Gestures and Insight in Advanced Mathematical Thinking
ERIC Educational Resources Information Center
Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy
2011-01-01
What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…
Advanced Mathematical Thinking and the Way to Enhance It
ERIC Educational Resources Information Center
Herlina, Elda; Batusangkar, Stain
2015-01-01
This journal article discusses Advanced Mathematical Thinking (AMT) and how to enhance it. AMT is ability in representing, abstracting, creative thinking, and mathematical proving. The importance of AMT ability development in accord with government expectation who realize about the importance of mathematical competency mastery for student's life.…
Advanced Mathematical Thinking in a Technological Workplace.
ERIC Educational Resources Information Center
Magajna, Zlatan; Monaghan, John
2003-01-01
Examines the use of mathematics in a computer-aided design and manufacturing setting, whether this mathematics is related to school mathematics, how technicians understand this mathematics, and the role of technology in the technicians' mathematics-related problem solving activities. Focuses on technician's calculations of the interval volume of…
Mathematical Proof as Formal Procept in Advanced Mathematical Thinking
ERIC Educational Resources Information Center
Chin, Erh-Tsung
2003-01-01
In this paper the notion of "procept" (in the sense of Gray & Tall, 1994) is extended to advanced mathematics by considering mathematical proof as "formal procept". The statement of a theorem as a symbol may theoretically evoke the proof deduction as a process that may contain sequential procedures and require the synthesis of distinct cognitive…
Student Learning in Linear Algebra: The Gateways To Advance Mathematical Thinking Project.
ERIC Educational Resources Information Center
Manes, Michelle
This document provides a preliminary report of the study Gateways To Advance Mathematical Thinking (GAMT) run by Educational Development Center, Inc. (EDC). The study was designed to see what types of reasoning students who have recently completed a linear algebra course apply to problems in algebraic thinking. Student interviews were used as the…
ERIC Educational Resources Information Center
Nabb, Keith A.
2013-01-01
The research literature has made calls for greater coherence and consistency with regard to the meaning and use of the term advanced mathematical thinking (AMT) in mathematics education (Artigue, Batanero, & Kent, 2007; Selden & Selden, 2005). Educators and researchers agree that students should be engaged in AMT but it is unclear…
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…
Supporting Mathematical Thinking
ERIC Educational Resources Information Center
Houssart, Jenny; Roaf, Caroline; Watson, Anne
2005-01-01
This book looks at how practitioners have focused on the fully educational application of intellect to the problem of developing mathematical thinking among one's pupils. Each chapter demonstrates reflective minds at work, relying on close observation, willingness to understand the student's thinking processes and patient commitment to students…
Cognitive Psychology and Mathematical Thinking.
ERIC Educational Resources Information Center
Greer, Brian
1981-01-01
This review illustrates aspects of cognitive psychology relevant to the understanding of how people think mathematically. Developments in memory research, artificial intelligence, visually mediated processes, and problem-solving research are discussed. (MP)
Mathematical thinking and origami
NASA Astrophysics Data System (ADS)
Wares, Arsalan
2016-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.
A Daunting Task for Pre-Service Mathematics Teachers: Developing Students' Mathematical Thinking
ERIC Educational Resources Information Center
Tataroglu Tasdan, Berna; Erduran, Ayten; Çelik, Adem
2015-01-01
The purpose of this study was to examine pre-service teachers' teaching practice in terms of providing suitable conditions for developing students' mathematical thinking in the frame of the Advancing Children's Thinking framework. In the study, Advancing Children's Thinking framework developed by Fraivillig et al. was adopted as theoretical…
The Transition to Formal Thinking in Mathematics
ERIC Educational Resources Information Center
Tall, David
2008-01-01
This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…
The Thinking Styles of University Mathematics Students
ERIC Educational Resources Information Center
Moutsios-Rentzos, Andreas; Simpson, Adrian
2010-01-01
In this paper, we focus on the relationship between studying university mathematics and the "thinking styles" of both undergraduate and postgraduate mathematics students. A cross-sectional quantitative study (N = 238) was conducted in a large Greek university, identifying the thinking styles of second, third and fourth year…
Visible Thinking in High School Mathematics
ERIC Educational Resources Information Center
Sliman, Emily
2013-01-01
If a teacher asked their students what thinking looks like, what would they say? Would they just look at the teacher quizzically? The question is challenging because thinking is largely an invisible endeavor, and developing thoughtful students can be a daunting task. However, the job of mathematics teachers is to develop students who think about…
Thinking Through Three Worlds of Mathematics
ERIC Educational Resources Information Center
Tall, David
2004-01-01
The major idea in this paper is the formulation of a theory of three distinct but interrelated worlds of mathematical thinking each with its own sequence of development of sophistication, and its own sequence of developing warrants for truth, that in total spans the range of growth from the mathematics of new-born babies to the mathematics of…
Assessing Higher Order Thinking in Mathematics.
ERIC Educational Resources Information Center
Kulm, Gerald, Ed.
This book explores current theory, research, practice, and policy in the assessment of higher order thinking in mathematics, focusing on the elementary and secondary grades. Current knowledge and research on mathematics learning and testing is synthesized. Examples of innovative test items for classroom use and state assessment programs are…
Inhibiting Intuitive Thinking in Mathematics Education
ERIC Educational Resources Information Center
Thomas, Michael O. J.
2015-01-01
The papers in this issue describe recent collaborative research into the role of inhibition of intuitive thinking in mathematics education. This commentary reflects on this research from a mathematics education perspective and draws attention to some of the challenges that arise in collaboration between research fields with different cultures,…
Screencasts: Formative Assessment for Mathematical Thinking
ERIC Educational Resources Information Center
Soto, Melissa; Ambrose, Rebecca
2016-01-01
Increased attention to reasoning and justification in mathematics classrooms requires the use of more authentic assessment methods. Particularly important are tools that allow teachers and students opportunities to engage in formative assessment practices such as gathering data, interpreting understanding, and revising thinking or instruction.…
Children's Mathematical Thinking in Different Classroom Cultures
ERIC Educational Resources Information Center
Wood, Terry; Williams, Gaye; McNeal, Betsy
2006-01-01
The relationship between normative patterns of social interaction and children's mathematical thinking was investigated in 5 classes (4 reform and 1 conventional) of 7- to 8-year-olds. In earlier studies, lessons from these classes had been analyzed for the nature of interaction broadly defined; the results indicated the existence of 4 types of…
Connecting Research to Teaching: The "MOST" Productive Student Mathematical Thinking
ERIC Educational Resources Information Center
Stockero, Shari L.; Peterson, Blake E.; Leatham, Keith R.; Van Zoest, Laura R.
2014-01-01
Instruction that meaningfully incorporates students' mathematical thinking is widely valued within the mathematics education community (NCTM 2000; Sherin, Louis, and Mendez 2000; Stein et al. 2008). Although being responsive to student thinking is important, not all student thinking has the same potential to support mathematical learning.…
Adding Structure to the Transition Process to Advanced Mathematical Activity
ERIC Educational Resources Information Center
Engelbrecht, Johann
2010-01-01
The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical…
Conceptualizing Mathematically Significant Pedagogical Opportunities to Build on Student Thinking
ERIC Educational Resources Information Center
Leatham, Keith R.; Peterson, Blake E.; Stockero, Shari L.; Van Zoest, Laura R.
2015-01-01
The mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. The authors conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical…
Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition
ERIC Educational Resources Information Center
Su, Hui Fang Huang; Ricci, Frederick A.; Mnatsakanian, Mamikon
2016-01-01
A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…
Researchers' Descriptions and the Construction of Mathematical Thinking
ERIC Educational Resources Information Center
Barwell, Richard
2009-01-01
Research in mathematics education is a discursive process: It entails the analysis and production of texts, whether in the analysis of what learners say, the use of transcripts, or the publication of research reports. Much research in mathematics education is concerned with various aspects of mathematical thinking, including mathematical knowing,…
Leveling Students' Creative Thinking in Solving and Posing Mathematical Problem
ERIC Educational Resources Information Center
Siswono, Tatag Yuli Eko
2010-01-01
Many researchers assume that people are creative, but their degree of creativity is different. The notion of creative thinking level has been discussed .by experts. The perspective of mathematics creative thinking refers to a combination of logical and divergent thinking which is based on intuition but has a conscious aim. The divergent thinking…
Helping Students Acquire Thinking Skills through Mathematics Instruction.
ERIC Educational Resources Information Center
Van Devender, Evelyn M.
1992-01-01
Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)
Level of Student's Creative Thinking in Classroom Mathematics
ERIC Educational Resources Information Center
Siswono, Tatag Yuli Eko
2011-01-01
It is reasonable to assume that people are creative, but the degree of creativity is different. The Idea of the level of student's creative thinking has been expressed by experts, such as Gotoh (2004), and Krulik and Rudnick (1999). The perspective of the mathematics creative thinking refers to a combination of logical and divergent thinking which…
Defining Computational Thinking for Mathematics and Science Classrooms
NASA Astrophysics Data System (ADS)
Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri
2016-02-01
Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new urgency has come to the challenge of defining computational thinking and providing a theoretical grounding for what form it should take in school science and mathematics classrooms. This paper presents a response to this challenge by proposing a definition of computational thinking for mathematics and science in the form of a taxonomy consisting of four main categories: data practices, modeling and simulation practices, computational problem solving practices, and systems thinking practices. In formulating this taxonomy, we draw on the existing computational thinking literature, interviews with mathematicians and scientists, and exemplary computational thinking instructional materials. This work was undertaken as part of a larger effort to infuse computational thinking into high school science and mathematics curricular materials. In this paper, we argue for the approach of embedding computational thinking in mathematics and science contexts, present the taxonomy, and discuss how we envision the taxonomy being used to bring current educational efforts in line with the increasingly computational nature of modern science and mathematics.
Conditional Inference and Advanced Mathematical Study: Further Evidence
ERIC Educational Resources Information Center
Inglis, Matthew; Simpson, Adrian
2009-01-01
In this paper, we examine the support given for the "theory of formal discipline" by Inglis and Simpson (Educational Studies Mathematics 67:187-204, "2008"). This theory, which is widely accepted by mathematicians and curriculum bodies, suggests that the study of advanced mathematics develops general thinking skills and, in particular, conditional…
Students' Thinking and the Depth of the Mathematics Curriculum
ERIC Educational Resources Information Center
Kent, Laura B.
2014-01-01
This article explores the impact of students' thinking centered professional development on mathematics teaching and learning. Purposeful pedagogy and problem posing are examined as mechanisms by which teachers can potentially deepen students' understanding of mathematics. A classroom example comparing student generated strategies versus…
Helping Prospective Teachers to Understand Children's Mathematical Thinking
ERIC Educational Resources Information Center
Hartman, Genevieve L.
2012-01-01
The primary aim of this study was to investigate the effects of two video-based interventions, one guided, the other non-guided, on pre-service early childhood education teachers' understanding of students' mathematical thinking. Five web-based lessons on various topics in children's mathematical development were created for this study. Each…
Defining Computational Thinking for Mathematics and Science Classrooms
ERIC Educational Resources Information Center
Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri
2016-01-01
Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new…
Uncovering Student Thinking in Mathematics: 25 Formative Assessment Probes
ERIC Educational Resources Information Center
Rose, Cheryl M.; Minton, Leslie; Arline, Carolyn B.
2006-01-01
Students learn at varying rates, and if a misconception in mathematics develops early, it may be carried from year to year and obstruct a student's progress. To identify fallacies in students' preconceived ideas, "Uncovering Student Thinking in Mathematics" offers educators a powerful diagnostic technique in the form of field-tested assessment…
Emergent Mathematical Thinking in the Context of Play
ERIC Educational Resources Information Center
van Oers, Bert
2010-01-01
In the attempt to improve mathematical thinking for safeguarding our future societal needs, there is a worldwide tendency in schools to start training mathematical and arithmetical operations at an earlier age in children's development. Recent theoretical developments and empirical research have pointed to alternative ways of approaching early…
Preparing Beginning Teachers to Elicit and Interpret Students' Mathematical Thinking
ERIC Educational Resources Information Center
Sleep, Laurie; Boerst, Timothy A.
2012-01-01
This study investigated how teacher education assignments can be designed to support beginning teachers in learning to do the work of teaching. We examined beginners' formative assessment practices--in particular, their eliciting and interpreting of students' mathematical thinking--in the context of an elementary mathematics methods assignment,…
Thinking and Creativity in Learning Mathematics Teaching
ERIC Educational Resources Information Center
Rosu, Luisa Maria
2010-01-01
Preparation to teach school mathematics should include developing an understanding of classroom mathematical interactions. The research literature and professional expertise agree that a teacher's ability to respond to classroom mathematical interactions depends on her understanding of the subject matter within pedagogical situations. As a…
Teacher Leaders: Advancing Mathematics Learning
ERIC Educational Resources Information Center
Kinzer, Cathy J.; Rincón, Mari; Ward, Jana; Rincón, Ricardo; Gomez, Lesli
2014-01-01
Four elementary school instructors offer insights into their classrooms, their unique professional roles, and their leadership approaches as they reflect on their journey to advance teacher and student mathematics learning. They note a "teacher leader" serves as an example to other educators and strives to impact student learning;…
ERIC Educational Resources Information Center
Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri
2013-01-01
This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…
Children thinking mathematically beyond authoritative identities
NASA Astrophysics Data System (ADS)
MacMillan, Agnes
1995-10-01
A study into the mathematics-related interactions and developing attitudes of young children during the transition period between pre-school and school is reported. Transcripts of interactions during a six-week observation period in one of two preschool sites are coded according to the classifications defined within a theoretical framework. Two separate episodes of construction play were analysed and one of these is used to examine the mathematical nature of the children's interactions within an emerging model of autonomous learning. The results of the analysis indicate that access to self-regulatory social relations is very closely linked to the accessibility of mathematical meanings.
Mathematical Language and Advanced Mathematics Learning
ERIC Educational Resources Information Center
Ferrari, Pier Luigi
2004-01-01
This paper is concerned with the role of language in mathematics learning at college level. Its main aim is to provide a perspective on mathematical language appropriate to effectively interpret students' linguistic behaviors in mathematics and to suggest new teaching ideas. Examples are given to show that the explanation of students' behaviors…
Using Questioning to Stimulate Mathematical Thinking
ERIC Educational Resources Information Center
Way, Jenni
2008-01-01
Good questioning techniques have long been regarded as a fundamental tool of effective teachers and research has found that "differences in students' thinking and reasoning could be attributed to the type of questions that teachers asked" (Wood, 2002). Past research shows that 93% of teacher questions were "lower order" knowledge-based questions…
Scaffolding Students' Thinking in Mathematical Investigations
ERIC Educational Resources Information Center
McCosker, Natalie; Diezmann, Carmel M.
2009-01-01
Mathematical investigations are loosely-defined, engaging problem-solving tasks that allow students to ask their own questions, explore their own interests and set their own goals. The value of investigations for students lies in their complexity. Scaffolding plays an important role in supporting students' high-level engagement by encouraging…
Thinking Process of Pseudo Construction in Mathematics Concepts
ERIC Educational Resources Information Center
Subanji; Nusantara, Toto
2016-01-01
This article aims at studying pseudo construction of student thinking in mathematical concepts, integer number operation, algebraic forms, area concepts, and triangle concepts. 391 junior high school students from four districts of East Java Province Indonesia were taken as the subjects. Data were collected by means of distributing the main…
Stretch-It! Creative Geoboard Tasks for Developing Mathematical Thinking.
ERIC Educational Resources Information Center
Linehan, Anne
The purpose of this book is to introduce the geoboard as an effective tool that can help young children understand geometry as they develop spatial sense and mathematical thinking. Activities are clustered into three main sections: beginning geoboard explorations, exploring polygons, and coordinates. Blackline masters are included. (MKR)
Activating Pre-Service Mathematics Teachers' Critical Thinking
ERIC Educational Resources Information Center
Applebaum, Mark
2015-01-01
Teachers' critical thinking skills are essential for fostering the development of the same skills in their students. To demonstrate how teachers' ability to examine solutions critically can be developed and supported, we analyse a classroom activity performed by a group of pre-service secondary school mathematics teachers (N = 37) who were asked:…
The Stakes of Movement: A Dynamic Approach to Mathematical Thinking
ERIC Educational Resources Information Center
Roth, Wolff-Michael; Maheux, Jean-François
2015-01-01
Standard approaches to thinking in the mathematics curriculum depict it as the result of some stable constructions in the mind of the person, constructions that are the results of individual efforts in the mind of subjects or of collective efforts that are then appropriated by and into the mind of individuals. Such work does not appreciate what…
Mathematical Critical Thinking Ability through Contextual Teaching and Learning Approach
ERIC Educational Resources Information Center
Kurniati; Kusumah, Yaya S.; Sabandar, Jozua; Herman, Tatang
2015-01-01
This research aimed to examine the effect of the application of contextual teaching and learning (CTL) approach to the enhance of mathematical critical thinking ability (MCTA) of Primary School Teacher Students (PSTS). This research is an experimental study with the population of all students PSTS who took algebra subject matter of one university…
ERIC Educational Resources Information Center
Rasiman
2015-01-01
This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…
Eliciting Mathematical Thinking of Students through Realistic Mathematics Education
ERIC Educational Resources Information Center
Anwar, Lathifu; Budayasa, I Ketut; Amin, Siti M.; de Haan, Dede
2012-01-01
This paper focuses on an implementation a sequence of instructional activities about addition of fractions that has been developed and implemented in grade four of primary school in Surabaya, Indonesia. The theory of Realistic Mathematics Education (RME) has been applied in the sequence, which aims to assist low attaining learners in supporting…
Cognitive Correlates of Performance in Advanced Mathematics
ERIC Educational Resources Information Center
Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin
2012-01-01
Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…
Selecting Video Clips to Promote Mathematics Teachers' Discussion of Student Thinking
ERIC Educational Resources Information Center
Sherin, Miriam Gamoran; Linsenmeier, Katherine A.; van Es, Elizabeth A.
2009-01-01
This study explores the use of video clips from teachers' own classrooms as a resource for investigating student mathematical thinking. Three dimensions for characterizing video clips of student mathematical thinking are introduced: the extent to which a clip provides "windows" into student thinking, the "depth" of thinking shown, and the…
A Framework for Mathematical Thinking: The Case of Linear Algebra
ERIC Educational Resources Information Center
Stewart, Sepideh; Thomas, Michael O. J.
2009-01-01
Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…
ERIC Educational Resources Information Center
Cardella, Monica E.
2008-01-01
While many engineering educators have proposed changes to the way that mathematics is taught to engineers, the focus has often been on mathematical content knowledge. Work from the mathematics education community suggests that it may be beneficial to consider a broader notion of mathematics: mathematical thinking. Schoenfeld identifies five…
ERIC Educational Resources Information Center
Hudson, Brian; Henderson, Sheila; Hudson, Alison
2015-01-01
This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011-2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of…
Student Produced Advanced Mathematical Software.
ERIC Educational Resources Information Center
Hogben, Leslie
The intent of this project was to develop a course for mathematics graduate students at Iowa State University. They would design and write computer programs for use by undergraduate mathematics students, and then offer the course and actually produce the software. Phase plane graphics for ordinary differential equations was selected as the topic.…
Advanced Mathematics from an Elementary Standpoint.
ERIC Educational Resources Information Center
Mosquera, Julio C.
1992-01-01
Presents four areas of advanced mathematical research (fuzzy set theory, subjective probability, search theory, and Voronoi diagrams) that are proposed for introduction into teacher education programs from an elementary, survey perspective without the intention of accomplishing formal mathematical research, thereby challenging teachers' beliefs…
ERIC Educational Resources Information Center
Jansen, Amanda; Spitzer, Sandy M.
2009-01-01
In this study, we examined prospective middle school mathematics teachers' reflective thinking skills to understand how they learned from their own teaching practice when engaging in a modified lesson study experience. Our goal was to identify variations among prospective teachers' descriptions of students' thinking and frequency of their…
Why Do Students Drop Advanced Mathematics?
ERIC Educational Resources Information Center
Horn, Ilana
2004-01-01
Students, especially black, Latino and Native American youth and students of low socio-economic status drop out of advanced mathematics. Teachers must coordinate their expectations, their knowledge of students and their teaching practices in order to stop struggling students from dropping out of advanced math classes.
A Study of Rural Preschool Practitioners' Views on Young Children's Mathematical Thinking
ERIC Educational Resources Information Center
Hunting, Robert P.; Mousley, Judith A.; Perry, Bob
2012-01-01
The project "Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice" aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian…
NASA Astrophysics Data System (ADS)
Didis, Makbule Gozde; Erbas, Ayhan Kursat; Cetinkaya, Bulent; Cakiroglu, Erdinc; Alacaci, Cengiz
2016-04-01
Researchers point out the importance of teachers' knowledge of student thinking and the role of examining student work in various contexts to develop a knowledge base regarding students' ways of thinking. This study investigated prospective secondary mathematics teachers' interpretations of students' thinking as manifested in students' work that embodied solutions of mathematical modelling tasks. The data were collected from 25 prospective mathematics teachers enrolled in an undergraduate course through four 2-week-long cycles. Analysis of data revealed that the prospective teachers interpreted students' thinking in four ways: describing, questioning, explaining, and comparing. Moreover, whereas some of the prospective teachers showed a tendency to increase their attention to the meaning of students' ways of thinking more while they engaged in students' work in depth over time and experience, some of them continued to focus on only judging the accuracy of students' thinking. The implications of the findings for understanding and developing prospective teachers' ways of interpreting students' thinking are discussed.
NASA Astrophysics Data System (ADS)
Fredenberg, Michael Duane
The idea that problems and tasks play a pivotal role in a mathematics lesson has a long standing in mathematics education research. Recent calls for teaching reform appeal for training teachers to better understand how students learn mathematics and to employ students' mathematical thinking as the basis for pedagogy (CCSSM, 2010; NCTM, 2000; NRC 1999). The teaching practices of (a) developing a task for a mathematics lesson and, (b) modifying the task for students while enacting the lesson fit within the scope of supporting students' mathematical thinking. Surprisingly, an extensive search of the literature did not yield any research aimed to identify and refine the constituent parts of the aforementioned teaching practices in the manner called for by Grossman and xiii colleagues (2009). Consequently, my research addresses the two questions: (a) what factors do exemplary elementary teachers consider when developing a task for a mathematics lesson? (b) what factors do they consider when they modify a task for a student when enacting a lesson? I conducted a multiple case study involving three elementary teachers, each with extensive training in the area of Cognitively Guided Instruction (CGI), as well as several years experience teaching mathematics following the principles of CGI (Carpenter et al., 1999). I recorded video of three mathematics lessons with each participant and after each lesson I conducted a semi-structured stimulated recall interview. A subsequent follow-up clinical interview was conducted soon thereafter to further explore the teacher's thoughts (Ginsberg, 1997). In addition, my methodology included interjecting myself at select times during a lesson to ask the teacher to explain her reasoning. Qualitative analysis led to a framework that identified four categories of influencing factors and seven categories of supporting objectives for the development of a task. Subsets of these factors and objectives emerged as particularly relevant when the
NASA Astrophysics Data System (ADS)
Osman, Sharifah; Mohammad, Shahrin; Abu, Mohd Salleh
2015-05-01
Mathematics and engineering are inexorably and significantly linked and essentially required in analyzing and accessing thought to make good judgment when dealing in complex and varied engineering problems. A study in the current engineering education curriculum to explore how the critical thinking and mathematical thinking relates to one another, is therefore timely crucial. Unfortunately, there is not much information available explicating about the link. This paper aims to report findings of a critical review as well as to provide brief description of an on-going research aimed to investigate the dispositions of critical thinking and the relationship and integration between critical thinking and mathematical thinking during the execution of civil engineering tasks. The first part of the paper reports an in-depth review on these matters based on rather limited resources. The review showed a considerable form of congruency between these two perspectives of thinking, with some prevalent trends of engineering workplace tasks, problems and challenges. The second part describes an on-going research to be conducted by the researcher to investigate rigorously the relationship and integration between these two types of thinking within the perspective of civil engineering tasks. A reasonably close non-participant observations and semi-structured interviews will be executed for the pilot and main stages of the study. The data will be analyzed using constant comparative analysis in which the grounded theory methodology will be adopted. The findings will serve as a useful grounding for constructing a substantive theory revealing the integral relationship between critical thinking and mathematical thinking in the real civil engineering practice context. The substantive theory, from an angle of view, is expected to contribute some additional useful information to the engineering program outcomes and engineering education instructions, aligns with the expectations of
ERIC Educational Resources Information Center
Berkley, Darrin K.
2012-01-01
This sequential explanatory mixed-methods study determined whether the game of chess can be used as an educational tool to improve critical thinking skills of developmental mathematics students and improve mathematics achievement for these students. Five research questions were investigated. These questions were as follows: (a) Is there a…
ERIC Educational Resources Information Center
Palinussa, Anderson L.
2013-01-01
This paper presents the findings of a quasi-experimental with pre-test-post-test design and control group that aims to assess students' critical mathematical thinking skills and character through realistic mathematics education (RME) culture-based. Subjects of this study were 106 junior high school students from two low and medium schools level in…
ERIC Educational Resources Information Center
Fatah, Abdul; Suryadi, Didi; Sabandar, Jozua; Turmudi
2016-01-01
The present study aims at examining the use of open-ended approach in cultivating senior high school students' mathematical creative thinking ability (MCTA) and self-esteem (SE) in mathematics viewed from school category. The subjects of this research were the students grade XI at three schools; high, middle and low category in Kota Serang, Banten…
ERIC Educational Resources Information Center
Henningsen, Marjorie; Stein, Mary Kay
1997-01-01
Examines and illustrates how classroom-based factors can shape students' engagement with mathematical tasks that encourage high-level mathematical thinking and reasoning. Among the factors influencing students are classroom norms, task conditions, teachers' instructional dispositions, and students' learning dispositions. (AIM)
A study of rural preschool practitioners' views on young children's mathematical thinking
NASA Astrophysics Data System (ADS)
Hunting, Robert P.; Mousley, Judith A.; Perry, Bob
2012-03-01
The project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian states. The questions focused on five broad themes: children's mathematics learning, support for mathematics teaching, technology and computers, attitudes and feelings, and assessment and record keeping. We review results from the interview data for each of these themes, discuss their importance, and outline recommendations related to teacher education as well as resource development and research.
Transfer of Algebraic and Graphical Thinking between Mathematics and Chemistry
ERIC Educational Resources Information Center
Potgieter, Marietjie; Harding, Ansie; Engelbrecht, Johann
2008-01-01
Students in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the…
What We Think We Know About Maya Mathematics and Astronomy
NASA Astrophysics Data System (ADS)
Van Stone, M.
2016-01-01
In most cultures, mathematics and astronomy are obscure and arcane. Not so to the ancient Maya. Despite what we consider technological “deficiencies”—they lacked both metal tools and the wheel—their public inscriptions paid uniquely sophisticated attention to these sciences. At any given monument, fully half the text is devoted to situating events in time, particularly specifying the precise number of days between events, whether historical or mythological. Often these intervals have numerological significance, and many are precise multiples of the periodicities of heavenly bodies. The Maya apparently were fully aware of the exact length of the tropical year, the sidereal year, the cycles of Venus, and eclipses; and there is evidence that they even celebrated events reflecting the 26,000-year precession cycle. However, Maya illuminati had an agenda quite alien to our way of thinking. Clues to their knowledge are arcane, rare, and often difficult for us to recognize with eyes clouded by our modern worldview. The body of work left to us consists of just a few tantalizing sherds of a once-rich and diverse astromythological tradition. Moreover, there was no single pan-Mayan mythos. An astronomical alignment seen repeatedly in one city will be completely absent in others. Each city-state emphasized specific and often unique features, and they often contradict one another. But we soldier on. The diversity we find so frustrating is simply the fine structure of their worldview. Intellectual historians have for too long been, like Procrustes, trying to force all Maya science and religion into a single universal straitjacket.
Developing the Mathematics Learning Management Model for Improving Creative Thinking in Thailand
ERIC Educational Resources Information Center
Sriwongchai, Arunee; Jantharajit, Nirat; Chookhampaeng, Sumalee
2015-01-01
The study purposes were: 1) To study current states and problems of relevant secondary students in developing mathematics learning management model for improving creative thinking, 2) To evaluate the effectiveness of model about: a) efficiency of learning process, b) comparisons of pretest and posttest on creative thinking and achievement of…
Connecting Research to Teaching: Lenses for Examining Students' Mathematical Thinking
ERIC Educational Resources Information Center
Linsenmeier, Katherine A.; Sherin, Miriam; Walkoe, Janet; Mulligan, Martha
2014-01-01
The authors present three strategies for making sense of students' mathematical thinking. These lenses make the abstract idea of "making sense of student thinking" more manageable and concrete. We start by taking an initial look at a student's idea, going deeper, and finally looking across several ideas.
Cultivating Divergent Thinking in Mathematics through an Open-Ended Approach
ERIC Educational Resources Information Center
Kwon, Oh Nam; Park, Jung Sook; Park, Jee Hyun
2006-01-01
The purpose of this study was to develop a program to help cultivate divergent thinking in mathematics based on open-ended problems and to investigate its effect. The participants were 398 seventh grade students attending middle schools in Seoul. A method of pre- and post-testing was used to measure mainly divergent thinking skills through…
ERIC Educational Resources Information Center
Aizikovitsh-Udi, Einav; Clarke, David; Kuntze, Sebastian
2014-01-01
Even though statistical thinking and critical thinking appear to have strong links from a theoretical point of view, empirical research into the intersections and potential interrelatedness of these aspects of competence is scarce. Our research suggests that thinking skills in both areas may be interdependent. Given this interconnection, it should…
Increasing Logico-Mathematical Thinking in Low SES Preschoolers
ERIC Educational Resources Information Center
Kirkland, Lynn D.; Manning, Maryann; Osaki, Kyoko; Hicks, Delyne
2015-01-01
Traditionally, children in low socioeconomic status (SES) inner-city areas in the United States lack experiences that prepare them for academic success, especially in math and science. The purpose of this research was to determine the extent to which a constructivist curriculum emphasizing logical thinking produces higher level thinking in low-SES…
ERIC Educational Resources Information Center
Anthony, Glenda; Hunter, Jodie; Hunter, Roberta
2015-01-01
In recent years there have been calls for ambitious mathematics teaching which places student thinking and reasoning at the centre of instruction. Drawing on a larger study concerning implementation of practice-based pedagogies within our initial teacher education mathematics programme, this paper examines the range of opportunities for…
Designing and Developing Assessments of Complex Thinking in Mathematics for the Middle Grades
ERIC Educational Resources Information Center
Graf, Edith Aurora; Arieli-Attali, Meirav
2015-01-01
Designing an assessment system for complex thinking in mathematics involves decisions at every stage, from how to represent the target competencies to how to interpret evidence from student performances. Beyond learning to solve particular problems in a particular area, learning mathematics with understanding involves comprehending connections…
Modifying a Board Game To Foster Kindergartners' Logico-Mathematical Thinking.
ERIC Educational Resources Information Center
Kamii, Constance
2003-01-01
This article describes the modifications that 12 early childhood educators in Japan made to the Sorry! board game to encourage kindergartners' logico-mathematical thinking. Logico-mathematical knowledge is described as including classification, seriation, numerical relationships, spatial relationships, and temporal relationships. Examples of seven…
Exploring the Possibilities of Using Tic-Tac-Toe to Think and Communicate about Mathematics
ERIC Educational Resources Information Center
Clarkson, Philip C.
2008-01-01
Doing mathematics, and thinking about how you are doing it at the same time, are not the easiest things to do. It is even more difficult if students are not aware that they should be attempting both processes at the same time. They are likely to concentrate on the immediate task of "doing" the mathematics, rather than trying to access the deeper…
Developing Student-Centered Learning Model to Improve High Order Mathematical Thinking Ability
ERIC Educational Resources Information Center
Saragih, Sahat; Napitupulu, Elvis
2015-01-01
The purpose of this research was to develop student-centered learning model aiming to improve high order mathematical thinking ability of junior high school students of based on curriculum 2013 in North Sumatera, Indonesia. The special purpose of this research was to analyze and to formulate the purpose of mathematics lesson in high order…
What Students Say about Their Mathematical Thinking When They Listen
ERIC Educational Resources Information Center
Kosko, Karl W.
2014-01-01
Mathematical listening is an important aspect of mathematical communication. Yet there are relatively few examinations of this phenomenon. Further, existing studies of students' mathematical listening come from observational data, lacking the student perspective. This study examined student replies to an open-response question regarding what…
Exploring Wind Power: Improving Mathematical Thinking through Digital Fabrication
ERIC Educational Resources Information Center
Tillman, Daniel A.; An, Song A.; Cohen, Jonathan D.; Kjellstrom, William; Boren, Rachel L.
2014-01-01
This mixed methods study examined the impacts of digital fabrication activities that were integrated into contextualized mathematics education. The study investigated the students' mathematics content knowledge and attitudes. Data analysis yielded two key findings regarding our intervention combined with the other mathematics activities…
ERIC Educational Resources Information Center
Husnaeni
2016-01-01
Critical thinking ability of students' mathematical is a component that must be mastered by the student. Learn to think critically means using mental processes, such as attention, categorize, selection, and rate/decide. Critical thinking ability in giving proper guidance in thinking and working, and assist in determining the relationship between…
ERIC Educational Resources Information Center
Sherman, Milan
2014-01-01
The use of instructional technology in secondary mathematics education has proliferated in the last decade, and students' mathematical thinking and reasoning has received more attention during this time as well. However, few studies have investigated the role of instructional technology in supporting students' mathematical thinking. In…
ERIC Educational Resources Information Center
Lince, Ranak
2016-01-01
Mathematical ability of students creative thinking is a component that must be mastered by the student. Mathematical creative thinking plays an important role, both in solving the problem and well, even in high school students. Therefore, efforts are needed to convey ideas in mathematics. But the reality is not yet developed the ability to…
ERIC Educational Resources Information Center
Stein, Mary Kay; Grover, Barbara W.; Henningsen, Majorie
1996-01-01
A sample of 144 mathematical tasks used during reform-oriented teaching was analyzed in terms of task features and cognitive demands. The ways cognitive demands of high-level tasks declined and factors associated with task changes were explored. Teachers used tasks that led to the development of students' thinking capacities. (MAK)
Using Literature To Support Mathematical Thinking in Middle School.
ERIC Educational Resources Information Center
Bintz, William P.; Moore, Sara Delano
2002-01-01
Addresses "text potential" as a tool to make interdisciplinary connections between language arts and mathematics by identifying literacy standards and identifying literature that has text potential for teaching mathematics. Describes literature that highlights aspects of geometry and measurement, and discusses the power and potential of using…
Connecting Science with Mathematics: Thinking Outside the Toolbox
ERIC Educational Resources Information Center
Wake, Geoff; Newton, Len
2014-01-01
Our view of learning takes into account how learners, when learning, are engaged in both doing science and mathematics and becoming mathematicians and scientists. Drawing on our work on a number of European projects that developed inquiry approaches across mathematics and science, we propose a new research and development agenda seeking new ways…
Research on Mathematical Thinking of Young Children: Six Empirical Studies.
ERIC Educational Resources Information Center
Steffe, Leslie P., Ed.
This volume includes reports of six studies of the thought processes of children aged four through eight. In the first paper Steffe and Smock outline a model for learning and teaching mathematics. Six reports on empirical studies are then presented in five areas of mathematics learning: (1) equivalence and order relations; (2) classification and…
NASA Astrophysics Data System (ADS)
Cable, John
2013-07-01
This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.
Elementary Teachers' Thinking about a Good Mathematics Lesson
ERIC Educational Resources Information Center
Li, Yeping
2011-01-01
In an effort to gain a better understanding of Chinese classroom teaching culture, this study aimed to examine elementary teachers' views about a good mathematics lesson in China. Through analyzing 57 teachers' essays collected from 7 elementary schools in 2 provinces, it is found that Chinese teachers emphasized the most about students and their…
Explicit versus Implicit Questioning: Inviting All Children to Think Mathematically
ERIC Educational Resources Information Center
Parks, Amy Noelle
2010-01-01
Background/Context: Open-ended, or implicit, questioning has been described as central to reform teaching in mathematics. However, concerns about equity have caused some researchers to question whether this kind of teaching is productive for all children. Purpose: This study explores the role that implicit and explicit questions played in…
Mathematical Thinking and Human Nature: Consonance and Conflict
ERIC Educational Resources Information Center
Leron, Uri
2004-01-01
Human nature had traditionally been the realm of novelists, philosophers, and theologicians, but has recently been studied by cognitive science, neuroscience, research on babies and on animals, anthropology, and evolutionary psychology. In this paper I will show--by surveying relevant research and by analyzing some mathematical "case studies"--how…
Enhancing Thinking Skills in the Sciences and Mathematics.
ERIC Educational Resources Information Center
Halpern, Diane F., Ed.
The need to provide an improved science and mathematics curriculum is imperative. Over recent years cognitive psychologists and educators have responded to this need by designing instructional programs that are more compatible with our knowledge of how people acquire, use, and retain knowledge. This book contains many of the guiding principles…
Improving Critical Thinking and Problem Solving in Fifth Grade Mathematics.
ERIC Educational Resources Information Center
Kjos, Ruth; Long, Kathryn
This report describes an intervention designed to assist students in creating and accepting divergent solutions to problems in mathematics. The targeted population consisted of fifth-grade students from a multicultural setting with varied economic backgrounds, and the sample included 171 fifth graders in two school districts. Underdeveloped…
Advanced Mathematics Course-Taking: A Focus on Gender Equifinality
ERIC Educational Resources Information Center
You, Sukkyung; Sharkey, Jill D.
2012-01-01
High school mathematics achievement predicts future success. Potentially different factors that lead to success for boys versus girls, termed equifinality, are not well understood. Such factors are needed to inform interventions to increase numbers of students taking advanced mathematics courses and going on into science and mathematics careers.…
Mathematical Thinking Process of Autistic Students in Terms of Representational Gesture
ERIC Educational Resources Information Center
Mustafa, Sriyanti; Nusantara, Toto; Subanji; Irawati, Santi
2016-01-01
The aim of this study is to describe the mathematical thinking process of autistic students in terms of gesture, using a qualitative approach. Data collecting is conducted by using 3 (three) audio-visual cameras. During the learning process, both teacher and students' activity are recorded using handy cam and digital camera (full HD capacity).…
ERIC Educational Resources Information Center
Kleiman, Glenn; Zweig, Karen
In this unit of the Seeing and Thinking Mathematically series, students use geometry to analyze buildings from around the world, design and build their own house models, create plans for their designs, and build from each other's plans. Students start out the unit building with cubes and later move to other geometric shapes. As they learn to…
ERIC Educational Resources Information Center
Sahin, Senar Alkin; Tunca, Nihal; Altinkurt, Yahya; Yilmaz, Kürsad
2016-01-01
The purpose of this study is to determine the relationship between the professional values and critical thinking disposition of science-technology and mathematics teachers working in middle schools. The survey research method was employed in the study. The sample of the study is comprised of 193 teachers (90 science-technology and 103 mathematics…
ERIC Educational Resources Information Center
Sevimli, Eyup; Delice, Ali
2012-01-01
Students' cognitive differences in problem solving have been the focus of much research. One classification of these differences is related to whether visualisation is used. Like mathematical thinking differences, multiple representation preferences are important when considering individual differences. Choosing an appropriate representation is an…
The Impact of Critical Thinking and Logico-Mathematical Intelligence on Algorithmic Design Skills
ERIC Educational Resources Information Center
Korkmaz, Ozgen
2012-01-01
The present study aims to reveal the impact of students' critical thinking and logico-mathematical intelligence levels of students on their algorithm design skills. This research was a descriptive study and carried out by survey methods. The sample consisted of 45 first-year educational faculty undergraduate students. The data was collected by…
An Initial Framework for the Language of Higher-Order Thinking Mathematics Practices
ERIC Educational Resources Information Center
Staples, Megan E.; Truxaw, Mary P.
2012-01-01
This article presents an examination of the language demands of cognitively demanding tasks and proposes an initial framework for the language demands of higher-order mathematics thinking practices. We articulate four categories for this framework: "language of generalisation," "language of comparison," "language of proportional reasoning," and…
ERIC Educational Resources Information Center
Imai, Toshihiro
2000-01-01
Aims to find the influence of overcoming fixation in mathematical problem-solving towards divergent thinking in open-ended mathematics problems. Presents findings from an investigation of Japanese junior high school students. Reports that students who can overcome fixation in mathematics can contribute varied and original ideas in open-ended…
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…
ERIC Educational Resources Information Center
Aguirre, Julia M.; Turner, Erin E.; Bartell, Tonya Gau; Kalinec-Craig, Crystal; Foote, Mary Q.; Roth McDuffie, Amy; Drake, Corey
2013-01-01
This study examines the ways prospective elementary teachers (PSTs) made connections to children's mathematical thinking and children's community funds of knowledge in mathematics lesson plans. We analyzed the work of 70 PSTs from across three university sites associated with an instructional module for elementary mathematics methods courses that…
ERIC Educational Resources Information Center
Cable, John
2014-01-01
This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which…
ERIC Educational Resources Information Center
Koichu, Boris
2010-01-01
This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…
ERIC Educational Resources Information Center
Gazit, Avikam
2012-01-01
The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical-mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th…
ERIC Educational Resources Information Center
Turner, Erin E.; Drake, Corey
2016-01-01
Researchers have studied the preparation of elementary teachers to teach mathematics to students from diverse racial, ethnic, and linguistic backgrounds by focusing either on teachers' learning about children's mathematical thinking (CMT) or, less frequently, about children's cultural funds of knowledge (CFoK) related to mathematics. Despite this…
ERIC Educational Resources Information Center
Gibney, Janette
2014-01-01
This action research project looks at what happened when a small group of adult numeracy teachers with widely different experiences of learning and teaching mathematics explored their own informal numeracy practices and undertook a series of collaborative mathematical tasks. Evidence from qualitative data collected during the enquiry suggests that…
ERIC Educational Resources Information Center
Paterson, Judy; Sneddon, Jamie
2011-01-01
This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…
ERIC Educational Resources Information Center
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
NASA Astrophysics Data System (ADS)
Bektasli, Behzat
Graphs have a broad use in science classrooms, especially in physics. In physics, kinematics is probably the topic for which graphs are most widely used. The participants in this study were from two different grade-12 physics classrooms, advanced placement and calculus-based physics. The main purpose of this study was to search for the relationships between student spatial ability, logical thinking, mathematical achievement, and kinematics graphs interpretation skills. The Purdue Spatial Visualization Test, the Middle Grades Integrated Process Skills Test (MIPT), and the Test of Understanding Graphs in Kinematics (TUG-K) were used for quantitative data collection. Classroom observations were made to acquire ideas about classroom environment and instructional techniques. Factor analysis, simple linear correlation, multiple linear regression, and descriptive statistics were used to analyze the quantitative data. Each instrument has two principal components. The selection and calculation of the slope and of the area were the two principal components of TUG-K. MIPT was composed of a component based upon processing text and a second component based upon processing symbolic information. The Purdue Spatial Visualization Test was composed of a component based upon one-step processing and a second component based upon two-step processing of information. Student ability to determine the slope in a kinematics graph was significantly correlated with spatial ability, logical thinking, and mathematics aptitude and achievement. However, student ability to determine the area in a kinematics graph was only significantly correlated with student pre-calculus semester 2 grades. Male students performed significantly better than female students on the slope items of TUG-K. Also, male students performed significantly better than female students on the PSAT mathematics assessment and spatial ability. This study found that students have different levels of spatial ability, logical thinking
All Students Need Advanced Mathematics. Math Works
ERIC Educational Resources Information Center
Achieve, Inc., 2013
2013-01-01
This fact sheet explains that to thrive in today's world, all students will need to graduate with very strong math skills. That can only mean one thing: advanced math courses are now essential math courses. Highlights of this paper include: (1) Advanced math equals college success; (2) Advanced math equals career opportunity; and (3) Advanced math…
Reassessing the Economic Value of Advanced Level Mathematics
ERIC Educational Resources Information Center
Adkins, Michael; Noyes, Andrew
2016-01-01
In the late 1990s, the economic return to Advanced level (A-level) mathematics was examined. The analysis was based upon a series of log-linear models of earnings in the 1958 National Child Development Survey (NCDS) and the National Survey of 1980 Graduates and Diplomates. The core finding was that A-level mathematics had a unique earnings premium…
Use and Recall of Advance Organizers in Mathematics Instruction
ERIC Educational Resources Information Center
Bright, George W.
1976-01-01
Two studies are described which (a) determined whether the generality and inclusiveness of advance organizers (AOs) were the same as the mathematical generality or abstractness of concepts that might be used as AOs and (b) measured the effect of programmed recall of AOs in enhancing the learning of a mathematical concept. (DT)
ERIC Educational Resources Information Center
Turner, Erin E.; Drake, Corey; McDuffie, Amy Roth; Aguirre, Julia; Bartell, Tonya Gau; Foote, Mary Q.
2012-01-01
Research repeatedly documents that teachers are underprepared to teach mathematics effectively in diverse classrooms. A critical aspect of learning to be an effective mathematics teacher for diverse learners is developing knowledge, dispositions, and practices that support building on children's mathematical thinking, as well as their cultural,…
ERIC Educational Resources Information Center
Ma, Xin
2010-01-01
Based on data from the Longitudinal Study of American Youth (LSAY), students were classified into high-, middle-, and low-ability students. The effects of early acceleration in mathematics on the most advanced mathematics coursework (precalculus and calculus) in high school were examined in each category. Results showed that although early…
ERIC Educational Resources Information Center
Clements, Douglas H., Ed.; DiBiase, Ann-Marie, Ed.; Sarama, Julie, Ed.
2004-01-01
This book brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and Kindergarten Mathematics Education, attended by representatives from almost every state developing standards for young children's…
NASA Astrophysics Data System (ADS)
Wilkie, Karina J.
2015-08-01
A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students' functional thinking through pattern generalisation. This aspect of algebra learning has been explicitly brought to the attention of upper primary teachers in the recently introduced Australian curriculum. Ten practising teachers participated over 1 year in a design-based research project involving a sequence of geometric pattern generalisation lessons with their classes. Initial and final survey responses and teachers' interactions in regular meetings and lessons were analysed from cognitive and situated perspectives on professional learning, using a theoretical model for the different types of knowledge needed for teaching mathematics. The teachers demonstrated an increase in certain aspects of their mathematical knowledge for teaching algebra as well as some residual issues. Implications for the professional learning of practising and pre-service teachers to develop their mathematics knowledge for teaching functional thinking, and challenges with operationalising knowledge categories for field-based research are presented.
NASA Astrophysics Data System (ADS)
Wilkie, Karina J.
2016-06-01
A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students' functional thinking through pattern generalisation. This aspect of algebra learning has been explicitly brought to the attention of upper primary teachers in the recently introduced Australian curriculum. Ten practising teachers participated over 1 year in a design-based research project involving a sequence of geometric pattern generalisation lessons with their classes. Initial and final survey responses and teachers' interactions in regular meetings and lessons were analysed from cognitive and situated perspectives on professional learning, using a theoretical model for the different types of knowledge needed for teaching mathematics. The teachers demonstrated an increase in certain aspects of their mathematical knowledge for teaching algebra as well as some residual issues. Implications for the professional learning of practising and pre-service teachers to develop their mathematics knowledge for teaching functional thinking, and challenges with operationalising knowledge categories for field-based research are presented.
ERIC Educational Resources Information Center
Tandiseru, Selvi Rajuaty
2015-01-01
The problem in this research is the lack of creative thinking skills of students. One of the learning models that is expected to enhance student's creative thinking skill is the local culture-based mathematical heuristic-KR learning model (LC-BMHLM). Heuristic-KR is a learning model which was introduced by Krulik and Rudnick (1995) that is the…
Understanding Mathematics and Science Matters. Studies in Mathematical Thinking and Learning Series
ERIC Educational Resources Information Center
Romberg, Thomas A., Ed.; Carpenter, Thomas P., Ed.; Dremock, Fae, Ed.
2005-01-01
The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics…
Global Perspectives: Developing Media Literacy Skills to Advance Critical Thinking
ERIC Educational Resources Information Center
Radeloff, Cheryl L.; Bergman, Barbara J.
2009-01-01
Women's studies and feminist curricula have been lauded for the development and application of critical thinking skills for social and political change in its students (Fisher; Kellner and Share; Mayberry). Critical thinking can be defined as the ability to identify and challenge assumptions, to search for alternative ways of thinking, and to…
ERIC Educational Resources Information Center
Widyatiningtyas, Reviandari; Kusumah, Yaya S.; Sumarmo, Utari; Sabandar, Jozua
2015-01-01
The study reported the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students' prior mathematical ability to student's mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from…
ERIC Educational Resources Information Center
Glazer, Evan
This resource book, written for mathematics teachers and school library media specialists, provides Web resources that promote critical thinking in the high school mathematics classroom. It consists of 153 activities that address topics in prealgebra, algebra, geometry, precalculus, calculus, probability, and statistics. Each activity has a…
Who Succeeds in Advanced Mathematics and Science Courses?
ERIC Educational Resources Information Center
Korpershoek, Hanke; Kuyper, Hans; van der Werf, Greetje; Bosker, Roel
2011-01-01
Few students (particularly few girls) currently choose to take their Final School Examination (FSE) in advanced mathematics, chemistry and physics, a combination of subjects that is the best preparation for a science-oriented study in higher education. Are these subjects attainable by more students than is currently the case? This study examined…
Advanced Mathematical Knowledge in Teaching Practice: Perceptions of Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Zazkis, Rina; Leikin, Roza
2010-01-01
For the purpose of our research we define Advanced Mathematical Knowledge (AMK) as knowledge of the subject matter acquired during undergraduate studies at colleges or universities. We examine the responses of secondary school teachers about their usage of AMK in teaching. We find that the majority of teachers focus on the purposes and advantages…
Students' Exploratory Thinking about a Nonroutine Calculus Task
ERIC Educational Resources Information Center
Nabb, Keith
2013-01-01
In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…
ERIC Educational Resources Information Center
Sezer, Renan
2008-01-01
Critical thinking receives increasing emphasis from educators looking to infuse analytical thinking skills into the curriculum. Many research projects have been conducted on the transferability of critical thinking skills to other disciplines and how critical thinking may be taught. There are numerous studies on teaching critical thinking, yet…
ERIC Educational Resources Information Center
Yuliani, Kiki; Saragih, Sahat
2015-01-01
The purpose of this research was to: 1) development of learning devices based guided discovery model in improving of understanding concept and critical thinking mathematically ability of students at Islamic Junior High School; 2) describe improvement understanding concept and critical thinking mathematically ability of students at MTs by using…
ERIC Educational Resources Information Center
Qudah, Ahmad Hassan
2016-01-01
This study aimed at identify the effect of using a proposed teaching strategy based on the selective thinking in acquire mathematical concepts by Classroom Teacher Students at Al- al- Bayt University, The sample of the study consisted of (74) students, equally distributed into a control group and an experimental group. The selective thinking…
ERIC Educational Resources Information Center
Koichu, Boris; Harel, Guershon; Manaster, Alfred
2013-01-01
Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…
ERIC Educational Resources Information Center
Abdullah, Nasarudin; Halim, Lilia; Zakaria, Effandi
2014-01-01
This study aimed to determine the impact of strategic thinking and visual representation approaches (VStops) on the achievement, conceptual knowledge, metacognitive awareness, awareness of problem-solving strategies, and student attitudes toward mathematical word problem solving among primary school students. The experimental group (N = 96)…
ERIC Educational Resources Information Center
Promraksa, Siwarak; Sangaroon, Kiat; Inprasitha, Maitree
2014-01-01
The objectives of this research were to study and analyze the characteristics of computational thinking about the estimation of the students in mathematics classroom applying lesson study and open approach. Members of target group included 4th grade students of 2011 academic year of Choomchon Banchonnabot School. The Lesson plan used for data…
Advancing socio-technical systems thinking: a call for bravery.
Davis, Matthew C; Challenger, Rose; Jayewardene, Dharshana N W; Clegg, Chris W
2014-03-01
Socio-technical systems thinking has predominantly been applied to the domains of new technology and work design over the past 60 years. Whilst it has made an impact, we argue that we need to be braver, encouraging the approach to evolve and extend its reach. In particular, we need to: extend our conceptualization of what constitutes a system; apply our thinking to a much wider range of complex problems and global challenges; and engage in more predictive work. To illustrate our agenda in novel domains, we provide examples of socio-technical perspectives on the management of crowd events and environmental sustainability. We also outline a research and development agenda to take the area forward. PMID:23664481
Gopnik, Alison
2012-09-28
New theoretical ideas and empirical research show that very young children's learning and thinking are strikingly similar to much learning and thinking in science. Preschoolers test hypotheses against data and make causal inferences; they learn from statistics and informal experimentation, and from watching and listening to others. The mathematical framework of probabilistic models and Bayesian inference can describe this learning in precise ways. These discoveries have implications for early childhood education and policy. In particular, they suggest both that early childhood experience is extremely important and that the trend toward more structured and academic early childhood programs is misguided. PMID:23019643
Thinking Ourselves to Liberation?: Advancing Sociopolitical Action in Critical Consciousness
ERIC Educational Resources Information Center
Watts, Roderick J.; Hipolito-Delgado, Carlos P.
2015-01-01
Freire advanced critical consciousness as a tool for the liberation of oppressed communities. Based on his ideas, scholars of theory and practice from myriad disciplines have written about how to advance critical consciousness (CC) among oppressed peoples. We reviewed CC theory and practice articles in scholarly journals with the goal of…
ERIC Educational Resources Information Center
Ercikan, Kadriye; McCreith, Tanya; Lapointe, Vanessa
2005-01-01
This article reports results of an exploratory study examining factors that might be associated with achievement in mathematics and participation in advanced mathematics courses in Canada, Norway, and the United States of America (USA). These factors, which were not directly related to schooling accounted for large degrees of variability, 24% to…
ERIC Educational Resources Information Center
Klein, Pnina S.; Adi-Japha, Esther; Hakak-Benizri, Simcha
2010-01-01
The objective of this study was to examine gender differences in the relations between verbal, spatial, mathematics, and teacher-child mathematics interaction variables. Kindergarten children (N = 80) were videotaped playing games that require mathematical reasoning in the presence of their teachers. The children's mathematics, spatial, and verbal…
Literacy in Language and Mathematics: More in Common Than You Think
ERIC Educational Resources Information Center
Thompson, Denisse R.; Rubenstein, Rheta N.
2014-01-01
This paper shares perspectives on literacy in mathematics, particularly highlighting commonalities with literacy in language arts. We discuss levels of language development appropriate for the mathematics classroom, issues related to mathematical definitions, implied meanings in many mathematics concepts, and the importance of justification. We…
ERIC Educational Resources Information Center
Pape, S. J.; Bell, C. V.; Yetkin, IE.
2003-01-01
Mathematics educators have found sociocultural models of teaching and learning to be powerful in their ability to describe and support the pursuit of instruction based on recent standards documents (e.g., National Council of Teachers of Mathematics [NCTM], 1989, 2000). These models of instruction, however, have been criticized for their lack of…
ERIC Educational Resources Information Center
Remillard, Janine T., Ed.; Herbel-Eisenmann, Beth A., Ed.; Lloyd, Gwendolyn M., Ed.
2011-01-01
This book compiles and synthesizes existing research on teachers' use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on--but not restricted to--those materials developed in the 1990s in response to the NCTM's Principles and Standards for School Mathematics. Despite…
ERIC Educational Resources Information Center
Jappinen, Aini-Kristiina
2005-01-01
This paper presents a study on thinking and learning processes of mathematics and science in teaching through a foreign language, in Finland. The entity of thinking and content learning processes is, in this study, considered as cognitional development. Teaching through a foreign language is here called Content and Language Integrated Learning or…
ERIC Educational Resources Information Center
Rasmussen, Chris; Kwon, Oh Nam; Allen, Karen; Marrongelle, Karen; Burtch, Mark
2006-01-01
This paper provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project and reports on the main results of a study that compared students' beliefs, skills, and understandings in IO-DE classes to more conventional approaches. The IO-DE project capitalizes on advances within mathematics and mathematics education, including the…
Promoting Critical-Thinking Dispositions by Using Problem Solving in Middle School Mathematics
ERIC Educational Resources Information Center
Leader, Lars F.; Middleton, James A.
2004-01-01
This review of research generates principles for the design of instructional programs that foster critical-thinking dispositions. The dispositional aspect of critical thinking may be considered part of attitudinal memory, readily activated if sufficiently strong. We describe evidence suggesting that ill-structured problem-solving can provide…
Issues in Designing Assessments of Historical Thinking
ERIC Educational Resources Information Center
Ercikan, Kadriye; Seixas, Peter
2015-01-01
Similar to educators in mathematics, science, and reading, history educators around the world have mobilized curricular reform movements toward including complex thinking in history education, advancing historical thinking, developing historical consciousness, and teaching competence in historical sense making. These reform movements, including…
Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…
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…
ERIC Educational Resources Information Center
Krummheuer, Götz
2013-01-01
This paper deals with one aspect of the endeavor to generate a theory of the development of mathematical thinking of children in the early years ages 3 to 10. By comparing two scenes, one from preschool and one from a first grade mathematics class, the relationship between diagrammatic and narrative argumentations among children and teachers is…
ERIC Educational Resources Information Center
Wickstrom, Megan H.
2015-01-01
Creating equitable opportunities so all students can learn and succeed mathematically has been a key focus of mathematics education across several decades. Central to student achievement are students' mathematical identity and their feelings of success during instruction. Researchers (e.g., Boaler & Staples, 2008) have shown that teachers can…
ERIC Educational Resources Information Center
Burris, Justin T.
2010-01-01
As one research priority for mathematics education is "to research how mathematical meanings are structured by tools available," the present study examined mathematical representations more closely by investigating instructional modes of representation (Noss, Healy & Hoyles, 1997). The study compared two modes of instruction of place value with…
Valuing Choice as an Alternative to Fixed-Ability Thinking and Teaching in Primary Mathematics
ERIC Educational Resources Information Center
Milik, Amy; Boylan, Mark
2013-01-01
This article offers a personal account of a primary mathematics teacher's current practice and how it developed through participation in a professional development programme. This alternative to fixed-ability teaching is based on creating opportunities for learners to exercise choice and on an understanding of mathematics as connected. Key…
ERIC Educational Resources Information Center
Norton, Anderson; McCloskey, Andrea; Hudson, Rick A.
2011-01-01
In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child's mathematics…
Inhibitory Control in Mathematical Thinking, Learning and Problem Solving: A Survey
ERIC Educational Resources Information Center
Van Dooren, Wim; Inglis, Matthew
2015-01-01
Inhibitory control--the ability to ignore salient but unhelpful stimuli and responses--seems to be important for learning mathematics. For instance there is now robust evidence that performance on classic measures of inhibition, such as the Stroop Task, correlate with school-level mathematics achievement. At the same time, a great deal of…
The Interaction between Intuitive and Formal Mathematical Thinking: A Case Study
ERIC Educational Resources Information Center
Farmaki, V.; Paschos, T.
2007-01-01
This paper reports studies of the interaction between the intuitive, the formal and the procedural aspects in the processes of mathematical understanding of Peter, a first-year undergraduate of Mathematics. Using an activity and an interview, an attempt is made to analyse his mental operations. The way in which he handles visual-graphic…
ERIC Educational Resources Information Center
Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim
2013-01-01
The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…
ERIC Educational Resources Information Center
Healey, Muriel
This study assesses the abilities of kindergarten children who attended the Mt. Druitt Early Childhood Project (MDECP) in Australia to apply logical processes to mathematic problems not generally found in the classroom. The mathematical abilities of 56 children enrolled in one of the MDECP's five programs (competency, cognitive, behaviorist,…
ERIC Educational Resources Information Center
DuBridge, Lee A.
An appeal for more research to determine how to educate children as effectively as possible is made. Mathematics teachers can readily examine the educational problems of today in their classrooms since learning progress in mathematics can easily be measured and evaluated. Since mathematics teachers have learned to think in quantitative terms and…
Thinking and Writing Mathematically: "Achilles and the Tortoise" as an Algebraic Word Problem.
ERIC Educational Resources Information Center
Martinez, Joseph G. R.
2001-01-01
Introduces Hogben's adaptation of Zeno's paradox, "Achilles and the Tortoise", as a thinking and writing exercise. Emphasizes engaging students' imagination with creative, thought-provoking problems and involving students in evaluating their word problem-solving strategies. Describes the paradox, logical solutions, and students' mathematical…
ERIC Educational Resources Information Center
Dyer, Elizabeth B.; Sherin, Miriam Gamoran
2016-01-01
Basing instruction on the substance of student thinking, or responsive teaching, is a critical strategy for supporting student learning. Previous research has documented responsive teaching by identifying observable teaching practices in a broad range of disciplines and classrooms. However, this research has not provided access to the teacher…
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…
ERIC Educational Resources Information Center
An, Shuhua; Wu, Zhonghe
2012-01-01
This study focuses on teacher learning of student thinking through grading homework, assessing and analyzing misconceptions. The data were collected from 10 teachers at fifth-eighth grade levels in the USA. The results show that assessing and analyzing misconceptions from grading homework is an important approach to acquiring knowledge of…
ERIC Educational Resources Information Center
Lew, Kristen; Fukawa-Connelly, Timothy Patrick; Mejía-Ramos , Juan Pablo; Weber, Keith
2016-01-01
We describe a case study in which we investigate the effectiveness of a lecture in advanced mathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he…
ERIC Educational Resources Information Center
Ma, Xin
2006-01-01
Using data from the Longitudinal Study of American Youth, this analysis tested whether changes during middle and high school in mathematics-related cognitive and affective factors influence participation in the most advanced mathematics course work, with control over confounding factors associated with student background. No significant…
ERIC Educational Resources Information Center
Anderson, Rick
2006-01-01
The focus of this paper is a group of rural high school students and the factors that contributed to their participation in mathematics classes beyond those minimally required for high school graduation. The author follows Gutierrez (2002) in referring to participation as course taking, particularly in elective and advanced mathematics classes.…
A National Dilemma: African American Students Underrepresented in Advanced Mathematics Courses
ERIC Educational Resources Information Center
Johnson, Clarence; Kritsonis, William Allan
2006-01-01
A lack of access to educational opportunities has been a reality for African American students. As a result, America's schools are facing a national dilemma. African American students are significantly underrepresented in advanced mathematics courses. One of the most segregated places in American society is the mathematics classroom. African…
Gender Differences in the Use and Benefit of Advanced Learning Technologies for Mathematics
ERIC Educational Resources Information Center
Arroyo, Ivon; Burleson, Winslow; Tai, Minghui; Muldner, Kasia; Woolf, Beverly Park
2013-01-01
We provide evidence of persistent gender effects for students using advanced adaptive technology while learning mathematics. This technology improves each gender's learning and affective predispositions toward mathematics, but specific features in the software help either female or male students. Gender differences were seen in the students' style…
Dropping Out of Advanced Mathematics: How Much Do Students and Schools Contribute to the Problem?
ERIC Educational Resources Information Center
Ma, Xin; Willms, J. Douglas
1999-01-01
Uses data from six waves of the Longitudinal Study of American Youth to discern when and why students drop out of advanced mathematics. Between grades 8 and 9, prior achievement plays a more important role than attitude or socioeconomic status, and between grades 11 and 12, student attitude toward mathematics is the most important factor. (SLD)
Origins of the brain networks for advanced mathematics in expert mathematicians.
Amalric, Marie; Dehaene, Stanislas
2016-05-01
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124
NASA Astrophysics Data System (ADS)
Bobis, Janette; Clarke, Barbara; Clarke, Doug; Thomas, Gill; Wright, Bob; Young-Loveridge, Jenny; Gould, Peter
2005-10-01
Recognition of the importance of the early childhood years in the development of numeracy is a significant characteristic of the New Zealand Numeracy Development Project, the Victorian Early Numeracy Research Project and the Count Me In Too program in New South Wales, Australia. This article outlines the background, key components and major impacts of these three innovative and successful professional development and research initiatives. Juxtaposing the three projects highlights important commonalities—research-based frameworks, diagnostic interviews, and whole-school approaches to professional development. Each program has been significant in rethinking what mathematics and how mathematics is taught to young children.
NASA Astrophysics Data System (ADS)
Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Hee, Pah Chin
2013-04-01
The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences. We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support . This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products. Guest Editors Nasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee The PDF contains the committee lists, board list and biographies of the plenary speakers.
Forecast: Changing Mathematics Curriculum and Increasing Pressure for Higher-Level Thinking Skills.
ERIC Educational Resources Information Center
Niess, Margaret L.
1993-01-01
Presents a unit developed by the 1991 Oregon Mathematics Teachers of Middle School project in which students investigate the average temperature, precipitation, and snowfall in their town using spreadsheets and graphing packages. Students compare the averages over a period of 30 years to a particular year. (MDH)
Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa
2014-01-01
Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students' apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students' understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students' inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students' biology learning. PMID:24591504
Mathematical thinking: challenging prospective teachers to do more than `talk the talk'
NASA Astrophysics Data System (ADS)
Prendergast, Mark; Johnson, Patrick; Fitzmaurice, Olivia; Liston, Miriam; O'Keeffe, Lisa; O'Meara, Niamh
2014-07-01
This paper reports on a research project which aims to improve prospective mathematics teachers' relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of the mathematics they are required to teach at second level. This paper describes a course designed by the authors to challenge such beliefs and encourage students to confront and possibly transform their ideas about teaching, while simultaneously improving their subject knowledge and relational understanding. Both content and pedagogical considerations for teaching second-level mathematics are integrated at all times. The course was originally optional and was piloted and implemented in a third-level Irish university. Apart from offering an insight into the design considerations when creating a course of this type, this paper also addresses some of the challenges faced when evaluating such a course. Overall participant feedback on the course is positive and both qualitative and quantitative results are provided to support this and also highlight the efficacy of the programme.
Increasing Cognitive Inhibition with a Difficult Prior Task: Implications for Mathematical Thinking
ERIC Educational Resources Information Center
Attridge, Nina; Inglis, Matthew
2015-01-01
Dual-process theories posit two distinct types of cognitive processing: Type 1, which does not use working memory making it fast and automatic, and Type 2, which does use working memory making it slow and effortful. Mathematics often relies on the inhibition of pervasive Type 1 processing to apply new skills or knowledge that require Type 2…
Seeing Relationships: Using Spatial Thinking to Teach Science, Mathematics, and Social Studies
ERIC Educational Resources Information Center
Newcombe, Nora S.
2013-01-01
The author discusses four specific strategies for enhancing and supporting the spatial aspects of the science, mathematics, and social studies curricula. However, these four strategies are examples of what can be done, not an exhaustive list. The overarching concept is to embrace the spatial visualizations used for discovery and communication in…
The School Library: A Space for Critical Thinking about Data and Mathematical Questions
ERIC Educational Resources Information Center
Kimmel, Sue C.
2012-01-01
Which potato chip is healthiest: (1) regular; (2) baked; or (3) sour cream and onion? This problem requires critical and numerical skills in order to read and compare nutrition labels. The question has applications in mathematics and science classrooms but also in teachers' lounges and school cafeterias. It is a problem that addresses the five…
ERIC Educational Resources Information Center
de Freitas, Elizabeth
2013-01-01
The primary aim of this article is to bring the work of Deleuze and Guattari to bear on the question of communication in the classroom. I focus on the mathematics classroom, where agency and subjectivity are highly regulated by the rituals of the discipline, and where neoliberal psychological frameworks continue to dominate theories of teaching…
ERIC Educational Resources Information Center
Sriraman, Bharath
2004-01-01
This article is the sequel to the use of "Flatland" with beginning algebra students reported in Sriraman (2003). The use of "Flatland" with beginning algebra students resulted in the positive outcomes of cultivating critical thinking in the students as well as providing the teacher with the context necessary to introduce sophisticated mathematical…
NASA Astrophysics Data System (ADS)
Bitner, Betty L.
To test the hypothesis that formal operational reasoning modes are predictors of critical thinking abilities and grades assigned by teachers in science and mathematics, in September 1986 the Group Assessment of Logical Thinking (GALT) and in December 1986 the Watson-Glaser Critical Thinking Appraisal (WGCTA) were administered to 101 rural students in Grades 9 through 12. The grades assigned by teachers were collected in May 1987. Construct and criterion-related validities and internal-consistency reliability using Cronbach's alpha method were established on the GALT. On the WGCTA, content and construct validities and internal consistency reliability using the split-half procedure, coefficient of stability, and coefficient of equivalence were established. The five formal operational reasoning modes in the GALT were found to be significant predictors of critical thinking abilities and grades assigned by teachers in science and mathematics. The variance in the five critical thinking abilities attributable to the five formal operational reasoning modes ranged between 28% and 70%. The five formal operational reasoning modes explained 29% of the variance in mathematics achievement and 62% of the variance in science achievement.
ERIC Educational Resources Information Center
Korkmaz, Özgen
2016-01-01
The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and…
ERIC Educational Resources Information Center
Cai, Jinfa, And Others
1996-01-01
Presents a conceptual framework for analyzing students' mathematical understanding, reasoning, problem solving, and communication. Analyses of student responses indicated that the tasks appear to measure the complex thinking and reasoning processes that they were designed to assess. Concludes that the QUASAR assessment tasks can capture changes in…
Advanced Mathematics. Training Module 1.303.3.77.
ERIC Educational Resources Information Center
Kirkwood Community Coll., Cedar Rapids, IA.
This document is an instructional module prepared in objective form for use by an instructor familiar with mathematics as applied to water and wastewater treatment plant operation. Included are objectives, instructor guides and student handouts. This is the third level of a three module series and is concerned with statistics, total head, steady…
Block Scheduling and Advanced Placement Mathematics: When Tradition and Reform Collide.
ERIC Educational Resources Information Center
Howard, Elizabeth
1997-01-01
This case study reflects block scheduling's effects on advanced-placement mathematics courses of one veteran teacher tracking personal progress since 1989. Block scheduling began in 1994, creating problems for the teacher, whose resistance to the reform was based on declining advanced-placement scores. Teacher attitude and insufficient…
Innovations in Science and Mathematics Education: Advanced Designs for Technologies of Learning.
ERIC Educational Resources Information Center
Jacobson, Michael J., Ed.; Kozma, Robert B., Ed.
This collection of essays consists of current work that addresses the challenge not just to put the newest technologies in schools, but to identify advanced ways to design and use these new technologies to advance learning. These essays are intended for science and mathematics educators, educational and cognitive researchers, instructional…
The Influence of Applied STEM Coursetaking on Advanced Mathematics and Science Coursetaking
ERIC Educational Resources Information Center
Gottfried, Michael A.
2015-01-01
Advanced mathematics and science course taking is critical in building the foundation for students to advance through the STEM pathway-from high school to college to career. To invigorate students' persistence in STEM fields, high schools have been introducing applied STEM courses into the curriculum as a way to reinforce concepts learned in…
Using the Common Core State Standards for Mathematics with Gifted and Advanced Learners
ERIC Educational Resources Information Center
Johnsen, Susan K., Ed.; Sheffield, Linda J., Ed.
2012-01-01
"Using the Common Core State Standards for Mathematics With Gifted and Advanced Learners" provides teachers and administrators examples and strategies to implement the new Common Core State Standards (CCSS) with advanced learners at all stages of development in K-12 schools. The book describes--and demonstrates with specific examples from the…
ERIC Educational Resources Information Center
Martin, Stu; Sharp, Janet; Zachary, Loren
2004-01-01
Most people think that engineering and mathematics go hand in hand. To many, being an engineer means manipulating equations and calculating measurements to design and build structures of all kinds. And they are right. Engineering does involve a great deal of mathematics. But, building structures to withstand certain environmental conditions or…
2016-01-01
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930
Recall of Advance Organizers as Part of Mathematics Instruction.
ERIC Educational Resources Information Center
Bright, George W.
This study was performed in order to test the author's notion that advance organizers operate because (1) they provide stable anchorage for concepts to be learned and (2) in order to operate they must be relatable by the student to the new material. To test this hypothesis the author constructed materials for each of ten treatments as defined by…
Project ACT (A Project to Advance Critical Thinking). Project Termination Report.
ERIC Educational Resources Information Center
Ahn, Chang-Yil
The goal of this project was to develop a sequential program for the development of critical thinking skills that could be extended to all the elementary schools in the school district. The major objectives were: (1) to enhance teachers' ability to think critically, practice in their classrooms teaching strategies to develop pupils' thinking, and…
NASA Astrophysics Data System (ADS)
Fiondella, F.; Davi, N. K.; Wattenberg, F.; Pringle, P. T.; Greidanus, I.; Oelkers, R.
2015-12-01
Tree-ring science provides an engaging, intuitive, and relevant entryway into understanding both climate change and environmental research. It also sheds light on the process of science--from inspiration, to fieldwork, to analysis, to publishing and communication. The basic premise of dendrochronology is that annual rings reflect year-to-year environmental conditions and that by studying long-lived trees we can learn about environmental and climatic conditions going back hundreds to thousands of years. Conceptually, this makes tree-ring studies accessible to students and faculty for a number of reasons. First, in order to collect their data, dendrochronologists often launch expeditions to stunningly picturesque and remote places in search of long-lived, climate sensitive trees. The exciting stories and images that scientists bring back from the field can help connect students to the studies, their motivation, and the data collected. Second, tree rings can be more easily explained as a proxy for climate than ice cores, speleothems and others. Most people have prior knowledge about trees and annual growth rings. It is even possible, for example, for non-expert audiences to see climate variability through time with the naked eye by looking at climate-sensitive tree cores. Third, tree rings are interdisciplinary and illustrate the interplay between the mathematical sciences, the biological sciences, and the geosciences—that is, they show that the biosphere is a fundamental component of the Earth system. Here, we present online, multi-media learning modules for undergraduates that introduce students to several foundational studies in tree-ring science. These include evaluating tree-ring cores from ancient hemlock trees growing on a talus slope in New Paltz, NY to learn about drought in the Northeastern US, evaluating long-term streamflow and drought of the Colorado River based on tree-ring records, and using tree-ring dating techniques to develop construction
ERIC Educational Resources Information Center
Grinstead, Mary L.
2013-01-01
This study explores the relationship between specific advanced mathematics courses and college readiness (as determined by ACT score). The ACT organization has found a consistent relationship between taking a minimum core number of mathematics courses and higher ACT scores (mathematics and composite) (ACT, Inc., 2012c). However, the extent to…
ERIC Educational Resources Information Center
Niess, Margaret; Gillow-Wiles, Henry
2013-01-01
This primarily online Master's degree program focused on advancing K-8 teachers' interdisciplinary mathematical and science content knowledge while integrating appropriate digital technologies as learning and teaching tools. The mixed-method, interpretive study examined in-service teachers' technological, pedagogical, and content knowledge (TPACK)…
ERIC Educational Resources Information Center
Davis, Cinda-Sue; And Others
This volume includes 10 reports that present findings and recommendations for advancing women in science, mathematics and engineering. Critical issues facing women in these disciplines are addressed, including demographic myths and realities at various educational levels; the educational pipeline for girls and women; involvement in education and…
ERIC Educational Resources Information Center
DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.
2015-01-01
This research examined the perspectives of teachers of students with visual impairments (TVIs) regarding the use and effectiveness of electronic assistive technology (EAT) purported to assist students who are blind in advanced mathematics subjects. The data for this study were collected via an online survey distributed to a convenience sample of…
ERIC Educational Resources Information Center
Hargreaves, Melanie; Homer, Matt; Swinnerton, Bronwen
2008-01-01
This paper explores gender differential performance in "gifted and talented" 9- and 13-year-olds in a mathematics assessment in England. Boys' and girls' attitudes to mathematics and their views about which gender is better at mathematics are also considered. The study employs the use of a matched sample of boys and girls so that school, age and…
Proceedings: Workshop on advanced mathematics and computer science for power systems analysis
Esselman, W.H.; Iveson, R.H. )
1991-08-01
The Mathematics and Computer Workshop on Power System Analysis was held February 21--22, 1989, in Palo Alto, California. The workshop was the first in a series sponsored by EPRI's Office of Exploratory Research as part of its effort to develop ways in which recent advances in mathematics and computer science can be applied to the problems of the electric utility industry. The purpose of this workshop was to identify research objectives in the field of advanced computational algorithms needed for the application of advanced parallel processing architecture to problems of power system control and operation. Approximately 35 participants heard six presentations on power flow problems, transient stability, power system control, electromagnetic transients, user-machine interfaces, and database management. In the discussions that followed, participants identified five areas warranting further investigation: system load flow analysis, transient power and voltage analysis, structural instability and bifurcation, control systems design, and proximity to instability. 63 refs.
ERIC Educational Resources Information Center
Sheldrake, Richard; Mujtaba, Tamjid; Reiss, Michael J.
2015-01-01
Increasing the number of students who study mathematics once it is no longer compulsory remains a priority for England. A longitudinal cohort from England (1085 students) was surveyed at Years 10 and 12. Students' self-beliefs of ability influenced their GCSE mathematics grades and their intended and actual mathematics subject-choices; the degree…
ERIC Educational Resources Information Center
Owens, Kay
2014-01-01
Identity as a mathematics teacher is enhanced when a teacher explores the cultural setting of their mathematics. The reports of projects that link culture and mathematics were analysed to explore the impact of sociocultural situations together with affective and cognitive aspects of self-regulation on identity. The reports were written by…
ERIC Educational Resources Information Center
Tularam, Gurudeo Anand; Hulsman, Kees
2015-01-01
This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The importance now placed on applied mathematics, however, means that students need to gain more conceptual and quantitative knowledge of mathematics in not…
ERIC Educational Resources Information Center
Hoffman, Bobby
2010-01-01
This study investigated the role of self-efficacy beliefs, mathematics anxiety, and working memory capacity in problem-solving accuracy, response time, and efficiency (the ratio of problem-solving accuracy to response time). Pre-service teachers completed a mathematics anxiety inventory measuring cognitive and affective dispositions for…
Non-Traditional Socio-Mathematical Norms in Undergraduate Real Analysis
ERIC Educational Resources Information Center
Dawkins, Paul Christian
2009-01-01
This study builds upon the framework of classroom norms (Cobb, Wood, & Yackel, 1993) and socio-mathematical norms (Cobb & Yackel, 1996) to understand how non-traditional socio-mathematical norms influence student reasoning and transitions to advanced mathematical thinking in undergraduate real analysis. The research involves a qualitative…
ERIC Educational Resources Information Center
Githua, Bernard N.; Nyabwa, Rachel Angela
2008-01-01
Students have continued to perform poorly in KCSE examinations in certain mathematics topics taught in secondary schools in Kenya. One such topic is commercial arithmetic. Successful teaching of mathematics depends partly on correct use of teaching methods in classroom settings. This study sought to examine how the use of advance organisers during…
Schissel, D.P.
1996-08-01
This report discusses advancing precollege science and mathematics education in San Diego Count. Described in this report are: curriculum and teacher development; pre-tour material; facility tour; student workbook; evaluation and assessment; and internet access.
ERIC Educational Resources Information Center
Boylan, Mark
2010-01-01
Actor-network theory is a way of describing and understanding the complexity of social change. This article explores its relevance to understanding teacher change in mathematics education by considering a single teacher change narrative. This is centred on a veteran teacher of mathematics who participated in a teacher led,…
ERIC Educational Resources Information Center
Blanton, Maria; Levi, Linda; Crites, Terry; Dougherty, Barbara; Zbiek, Rose Mary
2011-01-01
Like algebra at any level, early algebra is a way to explore, analyze, represent, and generalize mathematical ideas and relationships. This book shows that children can and do engage in generalizing about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential…
ERIC Educational Resources Information Center
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
ERIC Educational Resources Information Center
Borthwick, Alison
2012-01-01
What pupils think about mathematics often features in discussion between mathematics educators. But, how often is "what learners think about their mathematics lessons" a feature of enquiry? It could be a "high risk" strategy to garner honest comment that relates to the "classroom experience". Notions of "risk" apart, the process of collecting data…
Preschoolers' Thinking during Block Play
ERIC Educational Resources Information Center
Piccolo, Diana L.; Test, Joan
2010-01-01
Children build foundations for mathematical thinking in early play and exploration. During the preschool years, children enjoy exploring mathematical concepts--such as patterns, shape, spatial relationships, and measurement--leading them to spontaneously engage in mathematical thinking during play. Block play is one common example that engages…
ERIC Educational Resources Information Center
Weiss, Michael K.; Moore-Russo, Deborah
2012-01-01
What does it mean to think like a mathematician? One of the great paradoxes of mathematics education is that, although mathematics teachers are immersed in mathematical work every day of their professional lives, most of them nevertheless have little experience with the kind of work that research mathematicians do. Their ideas of what doing…
Not Available
1990-12-01
The issue of global warming and related climatic changes from increasing concentrations of greenhouse gases in the atmosphere has received prominent attention during the past few years. The Computer Hardware, Advanced Mathematics, and Model Physics (CHAMMP) Climate Modeling Program is designed to contribute directly to this rapid improvement. The goal of the CHAMMP Climate Modeling Program is to develop, verify, and apply a new generation of climate models within a coordinated framework that incorporates the best available scientific and numerical approaches to represent physical, biogeochemical, and ecological processes, that fully utilizes the hardware and software capabilities of new computer architectures, that probes the limits of climate predictability, and finally that can be used to address the challenging problem of understanding the greenhouse climate issue through the ability of the models to simulate time-dependent climatic changes over extended times and with regional resolution.
Mentoring for Administrative Advancement: A Study of What Mentors Do and Think.
ERIC Educational Resources Information Center
Mertz, Norma T.; And Others
Despite a profusion of mentoring publications, much information on the subject is opinion-based, retrospective, and reflective. In examining mentoring for career advancement, researchers have focused largely on proteges' experience. This study examined mentoring as a mechanism for career advancement, focusing on the mentor's perspective and…
NASA Astrophysics Data System (ADS)
Keller, Stacy Kathryn
This study examined how intermediate elementary students' mathematics and science background knowledge affected their interpretation of line graphs and how their interpretations were affected by graph question levels. A purposive sample of 14 6th-grade students engaged in think aloud interviews (Ericsson & Simon, 1993) while completing an excerpted Test of Graphing in Science (TOGS) (McKenzie & Padilla, 1986). Hand gestures were video recorded. Student performance on the TOGS was assessed using an assessment rubric created from previously cited factors affecting students' graphing ability. Factors were categorized using Bertin's (1983) three graph question levels. The assessment rubric was validated by Padilla and a veteran mathematics and science teacher. Observational notes were also collected. Data were analyzed using Roth and Bowen's semiotic process of reading graphs (2001). Key findings from this analysis included differences in the use of heuristics, self-generated questions, science knowledge, and self-motivation. Students with higher prior achievement used a greater number and variety of heuristics and more often chose appropriate heuristics. They also monitored their understanding of the question and the adequacy of their strategy and answer by asking themselves questions. Most used their science knowledge spontaneously to check their understanding of the question and the adequacy of their answers. Students with lower and moderate prior achievement favored one heuristic even when it was not useful for answering the question and rarely asked their own questions. In some cases, if students with lower prior achievement had thought about their answers in the context of their science knowledge, they would have been able to recognize their errors. One student with lower prior achievement motivated herself when she thought the questions were too difficult. In addition, students answered the TOGS in one of three ways: as if they were mathematics word problems
NASA Astrophysics Data System (ADS)
Leung, Shukkwan S.; Silver, Edward A.
1997-05-01
A Test of Arithmetic Problem Posing was developed by the authors to examine the arithmetic problem-posing behaviours of sixty-three prospective elementary school teachers. Results of analysis were then used to examine task format (i.e., the presence or absence of specific numerical information) on subjects' problem posing and the relationship between subjects' problem posing and their mathematics knowledge and verbal creativity. The major findings were that the test effectively evaluated arithmetic problem posing, and that most subjects were able to pose solvable and complex problems. In addition, problem-posing performance was better when the task contained specific numerical information than when it did not, and that problem-posing performance was significantly related to mathematical knowledge but not to verbal creativity.
NASA Astrophysics Data System (ADS)
Frankel, Felice
2010-02-01
The judgment and decision-making required to render science visual clarifies thinking. One must decide on a hierarchy of information--what must be included and what might be left out? What is the main point of the visual? Just as in writing an article or responding to an essay question, we must understand and then plan what we want to ``say'' in a drawing or other forms of representation. And since a visual representation of a scientific concept (or data) is a re-presentation, and not the thing itself, interpretation or translation is involved. The process tends to transcend barriers of linguistic facility and educational background; it attracts and communicates students and teachers of all backgrounds, where other methods intimidate. The rendered images are, in essence More Than Pretty Pictures. )
Mathematical Modeling of Food Supply for Long Term Space Missions Using Advanced Life Support
NASA Technical Reports Server (NTRS)
Cruthirds, John E.
2003-01-01
A habitat for long duration missions which utilizes Advanced Life Support (ALS), the Bioregenerative Planetary Life Support Systems Test Complex (BIO-Plex), is currently being built at JSC. In this system all consumables will be recycled and reused. In support of this effort, a menu is being planned utilizing ALS crops that will meet nutritional and psychological requirements. The need exists in the food system to identify specific physical quantities that define life support systems from an analysis and modeling perspective. Once these quantities are defined, they need to be fed into a mathematical model that takes into consideration other systems in the BIO-Plex. This model, if successful, will be used to understand the impacts of changes in the food system on the other systems and vice versa. The Equivalent System Mass (ESM) metric has been used to describe systems and subsystems, including the food system options, in terms of the single parameter, mass. There is concern that this approach might not adequately address the important issues of food quality and psychological impact on crew morale of a supply of fiesh food items. In fact, the mass of food can also depend on the quality of the food. This summer faculty fellow project will involve creating an appropriate mathematical model for the food plan developed by the Food Processing System for BIO-Plex. The desired outcome of this work will be a quantitative model that can be applied to the various options of supplying food on long-term space missions.
Intuitive vs Analytical Thinking: Four Perspectives
ERIC Educational Resources Information Center
Leron, Uri; Hazzan, Orit
2009-01-01
This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives--mathematics, mathematics education, cognitive psychology, and evolutionary psychology--each offering a different view on mathematical thinking and learning and, in particular, on the…
In-Situ Assays Using a New Advanced Mathematical Algorithm - 12400
Oginni, B.M.; Bronson, F.L.; Field, M.B.; Lamontagne, J.; LeBlanc, P.J.; Morris, K.E.; Mueller, W.F.; Atrashkevich, V.
2012-07-01
Current mathematical efficiency modeling software for in-situ counting, such as the commercially available In-Situ Object Calibration Software (ISOCS), typically allows the description of measurement geometries via a list of well-defined templates which describe regular objects, such as boxes, cylinder, or spheres. While for many situations, these regular objects are sufficient to describe the measurement conditions, there are occasions in which a more detailed model is desired. We have developed a new all-purpose geometry template that can extend the flexibility of current ISOCS templates. This new template still utilizes the same advanced mathematical algorithms as current templates, but allows the extension to a multitude of shapes and objects that can be placed at any location and even combined. In addition, detectors can be placed anywhere and aimed at any location within the measurement scene. Several applications of this algorithm to in-situ waste assay measurements, as well as, validations of this template using Monte Carlo calculations and experimental measurements are studied. Presented in this paper is a new template of the mathematical algorithms for evaluating efficiencies. This new template combines all the advantages of the ISOCS and it allows the use of very complex geometries, it also allows stacking of geometries on one another in the same measurement scene and it allows the detector to be placed anywhere in the measurement scene and pointing in any direction. We have shown that the template compares well with the previous ISOCS software within the limit of convergence of the code, and also compare well with the MCNPX and measured data within the joint uncertainties for the code and the data. The new template agrees with ISOCS to within 1.5% at all energies. It agrees with the MCNPX to within 10% at all energies and it agrees with most geometries within 5%. It finally agrees with measured data to within 10%. This mathematical algorithm can now be
ERIC Educational Resources Information Center
Parks, David J.
2016-01-01
The tallest hurdle in completing a doctoral degree is the dissertation, which continues to be the primary capstone experience for the degree. Dissertation research is a mystery to many considering an advanced degree and can be intimidating to those who are unfamiliar with the nature of universities and doctoral research. In this report, the author…
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
This text is the fourth of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This text begins with a brief discussion of quadratic equations which motivates the…
ERIC Educational Resources Information Center
Richardson, Sandra
2009-01-01
This article describes experiences from a professional development project designed to prepare in-service eighth-grade mathematics teachers to develop, explore, and advance technological pedagogical content knowledge (TPCK) in the teaching and learning of Algebra I. This article describes the process of the participating teachers' mathematical…
ERIC Educational Resources Information Center
Roschelle, Jeremy; Shechtman, Nicole; Tatar, Deborah; Hegedus, Stephen; Hopkins, Bill; Empson, Susan; Knudsen, Jennifer; Gallagher, Lawrence P.
2010-01-01
The authors present three studies (two randomized controlled experiments and one embedded quasi-experiment) designed to evaluate the impact of replacement units targeting student learning of advanced middle school mathematics. The studies evaluated the SimCalc approach, which integrates an interactive representational technology, paper curriculum,…
ERIC Educational Resources Information Center
Scarborough, Jule Dee
2004-01-01
This document (book) reports on the Strategic Alliance to Advance Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level, funded by National Science Foundation. It was a collaborative partnership involving the Rockford Public Schools, Rock Valley College, and Northern Illinois…
The Role of Symbols in Mathematical Communication: The Case of the Limit Notation
ERIC Educational Resources Information Center
Güçler, Beste
2014-01-01
Symbols play crucial roles in advanced mathematical thinking by providing flexibility and reducing cognitive load but they often have a dual nature since they can signify both processes and objects of mathematics. The limit notation reflects such duality and presents challenges for students. This study uses a discursive approach to explore how one…
ERIC Educational Resources Information Center
Ko, Yi-Yin; Knuth, Eric
2009-01-01
In advanced mathematical thinking, proving and refuting are crucial abilities to demonstrate whether and why a proposition is true or false. Learning proofs and counterexamples within the domain of continuous functions is important because students encounter continuous functions in many mathematics courses. Recently, a growing number of studies…
ERIC Educational Resources Information Center
Aneckstein, Laura; Baird, Andrea; Butler, Margaret; Chambers, David; Johnson, Wanda; Kraus, Rebecca; Mann, Eric; Trost, Tami; Zalokar, Nadja; Zieseniss, Mireille
This report focuses on the Office for Civil Rights' (OCR's) activities relating to Title IX and advanced mathematics, science, and technology education for girls. It examines some of the barriers and inequities that undermine girls' opportunities to choose college majors and enter careers in the advanced mathematics, science, and technology…
Computational thinking and thinking about computing
Wing, Jeannette M.
2008-01-01
Computational thinking will influence everyone in every field of endeavour. This vision poses a new educational challenge for our society, especially for our children. In thinking about computing, we need to be attuned to the three drivers of our field: science, technology and society. Accelerating technological advances and monumental societal demands force us to revisit the most basic scientific questions of computing. PMID:18672462
2014-01-01
Background Of the three million newborns that die each year, Uganda ranks fifth highest in neonatal mortality rates, with 43,000 neonatal deaths each year. Despite child survival and safe motherhood programmes towards reducing child mortality, insufficient attention has been given to this critical first month of life. There is urgent need to innovatively employ alternative solutions that take into account the intricate complexities of neonatal health and the health systems. In this paper, we set out to empirically contribute to understanding the causes of the stagnating neonatal mortality by applying a systems thinking approach to explore the dynamics arising from the neonatal health complexity and non-linearity and its interplay with health systems factors, using Uganda as a case study. Methods Literature reviews and interviews were conducted in two divisions of Kampala district with high neonatal mortality rates with mothers at antenatal clinics and at home, village health workers, community leaders, healthcare decision and policy makers, and frontline health workers from both public and private health facilities. Data analysis and brainstorming sessions were used to develop causal loop diagrams (CLDs) depicting the causes of neonatal mortality, which were validated by local and international stakeholders. Results We developed two CLDs for demand and supply side issues, depicting the range of factors associated with neonatal mortality such as maternal health, level of awareness of maternal and newborn health, and availability and quality of health services, among others. Further, the reinforcing and balancing feedback loops that resulted from this complexity were also examined. The potential high leverage points include special gender considerations to ensure that girls receive essential education, thereby increasing maternal literacy rates, improved socioeconomic status enabling mothers to keep healthy and utilise health services, improved supervision, and
Kasturirangan, Rajesh
2008-01-01
Philosophers as well lay people often think of beliefs as psychological states with dubious epistemic properties. Beliefs are conceptualized as unregulated conceptual structures, for the most part hypothetical and often fanciful or deluded. Thinking and reasoning on the other hand are seen as rational activities regulated by rules and governed by norms. Computational modeling of the mind has focused on rule-governed behavior, ultimately trying to reduce them to rules of logic. What if thinking is less like reasoning and more like believing? I argue that the classical model of thought as rational is mistaken and that thinking is fundamentally constituted by believing. This new approach forces us to re-evaluate classical epistemic concepts like "truth", "justification" etc. Furthermore, if thinking is believing, then it is not clear how thoughts can be modeled computationally. We need new mathematical ideas to model thought, ideas that are quite different from traditional logic-based mathematical structures. PMID:18166389
Analyzing the Teaching of Advanced Mathematics Courses via the Enacted Example Space
ERIC Educational Resources Information Center
Fukawa-Connelly, Timothy Patrick; Newton, Charlene
2014-01-01
Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in "Educational Studies in Mathematics" 69:77-79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the…
Students as Mathematics Consultants
ERIC Educational Resources Information Center
Jensen, Jennifer L.
2013-01-01
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
Algebraic Thinking: A Problem Solving Approach
ERIC Educational Resources Information Center
Windsor, Will
2010-01-01
Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…
Zlotnicki, Jason P.; Geeslin, Andrew G.; Murray, Iain R.; Petrigliano, Frank A.; LaPrade, Robert F.; Mann, Barton J.; Musahl, Volker
2016-01-01
Focal chondral defects of the articular surface are a common occurrence in the field of orthopaedics. These isolated cartilage injuries, if not repaired surgically with restoration of articular congruency, may have a high rate of progression to posttraumatic osteoarthritis, resulting in significant morbidity and loss of function in the young, active patient. Both isolated and global joint disease are a difficult entity to treat in the clinical setting given the high amount of stress on weightbearing joints and the limited healing potential of native articular cartilage. Recently, clinical interest has focused on the use of biologically active compounds and surgical techniques to regenerate native cartilage to the articular surface, with the goal of restoring normal joint health and overall function. This article presents a review of the current biologic therapies, as discussed at the 2015 American Orthopaedic Society for Sports Medicine (AOSSM) Biologics Think Tank, that are used in the treatment of focal cartilage deficiencies. For each of these emerging therapies, the theories for application, the present clinical evidence, and specific areas for future research are explored, with focus on the barriers currently faced by clinicians in advancing the success of these therapies in the clinical setting. PMID:27123466
ERIC Educational Resources Information Center
Parker, Sarah J.
The teaching of decision-making, problem-solving, and higher-order thinking skills is necessary to ensure adaptability to our world of accelerated change. Living skills in the technology and information age will include the understanding and application of higher level thinking skills, which will be the educational "basics" of tomorrow. Although…
ERIC Educational Resources Information Center
Fuson, Karen C.
2009-01-01
This article provides an overview of some perspectives about special issues in classroom mathematical teaching and learning that have stemmed from the huge explosion of research in children's mathematical thinking stimulated by Piaget. It concentrates on issues that are particularly important for less-advanced learners and for those who might be…
ERIC Educational Resources Information Center
Alsaeed, Maha Saad
2012-01-01
Teachers in Saudi Arabia are attempting to advance their teaching in mathematics to address specific reforms by the Ministry of Education. Saudi teachers must improve their students' thinking through engagement in problem solving. This qualitative study investigated how teachers use knowledge of student mathematical learning and how they…
Students in Rural Schools Have Limited Access to Advanced Mathematics Courses. Issue Brief No. 7
ERIC Educational Resources Information Center
Graham, Suzanne E.
2009-01-01
This Carsey brief reveals that students in rural areas and small towns have less access to higher-level mathematics courses than students in urban settings, which results in serious educational consequences, including lower scores on assessment tests and fewer qualified students entering science, technology, engineering, and mathematics (STEM) job…
ERIC Educational Resources Information Center
Hillman, Thomas
2014-01-01
This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…
METSAT: Advanced Microwave Sounding Unit-A2 (AMSU-A2) structural mathematical model
NASA Technical Reports Server (NTRS)
Ely, Wayne
1995-01-01
This plan describes the Structural Mathematical Model of the METSAT AMSU-A2 instrument. The model is used to verify the structural adequacy of the AMSU-A2 instrument for the specified loading environments.
ERIC Educational Resources Information Center
Wood, William B.
2002-01-01
A recently released National Research Council (NRC) report, "Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools", evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study,…
ERIC Educational Resources Information Center
Walshaw, Margaret
2014-01-01
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
The Creative Mathematics Teacher.
ERIC Educational Resources Information Center
Ediger, Marlow
The creative mathematics teacher who has love and enthusiasm for mathematics as a curriculum area should be in great demand in all schools. This paper discusses the characteristics of creative mathematics teachers, including those who guide students to engage in divergent thinking; have learners do much creative writing; and integrate creative…
Zeros and Ones in Advanced Mathematics: Transcending the Intimacy of Number.
ERIC Educational Resources Information Center
Nardi, Elena
2000-01-01
Examines how components of the concept of function (variable, domain, and range) and the process-object duality in its nature emerge as highly relevant to student learning in various mathematical contexts related to linear and abstract algebra. (Contains 22 references.) (ASK)
Clickers and Classroom Voting in a Transition to Advanced Mathematics Course
ERIC Educational Resources Information Center
Lockard, Shannon R.; Metcalf, Rebecca C.
2015-01-01
Clickers and classroom voting are used across a number of disciplines in a variety of institutions. There are several papers that describe the use of clickers in mathematics classrooms such as precalculus, calculus, statistics, and even differential equations. This paper describes a method of incorporating clickers and classroom voting in a…
ERIC Educational Resources Information Center
Montiel, Mariana; Bhatti, Uzma
2010-01-01
This article presents an overview of some issues that were confronted when delivering an online second Linear Algebra course (assuming a previous Introductory Linear Algebra course) to graduate students enrolled in a Secondary Mathematics Education program. The focus is on performance in one particular aspect of the course: "change of basis" and…
ERIC Educational Resources Information Center
Leddy, Mark H.
2010-01-01
Americans with disabilities are underemployed in science, technology, engineering and mathematics (STEM) at higher rates than their nondisabled peers. This article provides an overview of the National science Foundation's Research in Disabilities Education (RDE) program, of technology use by students with disabilities (SWD) in STEM, and of…
Learner-Centered Strategies and Advanced Mathematics: A Study of Students' Perspectives
ERIC Educational Resources Information Center
Ortiz-Robinson, Norma L.; Ellington, Aimee J.
2009-01-01
A number of learner-centered strategies were implemented during a two-semester course in real analysis that is traditionally taught in lecture format. We seek to understand the role that these strategies can have in this proof-intensive theoretical mathematics classroom and the perceived benefits by the students. Although learner-centered…
ERIC Educational Resources Information Center
Rasmussen, Ann Marie
2011-01-01
This article describes an undergraduate, German-language course that aimed to improve students' language skills, critical thinking, and declarative knowledge of German history and culture by studying multiple manifestations of the legend of Siegfried the Dragonslayer. The course used web-based e-learning tools to address two major learning…
ERIC Educational Resources Information Center
Izzo, Robert T.
2012-01-01
Researchers have explored teachers' differential expectations for minority and low-income students in an attempt to explain the achievement gap (Weinstein, 2002). New research uses models of deficit and dynamic thinking to reconceptualize and investigate teacher expectations. This study employs a framework that encompasses deficit and dynamic…
ERIC Educational Resources Information Center
Gough, Deborah
1991-01-01
This document summarizes five studies that offer insight into the nature of higher-order thinking skills and the most effective methods for teaching them to students. The reviews outline the conclusions, definitions, recommendations, specific methods of teaching, instructional strategies, and programs detailed in the documents themselves.…
ERIC Educational Resources Information Center
Callison, Daniel
1998-01-01
Distinguishes between critical and creative thinking and discusses critical-thinking in relation to modern instructional programs and information literacy. Outlines goals in critical-thinking curriculum, critical thinking skills (student disposition, interpretation, analysis, evaluation, inference, presenting argument, and reflection), and…
NASA Astrophysics Data System (ADS)
Perdigão, Rui A. P.
2016-04-01
The fundamental stochastic-dynamic coevolution laws governing complex coevolutionary systems are introduced in a mathematical physics framework formally unifying nonlinear stochastic physics with fundamental deterministic interaction laws among spatiotemporally distributed processes. The methodological developments are then used to shed light onto fundamental interactions underlying complex spatiotemporal behaviour and emergence in multiscale hydroclimate dynamics. For this purpose, a mathematical physics framework is presented predicting evolving distributions of hydrologic quantities under nonlinearly coevolving geophysical processes. The functional formulation is grounded on first principles regulating the dynamics of each system constituent and their interactions, therefore its applicability is general and data-independent, not requiring local calibrations. Moreover, it enables the dynamical estimation of hydroclimatic variations in space and time from knowledge at different spatiotemporal conditions, along with the associated uncertainties. This paves the way for a robust physically based prediction of hydroclimatic changes in unsupervised areas (e.g. ungauged basins). Validation is achieved by producing, with the mathematical physics framework, a comprehensive spatiotemporal legacy consistent with the observed distributions along with their statistic-dynamic relations. The similarity between simulated and observed distributions is further assessed with novel robust nonlinear information-theoretic diagnostics. The present study brings to light emerging signatures of structural change in hydroclimate dynamics arising from nonlinear synergies across multiple spatiotemporal scales, and contributes to a better dynamical understanding and prediction of spatiotemporal regimes, transitions, structural changes and extremes in complex coevolutionary systems. This study further sheds light onto a diversity of emerging properties from harmonic to hyper-chaotic in general
Ni, Bing-Jie; Yuan, Zhiguo
2015-12-15
Nitrous oxide (N2O) can be emitted from wastewater treatment contributing to its greenhouse gas footprint significantly. Mathematical modeling of N2O emissions is of great importance toward the understanding and reduction of the environmental impact of wastewater treatment systems. This article reviews the current status of the modeling of N2O emissions from wastewater treatment. The existing mathematical models describing all the known microbial pathways for N2O production are reviewed and discussed. These included N2O production by ammonia-oxidizing bacteria (AOB) through the hydroxylamine oxidation pathway and the AOB denitrification pathway, N2O production by heterotrophic denitrifiers through the denitrification pathway, and the integration of these pathways in single N2O models. The calibration and validation of these models using lab-scale and full-scale experimental data is also reviewed. We conclude that the mathematical modeling of N2O production, while is still being enhanced supported by new knowledge development, has reached a maturity that facilitates the estimation of site-specific N2O emissions and the development of mitigation strategies for a wastewater treatment plant taking into the specific design and operational conditions of the plant. PMID:26451976
Current Advances in Mathematical Modeling of Anti-Cancer Drug Penetration into Tumor Tissues
Kim, MunJu; Gillies, Robert J.; Rejniak, Katarzyna A.
2013-01-01
Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence. PMID:24303366
ERIC Educational Resources Information Center
Gough, John
2008-01-01
It is potentially arresting when a mathematical implication is offered in a non-mathematical book. This author contends that students are encouraged to develop mathematical thinking when they read mathematical challenges in books. Aspects of books such as time-lines, historical relationships, maps, journeys, cause-and-affect, deductive inference,…
Thinking Critically about Critical Thinking
ERIC Educational Resources Information Center
Mulnix, Jennifer Wilson
2012-01-01
As a philosophy professor, one of my central goals is to teach students to think critically. However, one difficulty with determining whether critical thinking can be taught, or even measured, is that there is widespread disagreement over what critical thinking actually is. Here, I reflect on several conceptions of critical thinking, subjecting…
Algebraic Thinking in Adult Education
ERIC Educational Resources Information Center
Manly, Myrna; Ginsburg, Lynda
2010-01-01
In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…
Geometrical Analogies in Mathematics Lessons
ERIC Educational Resources Information Center
Eid, Wolfram
2007-01-01
A typical form of thinking to approach problem solutions humanly is thinking in analogous structures. Therefore school, especially mathematical lessons should help to form and to develop corresponding heuristic abilities of the pupils. In the contribution, a summary of possibilities of mathematics lessons regarding this shall particularly be…
NASA Technical Reports Server (NTRS)
Aiken, E. W.
1980-01-01
A mathematical model of an advanced helicopter is described. The model is suitable for use in control/display research involving piloted simulation. The general design approach for the six degree of freedom equations of motion is to use the full set of nonlinear gravitational and inertial terms of the equations and to express the aerodynamic forces and moments as the reference values and first order terms of a Taylor series expansion about a reference trajectory defined as a function of longitudinal airspeed. Provisions for several different specific and generic flight control systems are included in the model. The logic required to drive various flight control and weapon delivery symbols on a pilot's electronic display is also provided. Finally, the model includes a simplified representation of low altitude wind and turbulence effects. This model was used in a piloted simulator investigation of the effects of control system and display variations for an attack helicopter mission.
ERIC Educational Resources Information Center
Ruthven, Kenneth
2014-01-01
Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims…
NASA Astrophysics Data System (ADS)
Campbell, D. Michael
The lack of preparation, participation, and equal access of students in mathematics and the science education continues to afflict America's high school system (Ratliff, 2001). Additionally, gender and ethnic status have become significant factors as females and minority subgroups such as African Americans and Hispanics continue to be underrepresented in these two subject fields. Recognizing and understanding these trends is extremely important for the future of this country. As fewer minorities and females become involved in advanced mathematics and science curriculum there will be a continued lack of minorities and females in mathematics and science careers. Additionally, this insufficient representation leads to fewer numbers of females and minorities in industry and educational leadership positions in mathematics and science to promote participation and equality in these fields. According to Brainard and Carlin (2003) as trends currently stand, these two groups will be under-represented in the fields of math and science and will continue to be denied economic and social power. Thus, a better understanding of these trends in participation in mathematics and science among these groups of students is warranted. This study is intended to accomplish four objectives. The first objective is to identify the extent to which opportunities are increasing or decreasing for students in high schools taking mathematics and science Advanced Placement exams by examining six years of student testing data from the College Board. A second objective is to identify features of high schools that relate to greater expansion in Advanced Placement test taking for females and minority groups in the areas of both math and science. A third objective is to explore whether, and to what extent, any social or educational features such as economic status, regional school and living locations, and ethnic backgrounds have enhanced or reduced Advanced Placement testing in these schools. Lastly
ERIC Educational Resources Information Center
Callison, Daniel
1998-01-01
Examines creative thinking in relation to modern instructional programs and information literacy and compares creative and critical thinking. Discusses teaching for thinking, techniques for sparking creativity, activities for creating a mental museum, synectics (a group creative process to create new insights), and creating meaning through story…
Dr. Edward de Bono's Six Thinking Hats and Numeracy
ERIC Educational Resources Information Center
Paterson, Anne
2006-01-01
In education, the term "metacognition" describes thinking about thinking. Within mathematics, the term "metacomputation" describes thinking about computational methods and tools. This article shows how Dr. Edward de Bono's Six Thinking Hats can be used to demonstrate metacognition and metacomputation in the primary classroom. The article suggests…
Mathematical Lens: Iron Gate, Metulla, Israel
ERIC Educational Resources Information Center
Mathematics Teacher, 2005
2005-01-01
The "Mathematical Lens" feature of "Mathematics Teacher," uses photographs as a springboard for mathematical inquiry. The goal of this feature is to encourage readers to see patterns and relationships that they can think about and extend in a mathematically playful way. In this edition of "Mathematical Lens," students analyze the shapes in an iron…
ERIC Educational Resources Information Center
Goldsmith, Lynn T.
2000-01-01
Parents can help ensure that their children are well-equipped with the necessary mathematical skills and understanding for the future by: having high expectations for their children's learning; helping their children see mathematical connections and applications in the world; being curious about their children's thinking; and being enthusiastic…
Business Mathematics Curriculum.
ERIC Educational Resources Information Center
EASTCONN Regional Educational Services Center, North Windham, CT.
This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…
Critically Thinking about Critical Thinking
ERIC Educational Resources Information Center
Weissberg, Robert
2013-01-01
In this article, the author states that "critical thinking" has mesmerized academics across the political spectrum and that even high school students are now being called upon to "think critically." He furthers adds that it is no exaggeration to say that "critical thinking" has quickly evolved into a scholarly…
Transforming Critical Thinking: Thinking Constructively.
ERIC Educational Resources Information Center
Thayer-Bacon, Barbara J.
This book presents a reconceptualization of critical thinking theory. Drawing on pragmatic, feminist, and postmodern philosophies, the book offers an overview of the history of critical thinking and identifies its major theorists. It critiques how critical thinking is conceptualized and applied in classrooms and offers a newly delineated platform…
ERIC Educational Resources Information Center
Lewis, Richard
2008-01-01
For their course, mathematics students at Bath Spa University were asked to choose a topic and explore the mathematics. As well as learning some mathematics, the author hoped that the assignment would shed light on the process of mathematical investigation itself. Their course leader had suggested that the topic of conic sections was rich, and…
Critical Thinking: A Stage Theory of Critical Thinking. Part I.
ERIC Educational Resources Information Center
Elder, Linda; Paul, Richard
1996-01-01
Discusses six stages of the development of critical thinkers: unreflective, challenged, beginning, practicing, advanced, and master thinkers. For each stage, describes the defining feature, the principle challenge, the knowledge or insight into thinking expressed, and the individual's skill in thinking. (AJL)
ERIC Educational Resources Information Center
Dori, Yehudit Judy; Dangur, Vered; Avargil, Shirly; Peskin, Uri
2014-01-01
Chemistry students in Israel have two options for studying chemistry: basic or honors (advanced placement). For instruction in high school honors chemistry courses, we developed a module focusing on abstract topics in quantum mechanics: Chemistry--From the Nanoscale to Microelectronics. The module adopts a visual-conceptual approach, which…
Mathematics in the Early Years.
ERIC Educational Resources Information Center
Copley, Juanita V., Ed.
Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining…
Go Figure! Mathematics through Sports.
ERIC Educational Resources Information Center
Farmer, Lesley S. J.
This book brings the notions of sports and mathematics together. Educators can use sports to provide a real-life context based on student interest. Not only do students become aware of mathematical thinking, but they can be "trained" to improve their mathematical skills and habits of mind through sports-related learning experiences in math. A…
Jitendra, Asha K; Dupuis, Danielle N; Star, Jon R; Rodriguez, Michael C
2016-07-01
This study examined the effect of schema-based instruction (SBI) on the proportional problem-solving performance of students with mathematics difficulties only (MD) and students with mathematics and reading difficulties (MDRD). Specifically, we examined the responsiveness of 260 seventh grade students identified as MD or MDRD to a 6-week treatment (SBI) on measures of proportional problem solving. Results indicated that students in the SBI condition significantly outperformed students in the control condition on a measure of proportional problem solving administered at posttest (g = 0.40) and again 6 weeks later (g = 0.42). The interaction between treatment group and students' difficulty status was not significant, which indicates that SBI was equally effective for both students with MD and those with MDRD. Further analyses revealed that SBI was particularly effective at improving students' performance on items related to percents. Finally, students with MD significantly outperformed students with MDRD on all measures of proportional problem solving. These findings suggest that interventions designed to include effective instructional features (e.g., SBI) promote student understanding of mathematical ideas. PMID:25312518
Thinking creatively is thinking critically.
Gruenfeld, Elizabeth
2010-01-01
The Cartoneras projects aim to promote the celebration of language, culture, and creativity through a collaboration between top literary minds and cardboard collectors in Buenos Aires and Lima. They produce and publish beautiful books with hand-painted cardboard covers that speak of the wonderful literature inside. Inspired by those projects, the Paper Picker Press (PPP) program in Boston aims to engage higher-order thinking through an arts-based approach to rediscovering literature through play. PPP starts with the premise that a student who is thinking creatively is also thinking critically. Creative play is critical thinking. PMID:20391619
ERIC Educational Resources Information Center
Chance, Paul
1986-01-01
As the world moves from the industrial age into the information age people become less dependent on basic facts and skills and more dependent on the ability to manipulate information. The higher level thinking skills that are needed in this new age must be taught in the schools. When selecting programs for teaching thinking, educators should…
Horsley, Helen L; Shepherd, Kate; Brown, Heather; Carey, Irene; Matthews, Beverley; O’Donoghue, Donal; Vinen, Katie; Murtagh, Felicity EM
2015-01-01
Background: There is a need to improve end-of-life care for people with end-stage kidney disease, particularly due to the increasingly elderly, frail and co-morbid end-stage kidney disease population. Timely, sensitive and individualised Advance Care Planning discussions are acceptable and beneficial for people with end-stage kidney disease and can help foster realistic hopes and goals. Aim: To explore the experiences of people with end-stage kidney disease regarding starting haemodialysis, its impact on quality of life and their preferences for future care and to explore the Advance Care Planning needs of this population and the timing of this support. Study design: Semi-structured qualitative interview study of people receiving haemodialysis. Interviews were analysed using thematic analysis. Recruitment ceased once data saturation was achieved. Setting/participants: A total of 20 patients at two UK National Health Service hospitals, purposively sampled by age, time on haemodialysis and symptom burden. Results: Themes emerged around: Looking Back, emotions of commencing haemodialysis; Current Experiences, illness and treatment burdens; and Looking Ahead, facing the realities. Challenges throughout the trajectory included getting information, communicating with staff and the ‘conveyor belt’ culture of haemodialysis units. Participants reported a lack of opportunity to discuss their future, particularly if their health deteriorated, and variable involvement in treatment decisions. However, discussion of these sensitive issues was more acceptable to some than others. Conclusion: Renal patients have considerable unmet Advance Care Planning needs. There is a need to normalise discussions about preferences and priorities in renal and haemodialysis units earlier in the disease trajectory. However, an individualised approach is essential – one size does not fit all. PMID:25527527
2014-01-01
make sense of policy intentions and incorporate them into their everyday routines and practices. This requires a leadership of sensemaking that enables front line staff to exercise their collective discretionary power in strengthening PHC. We hope this theoretically-framed analysis of one set of experiences stimulates wider thinking about the leadership needed to sustain primary health care in other settings. PMID:24935658
Murray, Iain R.; LaPrade, Robert F.; Musahl, Volker; Geeslin, Andrew G.; Zlotnicki, Jason P.; Mann, Barton J.; Petrigliano, Frank A.
2016-01-01
Rotator cuff tears are common and result in considerable morbidity. Tears within the tendon substance or at its insertion into the humeral head represent a considerable clinical challenge because of the hostile local environment that precludes healing. Tears often progress without intervention, and current surgical treatments are inadequate. Although surgical implants, instrumentation, and techniques have improved, healing rates have not improved, and a high failure rate remains for large and massive rotator cuff tears. The use of biologic adjuvants that contribute to a regenerative microenvironment have great potential for improving healing rates and function after surgery. This article presents a review of current and emerging biologic approaches to augment rotator cuff tendon and muscle regeneration focusing on the scientific rationale, preclinical, and clinical evidence for efficacy, areas for future research, and current barriers to advancement and implementation. PMID:27099865
ERIC Educational Resources Information Center
Rogness, Jonathan
2011-01-01
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
ERIC Educational Resources Information Center
Jackson, Philip W.
2012-01-01
Background: The intellectual context of this essay is the nature of human thought as examined by philosophers and psychologists past and present. Focus of study: The study focuses on the treatment of thinking by John Dewey in his two editions of "How We Think" and by William James in his "Talks to Teachers". Research Design: This is a…
Critical Thinking: Thinking with Concepts.
ERIC Educational Resources Information Center
Elder, Linda; Paul, Richard
2001-01-01
Urges education to help students learn through conceptual thinking. States that the first step must be to teach the subtleties of words--without a command of the language, important discriminations can be confused. Asserts that if students are to think well conceptually, surface language must dissolve, and alternative ways to communicate must be…
Computational Thinking Concepts for Grade School
ERIC Educational Resources Information Center
Sanford, John F.; Naidu, Jaideep T.
2016-01-01
Early education has classically introduced reading, writing, and mathematics. Recent literature discusses the importance of adding "computational thinking" as a core ability that every child must learn. The goal is to develop students by making them equally comfortable with computational thinking as they are with other core areas of…
Zlotnicki, Jason P; Geeslin, Andrew G; Murray, Iain R; Petrigliano, Frank A; LaPrade, Robert F; Mann, Barton J; Musahl, Volker
2016-04-01
Focal chondral defects of the articular surface are a common occurrence in the field of orthopaedics. These isolated cartilage injuries, if not repaired surgically with restoration of articular congruency, may have a high rate of progression to posttraumatic osteoarthritis, resulting in significant morbidity and loss of function in the young, active patient. Both isolated and global joint disease are a difficult entity to treat in the clinical setting given the high amount of stress on weightbearing joints and the limited healing potential of native articular cartilage. Recently, clinical interest has focused on the use of biologically active compounds and surgical techniques to regenerate native cartilage to the articular surface, with the goal of restoring normal joint health and overall function. This article presents a review of the current biologic therapies, as discussed at the 2015 American Orthopaedic Society for Sports Medicine (AOSSM) Biologics Think Tank, that are used in the treatment of focal cartilage deficiencies. For each of these emerging therapies, the theories for application, the present clinical evidence, and specific areas for future research are explored, with focus on the barriers currently faced by clinicians in advancing the success of these therapies in the clinical setting. PMID:27123466
ERIC Educational Resources Information Center
Shores, Melanie L.; Shannon, David M.; Smith, Tommy G.
2010-01-01
A total of 761 students (58.1% female) from selected fifth- and sixth-grade mathematics classrooms in Alabama were examined to investigate the relationships between individual learner variables (gender, ethnicity, socioeconomic status [SES]) and mathematics performance. Specifically, this portion of the study examined individual learner variables…
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…
Fostering Instructor Knowledge of Student Thinking Using the Flipped Classroom
ERIC Educational Resources Information Center
Strayer, Jeremy F.; Hart, James B.; Bleiler, Sarah K.
2015-01-01
In this article, we share a model of flipped instruction that allowed us to gain a window into our students' mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be…
Visual Thinking and Gender Differences in High School Calculus
ERIC Educational Resources Information Center
Haciomeroglu, Erhan Selcuk; Chicken, Eric
2012-01-01
This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…
NASA Astrophysics Data System (ADS)
Ligomenides, Panos A.
2009-05-01
The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.
2002-01-01
A recently released National Research Council (NRC) report, Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools, evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study, discipline-specific panels were formed to evaluate advanced programs in biology, chemistry, physics, and mathematics. Among the conclusions of the Content Panel for Biology were that AP courses in particular suffer from inadequate quality control as well as excessive pressure to fulfill their advanced placement function, which encourages teachers to attempt coverage of all areas of biology and emphasize memorization of facts rather than in-depth understanding. In this essay, the Panel's principal findings are discussed, with an emphasis on its recommendation that colleges and universities should be strongly discouraged from using performance on either the AP examination or the IB examination as the sole basis for automatic placement out of required introductory courses for biology majors and distribution requirements for nonmajors. PMID:12669097
Student Thinking Strategies in Reconstructing Theorems
ERIC Educational Resources Information Center
Siswono, Tatag Yuli Eko
2005-01-01
A mathematics university student as a future mathematician should have the ability to find "new" mathematics structures or construct theorems based on particular axioms. That ability can be created by using problem posing tasks. To do the tasks, students with different abilities will use different thinking strategies. To understand them exactly,…
Generalizing: The Core of Algebraic Thinking
ERIC Educational Resources Information Center
Kinach, Barbara M.
2014-01-01
Generalizing--along with conjecturing, representing, justifying, and refuting--are forms of mathematical reasoning important in all branches of mathematics (Lannin, Ellis, and Elliott 2011). Increasingly, however, generalizing is recognized as the essence of thinking in algebra (Mason, Graham, and Johnston-Wilder 2010; Kaput, Carraher, and Blanton…
ERIC Educational Resources Information Center
Brown, Kenneth E.; Johnson, Philip G.
1953-01-01
The Cooperative Committee on the Teaching of Science and Mathematics of the American Association for the Advancement of Science that participated in planning for and publishing this bulletin is composed of representatives of seventeen national scientific and mathematical societies including representatives from the associated teaching…
The Only Absolute Truth in Mathematics is the Myth of Mathematics as Universal
ERIC Educational Resources Information Center
Kantner, M. Joanne
2008-01-01
Culture and national origin can affect thinking about mathematics and mathematics learning. The myth that mathematics is objective and culture free becomes a barrier to adults learning mathematics. Adult educators must reflect upon culture's influence on learning and recognize the implications of universality myths on students' learning in…
Hunt, Tam
2014-01-01
Evolution as an idea has a lengthy history, even though the idea of evolution is generally associated with Darwin today. Rebecca Stott provides an engaging and thoughtful overview of this history of evolutionary thinking in her 2013 book, Darwin's Ghosts: The Secret History of Evolution. Since Darwin, the debate over evolution—both how it takes place and, in a long war of words with religiously-oriented thinkers, whether it takes place—has been sustained and heated. A growing share of this debate is now devoted to examining how evolutionary thinking affects areas outside of biology. How do our lives change when we recognize that all is in flux? What can we learn about life more generally if we study change instead of stasis? Carter Phipps’ book, Evolutionaries: Unlocking the Spiritual and Cultural Potential of Science's Greatest Idea, delves deep into this relatively new development. Phipps generally takes as a given the validity of the Modern Synthesis of evolutionary biology. His story takes us into, as the subtitle suggests, the spiritual and cultural implications of evolutionary thinking. Can religion and evolution be reconciled? Can evolutionary thinking lead to a new type of spirituality? Is our culture already being changed in ways that we don't realize by evolutionary thinking? These are all important questions and Phipps book is a great introduction to this discussion. Phipps is an author, journalist, and contributor to the emerging “integral” or “evolutionary” cultural movement that combines the insights of Integral Philosophy, evolutionary science, developmental psychology, and the social sciences. He has served as the Executive Editor of EnlightenNext magazine (no longer published) and more recently is the co-founder of the Institute for Cultural Evolution, a public policy think tank addressing the cultural roots of America's political challenges. What follows is an email interview with Phipps. PMID:26478766
ABCs of Early Mathematics Experiences
ERIC Educational Resources Information Center
Hensen, Laurie E.
2005-01-01
Children begin to develop mathematical thinking before they enter school. Art, baking, playing with blocks, counting numbers, games, puzzles, singing, playing with pretend money, water play all these early mathematical experiences help the children to learn in the elementary school years.
Glimm, J.
2009-10-14
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
ERIC Educational Resources Information Center
Whitin, Phyllis; Whitin, David J.
2011-01-01
The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…
Celebrate Mathematical Curiosity
ERIC Educational Resources Information Center
Redford, Christine
2011-01-01
Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
In this article, the author looks at ways of creating conditions to bring about learning. If one is to "arrange conditions to bring about learning," one needs written guidance and support systems. Two books that discusses how to arrange these conditions are: "Thinking Mathematically" by John Mason with Leone Burton and Kaye Stacey and "Starting…
Teaching Mathematics with Technology.
ERIC Educational Resources Information Center
Jensen, Robert J.
1988-01-01
Argues that calculator activities, even in the early grades, can present situations in which basic mathematical thinking processes come into play. The activity described involves developing efficient calculator guess-and-test strategies and requires only an introductory notion of the four basic operations of arithmetic. (PK)
ERIC Educational Resources Information Center
Berkeley, Viv
2008-01-01
Disability equality and improving life chances for disabled people are high on the U.K. Government's agenda at present. As someone who was once a practitioner and a manager in a busy further education environment, the author knows how difficult it is to find time to think about, and discuss with colleagues, the implications of policy. This article…
Serb, Chris
2008-08-01
Hospitals typically don't come to mind when you think about cutting-edge environmental programs, but that's changing. Rising energy costs, the need to replace older facilities, and a growing environmental consciousness have spurred hospitals nationwide to embrace a green ideology. The executive suite is a vocal and active player in these efforts. PMID:19062433
ERIC Educational Resources Information Center
Gibb, Dwight
2002-01-01
If history teachers' aim is to teach students how to think, why not ask: What forms of thought do historians use, and what specific techniques will inculcate these forms? In this article, the author proposes a fundamental shift, from courses with a focus on the mastery of data to courses with a priority on learning the historian's craft. The…
ERIC Educational Resources Information Center
Arnheim, Rudolf
Based on the more general principle that all thinking (including reasoning) is basically perceptual in nature, the author proposes that visual perception is not a passive recording of stimulus material but an active concern of the mind. He delineates the task of visually distinguishing changes in size, shape, and position and points out the…
A Mathematics Software Database Update.
ERIC Educational Resources Information Center
Cunningham, R. S.; Smith, David A.
1987-01-01
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
ERIC Educational Resources Information Center
Cohen, Jeremy A.
2012-01-01
This study concentrated on the characteristics of Grade 2 students' writing in mathematics class who used the Project M[superscript 2] units to learn geometry and measurement. Included in the study were students with high and low levels of content knowledge. Archived data from the Project M[superscript 2] study were analyzed to determine the…
ERIC Educational Resources Information Center
Rumsey, Chepina Witkowski
2012-01-01
The goals for this study were to investigate how fourth-grade students developed an understanding of the arithmetic properties when instruction promoted mathematical argumentation and to identify the characteristics of students' arguments. Using the emergent perspective as an overarching theoretical perspective helped distinguish between two…
NASA Technical Reports Server (NTRS)
Desoer, C. A.; Polak, E.; Zadeh, L. A.
1974-01-01
A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.
ERIC Educational Resources Information Center
National Science Foundation, 2006
2006-01-01
This booklet presents an overview of the Math Science Partnership program (MSP) at the National Science Foundation (NSF). This program responds to a growing national concern--the educational performance of U.S. children in mathematics and science. Through the MSP, NSF awards competitive, merit-based grants to teams composed of institutions of…
A New Start for Mathematics Curriculum.
ERIC Educational Resources Information Center
Tucker, Alan
Arguing that a major re-thinking of the mathematics curriculum is needed, this paper urges two-year colleges to take the lead in curriculum revision. Section I suggests that the pre-calculus orientation of high school mathematics may be inappropriate, viewing mathematics related to computers and dependent on computers for computation as more…
Promoting Mathematical Discourse: Learning from Classroom Examples.
ERIC Educational Resources Information Center
Manouchehri, Azita; Enderson, Mary C.
1999-01-01
Recommends that mathematics instruction should promote student discourse by orchestrating situations in which each individual's thinking is challenged and asking students to clarify and justify ideas. Provides a vignette of a heterogeneously grouped seventh-grade mathematics class to illustrate the process of mathematical discourse. (ASK)
A New World of Mathematics Thinking
ERIC Educational Resources Information Center
Schwartz, James E.
2010-01-01
The "flat" world described by Friedman (2006) is one of global supply chains and economic networks, outsourcing, international personal entrepreneurial opportunities, and nearly unlimited, universal information availability. American children will inherit a world in which their competition and opportunities are international. In light of these…
Stimulating Mathematical Thinking through Domino Games
ERIC Educational Resources Information Center
Gough, John
2015-01-01
Most readers would be familiar with the standard domino set which is played with rectangular domino tiles. The domino set, sometimes called a deck or pack, consists of 28 dominoes, colloquially nicknamed bones, cards, tiles, stones, or spinners. A domino set is a generic gaming device, similar to playing cards or dice, in that a variety of games…
Fractals Illustrate the Mathematical Way of Thinking.
ERIC Educational Resources Information Center
Nievergelt, Yves
1991-01-01
Presented are exercises that demonstrate the application of standard concepts in the design of algorithms for plotting certain fractals. The exercises can be used in any course that explains the concepts of bounded or unbounded planar sets and may serve as an application in a course on complex analysis. (KR)
ERIC Educational Resources Information Center
Reeve, Edward M.
2015-01-01
Science, Technology, Engineering, and Mathematics (STEM) is a term seen almost daily in the news. In 2009, President Obama launched the Educate to Innovate initiative to move American students from the middle to the top of the pack in science and math achievement over the next decade (The White House, n.d.). Learning about the attributes of STEM…
The materiality of mathematics: presenting mathematics at the blackboard.
Greiffenhagen, Christian
2014-09-01
Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. PMID:24620862
Young Children's Mathematics References during Free Play in Family Childcare Settings
ERIC Educational Resources Information Center
Hendershot, Shawnee M.; Berghout Austin, Ann M.; Blevins-Knabe, Belinda; Ota, Carrie
2016-01-01
Very little is known about children's discussion of mathematics topics during unstructured play. Ginsburg, Lin, Ness, and Seo [2003. Young American and Chinese children's everyday mathematical activity. Mathematical Thinking and Learning, 5(4), 235-258. Retrieved from…
NASA Astrophysics Data System (ADS)
Dickerson, David S.; Doerr, Helen M.
2014-12-01
Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were transferable to other fields of endeavor. We found teachers were divided on the characteristics (or features) of proofs that would serve these purposes. Teachers with less experience tended to believe that proofs in the high school should adhere to strict standards of language and reasoning while teachers with more experience tended to believe that proofs based on concrete or visual features were well suited for high school mathematics. This study has implications for teacher preparation because it appears that there is a wide variation in how teachers think about proof. It seems likely that students would experience proof very differently merely because they were seated in different classrooms.
On three forms of thinking: magical thinking, dream thinking, and transformative thinking.
Ogden, Thomas H
2010-04-01
The author believes that contemporary psychoanalysis has shifted its emphasis from the understanding of the symbolic meaning of dreams, play, and associations to the exploration of the processes of thinking, dreaming, and playing. In this paper, he discusses his understanding of three forms of thinking-magical thinking, dream thinking, and transformative thinking-and provides clinical illustrations in which each of these forms of thinking figures prominently. The author views magical thinking as a form of thinking that subverts genuine thinking and psychological growth by substituting invented psychic reality for disturbing external reality. By contrast, dream thinking--our most profound form of thinking-involves viewing an emotional experience from multiple perspectives simultaneously: for example, the perspectives of primary process and secondary process thinking. In transformative thinking, one creates a new way of ordering experience that allows one to generate types of feeling, forms of object relatedness, and qualities of aliveness that had previously been unimaginable. PMID:20496835
The Mathematical Education of Teachers. Issues in Mathematics Education. Volume 11 [and] Part I.
ERIC Educational Resources Information Center
Conference Board of the Mathematical Sciences, Washington, DC.
This report is designed to be a resource for mathematics faculty and other parties involved in the education of mathematics teachers. It provides a distillation of current thinking on curriculum and policy issues affecting the mathematical education of teachers with the goal of stimulating efforts on individual campuses to improve programs for…
A Constructive Response to "Where Mathematics Comes From."
ERIC Educational Resources Information Center
Schiralli, Martin; Sinclair, Nathalie
2003-01-01
Reviews the Lakoff and Nunez's book, "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (2000)," which provided many mathematics education researchers with a novel and startling perspective on mathematical thinking. Suggests that several of the book's flaws can be addressed through a more rigorous establishment of…
Hot Ideas. A Mathematical Response to a Piece of Text
ERIC Educational Resources Information Center
Grey, Melinda
2005-01-01
Children's literature can enhance mathematics lessons by providing a meaningful context, demonstrating that mathematics develops from human experiences and contributes an aesthetic dimension to learning mathematics. Written as a series of real life inspired snapshots of mathematical thinking, "Counting on Frank" (Rod Clement, 1990) provides a…
Integrating Mathematics across the Curriculum. NCTM-Aligned Activities.
ERIC Educational Resources Information Center
Martin, Hope
An effective curriculum gives students the opportunity to perceive relationships among different topics in mathematics, use mathematics in their everyday lives, and apply mathematical thinking and problem solving to other curriculum areas. This book contains fun and creative ways to integrate mathematics across the curriculum with a diversity of…
ERIC Educational Resources Information Center
Rowlett, Joel Everett
2013-01-01
This case study examined the beliefs of African American males on the psychosocial and pedagogical factors contributing to the underrepresentation of African American males in advanced high school math courses. Six 11th grade African American male juniors from a large, comprehensive, Southeastern high school served as individual cases. Within- and…
Fuzzy Thinking in Non-Fuzzy Situations: Understanding Students' Perspective.
ERIC Educational Resources Information Center
Zazkis, Rina
1995-01-01
In mathematics a true statement is always true, but some false statements are more false than others. Fuzzy logic provides a way of handling degrees of set membership and has implications for helping students appreciate logical thinking. (MKR)
ERIC Educational Resources Information Center
Wood, Eric
2004-01-01
The history of mathematics is full of rich examples that can help students to see the place of the discipline within our cultural heritage. Valuable as this can be, it also has the unfortunate side-effect of making students think that all the math has already been done and they do not get a sense that the subject is dynamic and growing.…
Lee, Stephen R
2010-01-01
Los Alamos National Laboratory will review its Computational Physics and Applied Mathematics (CPAM) capabilities in 2010. The goals of capability reviews are to assess the quality of science, technology, and engineering (STE) performed by the capability, evaluate the integration of this capability across the Laboratory and within the scientific community, examine the relevance of this capability to the Laboratory's programs, and provide advice on the current and future directions of this capability. This is the first such review for CPAM, which has a long and unique history at the laboratory, starting from the inception of the Laboratory in 1943. The CPAM capability covers an extremely broad technical area at Los Alamos, encompassing a wide array of disciplines, research topics, and organizations. A vast array of technical disciplines and activities are included in this capability, from general numerical modeling, to coupled mUlti-physics simulations, to detailed domain science activities in mathematics, methods, and algorithms. The CPAM capability involves over 12 different technical divisions and a majority of our programmatic and scientific activities. To make this large scope tractable, the CPAM capability is broken into the following six technical 'themes.' These themes represent technical slices through the CP AM capability and collect critical core competencies of the Laboratory, each of which contributes to the capability (and each of which is divided into multiple additional elements in the detailed descriptions of the themes in subsequent sections): (1) Computational Fluid Dynamics - This theme speaks to the vast array of scientific capabilities for the simulation of fluids under shocks, low-speed flow, and turbulent conditions - which are key, historical, and fundamental strengths of the laboratory; (2) Partial Differential Equations - The technical scope of this theme is the applied mathematics and numerical solution of partial differential equations
Learning with Touchscreen Devices: Game Strategies to Improve Geometric Thinking
ERIC Educational Resources Information Center
Soldano, Carlotta; Arzarello, Ferdinando
2016-01-01
The aim of this paper is to reflect on the importance of the students' game-strategic thinking during the development of mathematical activities. In particular, we hypothesise that this type of thinking helps students in the construction of logical links between concepts during the "argumentation phase" of the proving process. The…
2014-01-01
Background Although there is widespread agreement that strong district manager decision-making improves health systems, understanding about how the design and implementation of capacity-strengthening interventions work is limited. The Ghana Health Service has adopted the Leadership Development Programme (LDP) as one intervention to support the development of management and leadership within district teams. This paper seeks to address how and why the LDP ‘works’ when it is introduced into a district health system in Ghana, and whether or not it supports systems thinking in district teams. Methods We undertook a realist evaluation to investigate the outcomes, contexts, and mechanisms of the intervention. Building on two working hypotheses developed from our earlier work, we developed an explanatory case study of one rural district in the Greater Accra Region of Ghana. Data collection included participant observation, document review, and semi-structured interviews with district managers prior to, during, and after the intervention. Working backwards from an in-depth analysis of the context and observed short- and medium-term outcomes, we drew a causal loop diagram to explain interactions between contexts, outcomes, and mechanisms. Results The LDP was a valuable experience for district managers and teams were able to attain short-term outcomes because the novel approach supported teamwork, initiative-building, and improved prioritisation. However, the LDP was not institutionalised in district teams and did not lead to increased systems thinking. This was related to the context of high uncertainty within the district, and hierarchical authority of the system, which triggered the LDP’s underlying goal of organisational control. Conclusions Consideration of organisational context is important when trying to sustain complex interventions, as it seems to influence the gap between short- and medium-term outcomes. More explicit focus on systems thinking principles that
ERIC Educational Resources Information Center
Herman, Dan
1999-01-01
Explains how advances in diesel and alternative fuels has caused schools to reconsider their use for their bus fleets. Reductions in air pollution emissions, cost-savings developments, and the economies experienced from less downtime and maintenance requirements are explored. (GR)
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
ERIC Educational Resources Information Center
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
2016-01-01
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
Dahari, Harel; Layden-Almer, Jennifer E.; Kallwitz, Eric; Ribeiro, Ruy M.; Cotler, Scott J.; Layden, Thomas J.; Perelson, Alan S.
2010-01-01
Background & Aims Patients with baseline hepatitis C virus-RNA levels (bHCV-RNA) >6 log IU/ml or cirrhosis have a reduced probability of a sustained-virological response (SVR). We examined the relationship between bHCV-RNA, cirrhosis and SVR using a mathematical model that includes the critical-drug efficacy (εc; the efficacy required for a drug to clear HCV), the infection-rate constant (β) and the percentage of HCV-infected hepatocytes (π). Methods The relationship between baseline factors and SVR was evaluated in 1,000 in silico HCV-infected patients, generated by randomly assignment of realistic host and viral kinetic parameters. Model predictions were compared with clinical data from 170 non-cirrhotic and 75 cirrhotic patients. Results The ranges chosen for β and the viral production rate (p) resulted in bHCV-RNA levels that were in agreement with the distribution observed in US patients. Using these β and p values, higher bHCV-RNA levels led to higher εc, resulting in lower SVR rates. Alternatively, higher β values resulted in lower bHCV-RNA levels but higher π and εc, predicting lower rates of SVR. Cirrhotic patients had lower bHCV-RNA levels than non-cirrhotic patients (p=0.013) and more had bHCV-RNA levels <6 log IU/ml (p<0.001). Even cirrhotic patients with lower bHCV-RNA levels had lower SVR rates. An increase in β could explain the results observed in cirrhotic patients. Conclusions Our model predicts that higher bHCV-RNA levels lead to higher εc, reducing the chance of achieving SVR; cirrhotic patients have lower SVR rates because of large π values, caused by increased rates of hepatocyte infection. PMID:19208338
Gesture Supports Spatial Thinking in STEM
ERIC Educational Resources Information Center
Stieff, Mike; Lira, Matthew E.; Scopelitis, Stephanie A.
2016-01-01
The present article describes two studies that examine the impact of teaching students to use gesture to support spatial thinking in the Science, Technology, Engineering, and Mathematics (STEM) discipline of chemistry. In Study 1 we compared the effectiveness of instruction that involved either watching gesture, reproducing gesture, or reading…
Recognizing Creative Thinking Talent in the Classroom.
ERIC Educational Resources Information Center
Carroll, John; Howieson, Noel
1991-01-01
Forty-eight seventh grade children were divided into four groups based on creative thinking scores and intelligence scores. On some measures of problem solving, imagery, and mathematics, highest scores were achieved by the high-intelligence/high-creativity group. For other assessments, creativity did not add to performance and even appeared to…
Systemic Thinking To Support Dine Education.
ERIC Educational Resources Information Center
Rude, Harvey; Gorman, Roxanne
This paper describes systemic thinking in support of the recently established Navajo Nation Rural Systemic Initiative (RSI). The RSI aims to create a standards-based student-centered teaching and learning environment in mathematics, science, and technology in the 173 elementary and secondary schools on or near the Navajo Nation, including public,…
Developing Multiplicative Thinking from Additive Reasoning
ERIC Educational Resources Information Center
Tobias, Jennifer M.; Andreasen, Janet B.
2013-01-01
As students progress through elementary school, they encounter mathematics concepts that shift from additive to multiplicative situations (NCTM 2000). When they encounter fraction problems that require multiplicative thinking, they tend to incorrectly extend additive properties from whole numbers (Post et al. 1985). As a result, topics such as …
Theoretical Explanations in Mathematical Physics
NASA Astrophysics Data System (ADS)
Rivadulla, Andrés
Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.
ERIC Educational Resources Information Center
O'Donnell, Aislinn
2012-01-01
In this essay, I examine the concept of thinking in Hannah Arendt's writings. Arendt's interest in the experience of thinking allowed her to develop a concept of thinking that is distinct from other forms of mental activity such as cognition and problem solving. For her, thinking is an unending, unpredictable and destructive activity without fixed…
ERIC Educational Resources Information Center
Word's Worth: A Quarterly Newsletter of the Lifelong Learning Network, 1998
1998-01-01
This issue of a quarterly newsletter focuses on the theme of critical thinking skills. "Critical Thinking Skills: An Interview with Dr. Richard Paul" (Barbara Christopher) is the text of an interview in which the director of research at Sonoma State University's Center for Critical Thinking examines the meaning of critical thinking and the ways…
Brown, Tim
2008-06-01
In the past, design has most often occurred fairly far downstream in the development process and has focused on making new products aesthetically attractive or enhancing brand perception through smart, evocative advertising. Today, as innovation's terrain expands to encompass human-centered processes and services as well as products, companies are asking designers to create ideas rather than to simply dress them up. Brown, the CEO and president of the innovation and design firm IDEO, is a leading proponent of design thinking--a method of meeting people's needs and desires in a technologically feasible and strategically viable way. In this article he offers several intriguing examples of the discipline at work. One involves a collaboration between frontline employees from health care provider Kaiser Permanente and Brown's firm to reengineer nursing-staff shift changes at four Kaiser hospitals. Close observation of actual shift changes, combined with brainstorming and rapid prototyping, produced new procedures and software that radically streamlined information exchange between shifts. The result was more time for nursing, better-informed patient care, and a happier nursing staff. Another involves the Japanese bicycle components manufacturer Shimano, which worked with IDEO to learn why 90% of American adults don't ride bikes. The interdisciplinary project team discovered that intimidating retail experiences, the complexity and cost of sophisticated bikes, and the danger of cycling on heavily trafficked roads had overshadowed people's happy memories of childhood biking. So the team created a brand concept--"Coasting"--to describe a whole new category of biking and developed new in-store retailing strategies, a public relations campaign to identify safe places to cycle, and a reference design to inspire designers at the companies that went on to manufacture Coasting bikes. PMID:18605031
ERIC Educational Resources Information Center
Castro Superfine, Alison; Li, Wenjuan; Bragelman, John; Fisher, Amanda
2015-01-01
Noticing children's mathematical thinking is an important aspect of what teachers need to know. This study explores the role of videocases in supporting preservice elementary teachers' noticing of children's mathematical thinking. Findings from a quasi-experimental study of preservice teachers' engagement with videocases indicate no significant…
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…
Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process
ERIC Educational Resources Information Center
Bal, Aytgen Pinar; Doganay, Ahmet
2014-01-01
The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…
Discussion from a Mathematics Education Perspective
ERIC Educational Resources Information Center
Clements, Douglas; Sarama, Julie
2015-01-01
In a review of the special issue, we conclude that the articles are research gems in the domain of preschool mathematics education. Most share several features, such as their perspective on research methodology and their view of mathematics thinking and learning. They address the cognitive architecture and processes and the developmental levels…
Getting At The Mathematics: Sara's Journal
ERIC Educational Resources Information Center
Speiser, Bob; Walter, Chuck
2003-01-01
In this paper, we discuss issues in planning and conducting research into mathematics learning. We emphasize two central themes: (1) the learners' mathematics (especially the issues and ideas, in given problem situations, that learners choose to think about and to present; and (2) the kinds of knowledge that learners may be building (including…
Synopses for Modern Secondary School Mathematics.
ERIC Educational Resources Information Center
Organisation for Economic Cooperation and Development, Paris (France). Directorate for Scientific Affairs.
The 1959 Royaumont seminar "New Thinking in School Mathematics," having agreed on the need for modernization, recommended that a second group of experts work out detailed synopses of the entire subject matter of secondary school mathematics. This book is the report of the second seminar and contains the Dubrovnik Program which stimulated much…
Self and Peer Assessment of Mathematical Processes
ERIC Educational Resources Information Center
Onion, Alice; Javaheri, Elnaz
2011-01-01
This article explores using Bowland assessment tasks and Nuffield Applying Mathematical Processes (AMP) activities as part of a scheme of work. The Bowland tasks and Nuffield AMP activities are designed to develop students' mathematical thinking; they are focused on key processes. Unfamiliar demands are made on the students and they are challenged…
Mathematics Teacher TPACK Standards and Development Model
ERIC Educational Resources Information Center
Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis
2009-01-01
What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…
Mathematical Lens: Roller Coasters and Railways
ERIC Educational Resources Information Center
Daire, Sandra Arguelles
2009-01-01
This article uses photographs as a springboard for mathematical inquiry to encourage readers to see patterns and relationships that they can think about and extend in a mathematically playful way. Herein, two photographs are presented along with a discussion of the meaning of slopes and their relationship to gradient and pitch. (Contains 6…
Developing the Young Gifted Child's Mathematical Mind
ERIC Educational Resources Information Center
Fisher, Carol
2016-01-01
Schools seem firmly rooted in the emphasis on computational mastery, and seldom seem to have time to develop other areas of mathematical thinking, such as real-world problem solving and the application of mathematical concepts. All too often, children seem to do well in math in the early grades because they easily memorize the facts and the…
Making Mathematics Relevant for Students in Bali
ERIC Educational Resources Information Center
Sema, Pryde Nubea
2008-01-01
The reactions of students towards mathematics in Bali (in the NW Province of Cameroon) are appalling. This is due to a misconception regarding its uses. The author thinks that these problems derive partly from the influence that the Western curriculum has had in Bali--mathematical contexts are based around train times in Liverpool instead of from…
Governing Equality: Mathematics for All?
ERIC Educational Resources Information Center
Diaz, Jennifer D.
2013-01-01
With the notion of governmentality, this article considers how the equal sign (=) in the U.S. math curriculum organizes knowledge of equality and inscribes cultural rules for thinking, acting, and seeing in the world. Situating the discussion within contemporary math reforms aimed at teaching mathematics for all, I draw attention to how the…
Analogy, higher order thinking, and education.
Richland, Lindsey Engle; Simms, Nina
2015-01-01
Analogical reasoning, the ability to understand phenomena as systems of structured relationships that can be aligned, compared, and mapped together, plays a fundamental role in the technology rich, increasingly globalized educational climate of the 21st century. Flexible, conceptual thinking is prioritized in this view of education, and schools are emphasizing 'higher order thinking', rather than memorization of a cannon of key topics. The lack of a cognitively grounded definition for higher order thinking, however, has led to a field of research and practice with little coherence across domains or connection to the large body of cognitive science research on thinking. We review literature on analogy and disciplinary higher order thinking to propose that relational reasoning can be productively considered the cognitive underpinning of higher order thinking. We highlight the utility of this framework for developing insights into practice through a review of mathematics, science, and history educational contexts. In these disciplines, analogy is essential to developing expert-like disciplinary knowledge in which concepts are understood to be systems of relationships that can be connected and flexibly manipulated. At the same time, analogies in education require explicit support to ensure that learners notice the relevance of relational thinking, have adequate processing resources available to mentally hold and manipulate relations, and are able to recognize both the similarities and differences when drawing analogies between systems of relationships. PMID:26263071
Driven by History: Mathematics Education Reform
ERIC Educational Resources Information Center
Permuth, Steve; Dalzell, Nicole
2013-01-01
The advancement of modern societies is fueled by mathematics, and mathematics education provides the foundation upon which future scientists and engineers will build. Society dictates how mathematics will be taught through the development and implementation of mathematics standards. When examining the progression of these standards, it is…
Students' Interpretations of Mathematical Statements Involving Quantification
ERIC Educational Resources Information Center
Piatek-Jimenez, Katrina
2010-01-01
Mathematical statements involving both universal and existential quantifiers occur frequently in advanced mathematics. Despite their prevalence, mathematics students often have difficulties interpreting and proving quantified statements. Through task-based interviews, this study took a qualitative look at undergraduate mathematics students'…
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
Handwritten mathematical symbols dataset
Chajri, Yassine; Bouikhalene, Belaid
2016-01-01
Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975
Handwritten mathematical symbols dataset.
Chajri, Yassine; Bouikhalene, Belaid
2016-06-01
Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975
ERIC Educational Resources Information Center
National Council on Disability, Washington, DC.
This paper summarizes a May 2000 conference about advancing the civil and human rights of people with disabilities from diverse cultures. The conference included people with disabilities from diverse cultures and members of national civil rights organizations. The conference identified five priority areas for attention: (1) cultivating leadership…
Mathematization in introductory physics
NASA Astrophysics Data System (ADS)
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
Visual Thinking Strategies = Creative and Critical Thinking
ERIC Educational Resources Information Center
Moeller, Mary; Cutler, Kay; Fiedler, Dave; Weier, Lisa
2013-01-01
Implementation of Visual Thinking Strategies (VTS) into the Camelot Intermediate School curriculum in Brookings, South Dakota, has fostered the development of creative and critical thinking skills in 4th- and 5th-grade students. Making meaning together by observing carefully, deciphering patterns, speculating, clarifying, supporting opinions, and…
Investigating Mathematics through Digital Media: Cognitive Visual Perturbations
ERIC Educational Resources Information Center
Calder, Nigel
2011-01-01
How might investigating mathematical tasks through digital media influence students' learning trajectories, and hence their mathematical thinking? This article reports on elements of an ongoing study that examines how engaging mathematical phenomena through digital pedagogical media might influence understanding. As the students sought…
Provocative Mathematics Questions: Drawing Attention to a Lack of Attention
ERIC Educational Resources Information Center
Klymchuk, Sergiy
2015-01-01
The article investigates the role of attention in the reflective thinking of school mathematics teachers. It analyses teachers' ability to pay attention to detail and "use" their mathematical knowledge. The vast majority of teachers can be expected to have an excellent knowledge of mathematical techniques. The question examined here is…
Teacher Actions to Maximize Mathematics Learning Opportunities in Heterogeneous Classrooms
ERIC Educational Resources Information Center
Sullivan, Peter; Mousley, Judith; Zevenbergen, Robyn
2006-01-01
The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and…
Investigations in Mathematics Education. Volume 17, Number 3.
ERIC Educational Resources Information Center
Suydam, Marilyn N., Ed.; Kasten, Margaret L., Ed.
1984-01-01
This issue of "Investigations in Mathematics Education" contains: (1) a review of E. Fischbein's book "The Intuitive Sources of Probabilistic Thinking in Children;" (2) nine abstracts of research studies in mathematics education; (3) a list (by EJ number) of mathematics education research studies reported in the January to March 1984 issues of…
If This Is Our Mathematics, What Are Our Stories?
ERIC Educational Resources Information Center
Healy, Lulu; Sinclair, Nathalie
2007-01-01
This paper sets out to examine how narrative modes of thinking play a part in the claiming of mathematical territories as our own, in navigating mathematical landscapes and in conversing with the mathematical beings that inhabit them. We begin by exploring what constitutes the narrative mode, drawing principally on four characteristics identified…
Multiple Representations as Sites for Teacher Reflection about Mathematics Learning
ERIC Educational Resources Information Center
Ryken, Amy E.
2009-01-01
This documentary account situates teacher educator, prospective teacher, and elementary students' mathematical thinking in relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning skill--creating and analyzing representations. The author examines responses of prospective…
Gaber, David; Schlimm, Dirk
2015-01-01
Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. PMID:26263425
Foundations for Critical Thinking
ERIC Educational Resources Information Center
Bers, Trudy; Chun, Marc; Daly, William T.; Harrington, Christine; Tobolowsky, Barbara F.
2015-01-01
"Foundations for Critical Thinking" explores the landscape of critical-thinking skill development and pedagogy through foundational chapters and institutional case studies involving a range of students in diverse settings. By establishing a link between active learning and improved critical thinking, this resource encourages all higher…
Critical Thinking Concept Reconstructed
ERIC Educational Resources Information Center
Minter, Mary Kennedy
2010-01-01
This paper explores the proposition that teaching of critical thinking (CT) should include: (1) identifying and addressing the many environmental variables acting as barriers to our human thinking, i.e., an open system approach, and (2) utilizing the interrelatedness of the CT building blocks, i.e., creative thinking techniques, levels of…
ERIC Educational Resources Information Center
Hyde, Rod
1997-01-01
Effective Thinking Outdoors (ETO) is an organization that teaches thinking skills and strategies via significant outdoor experiences. Identifies the three elements of thinking as creativity, play, and persistence; presents a graphic depiction of the problem-solving process and aims; and describes an ETO exercise, determining old routes of travel…
Encouragement for Thinking Critically
ERIC Educational Resources Information Center
Olivares, Sonia; Saiz, Carlos; Rivas, Silvia F.
2013-01-01
Introduction: Here we report the results obtained in an innovative teaching experience that encourages the development of Critical Thinking skills through motivational intervention. Understanding Critical Thinking as a theory of action, "we think to solve problems", and accompanying this concept with a program aimed at teaching/learning…
ERIC Educational Resources Information Center
de Bono, Edward
1986-01-01
Suggests our society strongly needs thinking that is constructive, generative, and organizing; describes an educational program, CoRT (Cognitive Research Trust), which teaches creative thinking as a skill; and presents reasons for teaching thinking as a specific subject area. (MBR)
ERIC Educational Resources Information Center
Lovrich, Deborah
2004-01-01
Scientists and students often believe that if they just think harder about a problem, a solution will follow. However, thinking about one's thinking, or using metacognition, can be a more productive expenditure of mental energy. Introducing students to metacognition allows them to discover the value of reflection. This article presents a lesson on…
ERIC Educational Resources Information Center
Jones, Rachael Adams
2012-01-01
Too often, teachers scratch their heads and ask, "What were my students thinking?" then answer, "I don't want to know." But teachers should want to know, and students should question their own thinking, as well. Critical thinking involves not just problem solving, creativity, analysis, and synthesis but also self-awareness of learning and learning…
Mathematics Teaching: Where Are We at? NZCER Mathematics Seminar Proceedings (May 1998).
ERIC Educational Resources Information Center
Webber, Bev, Comp.
This publication contains the conference proceedings of the New Zealand Council for Educational Research's (NZCER) mathematics seminar in 1998. Practical insights are offered into topics such as Maori students' participation and performance in mathematics, a conceptual development for multiplication using thinking strategies, practical processes…
Financial Mathematical Tasks in a Middle School Mathematics Textbook Series: A Content Analysis
ERIC Educational Resources Information Center
Hamburg, Maryanna P.
2009-01-01
This content analysis examined the distribution of financial mathematical tasks (FMTs), mathematical tasks that contain financial terminology and require financially related solutions, across the National Standards in K-12 Personal Finance Education categories (JumpStart Coalition, 2007), the thinking skills as identified by "A Taxonomy for…
Improved Appreciation of Mathematics through an IBL Liberal Arts Mathematics Course
ERIC Educational Resources Information Center
Blyth, Russell D.
2015-01-01
The author has taught an inquiry-based liberal arts mathematics class using the text "The Heart of Mathematics: An Invitation to Effective Thinking" by Edward B. Burger and Michael Starbird a total of 20 times since Spring 2001. The students in this class have almost all been in non-technical majors and many started the semester with…
ERIC Educational Resources Information Center
Cambridge Conference on School Mathematics, Newton, MA.
These materials were written with the aim of reflecting the thinking of Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics K-6. In view of the experiences of other curriculum groups and of the general discussions since 1963, the present report initiates the next step in evolving the "Goals".…
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
ERIC Educational Resources Information Center
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
Towards a Dialogical Pedagogy: Some Characteristics of a Community of Mathematical Inquiry
ERIC Educational Resources Information Center
Kennedy, Nadia Stoyanova
2009-01-01
This paper discusses a teaching model called community of mathematical inquiry (CMI), characterized by dialogical and inquiry-driven communication and a dynamic structure of intertwined cognitive processes including distributed thinking, mathematical argumentation, integrated reasoning, conceptual transformation, internalization of critical…
ERIC Educational Resources Information Center
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Encouraging Young Women to Stay in the Mathematics Pipeline: Mathematics Camps for Young Women
ERIC Educational Resources Information Center
Chacon, Paul; Soto-Johnson, Hortensia
2003-01-01
For two summers, week-long residential mathematics programs were held for high school women, with the primary goal of encouraging them to continue their study of mathematics. The activities were designed to rekindle their excitement about mathematics and to support the idea that women should learn advanced mathematics. This paper reports the…
TIMSS Advanced 2008 Assessment Frameworks
ERIC Educational Resources Information Center
Garden, Robert A.; Lie, Svein; Robitaille, David F.; Angell, Carl; Martin, Michael O.; Mullis, Ina V.S.; Foy, Pierre; Arora, Alka
2006-01-01
Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advanced mathematics and one for physics. It also contains…
Mathematical E-Learning Using Interactive Mathematics on the Web.
ERIC Educational Resources Information Center
Bringslid, Odd
2002-01-01
Explains the use of the Web as an advanced calculator using numeric, graphic, and symbolic mathematics interactively with the development of XML-standard MathML. Suggests that the problem of decreasing achievement in mathematics courses can be solved using interactive and personalized documents on the Web and improve the understanding of…
Murray, Iain R; LaPrade, Robert F; Musahl, Volker; Geeslin, Andrew G; Zlotnicki, Jason P; Mann, Barton J; Petrigliano, Frank A
2016-03-01
Rotator cuff tears are common and result in considerable morbidity. Tears within the tendon substance or at its insertion into the humeral head represent a considerable clinical challenge because of the hostile local environment that precludes healing. Tears often progress without intervention, and current surgical treatments are inadequate. Although surgical implants, instrumentation, and techniques have improved, healing rates have not improved, and a high failure rate remains for large and massive rotator cuff tears. The use of biologic adjuvants that contribute to a regenerative microenvironment have great potential for improving healing rates and function after surgery. This article presents a review of current and emerging biologic approaches to augment rotator cuff tendon and muscle regeneration focusing on the scientific rationale, preclinical, and clinical evidence for efficacy, areas for future research, and current barriers to advancement and implementation. PMID:27099865
Scheme of thinking quantum systems
NASA Astrophysics Data System (ADS)
Yukalov, V. I.; Sornette, D.
2009-11-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
New Technologies in Mathematics.
ERIC Educational Resources Information Center
Sarmiento, Jorge
An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…
Audiovisual Materials in Mathematics.
ERIC Educational Resources Information Center
Raab, Joseph A.
This pamphlet lists five thousand current, readily available audiovisual materials in mathematics. These are grouped under eighteen subject areas: Advanced Calculus, Algebra, Arithmetic, Business, Calculus, Charts, Computers, Geometry, Limits, Logarithms, Logic, Number Theory, Probability, Soild Geometry, Slide Rule, Statistics, Topology, and…
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
ERIC Educational Resources Information Center
Wernet, Jamie L; Nurnberger-Haag, Julie
2015-01-01
Little research exists on young children's beliefs about mathematics, and current research perspectives on early mathematical activity may overlook a great deal of young children's sophisticated mathematical thinking. We argue this is attributable, in part, to a need for a broader view of what mathematics is, including cultural practices that are…
NASA Astrophysics Data System (ADS)
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Mole, John
2002-01-01
People in different cultures are taught to think differently. How we gather information, process, rationalise, justify and communicate our ideas is culturally determined. Europe is divided between the pragmatic, inductive thinking of North Sea cultures and the rationalist thinking of the rest of the continent. Westerners and Asians have different mental skills and capacities deriving from the nature of written and spoken language, the relative importance of learning by rote or investigation and the social environment. Western children are expected to ask questions and test ideas for themselves, while in Asia it is unacceptable to question anyone senior in age or authority, including teachers. Westerners base thinking on reason; Asians base thinking on harmony. Whenever people of different cultures work together, different ways of thinking create barriers to understanding and communication. This applies to many spheres of work, including the medical profession. PMID:12195863
Teaching Critical Thinking: Sense-Making, Explanations, Language, and Habits
ERIC Educational Resources Information Center
Maloney, David
2015-01-01
The conjunction of three events has encouraged me to devote significant time to thinking about the pedagogical framework in my introductory courses. The three events were: doing a workshop addressing the Advanced Placement restructuring of the Physics B course with a stronger focus on critical thinking, finding out that "The Physics…
Critical Thinking: Implications for Instruction of the Stage Theory.
ERIC Educational Resources Information Center
Paul, Richard; Elder, Linda
1997-01-01
Discusses the implications of the stage theory of critical thinking development. Argues that people actively pass through the predictable stages of unreflective, challenged, beginning, practicing, advanced, and master thinkers and that educators must bring critical thinking into instruction at the foundational level. Analyzes implications for…
Global Thinking, or the Utility of Trivia.
ERIC Educational Resources Information Center
Harris, John S.
2001-01-01
Suggests the case of the British Westland Lysander P12 Ground Strafer aircraft illustrates the problem of narrow thinking. Claims that had the initial designers approached the problem in a broad way, they would have seen in advance that the project would fail. Concludes the case is instructive as an industrial problem, but it also demonstrates the…
Lateral Thinking of Prospective Teachers
ERIC Educational Resources Information Center
Lawrence, A. S. Arul; Xavier, S. Amaladoss
2013-01-01
Edward de Bono who invented the term "lateral thinking" in 1967 is the pioneer of lateral thinking. Lateral thinking is concerned with the generation of new ideas. Liberation from old ideas and the stimulation of new ones are twin aspects of lateral thinking. Lateral thinking is a creative skills from which all people can benefit…
Special Section: Cognition and Instruction in Mathematics.
ERIC Educational Resources Information Center
Mayer, Richard E., Ed.
1989-01-01
This special section on cognition and mathematics contains an introduction and 13 articles on advances in the psychology of mathematics learning. The articles focus on how students learn to solve mathematics problems, including arithmetic computation problems, arithmetic word problems, and computer programing problems. (SLD)
Clinical Assessment in Mathematics: Learning the Craft.
ERIC Educational Resources Information Center
Hunting, Robert P.; Doig, Brian A.
1997-01-01
Discusses a professional development program called Clinical Approaches to Mathematics Assessment. Argues for the advanced training of mathematics teachers who understand knowledge construction processes of students; can use clinical tools for evaluating a student's unique mathematical "fingerprint"; and can create or adapt problems, tasks, or…
Action-Based Digital Tools: Mathematics Learning in 6-Year-Old Children
ERIC Educational Resources Information Center
Dejonckheere, Peter J. N.; Desoete, Annemie; Fonck, Nathalie; Roderiguez, Dave; Six, Leen; Vermeersch, Tine; Vermeulen, Lies
2014-01-01
Introduction: In the present study we used a metaphorical representation in order to stimulate the numerical competences of six-year-olds. It was expected that when properties of physical action are used for mathematical thinking or when abstract mathematical thinking is grounded in sensorimotor processes, learning gains should be more pronounced…
Statewide Mathematics Professional Development: Teacher Knowledge, Self-Efficacy, and Beliefs
ERIC Educational Resources Information Center
Carney, Michele B.; Brendefur, Jonathan L.; Thiede, Keith; Hughes, Gwyneth; Sutton, John
2016-01-01
We examined the impact of a state-mandated K-12 mathematics professional development course on knowledge, self-efficacy, and beliefs of nearly 4,000 teachers and administrators. Participants completed the Mathematical Thinking for Instruction course, emphasizing student thinking, problem-solving, and content knowledge specific to mathematics…
Reading the News: The Statistical Preparation of Pre-Service Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Chesler, Joshua
2015-01-01
Undergraduate mathematics programs must prepare teachers for the challenges of teaching statistical thinking as advocated in standards documents and statistics education literature. This study investigates the statistical thinking of pre-service secondary mathematics teachers at the end of their undergraduate educations. Although all had completed…
Experimental Mathematics and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
ERIC Educational Resources Information Center
Riding, R. J.; Powell, S. D.
1987-01-01
Reports on a study which investigated the possibility of improving five-year-olds' critical thinking skills in reading and mathematics by using computers. Results indicate improvement in the reading area but not in the mathematics area. (RKM)
ERIC Educational Resources Information Center
Maclennan, Ian
1977-01-01
Suggests that there exists a "finite" number of elementary concepts and distinguishable modes of thinking, that all human beings tend to acquire the same set of elements of thinking and the same strategies with which to understand and control their physical environment, and that the method of analysis used here is a standard scientific method.…
ERIC Educational Resources Information Center
Harden, Helen
2009-01-01
This article provides an overview of the "It Makes You Think" resource. The lessons provided by this resource show how students can learn about the global dimension through science. The "It Makes You Think" resource contains ten topics: (1) Metals in jewellery worldwide; (2) Global food market; (3) The worldwide travels of paper; (4) Mobile phones…
ERIC Educational Resources Information Center
Trimble, Ruth A.
It is proposed that a major obstacle for intermediate-level learners of English as a Second Language is the transition from thinking in the native language to thinking in English, that this transition must be made before proceeding from the intermediate level, and that it should begin as early as possible in language training. Early in-class…
Vitalistic thinking in adults.
Wilson, Stuart
2013-11-01
Vitalistic thinking has traditionally been associated with reasoning about biological phenomena. The current research aimed to investigate a broader range of vitalistic thinking than previously studied. Esoteric notions of 'energy' are frequently used by individuals when making causal attributions for strange occurrences, and previous literature has linked such thinking with paranormal, magical, and superstitious beliefs. Two experiments are described that aim to investigate whether adults are vitalistic when asked to make causal judgments, and whether this can be predicted by thinking styles and prior paranormal belief. Experiment 1 asked participants to rate three causal options (one of which was vitalistic) for six vignettes. Scores on one dimension of paranormal belief (New Age Philosophy) and analytical thinking significantly predicted vitalism, but scores on intuitive thinking and Traditional Paranormal Beliefs did not. Experiment 2 extended the findings by asking participants to generate their own causal responses. Again, paranormal belief was found to be the best predictor of vitalism, but this time Traditional Paranormal Beliefs were associated with vitalistic responses whilst both intuitive and analytical thinking were unable to significantly predict classification. Results challenge previous findings, suggesting that vitalistic thinking may operate differently when applied to everyday causal reasoning. PMID:24094281
Against Critical Thinking Pedagogy
ERIC Educational Resources Information Center
Hayes, David
2015-01-01
Critical thinking pedagogy is misguided. Ostensibly a cure for narrowness of thought, by using the emotions appropriate to conflict, it names only one mode of relation to material among many others. Ostensibly a cure for fallacies, critical thinking tends to dishonesty in practice because it habitually leaps to premature ideas of what the object…
ERIC Educational Resources Information Center
Hassard, Jack; Weisburg, Julie
1992-01-01
Describes the Global Thinking Project, a collaborative effort between Georgia State University and the Russian Academy of Pedagogical Sciences to develop strategies, methods, and teaching materials to help students think globally. Students are connected through the AppleLink network. Student and teacher attitudes toward the project are reported.…
Critical Thinking and Learning
ERIC Educational Resources Information Center
Mason, Mark
2007-01-01
This paper introduces some of the debates in the field of critical thinking by highlighting differences among thinkers such as Siegel, Ennis, Paul, McPeck, and Martin, and poses some questions that arise from these debates. Does rationality transcend particular cultures, or are there different kinds of thinking, different styles of reasoning? What…
ERIC Educational Resources Information Center
Downs, Christopher J.
2008-01-01
Critical thinking is of primary importance in higher education, yet the concept remains slippery and the skill elusive. The author argues that most current critical thinking textbooks are out of line with the seminal work of John Dewey. Rather than logical argument and justification, it is suggested that carefulness, open-mindedness and creativity…
Thinking Skills & Intelligence.
ERIC Educational Resources Information Center
Blai, Boris, Jr.
A review of research and the views of researchers prominent in the field of thinking skill development discusses the role of thinking skills in the ability to formulate problems, resolve issues, determine the most effective decisions, and create effective solutions to problems. The views of Edward deBono, Robert Ennis, Reuven Feuerstein, Matthew…
ERIC Educational Resources Information Center
Demski, Jennifer
2012-01-01
When one thinks of 21st century schools, one thinks of geometric modern architecture, sustainable building materials, and high-tech modular classrooms. It's rare, though, that a district has the space or the money to build that school from the ground up. Instead, the challenge for most is the transformation of the 20th century architecture to…
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
Siskiyou County Superintendent of Schools, Yreka, CA.
The purpose of this project was to raise the mathematics skills of 100 mathematically retarded students in grades one through eight by one year through the development of an inservice strategy prepared by four teacher specialists. Also used in the study was a control group of 100 students chosen from the median range of stanines on pretest scores…
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
Critical Thinking: Thinking to Some Purpose.
ERIC Educational Resources Information Center
Elder, Linda; Paul, Richard
2001-01-01
Argues that students should continuously question the purpose of their daily classroom activities and assignments. Explains that when students are required to consider purpose, they begin to develop important intellectual skills, and to bring relevance to their critical thinking and daily life. (NB)
Performance and Thinking Skills: The Battle between the Conscious and the Unconscious.
ERIC Educational Resources Information Center
Borchardt, Donald A.
Thinking skills and performance skills are compatible, and actors and directors should learn them both. If there are to be advances in performing arts there must be a clearer understanding of the processes of thinking and the practices of performing. Efforts to define thinking skills have tended to categorize the skills into four camps: critical…
ERIC Educational Resources Information Center
Box, Lorna; Watson, Anne
2010-01-01
This article presents an e-mail conversation between two teachers discussing how to have a "rich task" lesson in which they get to the heart of mathematical modeling and in which students are motivated into working on mathematics. One teacher emphasizes that the power of maths is in developing mathematical descriptions of situations by looking at…
A consensus statement on critical thinking in nursing.
Scheffer, B K; Rubenfeld, M G
2000-11-01
The purpose of this study was to define critical thinking in nursing. A Delphi technique with 5 rounds of input was used to achieve this purpose. An international panel of expert nurses from nine countries: Brazil, Canada, England, Iceland, Japan, Korea, Netherlands, Thailand, and 23 states in the U.S. participated in this study between 1995 and 1998. A consensus definition (statement) of critical thinking in nursing was achieved. The panel also identified and defined 10 habits of the mind (affective components) and 7 skills (cognitive components) of critical thinking in nursing. The habits of the mind of critical thinking in nursing included: confidence, contextual perspective, creativity, flexibility, inquisitiveness, intellectual integrity, intuition, open-mindedness, perseverance, and reflection. Skills of critical thinking in nursing included: analyzing, applying standards, discriminating, information seeking, logical reasoning, predicting and transforming knowledge. These findings can be used by practitioners, educators and researchers to advance understanding of the essential role of critical thinking in nursing. PMID:11103973
ERIC Educational Resources Information Center
Dalton, Ben; Ingels, Steven J.; Downing, Jane; Bozick, Robert
2007-01-01
While increased academic requirements for high school graduation have long been advocated, current research shows a mixed record in mathematics and science achievement among American middle and high school students relative to some of their international peers. In response to these concerns and other calls for reform, states have increased the…
Depastas, A.N.
1990-01-01
According to the practicalist school, thinking emerges from activity and each human practice is giving food to its own distinctive kinds of perception, conduct, and perspective of the world. The author, while studying and describing developments after the commencement of the nuclear age in many fields of human behavior and knowledge, including the social sciences, particularly psychology and international politics, became an adherent to the practicalist philosophy when he perceived new relevant thoughts coming to his mind at the same time. Indeed writing is a learning experience. He has, therefore, systematically included these thoughts in the following pages and synoptically characterized them in the title: Nuclear Age Thinking. He considers this kind of thinking as automatic, conscious activity which is gradually influencing our choices and decisions. The author has reservations as regards Albert Einstein's saying that the unleashed power of the atom changed everything save our modes of thinking, because the uncontrollability of nuclear energy is apparently in the subconscious of mankind nowadays, influencing the development of a new mode of thinking, and that is the nuclear age thinking which is the subject of this book. Nuclear age thinking drives from the collective fear of extinction of life on earth due to this new power at man's disposal, and it is not only limited to the change in the conventional meaning of the words war and peace.
NASA Astrophysics Data System (ADS)
Clarke, Doug; Roche, Anne; Wilkie, Karina; Wright, Vince; Brown, Jill; Downton, Ann; Horne, Marj; Knight, Rose; McDonough, Andrea; Sexton, Matthew; Worrall, Chris
2013-06-01
As part of a teacher professional learning project in mathematics education, university mathematics educators taught demonstration lessons in project primary schools. These lessons were part of a "pre-brief, teaching, and debrief" process, in which up to eight teachers observed each lesson. Using brief questionnaires completed in advance of the lesson, during the lesson, following the debrief, and several weeks later, data were collected on teachers' intended and actual observation foci and any anticipated changes in their beliefs and practices arising from the experience. There were several common themes in teachers' intended observations, including a focus on questioning, catering for individual differences, and building student engagement. As evident in other research, teachers' intended and actual observations gave greater attention to teacher actions and decision making than to student learning and thinking. In this paper, we situate demonstration lessons within teacher professional learning models, describe the features of our model, summarise teacher data, and discuss issues arising from our work.
ERIC Educational Resources Information Center
Donawa, Annette Mallory
2009-01-01
The enhancement of critical thinking skills is necessary for students pursuing degrees in science, technology, engineering, and mathematics (STEM) disciplines. A three-year mixed methods study conducted at a Historically Black College and University in Baltimore, Maryland focused on enhancing critical thinking skills for African American students.…
Picture This: Increasing Math and Science Learning by Improving Spatial Thinking
ERIC Educational Resources Information Center
Newcombe, Nora S.
2010-01-01
Spatial thinking--such as visualizing the earth rotating--is crucial to student success in science, technology, engineering, and mathematics (STEM). Since spatial thinking is associated with skill and interest in STEM fields (as well as in other areas, such as art, graphic design, and architecture), the immediate question is whether it can be…
Project IMPACT. Improve Minimal Proficiences by Activating Critical Thinking. Grades 7-12.
ERIC Educational Resources Information Center
Orange County Dept. of Education, Santa Ana, CA.
The major goal of Project IMPACT (Improve Minimal Proficiencies by Activating Critical Thinking) is to improve student achievement on district tests of basic skill competency. The program seeks to improve student performance on tests requiring critical thinking with emphasis on reading and mathematics. Students involved in Project IMPACT work in a…
Computational Thinking in K-12: A Review of the State of the Field
ERIC Educational Resources Information Center
Grover, Shuchi; Pea, Roy
2013-01-01
Jeannette Wing's influential article on computational thinking 6 years ago argued for adding this new competency to every child's analytical ability as a vital ingredient of science, technology, engineering, and mathematics (STEM) learning. What is computational thinking? Why did this article resonate with so many and serve as a rallying cry for…
The Thinking-about-Derivative Test for Undergraduate Students: Development and Validation
ERIC Educational Resources Information Center
Aydin, Utkun; Ubuz, Behiye
2015-01-01
Two studies were conducted for the development and validation of a multidimensional test to assess undergraduate students' mathematical thinking about derivative. The first study involved two phases: question generation and refinement of the Thinking-about-Derivative Test (TDT). The second study included four phases as follows: test…
ERIC Educational Resources Information Center
Ben Youssef, Belgacem; Berry, Barbara
2012-01-01
Spatial thinking skills are vital for success in everyday living and work, not to mention the centrality of spatial reasoning in scientific discoveries, design-based disciplines, medicine, geosciences and mathematics to name a few. This case study describes a course in spatial thinking and communicating designed and delivered by an…
Learning to Think Spatially: What Do Students "See" in Numeracy Test Items?
ERIC Educational Resources Information Center
Diezmann, Carmel M.; Lowrie, Tom
2012-01-01
Learning to think spatially in mathematics involves developing proficiency with graphics. This paper reports on 2 investigations of spatial thinking and graphics. The first investigation explored the importance of graphics as 1 of 3 communication systems (i.e. text, symbols, graphics) used to provide information in numeracy test items. The results…
ERIC Educational Resources Information Center
Luo, Yu L. L.; Kovas, Yulia; Haworth, Claire M. A.; Plomin, Robert
2011-01-01
The genetic and environmental origins of individual differences in mathematical self-evaluation over time and its association with later mathematics achievement were investigated in a UK sample of 2138 twin pairs at ages 9 and 12. Self-evaluation indexed how good children think they are at mathematical activities and how much they like those…
ERIC Educational Resources Information Center
McCammon, Richard B.
1979-01-01
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
The child may have problems in school, including behavior problems and loss of self-esteem. Some children with mathematics disorder become anxious or afraid when given math problems, making the problem even worse.
ERIC Educational Resources Information Center
Johnson, Jerry
1997-01-01
Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)
ERIC Educational Resources Information Center
Gardner, Martin
1978-01-01
Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)
What Hong Kong Teachers and Parents Think about Thinking.
ERIC Educational Resources Information Center
Lam, Mei-Yung Lam; Lim, Swee Eng; Ma, Jung Chen; Adams, Leah D.
2003-01-01
This study examined the perceptions of teachers and parents of preschoolers in Hong Kong regarding what constitutes thinking skills, the importance of thinking skills in children's lives, strategies they use to foster thinking skills in young children, and their perceived roles in facilitating thinking skills. Responses revealed the need for more…
Dialogue on Early Childhood Science, Mathematics, and Technology Education.
ERIC Educational Resources Information Center
American Association for the Advancement of Science, Washington, DC.
Educators, scholars, and researchers in the United States convened at the Forum on Early Childhood Science, Mathematics, and Technology Education to discuss how, when, and even if science, mathematics, and technology should be taught to pre-kindergarten children. The product of that forum, this book summarizes some of the latest thinking about…
Teacher Interventions in Cooperative-Learning Mathematics Classes
ERIC Educational Resources Information Center
Ding, Meixia; Li, Xiaobao; Piccolo, Diana; Kulm, Gerald
2007-01-01
The authors examined the extent to which teacher interventions focused on students' mathematical thinking in naturalistic cooperative-learning mathematics classroom settings. The authors also observed 6 videotapes about the same teaching content using similar curriculum from 2 states. They created 2 instruments for coding the quality of teacher…
The I Hate Mathematics! Book. A Brown Paper School Book.
ERIC Educational Resources Information Center
Burns, Marilyn
This 1975 book is written for children who do not like mathematics and presents activities which may help them to begin understanding mathematics. Activities are organized under the following headings: "Street Math"; "Maybe Grownups Aren't as Smart as You Think"; "Things to Do When You Have the Flu"; "A Math-Magic Show"; "How to Always Be a…
Graphing Calculators in the Mathematics Classroom. ERIC Digest.
ERIC Educational Resources Information Center
Smith, Jeffrey P.
Graphing calculators present a challenging task for mathematics teachers in the classroom. This digest offers four distinct methods for using graphing calculators in mathematics classrooms, including: (1) tools for expediency; (2) amplifiers for conceptual understanding; (3) catalysts for critical thinking; and (4) vehicles for integration.…
The Layering of Mathematical Interpretations through Digital Media
ERIC Educational Resources Information Center
Calder, Nigel
2012-01-01
How might understanding emerge when learners engage mathematical phenomena through digital technologies? This paper considers the ways children's mathematical thinking was influenced by their interpretations through various pedagogical discourses and how understanding emerged through those various filters. Current research into using digital…
When Teachers Know What Students Know: Integrating Mathematics Assessment
ERIC Educational Resources Information Center
Gearhart, Maryl; Saxe, Geoffrey B.
2004-01-01
The premise of this article is that excellent teaching requires ongoing assessment of student understanding--a commitment to knowing what students know. The Integrating Mathematics Assessment (IMA) program provides a well-researched example of professional development that helps teachers interpret children's mathematical thinking and guide…
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…
Conceptualizing Mathematics as Discourse in Different Educational Settings
ERIC Educational Resources Information Center
Güçler, Beste; Wang, Sasha; Kim, Dong-Joong
2015-01-01
In this work, we focus on a relatively new theory in mathematics education research, which views thinking as communication and characterizes mathematics as a form of discourse. We discuss how this framework can be utilized in different educational settings by giving examples from our own research to highlight the insights it provides in the…
Influence of Demographic Factors on Students' Beliefs in Learning Mathematics
ERIC Educational Resources Information Center
Tahir, Izah Mohd; Bakar, Nor Mazlina Abu
2009-01-01
Learning mathematics has been recognized by many as important. It does not only develop students' ability to think in quantitative terms but can also enhance skills such as analytical and problem solving skills. However, to enable us to tell our students how important mathematics is we have to understand students' beliefs in learning mathematics…
[Probability, Cambridge Conference on School Mathematics Feasibility Study No. 7.
ERIC Educational Resources Information Center
Davis, R.
These materials were written with the aim of reflecting the thinking of the Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics. They represent a practical response to a proposal by CCSM that some elements of probability be introduced in the elementary grades. These materials provide children…
Inquiry-Based Learning and the Art of Mathematical Discourse
ERIC Educational Resources Information Center
von Renesse, Christine; Ecke, Volker
2015-01-01
Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate…
Everyday Pedagogical Practices in Mathematical Play Situations in German "Kindergarten"
ERIC Educational Resources Information Center
Brandt, Birgit
2013-01-01
This study describes situations in German daycare facilities (Kindergarten) in which the development of mathematical thinking in children is specifically encouraged through examination of common play objects. Using micro-sociological methods of analysis, the mathematical potential of such interactions between teacher and child is elaborated within…
CASMI: Virtual Learning Collaborative Environment for Mathematical Enrichment
ERIC Educational Resources Information Center
Freiman, Viktor; Manuel, Dominic; Lirette-Pitre, Nicole
2007-01-01
Challenging problems can make mathematics more attractive to all learners, including the gifted. Application problems that one still finds in regular textbooks often can be resolved by applying a single mathematical concept, operation, or formula. These problems do not require a higher order of thinking. They are, therefore, less cognitively and…
From Static to Dynamic Mathematics: Historical and Representational Perspectives
ERIC Educational Resources Information Center
Moreno-Armella, Luis; Hegedus, Stephen J.; Kaput, James J.
2008-01-01
The nature of mathematical reference fields has substantially evolved with the advent of new types of digital technologies enabling students greater access to understanding the use and application of mathematical ideas and procedures. We analyze the evolution of symbolic thinking over time, from static notations to dynamic inscriptions in new…
Writing as a Tool to Demonstrate Mathematical Understanding
ERIC Educational Resources Information Center
Martin, Christie Lynn
2015-01-01
In this study, I examine how using a writers' workshop model in mathematics creates a space for students to write about their mathematical thinking and problem solving and how their writing impacts instruction. This case study of one classroom with one teacher spanned 6 weeks and included 18 implementations of an adapted version of the Writers'…
Crystalline Concepts in Long-Term Mathematical Invention and Discovery
ERIC Educational Resources Information Center
Tall, David
2011-01-01
This paper introduces the notion of "crystalline concept" as a focal idea in long-term mathematical thinking, bringing together the geometric development of Van Hiele, process-object encapsulation, and formal axiomatic systems. Each of these is a strand in the framework of "three worlds of mathematics" with its own special characteristics, but all…
Teaching Writing and Communication in a Mathematical Modeling Course
ERIC Educational Resources Information Center
Linhart, Jean Marie
2014-01-01
Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…
Equations and Inequalities: Making Mathematics Accessible to All. PISA
ERIC Educational Resources Information Center
Piacentini, Mario; Monticone, Chiara
2016-01-01
More than ever, students need to engage with mathematics concepts, think quantitatively and analytically, and communicate using mathematics. All these skills are central to a young person's preparedness to tackle problems that arise at work and in life beyond the classroom. But the reality is that many students are not familiar with basic…
Teaching Mathematics from a Chemist's Viewpoint.
ERIC Educational Resources Information Center
DeLorenzo, Ronald A.
This paper describes a chemistry professor's approach to teaching mathematics in the college classroom. Based on the assumption that the four main goals of the educational process in general are to teach students to communicate clearly, study regularly, master basic math skills, and think logically, a description is provided of the manner in which…
Pablo's Tree: Mathematics in a Different Light.
ERIC Educational Resources Information Center
Wickett, Maryann
1996-01-01
Relates mathematics to literature through the story "Pablo's Tree." The students turn flat paper into three-dimensional boxes through the use of riddles, reasoning, and communication, thereby providing the teacher an easy, informal way to assess their level of thinking and understanding. (AIM)
Graphing Calculators: The Newest Revolution in Mathematics.
ERIC Educational Resources Information Center
Clutter, Martha
1999-01-01
Asserts that there are numerous advantages to using graphing calculators, including the teaching of higher-level thinking skills and allowing students to draw conclusions about what they are learning. However, mathematics educators face such challenges as teaching students when it is appropriate to use graphing calculators, course-content…
NASA Astrophysics Data System (ADS)
Rodríguez, Nancy
2015-03-01
The use of mathematical tools has long proved to be useful in gaining understanding of complex systems in physics [1]. Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematical tools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].
Pre-Service Teachers' Opinions on Teaching Thinking Skills
ERIC Educational Resources Information Center
Akinoglu, Orhan; Karsantik, Yasemin
2016-01-01
The purpose of the present study is to determine pre-service teachers' opinions on teaching thinking skills. 134 senior pre-service pre-school, English and mathematics teachers studying at a state university in Istanbul participated in the study which is designed based on survey model. A questionnaire which was developed by the researchers was…
Science and the City: Thinking Geospatially about Opportunity to Learn
ERIC Educational Resources Information Center
Tate, William F.; Jones, Brittni D.; Thorne-Wallington, Elizabeth; Hogrebe, Mark C.
2012-01-01
The purpose of this article is to describe several conceptual areas that warrant attention by scholars and practitioners interested in improving access and opportunity to science, technology, engineering, and mathematics (STEM) learning in urban cities. Thinking conceptually about the urban context has been a part of intellectual traditions in the…
The Critical Thinking Workout.
ERIC Educational Resources Information Center
Masters, Terry McDaniel
1991-01-01
Presents a critical thinking exercise program, modeled on a physical exercise workout, for elementary teachers to use in the classroom. It includes warm-up exercises, a more strenuous workout, and a cool-down period for the brain. (SM)
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…
ERIC Educational Resources Information Center
Aguirre, Julia M.; Zavala, Maria del Rosario; Katanyoutanant, Tiffany
2012-01-01
This study documents and describes efforts to develop robust forms of pre-service teachers' pedagogical content knowledge through a culturally responsive mathematics teaching approach. Embedded in a university K-8 mathematics methods course emphasising the connections among mathematics, children's mathematical thinking, and…
Systems Thinking (and Systems Doing).
ERIC Educational Resources Information Center
Brethower, Dale M.; Dams, Peter-Cornelius
1999-01-01
Introduces human performance technology (HPT) by answering the following questions related to: what systems does; practical issues and questions to which systems thinking is relevant; research questions and answers with respect to systems thinking; how HPT practitioners can do systems thinking; systems thinking tools; what is and is not known…
ERIC Educational Resources Information Center
Martin, Daisy; Wineburg, Sam
2008-01-01
Teaching a way of thinking requires making thinking visible. Educators need to pull back the curtains from historical cognition to show students not only what historians think, but "how" they think. Given that many students believe that history is a single story to be committed to memory and that texts speak for themselves, teaching historical…
The Curiosity in Marketing Thinking
ERIC Educational Resources Information Center
Hill, Mark E.; McGinnis, John
2007-01-01
This article identifies the curiosity in marketing thinking and offers ways to teach for marketing thinking through an environment that fosters students' curiosity. The significance of curiosity in its relationship with thinking is that when curiosity is absent, so is thinking. Challenges are discussed in recognizing the fragility of curiosity…
The ‘structure-function’ relationship in glaucoma – past thinking and current concepts
Malik, Rizwan; Swanson, William H.; Garway-Heath, David F
2013-01-01
An understanding of the relationship between functional and structural measures in primary open angle glaucoma (POAG) is necessary for both grading the severity of disease and for understanding the natural history of the condition. This article outlines the current evidence for the nature of this relationship, and highlights the current mathematical models linking structure and function. Large clinical trials demonstrate that both structural and functional change are apparent in advanced stages of disease, while, at an individual level, detectable structural abnormality may precede functional abnormality in some patients whilst the converse in true in other patients. Although the exact nature of the ‘structure-function’ relationship in POAG is still the topic of scientific debate and the subject of continuing research, this article aims to provide the clinician with an understanding of the past concepts and contemporary thinking in relation to the structure-function relationship in POAG. PMID:22339936
Malkevitch, J. ); McCarthy, D. )
1990-01-01
The papers in this volume represent talks given at the monthly meetings of the Mathematics Section of the New York Academy of Sciences. They reflect the operating philosophy of the Section in its efforts to make a meaningful contribution to the mathematical life of a community that is exceedingly rich in cultural resources and intellectual opportunities. Each week during the academic year a dazzling abundance of mathematical seminars and colloquia is available in the New York metropolitan area. Most of these offer highly technical treatments intended for specialists. At the New York Academy we try to provide a forum of a different sort, where interesting ideas are presented in a congenial atmosphere to a broad mathematical audience. Many of the Section talks contain substantial specialized material, but we ask our speakers to include a strong expository component aimed at working mathematicians presumed to have no expert knowledge of the topic at hand. We urge speakers to try to provide the motivating interest they themselves would like to find in an introduction to a field other than their own. The same advice has been given to the authors of the present papers, with the goal of producing a collection that will be both accessible and stimulating to mathematical minds at large. We have tried to provide variety in the mathematical vistas offered; both pure and applied mathematics are well represented. Since the papers are presented alphabetically by author, some guidance seems appropriate as to what sorts of topics are treated, and where. There are three papers in analysis: those by Engber, Narici and Beckenstein, and Todd. Engber's deals with complex analysis on compact Riemann surfaces; Narici and Beckenstein provide an introduction to analysis on non-Archimendean fields; Todd surveys an area of contemporary functional analysis.
ERIC Educational Resources Information Center
Coffman, Diane M.
2013-01-01
Thinking skills have long been regarded as an essential outcome of the educational process. Yet, research shows that the teaching of thinking skills in K-12 education does not follow a coherent path. Several factors affect the teaching and use of thinking skills in the classroom, with teacher knowledge and beliefs about thinking skills among the…
ERIC Educational Resources Information Center
Slisko, Josip; Cruz, Adrian Corona
2013-01-01
There is a general agreement that critical thinking is an important element of 21st century skills. Although critical thinking is a very complex and controversial conception, many would accept that recognition and evaluation of assumptions is a basic critical-thinking process. When students use simple mathematical model to reason quantitatively…
The Progressive Development of Early Embodied Algebraic Thinking
NASA Astrophysics Data System (ADS)
Radford, Luis
2014-06-01
In this article I present some results from a 5-year longitudinal investigation with young students about the genesis of embodied, non-symbolic algebraic thinking and its progressive transition to culturally evolved forms of symbolic thinking. The investigation draws on a cultural-historical theory of teaching and learning—the theory of objectification. Within this theory, thinking is conceived of as a form of reflection and action that is simultaneously material and ideal: It includes inner and outer speech, sensuous forms of imagination and visualisation, gestures, rhythm, and their intertwinement with material culture (symbols, artifacts, etc.). The theory articulates a cultural view of development as an unfolding dialectic process between culturally and historically constituted forms of mathematical knowing and semiotically mediated classroom activity. Looking at the experimental data through these theoretical lenses reveals a developmental path where embodied forms of thinking are sublated or subsumed into more sophisticated ones through the mediation of properly designed classroom activity.
TIMSS Advanced 2015 Assessment Frameworks
ERIC Educational Resources Information Center
Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.
2014-01-01
The "TIMSS Advanced 2015 Assessment Frameworks" provides the foundation for the two international assessments to take place as part of the International Association for the Evaluation of Educational Achievement's TIMSS (Trends in International Mathematics and Science Study) Advanced 2015--Advanced Mathematics and Physics. Chapter 1 (Liv…
Lowi-Young, Mimi; DuBois-Wing, Gwen
2016-01-01
Amol Verma and Sacha Bhatia's (2016) paper presents policy recommendations that merit serious consideration on a system-wide level. While they make compelling arguments about why provincial governments are ideally suited to adapt Triple Aim innovation, we are concerned that the current health system climate limits this possibility. In our commentary, we present our thoughts about the authors' admittedly aspirational goals and the realities of the pan-Canadian healthcare system. We commence our commentary by confirming our agreement about the potential inherent within the Triple Aim framework. Second, we argue how important progress can take place that may not reflect a provincial-wide system. Next, we maintain that a learning health system is an essential ingredient to advancing Triple Aim and other health system-wide improvements. Third, we wonder whether the stewardship role of government is real and possible. Finally, we question the concept of our current health system's readiness for system change. While we have raised some questions about Verma and Bhatia's thinking around provincial adoption of the Triple Aim, we applaud their ideas. We believe that transformation in provincial health systems requires bold thinking. PMID:27009585
Schlimm, Dirk
2013-04-01
This article looks at recent work in cognitive science on mathematical cognition from the perspective of history and philosophy of mathematical practice. The discussion is focused on the work of Lakoff and Núñez, because this is the first comprehensive account of mathematical cognition that also addresses advanced mathematics and its history. Building on a distinction between mathematics as it is presented in textbooks and as it presents itself to the researcher, it is argued that the focus of cognitive analyses of historical developments of mathematics has been primarily on the former, even if they claim to be about the latter. PMID:23580452
ERIC Educational Resources Information Center
Dougherty, Barbara; Bryant, Diane Pedrotty; Bryant, Brian R.; Darrough, Rebecca L.; Pfannenstiel, Kathleen Hughes
2015-01-01
Many students with learning disabilities (LD) in mathematics receive their mathematics education in general education inclusive classes; therefore, these students must be capable of learning algebraic concepts, including developing algebraic thinking abilities, that are part of the general education curriculum. To help students develop algebraic…
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…
ERIC Educational Resources Information Center
Borden, Lisa Lunney
2011-01-01
As part of a larger project focused on transforming mathematics education for Aboriginal students in Atlantic Canada, this paper reports on the role of the Mi'kmaw language in mathematics teaching. Examining how mathematical concepts are described in Mi'kmaq gives insight into ways of thinking. Shifting classroom discussions to reflect Mi'kmaw…
ERIC Educational Resources Information Center
Bennett, Elaine; Weidner, Jenny
2011-01-01
Children are born naturally mathematical, so why is it sometimes so difficult to observe children being mathematical? Why do so many of us think we are "bad" at maths and how does this subconsciously affect the provision, experiences and opportunities we provide for young children who are starting their mathematical learning journey? This easily…
Textbook and Course Materials for 21-127 "Concepts of Mathematics"
ERIC Educational Resources Information Center
Sullivan, Brendan W.
2013-01-01
Concepts of Mathematics (21-127 at CMU) is a course designed to introduce students to the world of abstract mathematics, guiding them from more calculation-based math (that one learns in high school) to higher mathematics, which focuses more on abstract thinking, problem solving, and writing "proofs." This transition tends to be a shock:…
ERIC Educational Resources Information Center
Zelkowski, Jeremy
2010-01-01
This paper posits the position that if higher education and secondary schools wish to increase students' college readiness, specifically in mathematics and critical thinking skills, continuous enrollment in secondary mathematics is one avenue worth exploring as opposed to increasing mathematics graduation requirements only in terms of Carnegie…
ERIC Educational Resources Information Center
Bufford, Carolyn A.; Mettler, Everett; Geller, Emma H.; Kellman, Philip J.
2014-01-01
Mathematics requires thinking but also pattern recognition. Recent research indicates that perceptual learning (PL) interventions facilitate discovery of structure and recognition of patterns in mathematical domains, as assessed by tests of mathematical competence. Here we sought direct evidence that a brief perceptual learning module (PLM)…
Student Participation in Mathematics Discourse in a Standards-Based Middle Grades Classroom
ERIC Educational Resources Information Center
Lack, Brian
2010-01-01
The vision of K-12 standards-based mathematics reform embraces a greater emphasis on students' ability to communicate their understandings of mathematics by utilizing adaptive reasoning (i.e., reflection, explanation, and justification of thinking) through mathematics discourse. However, recent studies suggest that many students lack the…
Foundations of resilience thinking.
Curtin, Charles G; Parker, Jessica P
2014-08-01
Through 3 broad and interconnected streams of thought, resilience thinking has influenced the science of ecology and natural resource management by generating new multidisciplinary approaches to environmental problem solving. Resilience science, adaptive management (AM), and ecological policy design (EPD) contributed to an internationally unified paradigm built around the realization that change is inevitable and that science and management must approach the world with this assumption, rather than one of stability. Resilience thinking treats actions as experiments to be learned from, rather than intellectual propositions to be defended or mistakes to be ignored. It asks what is novel and innovative and strives to capture the overall behavior of a system, rather than seeking static, precise outcomes from discrete action steps. Understanding the foundations of resilience thinking is an important building block for developing more holistic and adaptive approaches to conservation. We conducted a comprehensive review of the history of resilience thinking because resilience thinking provides a working context upon which more effective, synergistic, and systems-based conservation action can be taken in light of rapid and unpredictable change. Together, resilience science, AM, and EPD bridge the gaps between systems analysis, ecology, and resource management to provide an interdisciplinary approach to solving wicked problems. PMID:24975863
Cognitive functioning in mathematical problem solving during early adolescence
NASA Astrophysics Data System (ADS)
Collis, Kevin F.; Watson, Jane M.; Campbell, K. Jennifer
1993-12-01
Problem-solving in school mathematics has traditionally been considered as belonging only to the concrete symbolic mode of thinking, the mode which is concerned with making logical, analytical deductions. Little attention has been given to the place of the intuitive processes of the ikonic mode. The present study was designed to explore the interface between logical and intuitive processes in the context of mathematical problem solving. Sixteen Year 9 and 10 students from advanced mathematics classes were individually assessed while they solved five mathematics problems. Each student's problem-solving path, for each problem, was mapped according to the type of strategies used. Strategies were broadly classified into Ikonic (IK) or Concrete Symbolic (CS) categories. Students were given two types of problems to solve: (i) those most likely to attract a concrete symbolic approach; and (ii) problems with a significant imaging or intuitive component. Students were also assessed as to the vividness and controllability of their imaging ability, and their creativity. Results indicated that the nature of the problem is a basic factor in determining the type of strategy used for its solution. Students consistently applied CS strategies to CS problems, and IK strategies to IK problems. In addition, students tended to change modes significantly more often when solving CS-type problems than when solving IK-type problems. A switch to IK functioning appeared to be particularly helpful in breaking an unproductive set when solving a CS-type problem. Individual differences in strategy use were also found, with students high on vividness of imagery using IK strategies more frequently than students who were low on vividness. No relationship was found between IK strategy use and either students' degree of controllability of imagery or their level of creativity. The instructional implications of the results are discussed.
ERIC Educational Resources Information Center
Lapointe, Archie E.; And Others
In 1990-91, 20 countries (Brazil, Canada, China, England, France, Hungary, Ireland, Israel, Italy, Jordan, Korea, Mozambique, Portugal, Scotland, Slovenia, Soviet Union, Spain, Switzerland, Taiwan, and the United States) surveyed the mathematics and science performance of 13-year-old students (and 14 countries also assessed 9-year-olds in the same…
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
ERIC Educational Resources Information Center
Catterton, Gene; And Others
This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…
Loughlin, Michael; Wyer, Peter; Tanenbaum, Sandra J
2016-08-01
Professor Jenicek's paper is confused in that his proposal to 'integrate' what he means by 'evidence-based scientific theory and cognitive approaches to medical thinking' actually embodies a contradiction. But, although confused, he succeeds in teaching us more about the EBM debate than those who seem keen to forge ahead without addressing the underlying epistemological problems that Jenicek brings to our attention. Fundamental questions about the relationship between evidence, knowledge and reason still require resolution if we are to see a genuine advance in this debate. PMID:27225855
ERIC Educational Resources Information Center
Berryman, Sue E.
This paper describes trends in and causes of minority and female representation among holders of advanced science and math degrees. The minority groups studied are Blacks, Hispanic Americans, American Indians, and Asian Americans, all of whom are compared with Whites. The degrees looked at include those in math, the computer sciences, physical…
Mathematical Connections and Their Relationship to Mathematics Knowledge for Teaching Geometry
ERIC Educational Resources Information Center
Eli, Jennifer A.; Mohr-Schroeder, Margaret J.; Lee, Carl W.
2013-01-01
Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that…
Teaching theoretical thinking for a sense of salience.
Hanna, Debra R
2011-08-01
Using a thought-provoking photograph, blank paper, and a series of questions, graduate students were asked to engage in an interactive classroom exercise that helps them understand the process and usefulness of theoretical thinking. This one-time exercise helps students envision ways they will be able to use theoretical thinking when they enter their advanced practice roles. The exercise is followed by a short, debriefing lecture on the four levels of theory as originally described by Dickoff, James, and Weidenbach. Students engage in a four-stage, systematic process of theoretical thinking that can be used as a model for clinical reasoning and problem solving, especially for ambiguous situations. PMID:21598862
Mathematics Curriculum Guide. Mathematics IV.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
J.K. Brimacombe; I.V. Samarasekera; E.B. Hawbolt; T.R. Meadowcroft; M. Militzer; W.J. Pool; D.Q. Jin
1999-07-31
This report describes the work of developing an integrated model used to predict the thermal history, deformation, roll forces, microstructural evolution and mechanical properties of steel strip in a hot-strip mill. This achievement results from a joint research effort that is part of the American Iron and Steel Institute's (AIS) Advanced Process Control Program, a collaboration between the U.S. DOE and fifteen North American Steelmakers.
Thinking Like a Ssssscientist!
ERIC Educational Resources Information Center
Scott, Catherine; Tomasek, Terry; Matthews, Catherine E.
2010-01-01
A fear of snakes developed into an opportunity to teach students about the process of science: formulating questions, collecting and analyzing data, and communicating findings to the public. By using snakes to help students "think like a scientist," the authors engaged students in a five-day unit on inquiry while providing information about snakes…