center

Ervin, Heather K.

2017-01-01

It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers and students need to have an understanding of rational number and related concepts such as fraction multiplication and division. This practitioner reference paper examines models that are important to…

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.

Mathematics and its value for engineering students: what are the implications for teaching?

NASA Astrophysics Data System (ADS)

Harris, Diane; Black, Laura; Hernandez-Martinez, Paul; Pepin, Birgit; Williams, Julian; with the TransMaths Team

2015-04-01

Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan.[1] This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme contexts. Our interviews with the students reveal how they understand the relation between engineering and mathematics and we draw on the concept of 'use- and exchange-value' to explore this relationship more fully. This paper challenges both the pedagogical practice of teaching non-contextualized mathematics and the lack of transparency regarding the significance of mathematics to engineering. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of first-year engineering.

Concepts of formal concept analysis

NASA Astrophysics Data System (ADS)

Žáček, Martin; Homola, Dan; Miarka, Rostislav

2017-07-01

The aim of this article is apply of Formal Concept Analysis on concept of world. Formal concept analysis (FCA) as a methodology of data analysis, information management and knowledge representation has potential to be applied to a verity of linguistic problems. FCA is mathematical theory for concepts and concept hierarchies that reflects an understanding of concept. Formal concept analysis explicitly formalizes extension and intension of a concept, their mutual relationships. A distinguishing feature of FCA is an inherent integration of three components of conceptual processing of data and knowledge, namely, the discovery and reasoning with concepts in data, discovery and reasoning with dependencies in data, and visualization of data, concepts, and dependencies with folding/unfolding capabilities.

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…

Policy versus Practice: The Role of the Home Language in Learning Mathematics and Science in English-Medium Classrooms

ERIC Educational Resources Information Center

Wildsmith-Cromarty, Rosemary; Gordon, Mary

2009-01-01

The focus of this paper is on the effects of the use of the home language (i.e. isiZulu) on teachers' and learners' understanding and use of core concepts in mathematics and science at the senior phase, in contexts where the language of instruction is English. It reports on a national, collaborative, multilingual research project which attempts to…

Toward physics of the mind: Concepts, emotions, consciousness, and symbols

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.

2006-03-01

Mathematical approaches to modeling the mind since the 1950s are reviewed, including artificial intelligence, pattern recognition, and neural networks. I analyze difficulties faced by these algorithms and neural networks and relate them to the fundamental inconsistency of logic discovered by Gödel. Mathematical discussions are related to those in neurobiology, psychology, cognitive science, and philosophy. Higher cognitive functions are reviewed including concepts, emotions, instincts, understanding, imagination, intuition, consciousness. Then, I describe a mathematical formulation, unifying the mind mechanisms in a psychologically and neuro-biologically plausible system. A mechanism of the knowledge instinct drives our understanding of the world and serves as a foundation for higher cognitive functions. This mechanism relates aesthetic emotions and perception of beauty to “everyday” functioning of the mind. The article reviews mechanisms of human symbolic ability. I touch on future directions: joint evolution of the mind, language, consciousness, and cultures; mechanisms of differentiation and synthesis; a manifold of aesthetic emotions in music and differentiated instinct for knowledge. I concentrate on elucidating the first principles; review aspects of the theory that have been proven in laboratory research, relationships between the mind and brain; discuss unsolved problems, and outline a number of theoretical predictions, which will have to be tested in future mathematical simulations and neuro-biological research.

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…

Improving conceptual and procedural knowledge: The impact of instructional content within a mathematics lesson.

PubMed

Rittle-Johnson, Bethany; Fyfe, Emily R; Loehr, Abbey M

2016-12-01

Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding. This study evaluated the effect of instruction on a math concept and procedure within the same lesson relative to a comparable amount of instruction on the concept alone. Direct instruction was provided before or after solving problems to evaluate whether the type of instruction interacted with the timing of instruction within a lesson. We worked with 180 second-grade children in the United States. In a randomized experiment, children received a classroom lesson on mathematical equivalence in one of four conditions that varied in instruction type (conceptual or combined conceptual and procedural) and in instruction order (instruction before or after solving problems). Children who received two iterations of conceptual instruction had better retention of conceptual and procedural knowledge than children who received both conceptual and procedural instruction in the same lesson. Order of instruction did not impact outcomes. Findings suggest that within a single lesson, spending more time on conceptual instruction may be more beneficial than time spent teaching a procedure when the goal is to promote more robust understanding of target concepts and procedures. © 2016 The British Psychological Society.

What’s about Peer Tutoring Learning Model?

NASA Astrophysics Data System (ADS)

Muthma'innah, M.

2017-09-01

Mathematics learning outcomes in Indonesia in general is still far from satisfactory. One effort that could be expected to solve the problem is to apply the model of peer tutoring learning in mathematics. This study aims to determine whether the results of students’ mathematics learning can be enhanced through peer tutoring learning models. This type of research is the study of literature, so that the method used is to summarize and analyze the results of relevant research that has been done. Peer tutoring learning model is a model of learning in which students learn in small groups that are grouped with different ability levels, all group members to work together and help each other to understand the material. By paying attention to the syntax of the learning, then learning will be invaluable peer tutoring for students who served as teachers and students are taught. In mathematics, the implementation of this learning model can make students understand each other mathematical concepts and help students in solving mathematical problems that are poorly understood, due to the interaction between students in learning. Then it will be able to improve learning outcomes in mathematics. The impact, it can be applied in mathematics learning.

Abstracting Sequences: Reasoning That Is a Key to Academic Achievement.

PubMed

Pasnak, Robert; Kidd, Julie K; Gadzichowski, K Marinka; Gallington, Debbie A; Schmerold, Katrina Lea; West, Heather

2015-01-01

The ability to understand sequences of items may be an important cognitive ability. To test this proposition, 8 first-grade children from each of 36 classes were randomly assigned to four conditions. Some were taught sequences that represented increasing or decreasing values, or were symmetrical, or were rotations of an object through 6 or 8 positions. Control children received equal numbers of sessions on mathematics, reading, or social studies. Instruction was conducted three times weekly in 15-min sessions for seven months. In May, the children taught sequences applied their understanding to novel sequences, and scored as well or better on three standardized reading tests as the control children. They outscored all children on tests of mathematics concepts, and scored better than control children on some mathematics scales. These findings indicate that developing an understanding of sequences is a form of abstraction, probably involving fluid reasoning, that provides a foundation for academic achievement in early education.

Dienes AEM as an alternative mathematics teaching aid to enhance Indonesian students’ understanding of algebra concept

NASA Astrophysics Data System (ADS)

Soro, S.; Maarif, S.; Kurniawan, Y.; Raditya, A.

2018-01-01

The aim of this study is to find out the effect of Dienes AEM (Algebra Experience Materials) on the ability of understanding concept of algebra on the senior high school student in Indonesia. This research is an experimental research with subject of all high school students in Indonesia. The samples taken were high school students in three provinces namely DKI Jakarta Province, West Java Province and Banten Province. From each province was taken senior high school namely SMA N 9 Bekasi West Java, SMA N 94 Jakarta and SMA N 5 Tangerang, Banten. The number of samples in this study was 114 high school students of tenth grade as experimental class and 115 high school students of tenth grade as control class. Learning algebra concept is needed in learning mathematics, besides it is needed especially to educate students to be able to think logically, systematically, critically, analytically, creatively, and cooperation. Therefore in this research will be developed an effective algebra learning by using Dienes AEM. The result of this research is that there is a significant influence on the students’ concept comprehension ability taught by using Dienes AEM learning as an alternative to instill the concept of algebra compared to the students taught by conventional learning. Besides, the students’ learning motivation increases because students can construct the concept of algebra with props.

Approach to mathematics in textbooks at tertiary level - exploring authors' views about their texts

NASA Astrophysics Data System (ADS)

Randahl, Mira

2012-10-01

The aim of this article is to present and discuss some results from an inquiry into mathematics textbooks authors' visions about their texts and approaches they choose when new concepts are introduced. Authors' responses are discussed in relation to results about students' difficulties with approaching calculus reported by previous research. A questionnaire has been designed and sent to seven authors of the most used calculus textbooks in Norway and four authors have responded. The responses show that the authors mainly view teaching in terms of transmission so they focus mainly on getting the mathematical content correct and 'clear'. The dominant view is that the textbook is intended to help the students to learn by explaining and clarifying. The authors prefer the approach to introduce new concepts based on the traditional way of perceiving mathematics as a system of definitions, examples and exercises. The results of this study may enhance our understanding of the role of the textbook at tertiary level. They may also form a foundation for further research.

Improving science and mathematics education with computational modelling in interactive engagement environments

NASA Astrophysics Data System (ADS)

Neves, Rui Gomes; Teodoro, Vítor Duarte

2012-09-01

A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed.

Longitudinal associations between reading and mathematics achievement.

PubMed

Grimm, Kevin J

2008-01-01

The association between early reading skills and changes in mathematics was examined in a large, low-income sample to determine whether students who have a greater level of reading skills in early elementary school exhibit more rapid gains in tests of mathematics. The longitudinal associations between third grade reading comprehension and changes in three components of mathematics achievement (Problem Solving and Data Interpretation, Mathematical Concepts and Estimation, Mathematical Computation) from third through eighth grade were examined. Latent growth models were fit to the repeated assessments of each mathematics component and the students' third grade reading and global mathematics scores were included as predictors of the intercept and slope. Gender, poverty status, and ethnicity were included in the models as control variables. The results showed males and African-American students tended to have shallower rates of change than females and non-African-American/non-Hispanic students. In terms of the effect of reading on changes in mathematics, third grade reading comprehension was found to be a positive significant predictor of change for each component of mathematics, suggesting students with a greater level of reading achievement in early elementary school change more rapidly in mathematics skills controlling for prior mathematics skills and student characteristics. The largest effects were shown for the Problem Solving and Data Interpretation test, a test focused on the applications of mathematics knowledge, and the Mathematical Concepts and Estimation test. Negligible effects were found for changes in Mathematical Computation. Thus, early reading comprehension was shown to be related to a conceptual understanding of mathematics and the application of mathematics knowledge. These findings lend support for the notion that early reading skills are important for success in mathematics.

Contribution of Auditory Learning Style to Students’ Mathematical Connection Ability

NASA Astrophysics Data System (ADS)

Karlimah; Risfiani, F.

2017-09-01

This paper presents the results of the research on the relation of mathematical concept with mathematics, other subjects, and with everyday life. This research reveals study result of the students who had auditory learning style and correlates it with their ability of mathematical connection. In this research, the researchers used a combination model or sequential exploratory design method, which is the use of qualitative and quantitative research methods in sequence. The result proves that giving learning facilities which are not suitable for the class whose students have the auditory learning style results in the barely sufficient math connection ability. The average mathematical connection ability of the auditory students was initially in the medium level of qualification. Then, the improvement in the form of the varied learning that suited the auditory learning style still showed the average ability of mathematical connection in medium level of qualification. Nevertheless, there was increase in the frequency of students in the medium level of qualification and decrease in the very low and low level of qualification. This suggests that the learning facilities, which are appropriate for the student’s auditory learning style, contribute well enough to the students’ mathematical connection ability. Therefore, the mathematics learning for students who have an auditory learning style should consist of particular activity that is understanding the concepts of mathematics and their relations.

Literacy Strategies for Improving Mathematics Instruction

ERIC Educational Resources Information Center

Kenney, Joan M.; Hancewicz, Euthecia; Heuer, Loretta; Metsisto, Diana; Tuttle, Cynthia L.

2005-01-01

One of the best ways to give students the background knowledge they need to understand math concepts is to teach them the vocabulary and comprehension skills that are essential to understanding math. So here's a book that explains how to do that and provides teachers with lots of classroom-proven ways to prepare students to be successful math…

Can Slope Be Negative in 3-Space? Studying Concept Image of Slope through Collective Definition Construction

ERIC Educational Resources Information Center

Moore-Russo, Deborah; Conner, AnnaMarie; Rugg, Kristina I.

2011-01-01

Developing deep conceptual understanding of what Ma (1999) calls fundamental mathematics is a well-accepted goal of teacher education. This paper presents a microanalysis of an intriguing episode within a course designed to encourage such understanding. An adaptation of Krummheuer's (1995) elaboration of Toulmin's (1958/2003) diagrams is used to…

A Districtwide Study of Automaticity When Included in Concept-Based Elementary School Mathematics Instruction

ERIC Educational Resources Information Center

McGee, Daniel; Richardson, Patrick; Brewer, Meredith; Gonulates, Funda; Hodgson, Theodore; Weinel, Rebecca

2017-01-01

While conceptual understanding of properties, operations, and the base-ten number system is certainly associated with the ability to access math facts fluently, the role of math fact memorization to promote conceptual understanding remains contested. In order to gain insight into this question, this study looks at the results when one of three…

Technologies to Enhance and Extend Children's Understanding of Geometry: A Configurative Thematic Synthesis of the Literature

ERIC Educational Resources Information Center

Crompton, Helen; Grant, Melva R.; Shraim, Khitam Y. H.

2018-01-01

Empirical evidence indicates that students are not learning geometry with relational understanding of the concepts. Studies have shown that digital technologies can support students in mathematics. The purpose of this study was to find which technologies and technological affordances are specific to learners of geometry. This paper presents the…

Developing a Theoretical Framework for Examining Student Understanding of Fractional Concepts: An Historical Accounting

ERIC Educational Resources Information Center

Cooper, Susan M.; Wilkerson, Trena L.; Montgomery, Mark; Mechell, Sara; Arterbury, Kristin; Moore, Sherrie

2012-01-01

In 2007, a group of mathematics educators and researchers met to examine rational numbers and why children have such an issue with them. An extensive review of the literature on fractional understanding was conducted. The ideas in that literature were then consolidated into a theoretical framework for examining fractions. Once that theoretical…

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.

Constructing the integral concept on the basis of the idea of accumulation: suggestion for a high school curriculum

NASA Astrophysics Data System (ADS)

Kouropatov, Anatoli; Dreyfus, Tommy

2013-07-01

Students have a tendency to see integral calculus as a series of procedures with associated algorithms and many do not develop a conceptual grasp giving them the desirable versatility of thought. Thus, instead of a proceptual view of the symbols in integration, they have, at best, a process-oriented view. On the other hand, it is not surprising that many students find concepts such as the integral difficult when they are unable to experience these processes directly in the classroom. With a view towards improving this situation, constructing the integral concept on the basis of the idea of accumulation has been proposed (Educ Stud Math. 1994;26:229-274; Integral as accumulation: a didactical perspective for school mathematics; Thessaloniki: PME; 2009. p. 417-424). In this paper, we discuss a curriculum that is based on this idea and a design for curriculum materials that are intended to develop an improved cognitive base for a flexible proceptual understanding of the integral and integration in high school. The main focus is on how we (mathematics teachers and mathematics educators) might teach the integral concept in order to help high school students to construct meaningful knowledge alongside acquiring technical abilities.

Enhancing student engagement to positively impact mathematics anxiety, confidence and achievement for interdisciplinary science subjects

NASA Astrophysics Data System (ADS)

Everingham, Yvette L.; Gyuris, Emma; Connolly, Sean R.

2017-11-01

Contemporary science educators must equip their students with the knowledge and practical know-how to connect multiple disciplines like mathematics, computing and the natural sciences to gain a richer and deeper understanding of a scientific problem. However, many biology and earth science students are prejudiced against mathematics due to negative emotions like high mathematical anxiety and low mathematical confidence. Here, we present a theoretical framework that investigates linkages between student engagement, mathematical anxiety, mathematical confidence, student achievement and subject mastery. We implement this framework in a large, first-year interdisciplinary science subject and monitor its impact over several years from 2010 to 2015. The implementation of the framework coincided with an easing of anxiety and enhanced confidence, as well as higher student satisfaction, retention and achievement. The framework offers interdisciplinary science educators greater flexibility and confidence in their approach to designing and delivering subjects that rely on mathematical concepts and practices.

Chaos Theory for the Practical Military Mind

DTIC Science & Technology

1997-03-01

kept at a conceptual level for the benefit of the novice looking to understand the ‘big picture’ before pursuing the topic further, and for those...individuals who do not need to work at a more mathematical level . Examples of Chaotic systems of military interest are given. This work also addresses...we’ll keep the level conceptual and as non- mathematical as practical. While we will develop definitions throughout this paper, key concepts that are

Representations in Calculus: Two Contrasting Cases.

ERIC Educational Resources Information Center

Aspinwall, Leslie; Shaw, Kenneth L.

2002-01-01

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

A Characterization of a Unified Notion of Mathematical Function: The Case of High School Function and Linear Transformation

ERIC Educational Resources Information Center

Zandieh, Michelle; Ellis, Jessica; Rasmussen, Chris

2017-01-01

As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear…

Using Game Theory Techniques and Concepts to Develop Proprietary Models for Use in Intelligent Games

ERIC Educational Resources Information Center

Christopher, Timothy Van

2011-01-01

This work is about analyzing games as models of systems. The goal is to understand the techniques that have been used by game designers in the past, and to compare them to the study of mathematical game theory. Through the study of a system or concept a model often emerges that can effectively educate students about making intelligent decisions…

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…

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

Paint Bucket Polygons

ERIC Educational Resources Information Center

Edwards, Michael Todd; Harper, Suzanne R.

2010-01-01

During a two-week summer professional development workshop, teams of intermediate-level school teachers and college methods instructors crafted mathematics learning modules--activities, lesson plans, work sheets, and technology-oriented tasks--with the primary goal of strengthening students' understanding of various geometric concepts. They recast…

Developing a Kindergartener's Concept of Cardinality

ERIC Educational Resources Information Center

Throndsen, Jennifer; MacDonald, Beth; Hunt, Jessica

2017-01-01

Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.

Using a Topological Model in Psychology: Developing Sense and Choice Categories.

PubMed

Mammen, Jens

2016-06-01

A duality of sense categories and choice categories is introduced to map two distinct but co-operating ways in which we as humans are relating actively to the world. We are sensing similarities and differences in our world of objects and persons, but we are also as bodies moving around in this world encountering, selecting, and attaching to objects beyond our sensory interactions and in this way also relating to the individual objects' history. This duality is necessary if we shall understand man as relating to the historical depth of our natural and cultural world, and to understand our cognitions and affections. Our personal affections and attachments, as well as our shared cultural values are centered around objects and persons chosen as reference points and landmarks in our lives, uniting and separating, not to be understood only in terms of sensory selections. The ambition is to bridge the gap between psychology as part of Naturwissenschaft and of Geisteswissenschaft, and at the same time establish a common frame for understanding cognition and affection, and our practical and cultural life (Mammen and Mironenko 2015). The duality of sense and choice categories can be described formally using concepts from modern mathematics, primarily topology, surmounting the reductions rooted in the mechanistic concepts from Renaissance science and mathematics. The formal description is based on 11 short and simple axioms held in ordinary language and visualized with instructive figures. The axioms are bridging psychology and mathematics and not only enriching psychology but also opening for a new interpretation of parts of the foundation of mathematics and logic.

Mathematics learning on geometry for children with autism

NASA Astrophysics Data System (ADS)

Widayati, F. E.; Usodo, B.; Pamudya, I.

2017-12-01

The purpose of this research is to describe: (1) the mathematics learning process in an inclusion class and (2) the obstacle during the process of mathematics learning in the inclusion class. This research is a descriptive qualitative research. The subjects were a mathematics teacher, children with autism, and a teacher assistant. Method of collecting data was observation and interview. Data validation technique is triangulation technique. The results of this research are : (1) There is a modification of lesson plan for children with autism. This modification such as the indicator of success, material, time, and assessment. Lesson plan for children with autism is arranged by mathematics teacher and teacher assistant. There is no special media for children with autism used by mathematics teacher. (2) The obstacle of children with autism is that they are difficult to understand mathematics concept. Besides, children with autism are easy to lose their focus.

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…

The Effects of Dynamic Graphing Utilities on Student Attitudes and Conceptual Understanding in College Algebra

ERIC Educational Resources Information Center

Thomas, Ryan Vail

2016-01-01

The goal of this study is to explore and characterize the effects of using a dynamic graphing utility (DGU) on conceptual understanding and attitudes toward mathematics, measured by the responses of college algebra students to an attitude survey and concepts assessment. Two sections of college algebra taught by the primary researcher are included…

Investigating Preservice Teachers' Understanding of Balance Concepts Utilizing a Clinical Interview Method and a Virtual Tool

ERIC Educational Resources Information Center

Wilhelm, Jennifer; Matteson, Shirley; She, Xiaobo

2013-01-01

Our study was enacted in university mathematics education classes in the USA with preservice teachers (PSTs). This research focused on PSTs' interview responses that were used to assess their understanding of balance when challenged with tasks involving virtual manipulatives. Siegler's rules were used in analyzing PSTs' responses to…

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.

Advanced mathematics communication beyond modality of\\xA0sight

NASA Astrophysics Data System (ADS)

Sedaghatjou, Mina

2018-01-01

This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access to visual fields in an advanced mathematics course does not obstruct a blind student's ability to visualize, but transforms it. The goal of this study is not to compare the visually impaired student with non-visually impaired students to address the 'differences' in understanding; instead, I discuss the challenges that a blind student, named Anthony, has encountered and the ways that we tackled those problems. I also demonstrate how the proper and precisely crafted tactile materials empowered Anthony to learn mathematical functions.

Learning difficulties of senior high school students based on probability understanding levels

NASA Astrophysics Data System (ADS)

Anggara, B.; Priatna, N.; Juandi, D.

2018-05-01

Identifying students' difficulties in learning concept of probability is important for teachers to prepare the appropriate learning processes and can overcome obstacles that may arise in the next learning processes. This study revealed the level of students' understanding of the concept of probability and identified their difficulties as a part of the epistemological obstacles identification of the concept of probability. This study employed a qualitative approach that tends to be the character of descriptive research involving 55 students of class XII. In this case, the writer used the diagnostic test of probability concept learning difficulty, observation, and interview as the techniques to collect the data needed. The data was used to determine levels of understanding and the learning difficulties experienced by the students. From the result of students' test result and learning observation, it was found that the mean cognitive level was at level 2. The findings indicated that students had appropriate quantitative information of probability concept but it might be incomplete or incorrectly used. The difficulties found are the ones in arranging sample space, events, and mathematical models related to probability problems. Besides, students had difficulties in understanding the principles of events and prerequisite concept.

Unlocking the black box: teaching mathematical modeling with popular culture.

PubMed

Lofgren, Eric T

2016-10-01

Mathematical modeling is an important tool in biological research, allowing for the synthesis of results from many studies into an understanding of a system. Despite this, the need for extensive subject matter knowledge and complex mathematics often leaves modeling as an esoteric subspecialty. A 2-fold approach can be used to make modeling more approachable for students and those interested in obtaining a functional knowledge of modeling. The first is the use of a popular culture disease system-a zombie epidemic-to allow for exploration of the concepts of modeling using a flexible framework. The second is the use of available interactive and non-calculus-based tools to allow students to work with and implement models to cement their understanding. © FEMS 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Sediment in Lake Coeur d'Alene, Idaho.

ERIC Educational Resources Information Center

Nord, Gail; Nord, John

1998-01-01

Describes how a mathematical model can be constructed and used to better understand human impact on natural resources. Uses the source of many current discussions in northern Idaho to present algebraic concepts and show an application of exponential functions. Contains 13 references. (ASK)

The effectiveness of resources created by students as partners in explaining the relevance of mathematics in engineering education

NASA Astrophysics Data System (ADS)

Dunn, Michelle; Loch, Birgit; Scott, Wendy

2018-01-01

First-year engineering students often struggle to see the relevance of theoretical mathematical concepts for their future studies and professional careers. This is an issue, as students who do not see relevance in fundamental parts of their studies may disengage from these parts and focus their efforts on other subjects they think will be more useful to them. In this study, we surveyed engineering students enrolled in a first-year mathematics subject on their perceptions of the relevance of the individual mathematical topics taught. Surveys were administered at the start of semester when some of these topics were unknown to them, and again at the end of semester when students had not only studied all these topics but also watched a set of animated videos. These videos had been produced by higher-year students to explain where they had seen applications of the mathematical concepts presented in the first year. We notice differences between the perceived relevance of topics for future study and for professional careers, with relevance to study rated higher than relevance to careers. We also find that the animations are seen as helpful in understanding the relevance of first-year mathematics. The majority of students indicated that lecturers with students as partners should work collaboratively to produce future videos.

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.

Prospective mathematics teachers' understanding of the base concept

NASA Astrophysics Data System (ADS)

Horzum, Tuğba; Ertekin, Erhan

2018-02-01

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 by PMTs. As a result, it was determined that PMTs dealt with the BC in a broad range of seven different images. It was also determined that the base perception of PMTs was limited mostly to their usage in daily life and in this context, they have position-dependent and word-dependent images. It was also determined that PMTs named the base to explain the BC or paid attention to the naming of three-dimensional geometric figures through the statement: 'objects are named according to their bases'. At the same time, it was also determined that PMTs had more than one concept imageswhich were contradicting with each other. According to these findings, potential explanations and advices were given.

Performing mathematics activities with non-standard units of measurement using robots controlled via speech-generating devices: three case studies.

PubMed

Adams, Kim D; Cook, Albert M

2017-07-01

Purpose To examine how using a Lego robot controlled via a speech-generating device (SGD) can contribute to how students with physical and communication impairments perform hands-on and communicative mathematics measurement activities. This study was a follow-up to a previous study. Method Three students with cerebral palsy used the robot to measure objects using non-standard units, such as straws, and then compared and ordered the objects using the resulting measurement. Their performance was assessed, and the manipulation and communication events were observed. Teachers and education assistants were interviewed regarding robot use. Results Similar benefits to the previous study were found in this study. Gaps in student procedural knowledge were identified such as knowing to place measurement units tip-to-tip, and students' reporting revealed gaps in conceptual understanding. However, performance improved with repeated practice. Stakeholders identified that some robot tasks took too long or were too difficult to perform. Conclusions Having access to both their SGD and a robot gave the students multiple ways to show their understanding of the measurement concepts. Though they could participate actively in the new mathematics activities, robot use is most appropriate in short tasks requiring reasonable operational skill. Implications for Rehabilitation Lego robots controlled via speech-generating devices (SGDs) can help students to engage in the mathematics pedagogy of performing hands-on activities while communicating about concepts. Students can "show what they know" using the Lego robots, and report and reflect on concepts using the SGD. Level 1 and Level 2 mathematics measurement activities have been adapted to be accomplished by the Lego robot. Other activities can likely be accomplished with similar robot adaptations (e.g., gripper, pen). It is not recommended to use the robot to measure items that are long, or perform measurements that require high operational competence in order to be successful.

Thai Grade 11 students' alternative conceptions for acid-base chemistry

NASA Astrophysics Data System (ADS)

Artdej, Romklao; Ratanaroutai, Thasaneeya; Coll, Richard Kevin; Thongpanchang, Tienthong

2010-07-01

This study involved the development of a two-tier diagnostic instrument to assess Thai high school students' understanding of acid-base chemistry. The acid-base diagnostic test (ABDT) comprising 18 items was administered to 55 Grade 11 students in a science and mathematics programme during the second semester of the 2008 academic year. Analysis of students' responses from this study followed the methodology outlined by Çalik and Ayas. The research findings suggest that the ABDT, the multiple choice diagnostic instrument, enables researchers and teachers to classify students' understanding at different levels. Most students exhibited alternative conceptions for several concepts: acid-base theory, dissociation of strong acids or bases, and dissociation of weak acids/bases. Interestingly, one of the concepts that students appeared to find most difficult, and for which they exhibited the most alternative conceptions, was acid-base theory. Some alternative conceptions revealed in this study differ from earlier reports, such as the concept of electrolyte and non-electrolyte solutions as well as the concentration changes of H3O+and OH- in water. These research findings present valuable information for facilitating better understanding of acid-base chemistry by providing insight into the preventable and correctable alternative conceptions exhibited by students.

Effect of problem type toward students’ conceptual understanding level on heat and temperature

NASA Astrophysics Data System (ADS)

Ratnasari, D.; Sukarmin; Suparmi, S.

2017-11-01

The aim of this research is to analyze the level of students’ understanding of heat and temperature concept and effect of problem type toward students’ conceptual understanding of heat and temperature. This research is descriptive research with the subjects of the research are 96 students from high, medium, and low categorized school in Surakarta. Data of level of students’ conceptual understanding is from students’ test result using essay instrument (arranged by researcher and arranged by the teacher) and interview. Before being tested in the samples, essay instrument is validated by the experts. Based on the result and the data analysis, students’ conceptual understanding level of 10th grade students on heat and temperature is as follows: (1) Most students have conceptual understanding level at Partial Understanding with a Specific Misconception (PUSM) with percentage 28,85%; (2) Most students are able to solve mathematic problem from teacher, but don’t understand the underlying concept.

Study ethnomathematics of aboge (alif, rebo, wage) calendar as determinant of the great days of Islam and traditional ceremony in Cirebon Kasepuhan Palace

NASA Astrophysics Data System (ADS)

Syahrin, Muhammad Alfi; Turmudi, Puspita, Entit

2016-02-01

This research attempts to show about the relationship between mathematics and culture. Paradigm that emerged currently, that mathematics is an abstract concept and difficult, therefore mathematics is not favored by most students. In the reality, indirectly mathematics is present in a culture of a society. Ethnomathematics study is a study to examine how does a group of people in a particular culture understand, express, and use the concepts and practices of culture that depicted mathematically. This research was conducted in Cirebon precisely in Kasepuhan Palace, which was in RW 04, Kasepuhan village, Lemah Wungkuk district, Cirebon city, West Java. The focus of the study and research purposes was the application of aboge (alif rebo wage) calendar as the calculation of days and the calendar rules determine the time of days, great days of Islam and traditional ceremony in Kasepuhan Palace. Qualitative methods with the principles of ethnography such as studies in ethnomathematics i.e observation, interviews, documentation and fieldnotes were used in this research. The findings of this ethnomathematics study show that the determining great days of Islam and the days of palace traditional ceremony have a close relationship with the counts and principles in mathematics. This study provides recommendations that mathematics is closely related to culture due to ethnomathematics.

Heuristic for learning common emitter amplification with bipolar transistors

NASA Astrophysics Data System (ADS)

Staffas, Kjell

2017-11-01

Mathematics in engineering education causes many thresholds in the courses because of the demand of abstract conceptualisation. Electronics depend heavily on more or less complex mathematics. Therefore the concepts of analogue electronics are hard to learn since a great deal of students struggle with the calculations and procedures needed. A survey was done focusing on students' struggle to pass a course in analogue electronics by introducing a top-down perspective and the revised taxonomy of Bloom. From a top-down perspective you can create learning environments from any spot in the taxonomy using a step-by-step approach of the verbs understand and apply. Three textbooks with a top-down perspective on analogue electronics are analysed on the concept of amplifying with a transistor circuit. The study claims issues when losing the top-down perspective to present concepts and procedures of the content to be learned.

ITEMS Project: An online sequence for teaching mathematics and astronomy

NASA Astrophysics Data System (ADS)

Martínez, Bernat; Pérez, Josep

2010-10-01

This work describes an elearning sequence for teaching geometry and astronomy in lower secondary school created inside the ITEMS (Improving Teacher Education in Mathematics and Science) project. It is based on results from the astronomy education research about studentsŠ difficulties in understanding elementary astronomical observations and models. The sequence consists of a set of computer animations embedded in an elearning environment aimed at supporting students in learning about astronomy ideas that require the use of geometrical concepts and visual-spatial reasoning.

The Math Gap: a description of the mathematics performance of preschool-aged deaf/hard-of-hearing children.

PubMed

Pagliaro, Claudia M; Kritzer, Karen L

2013-04-01

Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures were used to assess understanding in number, geometry, measurement, problem solving, and patterns, reasoning and algebra. Results present strong evidence that d/hh students' difficulty in mathematics may begin prior to the start of formal schooling. Findings also show areas of strength (geometry) and weakness (problem solving and measurement) for these children. Evidence of poor foundational performance may relate to later academic achievement.

Understanding Scientific Ideas: An Honors Course.

ERIC Educational Resources Information Center

Capps, Joan; Schueler, Paul

At Raritan Valley Community College (RVCC) in New Jersey, an honors philosophy course was developed which taught mathematics and science concepts independent of computational skill. The course required that students complete a weekly writing assignment designed as a continuous refinement of logical reasoning development. This refinement was…

Hemispheric Laterality in Music and Math

ERIC Educational Resources Information Center

Szirony, Gary Michael; Burgin, John S.; Pearson, L. Carolyn

2008-01-01

Hemispheric laterality may be a useful concept in teaching, learning, training, and in understanding more about human development. To address this issue, a measure of hemispheric laterality was compared to musical and mathematical ability. The Human Information Processing Survey (HIPS) instrument, designed to measure hemispheric laterality, was…

Knot theory in modern chemistry.

PubMed

Horner, Kate E; Miller, Mark A; Steed, Jonathan W; Sutcliffe, Paul M

2016-11-21

Knot theory is a branch of pure mathematics, but it is increasingly being applied in a variety of sciences. Knots appear in chemistry, not only in synthetic molecular design, but also in an array of materials and media, including some not traditionally associated with knots. Mathematics and chemistry can now be used synergistically to identify, characterise and create knots, as well as to understand and predict their physical properties. This tutorial review provides a brief introduction to the mathematics of knots and related topological concepts in the context of the chemical sciences. We then survey the broad range of applications of the theory to contemporary research in the field.

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.

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.

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.

Measuring and factors influencing mathematics teachers' technological pedagogical and content knowledge (TPACK) in three southernmost provinces, Thailand

NASA Astrophysics Data System (ADS)

Adulyasas, Lilla

2017-08-01

Technology becomes an important role in teaching and learning mathematics nowadays. Integrating technology in the classroom helps students have better understanding in many of mathematics concepts. One of the major framework for assessing the knowledge of integrating technology with the pedagogy and content in the classroom is Technological Pedagogical and Content Knowledge (TPACK) framework. This study aimed to measure mathematics teachers' TPACK in three southernmost provinces, Thailand and to study on factors influencing their TPACK. A quantitative study was carried out with 210 secondary level mathematics teachers in the three southernmost provinces, Thailand which were random by two stage sampling technique. Data were collected by using a questionnaire to identify the level of mathematics teachers' TPACK and the factors influencing their TPACK. Descriptive statistics, Pearson product moment correlation and multiple regression analysis were used for analysing data. Findings reveal that the mean score of mathematics teachers' TPACK is 3.33 which is in the medium level and the three factors which have positive correlation at .05 level of significant with the level of TPACK are teaching experience factor, individual specialization factor and personal & organization factor. However, there are only two factors influencing mathematics teachers' TPACK. The two factors are individual specialization factor and personal & organization factors. These give better understanding on mathematics teachers' knowledge in integrating technology with the pedagogy and content which will be the important information for improving mathematics teachers' TPACK.

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…

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.

Can Computers be Social?

NASA Astrophysics Data System (ADS)

Ekdahl, Bertil

2002-09-01

Of main concern in agent based computing is the conception that software agents can attain socially responsible behavior. This idea has its origin in the need for agents to interact with one another in a cooperating manner. Such interplay between several agents can be seen as a combinatorial play where the rules are fixed and the actors are supposed to closely analyze the play in order to behave rational. This kind of rationality has successfully being mathematically described. When the social behavior is extended beyond rational behavior, mere mathematical analysis falls short. For such behavior language is decisive for transferring concepts and language is a holistic entity that cannot be analyzed and defined mathematically. Accordingly, computers cannot be furnished with a language in the sense that meaning can be conveyed and consequently they lack all the necessary properties to be made social. The attempts to postulate mental properties to computer programs are a misconception that is blamed the lack of true understanding of language and especially the relation between formal system and its semantics.

Siphons, Water Clocks, Cooling Coffee, and Leaking Capacitors: Classroom Activities and a Few Equations to Help Students Understand Radioactive Decay and Other Exponential Processes

ERIC Educational Resources Information Center

Brady, John B.

2009-01-01

Although an understanding of radiometric dating is central to the preparation of every geologist, many students struggle with the concepts and mathematics of radioactive decay. Physical demonstrations and hands-on experiments can be used to good effect in addressing this teaching conundrum. Water, heat, and electrons all move or flow in response…

Digital education reform for improving interaction between students and instructors

NASA Astrophysics Data System (ADS)

Deng, Qiansong; Li, Yuanjie; Zheng, Lixin

2017-08-01

Nowadays it is difficult to attract undergraduate students' interesting to put sufficient time to learn major courses in China, which are too hard for them to quick grasp and fully understanding. Here we report a digital education reform for improving interactions between students and instructors, in which we transform the abstract, obscure and boring knowledge, such as physical, mathematical, electronic or optical concepts into direct and dynamic 3-D model and flash. Therefore, this method can convert theoretical concepts into easy understanding pictures. Our several years' experience shows that this education mode can make students' willing to think and practice, then it is helpful for attracting their learning interests. Most students benefit from this education mode which can greatly enhance their understanding abilities.

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.

Mathematical Language Skills of Mathematics Prospective Teachers

ERIC Educational Resources Information Center

Gürefe, Nejla

2018-01-01

Effective mathematics teaching can be actualized only with correct use of the mathematical content language which comprises mathematical rules, concepts, symbols and terms. In this research, it was aimed to examine the mathematics prospective teachers' content language skills in some basic geometric concepts which are ray, angle, polygon,…

Challenges in assessing college students' conception of duality: the case of infinity

NASA Astrophysics Data System (ADS)

Babarinsa-Ochiedike, Grace Olutayo

Interpreting students' views of infinity posits a challenge for researchers due to the dynamic nature of the conception. There is diversity and variation among students' process-object perceptions. The fluctuations between students' views however reveal an undeveloped duality conception. This study examined college students' conception of duality in understanding and representing infinity with the intent to design strategies that could guide researchers in categorizing students' views of infinity into different levels. Data for the study were collected from N=238 college students enrolled in Calculus sequence courses (Pre-Calculus, Calculus I through Calculus III) at one of the southwestern universities in the U.S. using self-report questionnaires and semi-structured individual task-based interviews. Data was triangulated using multiple measures analyzed by three independent experts using self-designed coding sheets to assess students' externalization of the duality conception of infinity. Results of this study reveal that college students' experiences in traditional Calculus sequence courses are not supportive of the development of duality conception. On the contrary, it strengthens the singularity perspective on fundamental ideas of mathematics such as infinity. The study also found that coding and assessing college students' conception of duality is a challenging and complex process due to the dynamic nature of the conception that is task-dependent and context-dependent. Practical significance of the study is that it helps to recognize misconceptions and starts addressing them so students will have a more comprehensive view of fundamental mathematical ideas as they progress through the Calculus coursework sequence. The developed duality concept development framework called Action-Process-Object-Duality (APOD) adapted from the APOS theory could guide educators and researchers as they engage in assessing students' conception of duality. The results of this study could serve as a facilitating instrument to further analyze cognitive obstacles in college students' understanding of the infinity concept.

American hydrogeology at the millennium: An annotated chronology of 100 most influential papers

USGS Publications Warehouse

Back, W.; Herman, J.S.

1997-01-01

Hydrogeology developed as scientists undertook activities to describe how a groundwater system functions to explain why it is that way, in order to solve practical problems of water supply. This paper demonstrates the evolutionary nature and growth of hydrogeology in the United States on the basis of a selection of one hundred papers that had a significant impact on subsequent activities. We have identified three revolutionary concepts that resulted directly from this evolutionary understanding and have selected papers that demonstrate important consequences. These three concepts are 1) that the mathematical expression for heat flow can be paraphrased for groundwater and used in transient flow conditions to determine aquifer characteristics; 2) that the distribution of fluid potential can be formulated in mathematical equations suitable for solution by various analytical techniques; and 3) that chemical thermodynamics can be applied to hydrogeologic systems in order to understand the processes controlling the chemical character of groundwater. One purpose of this paper is to encourage scientists to gain an additional dimension of satisfaction from their work by being aware of the contributions of those who went before them and to see how their own work fits into the current understanding of hydrogeology.

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.

Let's Cut the Cake

ERIC Educational Resources Information Center

Zeybek, Zulfiye; Cross Francis, Dionne I.

2017-01-01

Measurement is an important component of K-grade 12 mathematics curricula. The concepts of area and perimeter of polygons are first introduced in third grade and serve as the basis for teaching in the upper grades. Without a strong understanding of measurement, students will struggle to meaningfully grasp three-dimensional measurement concepts…

Understanding the Theory of Multiple Intelligences. Staff Workshop Handout

ERIC Educational Resources Information Center

Early Childhood Today, 2005

2005-01-01

In his "Theory of Multiple Intelligences," Dr. Howard Gardner expands the concept of intelligence to include such areas as music, spatial relations, and interpersonal knowledge in addition to the traditional view of two intelligences--mathematical and linguistic. Using biological as well as cultural research, Gardner formulated a list of seven…

Sawtooth Functions. Classroom Notes

ERIC Educational Resources Information Center

Hirst, Keith

2004-01-01

Using MAPLE enables students to consider many examples which would be very tedious to work out by hand. This applies to graph plotting as well as to algebraic manipulation. The challenge is to use these observations to develop the students' understanding of mathematical concepts. In this note an interesting relationship arising from inverse…

Technology's Impact on Fraction Learning: An Experimental Comparison of Virtual and Physical Manipulatives

ERIC Educational Resources Information Center

Mendiburo, Maria; Hasselbring, Ted

2011-01-01

Fractions are among the most difficult mathematical concepts for elementary school students to master (Behr, Harel, Post, & Lesh, 1992; Bezuk & Cramer, 1989; Moss & Case, 1999). Research indicates that manipulatives (e.g. fractions circles, fractions strips) positively impact students' conceptual and procedural understanding of…

Student Understanding of Taylor Series Expansions in Statistical Mechanics

ERIC Educational Resources Information Center

Smith, Trevor I.; Thompson, John R.; Mountcastle, Donald B.

2013-01-01

One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann…

Revisiting Mr. Tall and Mr. Short

ERIC Educational Resources Information Center

Riehl, Suzanne M.; Steinthorsdottir, Olof Bjorg

2014-01-01

Ratio, rate, and proportion are central ideas in the Common Core State Standards (CCSS) for middle-grades mathematics (CCSSI 2010). These ideas closely connect to themes in earlier grades (pattern building, multiplicative reasoning, rational number concepts) and are the foundation for understanding linear functions as well as many high school…

Students' Development and Use of Internal Representations When Solving Algebraic Tasks

ERIC Educational Resources Information Center

Cross, Laban J.

2013-01-01

The difficulty in observing, recording, and examining internal representations has been well documented (Goldin & Shteingold, 2001). However, the important role that these internal representations play in the learning and understanding of mathematical concepts has been noted (Yackel, 2000). This study sought to develop a framework for…

Effects of Perceptually Rich Manipulatives on Preschoolers' Counting Performance: Established Knowledge Counts

ERIC Educational Resources Information Center

Petersen, Lori A.; McNeil, Nicole M.

2013-01-01

Educators often use concrete objects to help children understand mathematics concepts. However, findings on the effectiveness of concrete objects are mixed. The present study examined how two factors--perceptual richness and established knowledge of the objects--combine to influence children's counting performance. In two experiments, preschoolers…

A Historical Perspective on Teaching and Learning Calculus

ERIC Educational Resources Information Center

Doorman, Michiel; van Maanen, Jan

2008-01-01

Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student…

Student Difficulties Regarding Symbolic and Graphical Representations of Vector Fields

ERIC Educational Resources Information Center

Bollen, Laurens; van Kampen, Paul; Baily, Charles; Kelly, Mossy; De Cock, Mieke

2017-01-01

The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person's understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing,…

Zooming in on Children's Thinking

ERIC Educational Resources Information Center

Tucker, Steven; Shumway, Jessica F.; Moyer-Packenham, Patricia S.; Jordan, Kerry E.

2016-01-01

Teachers increasingly use virtual manipulatives and other apps on touch-screen devices (e.g., "iPads") in an effort to help students understand mathematics concepts. However, students experience these apps and their affordances in different ways. The purpose of this article is to inform teachers' decisions about app implementation in the…

Technology Focus: Using Technology to Explore Statistical Inference

ERIC Educational Resources Information Center

Garofalo, Joe; Juersivich, Nicole

2007-01-01

There is much research that documents what many teachers know, that students struggle with many concepts in probability and statistics. This article presents two sample activities the authors use to help preservice teachers develop ideas about how they can use technology to promote their students' ability to understand mathematics and connect…

Naive Analysis of Variance

ERIC Educational Resources Information Center

Braun, W. John

2012-01-01

The Analysis of Variance is often taught in introductory statistics courses, but it is not clear that students really understand the method. This is because the derivation of the test statistic and p-value requires a relatively sophisticated mathematical background which may not be well-remembered or understood. Thus, the essential concept behind…

On Problematic Aspects in Learning Trigonometry

ERIC Educational Resources Information Center

Kamber, Dina; Takaci, Djurdjica

2018-01-01

In this paper, research on some problematic aspects high school students have in learning trigonometry is presented. It is based on making sense of mathematics through perception, operation and reason in the case of trigonometry. We analyzed students' understanding of trigonometric concepts in the frame of triangle and circle trigonometry…

Scale and the evolutionarily based approximate number system: an exploratory study

NASA Astrophysics Data System (ADS)

Delgado, Cesar; Jones, M. Gail; You, Hye Sun; Robertson, Laura; Chesnutt, Katherine; Halberda, Justin

2017-05-01

Crosscutting concepts such as scale, proportion, and quantity are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such as measurement units may be built on evolutionarily-based systems of number such as the approximate number system (ANS), which processes approximate representations of numerical magnitude. ANS is related to mathematical achievement in pre-school and early elementary students, but there is little research on ANS among older students or in science-related areas such as scale. Here, we investigate the relationship between ANS precision in public school U.S. seventh graders and their accuracy estimating the length of standard units of measurement in SI and U.S. customary units. We also explored the relationship between ANS and science and mathematics achievement. Accuracy estimating the metre was positively and significantly related to ANS precision. Mathematics achievement, science achievement, and accuracy estimating other units were not significantly related to ANS. We thus suggest that ANS precision may be related to mathematics understanding beyond arithmetic, beyond the early school years, and to the crosscutting concepts of scale, proportion, and quantity.

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…

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.

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.

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…

Developing mathematical practices through reflection cycles

NASA Astrophysics Data System (ADS)

Reinholz, Daniel L.

2016-09-01

This paper focuses on reflection in learning mathematical practices. While there is a long history of research on reflection in mathematics, it has focused primarily on the development of conceptual understanding. Building on notion of learning as participation in social practices, this paper broadens the theory of reflection in mathematics learning. To do so, it introduces the concept of reflection cycles. Each cycle begins with prospective reflection, which guides one's actions during an experience, and ends with retrospective reflection, which consolidates the experience and informs the next reflection cycle. Using reflection cycles as an organizing framework, this paper synthesizes the literature on reflective practices at a variety of levels: (1) metacognition, (2) self-assessment, (3) noticing, and (4) lifelong learning. These practices represent a spectrum of reflection, ranging from the micro level (1) to macro level (4).

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…

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

2014-01-01

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

Technological pedagogical content knowledge of junior high school mathematics teachers in teaching linear equation

NASA Astrophysics Data System (ADS)

Wati, S.; Fitriana, L.; Mardiyana

2018-04-01

Linear equation is one of the topics in mathematics that are considered difficult. Student difficulties of understanding linear equation can be caused by lack of understanding this concept and the way of teachers teach. TPACK is a way to understand the complex relationships between teaching and content taught through the use of specific teaching approaches and supported by the right technology tools. This study aims to identify TPACK of junior high school mathematics teachers in teaching linear equation. The method used in the study was descriptive. In the first phase, a survey using a questionnaire was carried out on 45 junior high school mathematics teachers in teaching linear equation. While in the second phase, the interview involved three teachers. The analysis of data used were quantitative and qualitative technique. The result PCK revealed teachers emphasized developing procedural and conceptual knowledge through reliance on traditional in teaching linear equation. The result of TPK revealed teachers’ lower capacity to deal with the general information and communications technologies goals across the curriculum in teaching linear equation. The result indicated that PowerPoint constitutes TCK modal technological capability in teaching linear equation. The result of TPACK seems to suggest a low standard in teachers’ technological skills across a variety of mathematics education goals in teaching linear equation. This means that the ability of teachers’ TPACK in teaching linear equation still needs to be improved.

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…

Neural mechanisms of the mind, Aristotle, Zadeh, and fMRI.

PubMed

Perlovsky, Leonid I

2010-05-01

Processes in the mind: perception, cognition, concepts, instincts, emotions, and higher cognitive abilities for abstract thinking, beautiful music are considered here within a neural modeling fields (NMFs) paradigm. Its fundamental mathematical mechanism is a process "from vague-fuzzy to crisp," called dynamic logic (DL). This paper discusses why this paradigm is necessary mathematically, and relates it to a psychological description of the mind. Surprisingly, the process from "vague to crisp" corresponds to Aristotelian understanding of mental functioning. Recent functional magnetic resonance imaging (fMRI) measurements confirmed this process in neural mechanisms of perception.

What is information?†

PubMed Central

2016-01-01

Information is a precise concept that can be defined mathematically, but its relationship to what we call ‘knowledge’ is not always made clear. Furthermore, the concepts ‘entropy’ and ‘information’, while deeply related, are distinct and must be used with care, something that is not always achieved in the literature. In this elementary introduction, the concepts of entropy and information are laid out one by one, explained intuitively, but defined rigorously. I argue that a proper understanding of information in terms of prediction is key to a number of disciplines beyond engineering, such as physics and biology. PMID:26857663

Language and counting: Some recent results

NASA Astrophysics Data System (ADS)

Bell, Garry

1990-02-01

It has long been recognised that the language of mathematics is an important variable in the learning of mathematics, and there has been useful work in isolating and describing the linkage. Steffe and his co-workers at Georgia, for example, (Steffe, von Glasersfeld, Richardson and Cobb, 1983) have suggested that young children may construct verbal countable items to count objects which are hidden from their view. Although there has been a surge of research interest in counting and early childhood mathematics, and in cultural differences in mathematics attainment, there has been little work reported on the linkage between culture as exemplified by language, and initial concepts of numeration. This paper reports on some recent clinical research with kindergarten children of European and Asian background in Australia and America. The research examines the influence that number naming grammar appears to have on young children's understandings of two-digit numbers and place value. It appears that Transparent Standard Number Word Sequences such as Japanese, Chinese and Vietnamese which follow the numerical representation pattern by naming tens and units in order ("two tens three"), may be associated with distinctive place value concepts which may support sophisticated mental algorithms.

Behaviour of mathematics and physics students in solving problem of Vector-Physics context

NASA Astrophysics Data System (ADS)

Sardi; Rizal, M.; Mansyur, J.

2018-04-01

This research aimed to describe behaviors of mathematics and physics students in solving problem of the vector concept in physics context. The subjects of the research were students who enrolled in Mathematics Education Study Program and Physics Education Study Program of FKIP Universitas Tadulako. The selected participants were students who received the highest score in vector fundamental concept test in each study program. The data were collected through thinking-aloud activity followed by an interview. The steps of data analysis included data reduction, display, and conclusion drawing. The credibility of the data was tested using a triangulation method. Based on the data analysis, it can be concluded that the two groups of students did not show fundamental differences in problem-solving behavior, especially in the steps of understanding the problem (identifying, collecting and analyzing facts and information), planning (looking for alternative strategies) and conducting the alternative strategy. The two groups were differ only in the evaluation aspect. In contrast to Physics students who evaluated their answer, mathematics students did not conducted an evaluation activity on their work. However, the difference was not caused by the differences in background knowledge.

Modelling the human immunodeficiency virus (HIV) epidemic: A review of the substance and role of models in South Africa

PubMed Central

2018-01-01

We review key mathematical models of the South African human immunodeficiency virus (HIV) epidemic from the early 1990s onwards. In our descriptions, we sometimes differentiate between the concepts of a model world and its mathematical or computational implementation. The model world is the conceptual realm in which we explicitly declare the rules – usually some simplification of ‘real world’ processes as we understand them. Computing details of informative scenarios in these model worlds is a task requiring specialist knowledge, but all other aspects of the modelling process, from describing the model world to identifying the scenarios and interpreting model outputs, should be understandable to anyone with an interest in the epidemic. PMID:29568647

All biology is computational biology.

PubMed

Markowetz, Florian

2017-03-01

Here, I argue that computational thinking and techniques are so central to the quest of understanding life that today all biology is computational biology. Computational biology brings order into our understanding of life, it makes biological concepts rigorous and testable, and it provides a reference map that holds together individual insights. The next modern synthesis in biology will be driven by mathematical, statistical, and computational methods being absorbed into mainstream biological training, turning biology into a quantitative science.

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…

Students’ conceptions analysis on several electricity concepts

NASA Astrophysics Data System (ADS)

Saputro, D. E.; Sarwanto, S.; Sukarmin, S.; Ratnasari, D.

2018-05-01

This research is aimed to analyse students’ conceptions on several electricity concept. This is a descriptive research with the subjects of new students of Sebelas Maret University. The numbers of the subject were 279 students that consisted of several departments such as science education, physics education, chemistry education, biology education and mathematics education in the academic year of 2017/2018. The instrument used in this research was the multiple-choice test with arguments. Based on the result of the research and analysis, it can be concluded that most of the students still find misconceptions and do not understand electricity concept on sub-topics such as electric current characteristic in the series and parallel arrangement, the value of capacitor capacitance, the influence of the capacitor charge and discharge towards the loads, and the amount of capacitor series arrangement. For the future research, it is suggested to improve students’ conceptual understanding with appropriate learning method and assessment instrument because electricity is one of physics material that closely related with students’ daily life.

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)

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…

Learning Trajectories in Teacher Education: Supporting Teachers' Understandings of Students' Mathematical Thinking

ERIC Educational Resources Information Center

Wilson, P. Holt; Mojica, Gemma F.; Confrey, Jere

2013-01-01

Recent work by researchers has focused on synthesizing and elaborating knowledge of students' thinking on particular concepts as core progressions called learning trajectories. Although useful at the level of curriculum development, assessment design, and the articulation of standards, evidence is only beginning to emerge to suggest how learning…

Useful Material Efficiency Green Metrics Problem Set Exercises for Lecture and Laboratory

ERIC Educational Resources Information Center

Andraos, John

2015-01-01

A series of pedagogical problem set exercises are posed that illustrate the principles behind material efficiency green metrics and their application in developing a deeper understanding of reaction and synthesis plan analysis and strategies to optimize them. Rigorous, yet simple, mathematical proofs are given for some of the fundamental concepts,…

Strategies for Reducing Math Anxiety. Information Capsule. Volume 1102

ERIC Educational Resources Information Center

Blazer, Christie

2011-01-01

Approximately 93 percent of Americans indicate that they experience some level of math anxiety. Math anxiety is defined as negative emotions that interfere with the solving of mathematical problems. Studies have found that some students who perform poorly on math assessments actually have a full understanding of the concepts being tested; however,…

Taking Math Beyond Counting in Preschool: Thinking About the Same Object, Different State!

ERIC Educational Resources Information Center

Chafel, Judith A.; Olmsted, Judith

In order to help preschool children understand mathematical principles, five different learning activities designed to help them think about physical transformation or change are described. Introductory remarks focus on Piaget's concept of transformation and on various strategies teachers can use to help children consider changes in the state of…

Incorporating GeoGebra into Geometry Learning--A Lesson from India

ERIC Educational Resources Information Center

Bhagat, Kaushal Kumar; Chang, Chun-Yen

2015-01-01

Students often find geometrical concepts abstract and difficult to understand. This results in poor performance, which contributes in the declining interest in geometry. The aim of this study was to examine the impact of using the free educational software program, "GeoGebra" on 9th grade student's mathematics achievement in learning…

Discrete and Continuous Reasoning about Change in Primary School Classrooms

ERIC Educational Resources Information Center

de Beer, Huub; Gravemeijer, Koeno; van Eijck, Michiel

2015-01-01

To prepare students for participation in our society, where interpreting, representing, and manipulating of dynamic phenomena are becoming key activities, we believe that one should start developing a mathematical understanding of change at an early age. We therefore started a design research project to teach the concept of instantaneous speed in…

Understanding Introductory Students' Application of Integrals in Physics from Multiple Perspectives

ERIC Educational Resources Information Center

Hu, Dehui

2013-01-01

Calculus is used across many physics topics from introductory to upper-division level college courses. The concepts of differentiation and integration are important tools for solving real world problems. Using calculus or any mathematical tool in physics is much more complex than the straightforward application of the equations and algorithms that…

The History of the Calculus

ERIC Educational Resources Information Center

Harding, Simon; Scott, Paul

2004-01-01

Calculus is a mathematical concept that is fundamental to how we understand the world around us. Whether it is in the world of technology, finance, astronomy, sociology, medicine, calculus in one form or another can be found. This brief article describes the origins of calculus in Greece, further developments by Newton and Leibniz, and the…

Exploring Links between Pedagogical Knowledge Practices and Student Outcomes in STEM Education for Primary Schools

ERIC Educational Resources Information Center

Hudson, Peter; English, Lyn; Dawes, Les; King, Donna; Baker, Steve

2015-01-01

Science, technology, engineering, and mathematics (STEM) education is an emerging initiative in Australia, particularly in primary schools. This qualitative research aimed to understand Year 4 students' involvement in an integrated STEM education unit that focused on science concepts (e.g., states of matter, testing properties of materials) and…

Visual Criterion for Understanding the Notion of Convergence if Integrals in One Parameter

ERIC Educational Resources Information Center

Alves, Francisco Regis Vieira

2014-01-01

Admittedly, the notion of generalized integrals in one parameter has a fundamental role. En virtue that, in this paper, we discuss and characterize an approach for to promote the visualization of this scientific mathematical concept. We still indicate the possibilities of graphical interpretation of formal properties related to notion of…

Conceptualizing Routines of Practice That Support Algebraic Reasoning in Elementary Schools: A Constructivist Grounded Theory

ERIC Educational Resources Information Center

Store, Jessie Chitsanzo

2012-01-01

There is ample literature documenting that, for many decades, high school students view algebra as difficult and do not demonstrate understanding of algebraic concepts. Algebraic reasoning in elementary school aims at meaningfully introducing algebra to elementary school students in preparation for higher-level mathematics. While there is research…

Children's Concepts of Average and Representativeness.

ERIC Educational Resources Information Center

Mokros, Jan; Russell, Susan Jo

This paper reports a study to address two questions concerning children's understanding of average: How do children construct and interpret representativeness within the context of data sets? and How do children think about the mean as a particular mathematical definition and relationship? Twenty-one students (seven each of 4th, 6th, and 8th…

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. …

Teaching and Learning Calculus in Secondary Schools with the TI-Nspire

ERIC Educational Resources Information Center

Parrot, Mary Ann Serdina; Eu, Leong Kwan

2014-01-01

Technology can help develop understanding of abstract mathematical concepts through visualisation and graphic representation. The teaching and learning of calculus can be challenging as it involves abstract and complex ideas. The purpose of this study was to investigate how students and teachers attempt to use TI-Nspire, the latest graphing…

Numerical Integration with GeoGebra in High School

ERIC Educational Resources Information Center

Herceg, Dorde; Herceg, Dragoslav

2010-01-01

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

Reversibility of Thought: An Instance in Multiplicative Tasks

ERIC Educational Resources Information Center

Ramful, Ajay; Olive, John

2008-01-01

In line with current efforts to understand the piece-by-piece structure and articulation of children's mathematical concepts, this case study compares the reversibility schemes of two eighth-grade students. The aim of the study was to identify the mechanism through which students reverse their thought processes in a multiplicative situation. Data…

A Visualisation-Based Semiotic Analysis of Learners' Conceptual Understanding of Graphical Functional Relationships

ERIC Educational Resources Information Center

Mudaly, Vimolan

2014-01-01

Within the South African school curriculum, the section on graphical functional relationships consists of signs which include symbols, notation and imagery. In a previous article we explored the role visualisation played in the way learners understood mathematical concepts. That paper reported on the learners' fixation with the physical features…

Mat-Rix-Toe: Improving Writing through a Game-Based Project in Linear Algebra

ERIC Educational Resources Information Center

Graham-Squire, Adam; Farnell, Elin; Stockton, Julianna Connelly

2014-01-01

The Mat-Rix-Toe project utilizes a matrix-based game to deepen students' understanding of linear algebra concepts and strengthen students' ability to express themselves mathematically. The project was administered in three classes using slightly different approaches, each of which included some editing component to encourage the…

Student's Concept of Infinity in the Context of a Simple Geometrical Construct

ERIC Educational Resources Information Center

Jirotkova, Darina; Littler, Graham

2003-01-01

The research described in this paper was undertaken to determine student-teachers' understanding of infinity in a geometrical context. The methods of analysis of students' responses is presented and these were found to be universally applicable. The findings show that school mathematics does not generally develop the students' ideas of infinity…

An Application of Fuzzy Analytic Hierarchy Process (FAHP) for Evaluating Students' Project

ERIC Educational Resources Information Center

Çebi, Ayça; Karal, Hasan

2017-01-01

In recent years, artificial intelligence applications for understanding the human thinking process and transferring it to virtual environments come into prominence. The fuzzy logic which paves the way for modeling human behaviors and expressing even vague concepts mathematically, and is also regarded as an artificial intelligence technique has…

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…

Science Shorts: Sort It out

ERIC Educational Resources Information Center

Adams, Barbara

2007-01-01

Many children enjoy collecting items such as seashells, state quarters, and trading cards. Asking students to think about the ways in which similar items differ, how objects can be grouped by a common characteristic, and how groups can be subsets of a larger category leads to an understanding of fundamental mathematics and science concepts: sets,…

Software-aided discussion about classical picture of Mach-Zehnder interferometer

NASA Astrophysics Data System (ADS)

Cavalcanti, C. J. H.; Ostermann, F.; Lima, N. W.; Netto, J. S.

2017-11-01

The Mach-Zehnder interferometer has played an important role both in quantum and classical physics research over the years. In physics education, it has been used as a didactic tool for quantum physics teaching, allowing fundamental concepts, such as particle-wave duality, to be addressed from the very beginning. For a student to understand the novelties of the quantum scenario, it is first worth introducing the classical picture. In this paper, we introduce a new version of the software developed by our research group to deepen the discussion on the classical picture of the Mach-Zehnder interferometer. We present its equivalence with the double slit experiment and we derive the mathematical expressions relating to the interference pattern. We also explore the concept of visibility (which is very important for understanding wave-particle complementarity in quantum physics) to help students become familiar with this experiment and to enhance their knowledge of its counterintuitive aspects. We use the software articulated by the mathematical formalism and phenomenological features. We also present excerpts of the discursive interactions of students using the software in didactic situations.

What Physicists Mean By the Equals Sign in Undergraduate Education

NASA Astrophysics Data System (ADS)

Kornick, Kellianne; Alaee, Dina; Sayre, Eleanor; Franklin, Scott

2017-01-01

Mathematical syntax allows for the description of meaningful concepts in the physical sciences, and having nuanced proficiency in mathematical formalism is closely tied to communication and understanding of physical principles. The concept of equality is especially important, as it constrains and dictates the relationships between two equated expressions, and a student with detailed understanding of these relationships can derive physical meaning from syntactical expressions mediated by equals signs by knowing the ``meaning'' of equals signs. We delineate types of equals signs as used in undergraduate textbooks and develop a categorization scheme in order to investigate how equals signs are used paradigmatically and culturally in textbooks to convey physical meaning. We classify equals signs into general clusters (causal, definitional, assignment, balancing, and ``just math''), each cluster containing more detailed types. We investigate differences across various topics and between introductory and upper-division textbooks. We found that upper division textbooks are more likely to use balancing, definitional, and more complex kinds of assignment forms, while introductory texts have much higher frequencies of simple assignment and ``just math'' types.

On supporting students' understanding of solving linear equation by using flowchart

NASA Astrophysics Data System (ADS)

Toyib, Muhamad; Kusmayadi, Tri Atmojo; Riyadi

2017-05-01

The aim of this study was to support 7th graders to gradually understand the concepts and procedures of solving linear equation. Thirty-two 7th graders of a Junior High School in Surakarta, Indonesia were involved in this study. Design research was used as the research approach to achieve the aim. A set of learning activities in solving linear equation with one unknown were designed based on Realistic Mathematics Education (RME) approach. The activities were started by playing LEGO to find a linear equation then solve the equation by using flowchart. The results indicate that using the realistic problems, playing LEGO could stimulate students to construct linear equation. Furthermore, Flowchart used to encourage students' reasoning and understanding on the concepts and procedures of solving linear equation with one unknown.

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.

In-Service Teachers’ Understanding on the Concept of Limits and Derivatives and the Way They Deliver the Concepts to Their High School Students

NASA Astrophysics Data System (ADS)

Desfitri, Rita

2016-02-01

The aim of this study was to analyze the teachers’ understanding on the concept of limits and derivative and the way they deliver the subjects to their students. The study was divided into two main phases during two years of research. This research was conducted in 7 high schools vary from general, Islamic and occasional schools. The participants of the study were 20 in-service mathematics teachers from 7 high schools. Questioners were given to find out how teachers’ understanding on the concepts and how they organized their class. The teachers’ level of complexity on the subject was analyzed by Structure of the Observed Learning Outcome (SOLO) Taxonomy, and teachers’ class organizations was analyzed by assessing and classifying their responds written on the questioner sheets and discussion with the selected participants.. Based on the data, it can be figured out that the most teachers’ position were on third level out of five level of SOLO Taxonomy. Data also told us that half of the teachers experienced the difficulties in teaching the concept due to their limitations on mastering subject. Data also showed that there is a relevance between teachers’ level of understanding and teachers’ ability in delivering subject to their students.

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,…

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.

Using structured games to teach early fraction concepts to students who are deaf or hard of hearing.

PubMed

Markey, Carmel; Power, Des; Booker, George

2003-01-01

The study focused on the development of the concept of fractions in a group of 11- and 12-year-old students who were deaf or hard of hearing. The approach implemented in the study relied extensively on the use of games with very little formal instruction. It emphasized the development of appropriate language to facilitate an understanding of the notion of fractions through the investigation of concrete materials, pictorial representations, and interactions between students and teacher. The progress achieved by means of this approach is reported, and the implications of developing an understanding of fractions (and mathematics generally) among students who are deaf or hard of hearing are noted.

The development of a valid discovery-based learning module to improve students' mathematical connection

NASA Astrophysics Data System (ADS)

Kuneni, Erna; Mardiyana, Pramudya, Ikrar

2017-08-01

Geometry is the most important branch in mathematics. The purpose of teaching this material is to develop students' level of thinking for a better understanding. Otherwise, geometry in particular, has contributed students' failure in mathematics examinations. This problem occurs due to special feature in geometry which has complexity of correlation among its concept. This relates to mathematical connection. It is still difficult for students to improve this ability. This is because teachers' lack in facilitating students towards it. Eventhough, facilitating students can be in the form of teaching material. A learning module can be a solution because it consists of series activities that should be taken by students to achieve a certain goal. A series activities in this case is adopted by the phases of discovery-based learning model. Through this module, students are facilitated to discover concept by deep instruction and guidance. It can build the mathematical habits of mind and also strengthen the mathematical connection. Method used in this research was ten stages of research and development proposed by Bord and Gall. The research purpose is to create a valid learning module to improve students' mathematical connection in teaching quadrilateral. The retrieved valid module based on media expert judgment is 2,43 for eligibility chart aspect, 2,60 for eligibility presentation aspect, and 3,00 for eligibility contents aspect. Then the retrieved valid module based on material expert judgment is 3,10 for eligibility content aspect, 2,87 for eligibility presentation aspect, and 2,80 for eligibility language and legibility aspect.

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)

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…

Causality

NASA Astrophysics Data System (ADS)

Pearl, Judea

2000-03-01

Written by one of the pre-eminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, philosophy, cognitive science, and the health and social sciences. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artifical intelligence, business, epidemiology, social science and economics. Students in these areas will find natural models, simple identification procedures, and precise mathematical definitions of causal concepts that traditional texts have tended to evade or make unduly complicated. This book will be of interest to professionals and students in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable.

The (kinetic) theory of active particles applied to learning dynamics. Comment on "Collective learning modeling based on the kinetic theory of active particles" by D. Burini et al.

NASA Astrophysics Data System (ADS)

Nieto, J.

2016-03-01

The learning phenomena, their complexity, concepts, structure, suitable theories and models, have been extensively treated in the mathematical literature in the last century, and [4] contains a very good introduction to the literature describing the many approaches and lines of research developed about them. Two main schools have to be pointed out [5] in order to understand the two -not exclusive- kinds of existing models: the stimulus sampling models and the stochastic learning models. Also [6] should be mentioned as a survey where two methods of learning are pointed out, the cognitive and the social, and where the knowledge looks like a mathematical unknown. Finally, as the authors do, we refer to the works [9,10], where the concept of population thinking was introduced and which motivate the game theory rules as a tool (both included in [4] to develop their theory) and [7], where the ideas of developing a mathematical kinetic theory of perception and learning were proposed.

Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management

NASA Astrophysics Data System (ADS)

Bellomo, N.; Clarke, D.; Gibelli, L.; Townsend, P.; Vreugdenhil, B. J.

2016-09-01

This paper proposes an essay concerning the understanding of human behaviours and crisis management of crowds in extreme situations, such as evacuation through complex venues. The first part focuses on the understanding of the main features of the crowd viewed as a living, hence complex system. The main concepts are subsequently addressed, in the second part, to a critical analysis of mathematical models suitable to capture them, as far as it is possible. Then, the third part focuses on the use, toward safety problems, of a model derived by the methods of the mathematical kinetic theory and theoretical tools of evolutionary game theory. It is shown how this model can depict critical situations and how these can be managed with the aim of minimizing the risk of catastrophic events.

Integrated learning of mathematics, science and technology concepts through LEGO/Logo projects

NASA Astrophysics Data System (ADS)

Wu, Lina

This dissertation examined integrated learning in the domains of mathematics, science and technology based on Piaget's constructivism, Papert's constructionism, and project-based approach to education. Ten fifth grade students were involved in a two-month long after school program where they designed and built their own computer-controlled LEGO/Logo projects that required the use of gears, ratios and motion concepts. The design of this study centered on three notions of integrated learning: (1) integration in terms of what educational materials/settings provide, (2) integration in terms of students' use of those materials, and (3) integration in the psychological sense. In terms of the first notion, the results generally showed that the LEGO/Logo environment supported the integrated learning of math, science and technology concepts. Regarding the second notion, the students all completed impressive projects of their own design. They successfully combined gears, motors, and LEGO parts together to create motion and writing control commands to manipulate the motion. But contrary to my initial expectations, their successful designs did not require numerical reasoning about ratios in designing effective gear systems. When they did reason about gear relationships, they worked with "qualitative" ratios, e.g., "a larger driver gear with a smaller driven gear increases the speed." In terms of the third notion of integrated learning, there was evidence in all four case study students of the psychological processes involved in linking mathematical, scientific, and/or technological concepts together to achieve new conceptual units. The students not only made connections between ideas and experiences, but also recognized decisive patterns and relationships in their project work. The students with stronger overall project performances showed more evidence of synthesis than the students with relatively weaker performances did. The findings support the conclusion that all three notions of the integrated learning are important for understanding what the students learned from their project work. By considering these notions together, and by deliberating about their interrelations, we take a step towards understanding the integrated learning.

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

Mathematical difficulties as decoupling of expectation and developmental trajectories

PubMed Central

McLean, Janet F.; Rusconi, Elena

2014-01-01

Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science. PMID:24567712

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…

The Catalytic Pellet: A Rich Prototype for Engineering Up-Scaling

ERIC Educational Resources Information Center

Arce, Pedro E.; Oyanader, Mario; Whitaker, Stephen

2007-01-01

This paper focuses on the use of scaling aspects for understanding transport processes with reaction in catalytic pores and pellets. The idea is to identify a systematic up-scaling approach in the learning process to help students with several concepts related to the transport-reaction process and the mathematical description associated with them.…

Developing Learning Materials Using an Ontology of Mathematical Logic

ERIC Educational Resources Information Center

Boyatt, Russell; Joy, Mike

2012-01-01

Ontologies describe a body of knowledge and give formal structure to a domain by describing concepts and their relationships. The construction of an ontology provides an opportunity to develop a shared understanding and a consistent vocabulary to be used for a given activity. This paper describes the construction of an ontology for an area of…

Abduction--A Logical View for Investigating and Initiating Processes of Discovering Mathematical Coherences

ERIC Educational Resources Information Center

Meyer, Michael

2010-01-01

According to theoretical concepts like constructivism, each learner has to build up knowledge on his or her own. The learner creates hypotheses in order to explain "facts". Hypotheses do not guarantee certainty. They have to be verified. In this article, a theoretical framework will be presented which can help to understand and analyse the…

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…

"Gaa-Noodin-Oke" (Alternative Energy/Wind Power): A Curriculum Implementation on the White Earth Reservation

ERIC Educational Resources Information Center

Guzey, Siddika Selcen; Nyachwaya, James; Moore, Tamara J.; Roehrig, Gillian H.

2014-01-01

A wind energy focused curriculum for grades 4-8 was designed and implemented to promote the understanding of wind energy concepts with American Indian students. 57 students who participated in the 2009 summer program of the "Reach for the Sky" (RFTS) Science, Technology, Engineering, and Mathematics (STEM) received the curriculum. The…

Changing the Metacognitive Orientation of a Classroom Environment to Stimulate Metacognitive Reflection Regarding the Nature of Physics Learning

ERIC Educational Resources Information Center

Thomas, Gregory P.

2013-01-01

Problems persist with physics learning in relation to students' understanding and use of representations for making sense of physics concepts. Further, students' views of physics learning and their physics learning processes have been predominantly found to reflect a "surface" approach to learning that focuses on mathematical aspects of…

Teaching Directed Numbers at Secondary School Level. Series of Caribbean Volunteer Publications, No. 7.

ERIC Educational Resources Information Center

Voluntary Services Overseas, Castries (St. Lucia).

This book is a collection of teaching strategies and activities for teachers of secondary mathematics. This volume is the product of a workshop that focused on student understanding of directed numbers. Suggested teaching methods include introducing the number concept, using a number line, number strips, monograms, bottle top addition and…

Eliciting and Developing Teachers' Conceptions of Random Processes in a Probability and Statistics Course

ERIC Educational Resources Information Center

Smith, Toni M.; Hjalmarson, Margret A.

2013-01-01

The purpose of this study is to examine prospective mathematics specialists' engagement in an instructional sequence designed to elicit and develop their understandings of random processes. The study was conducted with two different sections of a probability and statistics course for K-8 teachers. Thirty-two teachers participated. Video analyses…

The Combination of Just-in-Time Teaching and Wikispaces in Physics Classrooms

ERIC Educational Resources Information Center

Mohottala, Hashini E.

2013-01-01

The general student population enrolled in today's physics classrooms is diverse. They come from a variety of different educational backgrounds. Some demonstrate a good knowledge of natural laws of physics with a better understanding of mathematical concepts, while others show a fair knowledge in fundamentals of physics with a minimum knowledge in…