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Sample records for advanced mathematical thinking

  1. 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.…

  2. 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.…

  3. 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…

  4. 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…

  5. 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…

  6. An Empirical Grounded Theory Approach to Characterizing Advanced Mathematical Thinking in College Calculus

    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…

  7. 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…

  8. 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)

  9. 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.

  10. 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…

  11. 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…

  12. Mathematical Thinking: From Cacophony to Consensus

    ERIC Educational Resources Information Center

    Argyle, Sean F.

    2012-01-01

    Various standards have demanded that teachers improve "mathematical thinking," but definitions are vague--if present at all. What little research on the subject exists is disjointed and dissenting, leading some researchers to lament the possibility of ever coming to an agreement on how to define "mathematical thinking" as a…

  13. 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…

  14. 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…

  15. 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…

  16. Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

    ERIC Educational Resources Information Center

    Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

    2016-01-01

    This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

  17. 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,…

  18. 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…

  19. 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.…

  20. Adding structure to the transition process to advanced mathematical activity

    NASA Astrophysics Data System (ADS)

    Engelbrecht, Johann

    2010-03-01

    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 deductive reasoning, required in advanced mathematics. It is necessary to assist students in this transition process, in moving from general to mathematical thinking. In this article some structure is suggested for this transition period. This essay is an argumentative exposition supported by personal experience and international literature. This makes this study theoretical rather than empirical.

  1. 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.…

  2. 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…

  3. Extending Students' Mathematical Thinking during Whole-Group Discussions

    ERIC Educational Resources Information Center

    Cengiz, Nesrin; Kline, Kate; Grant, Theresa J.

    2011-01-01

    Studies show that extending students' mathematical thinking during whole-group discussions is a challenging undertaking. To better understand what extending student thinking looks like and how teachers' mathematical knowledge for teaching (MKT) supports teachers in their efforts to extend student thinking, the teaching of six experienced…

  4. 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…

  5. 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…

  6. Advanced Analytic Cognition: Critical Thinking

    DTIC Science & Technology

    2013-09-01

    Published online ahead of print: 12/16/2010) 39 Beyer, B.K. Practical Strategies for the Teaching of Thinking, Allyn and Bacon , Boston, MA, 1987, p. 32...or critical thinking as such has no part in this linkage.78 David Schum and Francis Hume discussed critical reasoning within the context of...Teaching of Thinking, Allyn and Bacon , Boston, MA, 1987, p. 211. 110 Dewey, J. How We Think: A Restatement of the Relation of Reflective Thinking to

  7. 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…

  8. 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,…

  9. 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…

  10. 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…

  11. 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.

  12. Racial Differences in Mathematics Test Scores for Advanced Mathematics Students

    ERIC Educational Resources Information Center

    Minor, Elizabeth Covay

    2016-01-01

    Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…

  13. 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;…

  14. Advanced Analytic Cognition: Thinking Dispositions

    DTIC Science & Technology

    2013-09-01

    contributors to individual differences in cognitive processing . The experiments they conducted tended to be much more focused with clearer...21  4.2.1.   General Experiments into the Impact of Thinking Dispositions on Cognitive Performance...21 May 2014 1.0 SUMMARY Everyone agrees that intelligence analysis is an intensely cognitive process and that the quality of an analyst’s

  15. Think3d!: Improving mathematics learning through embodied spatial training.

    PubMed

    Burte, Heather; Gardony, Aaron L; Hutton, Allyson; Taylor, Holly A

    2017-01-01

    Spatial thinking skills positively relate to Science, Technology, Engineering, and Math (STEM) outcomes, but spatial training is largely absent in elementary school. Elementary school is a time when children develop foundational cognitive skills that will support STEM learning throughout their education. Spatial thinking should be considered a foundational cognitive skill. The present research examined the impact of an embodied spatial training program on elementary students' spatial and mathematical thinking. Students in rural elementary schools completed spatial and math assessments prior to and after participating in an origami and pop-up paper engineering-based program, called Think3d!. Think3d! uses embodied tasks, such as folding and cutting paper, to train two-dimensional to three-dimensional spatial thinking. Analyses explored spatial thinking gains, mathematics gains - specifically for problem types expected to show gains from spatial training - and factors predicting mathematics gains. Results showed spatial thinking gains in two assessments. Using a math categorization to target problems more and less likely to be impacted by spatial training, we found that all students improved on real-world math problems and older students improved on visual and spatial math problems. Further, the results are suggestive of developmental time points for implementing embodied spatial training related to applying spatial thinking to math. Finally, the spatial thinking assessment that was most highly related to training activities also predicted math performance gains. Future research should explore developmental issues related to how embodied spatial training might support STEM learning and outcomes.

  16. 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…

  17. 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…

  18. 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…

  19. 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,…

  20. A Mathematical Mystery Tour: Higher-Thinking Math Tasks.

    ERIC Educational Resources Information Center

    Wahl, Mark

    This book contains mathematics activities based upon the concepts of Fibonacci numbers and the Golden Ratio. The activities include higher order thinking skills, calculation practice, integration with different subject areas, mathematics history, extensions and home tasks, teaching notes, and questions for thought and comprehension. A visual map…

  1. Picture Books as an Impetus for Kindergartners' Mathematical Thinking

    ERIC Educational Resources Information Center

    van den Heuvel-Panhuizen, Marja; van den Boogaard, Sylvia

    2008-01-01

    Although there is evidence that the use of picture books affects young children's achievement scores in mathematics, little is known about the cognitive engagement and, in particular, the mathematical thinking that is evoked when young children are read a picture book. The focus of the case study reported in this article is on the cognitive…

  2. 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…

  3. An Analysis of Mathematics Teacher Candidates' Critical Thinking Dispositions and Their Logical Thinking Skills

    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…

  4. Conversations about curriculum change: mathematical thinking and team-based learning in a discrete mathematics course

    NASA Astrophysics Data System (ADS)

    Paterson, Judy; Sneddon, Jamie

    2011-10-01

    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 on what he calls the 'unspoken curriculum': mathematical thinking. We consider the ways in which the TBL model promoted and enabled this in the light of literature on mathematical thinking, sense-making and behaviours, and strongly suggest that this approach warrants more attention from the mathematics teaching community. We also discuss shifts in the mathematician's thinking about task construction as he refined the tasks to encourage students to think and behave like mathematicians.

  5. 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…

  6. Educational interventions to advance children's scientific thinking.

    PubMed

    Klahr, David; Zimmerman, Corinne; Jirout, Jamie

    2011-08-19

    The goal of science education interventions is to nurture, enrich, and sustain children's natural and spontaneous interest in scientific knowledge and procedures. We present taxonomy for classifying different types of research on scientific thinking from the perspective of cognitive development and associated attempts to teach science. We summarize the literature on the early--unschooled--development of scientific thinking, and then focus on recent research on how best to teach science to children from preschool to middle school. We summarize some of the current disagreements in the field of science education and offer some suggestions on ways to continue to advance the science of science instruction.

  7. Technology and Versatile Thinking in Mathematics.

    ERIC Educational Resources Information Center

    Tall, David

    Today's technology gives us a great opportunity to complement the subtlety of human thought with the power and accuracy of modern computers. In this presentation I consider fundamental modes of human thinking to see how enactive, visual and symbolic methods can be used in a versatile way with the support of well-designed software. My analysis…

  8. Conquer Mathematics Concepts by Developing Visual Thinking.

    ERIC Educational Resources Information Center

    Hershkowitz, Rina; Markovits, Zvia

    1992-01-01

    Describes the Agam program, a 36-unit curriculum program to introduce students to basic visual concepts and that applies visual abilities and visual thinking to learning tasks. Describes two units at the third grade level, "Ratio and Proportion" and "Numerical Intuition," and makes observations of the students' learning. (MDH)

  9. Inversion in Mathematical Thinking and Learning

    ERIC Educational Resources Information Center

    Greer, Brian

    2012-01-01

    Inversion is a fundamental relational building block both within mathematics as the study of structures and within people's physical and social experience, linked to many other key elements such as equilibrium, invariance, reversal, compensation, symmetry, and balance. Within purely formal arithmetic, the inverse relationships between addition and…

  10. Embedding Algebraic Thinking throughout the Mathematics Curriculum

    ERIC Educational Resources Information Center

    Vennebush, G. Patrick; Marquez, Elizabeth; Larsen, Joseph

    2005-01-01

    This article explores the algebra that can be uncovered in many middle-grades mathematics tasks that, on first inspection, do not appear to be algebraic. It shows connections to the other four Standards that occur in traditional algebra problems, and it offers strategies for modifying activities so that they can be used to foster algebraic…

  11. 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…

  12. 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…

  13. Teachers' Perceptions of Examining Students' Thinking: Changing Mathematics Instructional Practice

    ERIC Educational Resources Information Center

    Anderson-Pence, Katie L.

    2015-01-01

    This paper seeks to illuminate teachers' perceptions of the challenges and benefits of systematically examining students' thinking as part of a professional development program in elementary mathematics education. Using a framework of models of conceptual change and principles of discomfort, three elementary teachers' perceptions of their…

  14. 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…

  15. 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:…

  16. Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

    ERIC Educational Resources Information Center

    Mairing, Jackson Pasini

    2017-01-01

    Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…

  17. Teachers' Considerations of Students' Thinking during Mathematics Lesson Design

    ERIC Educational Resources Information Center

    Amador, Julie M.

    2016-01-01

    Teachers' abilities to design mathematics lessons are related to their capability to mobilize resources to meeting intended learning goals based on their noticing. In this process, knowing how teachers consider Students' thinking is important for understanding how they are making decisions to promote student learning. While teaching, what teachers…

  18. Leveling of Critical Thinking Abilities of Students of Mathematics Education in Mathematical Problem Solving

    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…

  19. 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…

  20. Teaching Thinking and Problem Solving. An Annotated Bibliography on Thinking Skills in Mathematics. A Cross-Laboratory Project on Teaching Thinking.

    ERIC Educational Resources Information Center

    Boswell, Anthony; Coan, Boyd

    This bibliography presents 21 references and abstracts for improving mathematics instruction in two ways. The first aim is to serve as a guide in locating higher-order thinking skills material in mathematics; the second is to encourage the integration of higher-order thinking skills techniques into the mathematics curriculum. Entries are included…

  1. 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.…

  2. Advanced Numerical-Algebraic Thinking: Constructing the Concept of Covariation as a Prelude to the Concept of Function

    ERIC Educational Resources Information Center

    Hitt, Fernando; Morasse, Christian

    2009-01-01

    Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…

  3. Developing Mathematical Thinking in the Primary Classroom: Liberating Students and Teachers as Learners of Mathematics

    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…

  4. 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…

  5. Chance Encounters: Probability in Games and Simulations. Seeing and Thinking Mathematically in the Middle Grades.

    ERIC Educational Resources Information Center

    Kleiman, Glenn; Zweig, Karen

    With the Seeing and Thinking Mathematically materials, students learn mathematics by doing mathematics, by using and connecting mathematical ideas, and by actively constructing their own understandings. In this unit students learn to see probability through a mathematical lens by exploring and creating games and simulations and by applying the…

  6. Prospective Middle School Mathematics Teachers' Reflective Thinking Skills: Descriptions of Their Students' Thinking and Interpretations of Their Teaching

    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…

  7. Advanced mathematical study and the development of conditional reasoning skills.

    PubMed

    Attridge, Nina; Inglis, Matthew

    2013-01-01

    Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general 'thinking skills'. Today, this argument, known as the 'Theory of Formal Discipline' is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought.

  8. Exploring Prospective Secondary Mathematics Teachers' Interpretation of Student Thinking through Analysing Students' Work in Modelling

    ERIC Educational Resources Information Center

    Didis, Makbule Gozde; Erbas, Ayhan Kursat; Cetinkaya, Bulent; Cakiroglu, Erdinc; Alacaci, Cengiz

    2016-01-01

    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…

  9. Exploring prospective secondary mathematics teachers' interpretation of student thinking through analysing students' work in modelling

    NASA Astrophysics Data System (ADS)

    Didis, Makbule Gozde; Erbas, Ayhan Kursat; Cetinkaya, Bulent; Cakiroglu, Erdinc; Alacaci, Cengiz

    2016-09-01

    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.

  10. Factors Considered by Elementary Teachers When Developing and Modifying Mathematical Tasks to Support Children's Mathematical Thinking

    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

  11. A preliminary study on the integral relationship between critical thinking and mathematical thinking among practicing civil engineers

    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

  12. The Impact of Chess Instruction on the Critical Thinking Ability and Mathematical Achievement of Developmental Mathematics Students

    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…

  13. Open-Ended Approach: An Effort in Cultivating Students' Mathematical Creative Thinking Ability and Self-Esteem in Mathematics

    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…

  14. 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.

  15. 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…

  16. 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.

  17. 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.

  18. What Secondary Teachers Think and Do about Student Engagement in Mathematics

    ERIC Educational Resources Information Center

    Skilling, Karen; Bobis, Janette; Martin, Andrew J.; Anderson, Judy; Way, Jennifer

    2016-01-01

    What teachers' think about student engagement influences the teaching practices they adopt, their responses to students and the efforts they make in the classroom. Interviews were conducted with 31 mathematics teachers from ten high schools to investigate their perceptions and beliefs about student engagement in mathematics. Teachers also reported…

  19. 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…

  20. 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…

  1. 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…

  2. Elementary Preservice Teachers' Changing Beliefs and Instructional Use of Children's Mathematical Thinking.

    ERIC Educational Resources Information Center

    Vacc, Nancy Nesbitt; Bright, George W.

    1999-01-01

    Examines changes in preservice elementary teachers' beliefs about teaching and learning mathematics and their ability to provide mathematics instruction that is based on children's thinking. Reports that, after participants were introduced to Cognitively Guided Instruction (CGI), significant changes in their beliefs and perceptions about…

  3. Supporting Prospective Teachers to Notice Students' Mathematical Thinking through Rehearsal Activities

    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…

  4. Hybrid Tasks: Promoting Statistical Thinking and Critical Thinking through the Same Mathematical Activities

    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…

  5. 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…

  6. The Role of Technology in Supporting Students' Mathematical Thinking: Extending the Metaphors of Amplifier and Reorganizer

    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…

  7. Creative Thinking Ability to Increase Student Mathematical of Junior High School by Applying Models Numbered Heads Together

    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…

  8. The Enhancement of Mathematical Critical Thinking Ability of Aliyah Madrasas Student Model Using Gorontalo by Interactive Learning Setting Cooperative Model

    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…

  9. 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…

  10. 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 resulted…

  11. 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.…

  12. Secondary School Advanced Mathematics, Chapter 3, Formal Geometry. Student's Text.

    ERIC Educational Resources Information Center

    Stanford Univ., CA. School Mathematics Study Group.

    This text is the second 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 volume is devoted to a rigorous development of theorems in plane geometry from 22…

  13. 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…

  14. Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School.

    ERIC Educational Resources Information Center

    Carpenter, Thomas P.; Franke, Megan Loef; Levi, Linda

    This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…

  15. Attributes of Instances of Student Mathematical Thinking That Are Worth Building on in Whole-Class Discussion

    ERIC Educational Resources Information Center

    Van Zoest, Laura R.; Stockero, Shari L.; Leatham, Keith R.; Peterson, Blake E.; Atanga, Napthalin A.; Ochieng, Mary A.

    2017-01-01

    This study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners' understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative…

  16. La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

    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.

  17. Sources of mathematical thinking: behavioral and brain-imaging evidence.

    PubMed

    Dehaene, S; Spelke, E; Pinel, P; Stanescu, R; Tsivkin, S

    1999-05-07

    Does the human capacity for mathematical intuition depend on linguistic competence or on visuo-spatial representations? A series of behavioral and brain-imaging experiments provides evidence for both sources. Exact arithmetic is acquired in a language-specific format, transfers poorly to a different language or to novel facts, and recruits networks involved in word-association processes. In contrast, approximate arithmetic shows language independence, relies on a sense of numerical magnitudes, and recruits bilateral areas of the parietal lobes involved in visuo-spatial processing. Mathematical intuition may emerge from the interplay of these brain systems.

  18. 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…

  19. 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…

  20. 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…

  1. Relationship between Professional Values and Critical Thinking Disposition of Science-Technology and Mathematics Teachers

    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…

  2. Responding to Children's Mathematical Thinking in the Moment: An Emerging Framework of Teaching Moves

    ERIC Educational Resources Information Center

    Jacobs, Victoria R.; Empson, Susan B.

    2016-01-01

    This case study contributes to efforts to characterize teaching that is responsive to children's mathematical thinking. We conceptualize "responsive teaching" as a type of teaching in which teachers' instructional decisions about what to pursue and how to pursue it are continually adjusted during instruction in response to children's…

  3. Development of an Instrument to Measure Higher Order Thinking Skills in Senior High School Mathematics Instruction

    ERIC Educational Resources Information Center

    Tanujaya, Benidiktus

    2016-01-01

    The purpose of this research was to develop an instrument that can be used to measure higher-order thinking skills (HOTS) in mathematics instruction of high school students. This research was conducted using a standard procedure of instrument development, from the development of conceptual definitions, development of operational definitions,…

  4. The Relationship between Students' Mathematical Thinking Types and Representation Preferences in Definite Integral Problems

    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…

  5. 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…

  6. Designing Spaces: Visualizing, Planning, and Building. Seeing and Thinking Mathematically in the Middle Grades.

    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…

  7. Examination of Gifted Students' Probability Problem Solving Process in Terms of Mathematical Thinking

    ERIC Educational Resources Information Center

    Baltaci, Serdal

    2016-01-01

    It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students' probability…

  8. 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…

  9. 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).…

  10. Making Connections in Practice: How Prospective Elementary Teachers Connect to Children's Mathematical Thinking and Community Funds of Knowledge in Mathematics Instruction

    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…

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

    ERIC Educational Resources Information Center

    van Velzen, Joke H.

    2016-01-01

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

  12. 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…

  13. 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…

  14. La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

    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…

  15. Promoting Equity in Mathematics Teacher Preparation: A Framework for Advancing Teacher Learning of Children's Multiple Mathematics Knowledge Bases

    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,…

  16. Effects of Early Acceleration of Students in Mathematics on Taking Advanced Mathematics Coursework in High School

    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…

  17. A Review of Research on Prospective Teachers' Learning about Children's Mathematical Thinking and Cultural Funds of Knowledge

    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…

  18. Students' Conceptual Understanding and Critical Thinking: A Case for Concept Maps and Vee-Diagrams in Mathematics Problem Solving

    ERIC Educational Resources Information Center

    Afamasaga-Fuata'i, Karoline

    2008-01-01

    With the current focus in mathematics education on the importance of developing students' conceptual understanding, fluency with the language of mathematics, critical thinking, and working mathematically, teachers are constantly expected to design challenging and investigative tasks that can engage and motivate students in their learning of…

  19. Carpenter, Tractors and Microbes for the Development of Logical-Mathematical Thinking--The Way 10th Graders and Pre-Service Teachers Solve Thinking Challenges

    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…

  20. Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

    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…

  1. Motivating Prospective Elementary School Teachers to Learn Mathematics by Focusing upon Children's Mathematical Thinking

    ERIC Educational Resources Information Center

    Philipp, Randolph A.

    2008-01-01

    Elementary school children in the United States are not developing acceptable levels of mathematical proficiency (National Center for Education Statistics, 1999), and a major concern of teacher educators is that teachers lack the depth and flexibility of mathematical understanding and the corresponding beliefs they need to teach for proficiency…

  2. Neuroscientific Studies of Mathematical Thinking and Learning: A Critical Look from a Mathematics Education Viewpoint

    ERIC Educational Resources Information Center

    Verschaffel, Lieven; Lehtinen, Erno; Van Dooren, Wim

    2016-01-01

    In this commentary we take a critical look at the various studies being reported in this issue about the relationship between cognitive neuroscience and mathematics, from a mathematics education viewpoint. After a discussion of the individual contributions, which we have grouped into three categories--namely neuroscientific studies of (a)…

  3. Provoking Mathematical Thinking: Experiences of Doing Realistic Mathematics Tasks with Adult Numeracy Teachers

    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…

  4. What secondary teachers think and do about student engagement in mathematics

    NASA Astrophysics Data System (ADS)

    Skilling, Karen; Bobis, Janette; Martin, Andrew J.; Anderson, Judy; Way, Jennifer

    2016-12-01

    What teachers' think about student engagement influences the teaching practices they adopt, their responses to students and the efforts they make in the classroom. Interviews were conducted with 31 mathematics teachers from ten high schools to investigate their perceptions and beliefs about student engagement in mathematics. Teachers also reported the practices they used to engage their students during mathematics lessons. Teacher perceptions of student engagement were categorised according to recognised `types' (behavioural, emotional and cognitive) and `levels' (ranging from disengaged to engaged). The teachers' reports emphasised immediate attention being paid to students' behaviours and overt emotions towards mathematics with fewer and less extensive reports made about students' cognitive engagement. Teachers' abilities to implement practices considered supportive of student engagement were linked to a number of elements, including their self-efficacy. Perceptions of being powerless to engage their students resulted in many teachers limiting their efforts to attempt some form of intervention.

  5. An initial framework for the language of higher-order thinking mathematics practices

    NASA Astrophysics Data System (ADS)

    Staples, Megan E.; Truxaw, Mary P.

    2012-09-01

    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 language of analysing impact. These categories were developed out of our collaborative work to design and implement higher-order thinking tasks with a group of Grade 9 (14- and 15-year-olds) teachers teaching in a linguistically diverse setting; analyses of student work samples on these tasks; and our knowledge of the literature. We describe each type of language demand and then analyse student work in each category to reveal linguistic challenges facing students as they engage these mathematical tasks. Implications for teaching and professional development are discussed.

  6. Computer Simulations and the Transition from Concrete Manipulation of Objects to Abstract Thinking in Elementary School Mathematics.

    ERIC Educational Resources Information Center

    Berlin, Donna; White, Arthur

    1986-01-01

    This study investigated the effects of combining interactive microcomputer simulations and concrete activities on the development of abstract thinking in elementary school mathematics. Students in grades 2-4 were assessed on tasks involving designs and patterns. (MNS)

  7. 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…

  8. Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education. Studies in Mathematical Thinking and Learning Series

    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…

  9. The Effectiveness of Local Culture-Based Mathematical Heuristic-KR Learning towards Enhancing Student's Creative Thinking Skill

    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…

  10. Learning to teach upper primary school algebra: changes to teachers' mathematical knowledge for teaching functional thinking

    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.

  11. 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…

  12. 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…

  13. The Impact of Problem-Based Learning Approach to Senior High School Students' Mathematics Critical Thinking Ability

    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…

  14. Using Internet Primary Sources To Teach Critical Thinking Skills in Mathematics. Greenwood Professional Guides in School Librarianship.

    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…

  15. Advanced Mathematical Tools in Metrology III

    NASA Astrophysics Data System (ADS)

    Ciarlini, P.

    The Table of Contents for the book is as follows: * Foreword * Invited Papers * The ISO Guide to the Expression of Uncertainty in Measurement: A Bridge between Statistics and Metrology * Bootstrap Algorithms and Applications * The TTRSs: 13 Oriented Constraints for Dimensioning, Tolerancing & Inspection * Graded Reference Data Sets and Performance Profiles for Testing Software Used in Metrology * Uncertainty in Chemical Measurement * Mathematical Methods for Data Analysis in Medical Applications * High-Dimensional Empirical Linear Prediction * Wavelet Methods in Signal Processing * Software Problems in Calibration Services: A Case Study * Robust Alternatives to Least Squares * Gaining Information from Biomagnetic Measurements * Full Papers * Increase of Information in the Course of Measurement * A Framework for Model Validation and Software Testing in Regression * Certification of Algorithms for Determination of Signal Extreme Values during Measurement * A Method for Evaluating Trends in Ozone-Concentration Data and Its Application to Data from the UK Rural Ozone Monitoring Network * Identification of Signal Components by Stochastic Modelling in Measurements of Evoked Magnetic Fields from Peripheral Nerves * High Precision 3D-Calibration of Cylindrical Standards * Magnetic Dipole Estimations for MCG-Data * Transfer Functions of Discrete Spline Filters * An Approximation Method for the Linearization of Tridimensional Metrology Problems * Regularization Algorithms for Image Reconstruction from Projections * Quality of Experimental Data in Hydrodynamic Research * Stochastic Drift Models for the Determination of Calibration Intervals * Short Communications * Projection Method for Lidar Measurement * Photon Flux Measurements by Regularised Solution of Integral Equations * Correct Solutions of Fit Problems in Different Experimental Situations * An Algorithm for the Nonlinear TLS Problem in Polynomial Fitting * Designing Axially Symmetric Electromechanical Systems of

  16. Mathematical foundations of quantum mechanics: An advanced short course

    NASA Astrophysics Data System (ADS)

    Moretti, Valter

    2016-08-01

    This paper collects and extends the lectures I gave at the “XXIV International Fall Workshop on Geometry and Physics” held in Zaragoza (Spain) during September 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C∗-) algebraic formulation of quantum theories.

  17. Thinking.

    PubMed

    Smythe, Elizabeth A

    2004-05-01

    This paper argues that thinking is assumed within nursing education. There are strategies to promote thinking: reflective practice, critical analysis and problem solving. I suggest that by categorising thinking into such boxes there may be a danger of limiting the rich possibilities of simply 'thinking'. The writings of Heidegger (1889-1976) are cited, highlighting the need to 'call' thinking, and to meditate or ponder on the things that matter. The paper comes from research that asked the question 'What calls for thinking in postgraduate education?' Findings reveal examples of teachers and students recalling 'thinking experiences' but also suggest there is a danger that students do not have time to think in a busy classroom situation. It appears that thinking is more likely to happen outside of the classroom, with peers, in assignment writing, or when thoughts simply come. The challenge to nursing education is that not only may teachers be limiting students thinking opportunities, but they may be directing thinking in a way that maintains the status quo. If nursing is to equip itself as a dynamic profession and take initiative for shaping its own future, then close attention must be paid to enabling thinking.

  18. 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.…

  19. Listening to and Learning from Student Thinking

    ERIC Educational Resources Information Center

    Kazemi, Elham; Gibbons, Lynsey K.; Lomax, Kendra; Franke, Megan L.

    2016-01-01

    Eliciting, responding to, and advancing students' mathematical thinking all lie at the heart of great teaching. In this article, the authors describe a formative assessment approach that teachers can use to learn more about their students' mathematical thinking and inform their instructional decisions. This assessment approach draws on a widely…

  20. Carpenter, tractors and microbes for the development of logical-mathematical thinking - the way 10th graders and pre-service teachers solve thinking challenges

    NASA Astrophysics Data System (ADS)

    Gazit, Avikam

    2012-12-01

    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 graders was higher than that of the pre-service teachers. Unlike the 10th graders, some of whom used various strategies for representing the problem, most of the pre-service teachers' answers were based on a technical algorithm, without using control processes. The obvious conclusion drawn from the findings supports and recommends expanding and enhancing the development of logical-mathematical thinking, both in specific lessons and as an integral part of other lessons in pre-service frameworks.

  1. Teaching students to think spatially through embodied actions: Design principles for learning environments in science, technology, engineering, and mathematics.

    PubMed

    DeSutter, D; Stieff, M

    2017-01-01

    Spatial thinking is a vital component of the science, technology, engineering, and mathematics curriculum. However, to date, broad development of learning environments that target domain-specific spatial thinking is incomplete. The present article visits the problem of improving spatial thinking by first reviewing the evidence that the human mind is embodied: that cognition, memory, and knowledge representation maintain traces of sensorimotor impressions from acting and perceiving in a physical environment. In particular, we review the evidence that spatial cognition and the ways that humans perceive and conceive of space are embodied. We then propose a set of design principles to aid researchers, designers, and practitioners in creating and evaluating learning environments that align principled embodied actions to targets of spatial thinking in science, technology, engineering, and mathematics.

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

    ERIC Educational Resources Information Center

    Yuliani, Kiki; Saragih, Sahat

    2015-01-01

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

  3. Integration of Critical Thinking Skills into Elementary School Teacher Education Courses in Mathematics

    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…

  4. Advancing socio-technical systems thinking: a call for bravery.

    PubMed

    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.

  5. The Role of Analogical Thinking in Designing Tasks for Mathematics Teacher Education: An Example of a Pedagogical Ad Hoc Task

    ERIC Educational Resources Information Center

    Peled, Irit

    2007-01-01

    This article discusses the design of tasks for teacher education. It focuses on tasks that are used in a university course for pre-service secondary school mathematics teachers. Special attention is given to tasks that use analogical thinking in their construction or implementation. These tasks are categorized by type of teacher education goal and…

  6. Mathematics Teachers' Level of Knowledge and Practice on the Implementation of Higher-Order Thinking Skills (HOTS)

    ERIC Educational Resources Information Center

    Abdullah, Abdul Halim; Mokhtar, Mahani; Halim, Noor Dayana Abd; Ali, Dayana Farzeeha; Tahir, Lokman Mohd; Kohar, Umar Haiyat Abdul

    2017-01-01

    This study aims to identify the level of knowledge and practice on the implementation of higher-order thinking skills (HOTS) among mathematics teachers at a secondary school in the district of Terengganu. The study focused on the aspects of curriculum, pedagogy and assessment and compared them with demographic factors of the respondents. It used…

  7. VStops: A Thinking Strategy and Visual Representation Approach in Mathematical Word Problem Solving toward Enhancing STEM Literacy

    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)…

  8. Characteristics of Computational Thinking about the Estimation of the Students in Mathematics Classroom Applying Lesson Study and Open Approach

    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…

  9. Ways of Thinking Associated with Mathematics Teachers' Problem Posing in the Context of Division of Fractions

    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…

  10. Scientific thinking in young children: theoretical advances, empirical research, and policy implications.

    PubMed

    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.

  11. Systems Thinking: An Approach for Advancing Workplace Information Literacy

    ERIC Educational Resources Information Center

    Somerville, Mary M.; Howard, Zaana

    2008-01-01

    As the importance of information literacy has gained increased recognition, so too have academic library professionals intensified their efforts to champion, activate, and advance these capabilities in others. To date, however, little attention has focused on advancing these essential competencies amongst practitioner advocates. This paper helps…

  12. 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…

  13. Capitalizing on Advances in Mathematics and K-12 Mathematics Education in Undergraduate Mathematics: An Inquiry-Oriented Approach to Differential Equations

    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…

  14. Mathematical Foresight: Thinking in the Future to Work in the Present

    ERIC Educational Resources Information Center

    Maciejewski, Wes; Barton, Bill

    2016-01-01

    Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes's reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical…

  15. CEEB Advanced Placement Mathematics Examination Results and Performance in First-Quarter UW Calculus Course.

    ERIC Educational Resources Information Center

    de Wolf, Virginia A.

    Freshmen placed into the second or third quarter of the first year calculus sequence at the University of Washington were studied. Two major findings were: freshmen eligible for advanced placement earned mean mathematics Grade Point Averages (GPAs) which were quite high; and advanced placement students earned mean mathematics GPAs substantially…

  16. A Cross-National Comparison of Reported Effort and Mathematics Performance in TIMSS Advanced

    ERIC Educational Resources Information Center

    Eklöf, Hanna; Pavešic, Barbara Japelj; Grønmo, Liv Sissel

    2014-01-01

    The purpose of the study was to measure students' reported test-taking effort and the relationship between reported effort and performance on the Trends in International Mathematics and Science Study (TIMSS) Advanced mathematics test. This was done in three countries participating in TIMSS Advanced 2008 (Sweden, Norway, and Slovenia), and the…

  17. Thinking and Content Learning of Mathematics and Science as Cognitional Development in Content and Language Integrated Learning (CLIL): Teaching Through a Foreign Language in Finland

    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…

  18. What do trainees think about advanced trauma life support (ATLS)?

    PubMed Central

    Campbell, B.; Heal, J.; Evans, S.; Marriott, S.

    2000-01-01

    Advanced trauma life support (ATLS) has become a desirable or even essential part of training for many surgeons and anaesthetists, but aspects of the ATLS course have attracted criticism. In the absence of published data on the views of trainees, this study sought their opinions in a structured questionnaire, which was completed by trainees in accident and emergency (A & E) (26), anaesthetic (82), general surgical (26), orthopaedic (42) and other (5) posts in different hospitals (response rate 66%). Of the trainees, 78% had done an ATLS course and, of these, 83% considered ATLS a 'major advantage' or 'essential' for practising their proposed specialty--100% for A & E, 94% for orthopaedics, 92% for general surgery, and 75% for anaesthetics. ATLS was considered a major curriculum vitae (CV) advantage by 94%, 85%, 50%, and 45%, respectively. Over 90% had positive attitudes towards ATLS, and 74% selected 'genuine improvement of management of trauma patients' as the most important reason for doing the course: 93% thought ATLS saved lives. Of the respondents, 83% thought that all existing consultants dealing with trauma patients should have done the course, and 41% thought it offered major advantages to doctors not involved in trauma. Funding problems for ATLS courses had been experienced by 14% trainees. This survey has shown that most trainees view ATLS positively. They believe that it provides genuine practical benefit for patients, and very few regard ATLS primarily as a career advantage or mandate. PMID:10932661

  19. Mathematical Thinking of Kindergarten Boys and Girls: Similar Achievement, Different Contributing Processes

    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…

  20. 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…

  1. Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction. Studies in Mathematical Thinking and Learning Series

    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…

  2. Developing Mathematical Thinking and Self-Regulated Learning: A Teaching Experiment in a Seventh-Grade Mathematics Classroom

    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…

  3. 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…

  4. Some observations on the interdigitation of advances in medical science and mathematics.

    PubMed

    Glamore, Michael James; West, James L; O'leary, James Patrick

    2013-12-01

    The immense advancement of our understanding of disease processes has not been a uniform progression related to the passage of time. Advances have been made in "lurches" and "catches" since the advent of the written word. There has been a remarkable interdependency between such advances in medicine and advances in mathematics that has proved beneficial to both. This work explores some of these critical relationships and documents how the individuals involved contributed to advances in each.

  5. 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…

  6. Third Graders' Mathematical Thinking of Place Value through the Use of Concrete and Virtual Manipulatives

    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…

  7. Challenging a Teacher's Perceptions of Mathematical Smartness through Reflections on Students' Thinking

    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…

  8. Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey

    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…

  9. 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…

  10. Origins of the brain networks for advanced mathematics in expert mathematicians

    PubMed Central

    Amalric, Marie; Dehaene, Stanislas

    2016-01-01

    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

  11. PREFACE: International Conference on Advancement in Science and Technology 2012 (iCAST): Contemporary Mathematics, Mathematical Physics and their Applications

    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.

  12. Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL

    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…

  13. Prediction Assessments: Using Video-Based Predictions to Assess Prospective Teachers' Knowledge of Students' Mathematical Thinking

    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…

  14. "Change My Thinking Patterns towards Maths": A Bibliotherapy Workshop for Pre-Service Teachers' Mathematics Anxiety

    ERIC Educational Resources Information Center

    Wilson, Sue; Raven, Monica

    2014-01-01

    In small-group workshops, a joint initiative of the researcher and the student counsellor, primary (elementary) pre-service teachers (PSTs) wrote about critical incidents in their mathematics learning, and shared them with the group. Then, PSTs read extracts about mathematics anxiety (maths anxiety), and wrote and shared their reflections…

  15. Connecting Social and Mathematical Thinking: The Use of "Real Life" Contexts

    ERIC Educational Resources Information Center

    Sawatzki, Carly

    2014-01-01

    This paper reports the findings of research into an educational intervention featuring open-ended mathematical problems situated in "real life" contexts and associated pedagogies. "Money and financial mathematics" is the topic in focus, with tasks termed "financial dilemmas" being trialled by 35 teachers in 16…

  16. 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…

  17. Using the Learners World to Construct and Think in a System of Mathematical Symbols

    ERIC Educational Resources Information Center

    Kerekes, Judit

    2005-01-01

    According to Dutch mathematician and educator Hans Freudenthal, mathematics is a human activity that unfolds in a process and can be best learned through personal experience (Gravemeijer & Treffers, 2000). Such experience involves the solving of real life problems; they require mathematization based on reality. Students should therefore be given…

  18. Middle School Mathematics: 2006-07 to 2008-09. Impact Evaluation. E&R Report No. 10.11

    ERIC Educational Resources Information Center

    Paeplow, Colleen

    2010-01-01

    In 2006-07, seven Wake County Public School System (WCPSS) middle schools piloted Algebraic Thinking as an alternate approach to teaching middle school mathematics. Algebraic Thinking was developed to help students in grade 6 reach higher mathematics courses by combining the regular and advanced middle school mathematics courses into one…

  19. Mathematics and Literature (the Sequel): Imagination as a Pathway to Advanced Mathematical Ideas and Philosophy

    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…

  20. 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…

  1. 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…

  2. 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…

  3. 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…

  4. Instructional Reasoning about Interpretations of Student Thinking That Supports Responsive Teaching in Secondary Mathematics

    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…

  5. Enhancing Mathematics Teachers' Knowledge of Students' Thinking from Assessing and Analyzing Misconceptions in Homework

    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…

  6. Mathematical Thinking Intervention Programmes for Preschool Children with Normal and Low Number Sense

    ERIC Educational Resources Information Center

    Aunio, Pirjo; Hautamaki, Jarkko; Van Luit, Johannes E. H.

    2005-01-01

    This study investigated the possibility of enhancing the level of preschoolers number sense by introducing two intervention programmes, "Lets think!" and "Young children with special educational needs count, too!" Forty-five preschoolers, mean age 66.4 months, were randomly assigned to the experimental and control groups. The…

  7. 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…

  8. Mathematics in the Early Grades: Operations & Algebraic Thinking. Interactive STEM Research + Practice Brief

    ERIC Educational Resources Information Center

    Education Development Center, Inc., 2016

    2016-01-01

    In the domain of "Operations & Algebraic Thinking," Common Core State Standards indicate that in kindergarten, first grade, and second grade, children should demonstrate and expand their ability to understand, represent, and solve problems using the operations of addition and subtraction, laying the foundation for operations using…

  9. An Investigation into Logical Thinking Skills and Proof Writing Levels of Prospective Mathematics Teachers

    ERIC Educational Resources Information Center

    Özdemir, Emine; Övez, Filiz Tuba Dikkartin

    2017-01-01

    The cognitive development of prospective teacher needs to be taken into estimate so that proofs are presented in forms that are potentially meaningful for them. This requires educators and mathematicians to rethink consider the use of types of proof related to the logical thinking improvement of the singular. The purpose of the study is to…

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

    ERIC Educational Resources Information Center

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

    2013-01-01

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

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

    PubMed

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

    2016-09-01

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

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

    PubMed Central

    2016-01-01

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

  13. Supporting teachers in the development of young children's mathematical thinking: Three large scale cases

    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.

  14. 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…

  15. Integrating quantitative thinking into an introductory biology course improves students' mathematical reasoning in biological contexts.

    PubMed

    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.

  16. Assessing the Mathematical Thinking of Young Children in New Zealand: The Initial School Years

    ERIC Educational Resources Information Center

    Young-Loveridge, Jenny

    2011-01-01

    This paper provides an overview of assessment policy and practice in mathematics for early years classrooms in New Zealand between 1993 and the present day. It describes the introduction of school entry assessment for children starting school at age five. A numeracy initiative, the Numeracy Development Projects (NDP), for students in Years 1-10…

  17. 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…

  18. What Were You Thinking? A Deleuzian/Guattarian Analysis of Communication in the Mathematics Classroom

    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…

  19. Learning to Teach Upper Primary School Algebra: Changes to Teachers' Mathematical Knowledge for Teaching Functional Thinking

    ERIC Educational Resources Information Center

    Wilkie, Karina J.

    2016-01-01

    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…

  20. 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.

  1. 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)

  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…

  3. The Effect of Scratch- and Lego Mindstorms Ev3-Based Programming Activities on Academic Achievement, Problem-Solving Skills and Logical-Mathematical Thinking Skills of Students

    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…

  4. A Cognition Analysis of QUASAR's Mathematics Performance Assessment Tasks and Their Sensitivity to Measuring Changes in Middle School Students' Thinking and Reasoning.

    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…

  5. Evaluating the Effects of Lesson Study as a Way to Help Student Teachers Learn How to Use Student Thinking when Planning and Revising Mathematics Lesson Plans

    ERIC Educational Resources Information Center

    Sisofo, Eric Joseph

    2010-01-01

    The use of student thinking in teaching has been linked to improved instruction and learning. It is reasonable to assume that the University of Delaware's undergraduate program might be interested in figuring out ways to develop this skill in its mathematics specialist pre-service teachers. Currently, the student teaching experience at the…

  6. Development of Analytical Thinking Ability and Attitudes towards Science Learning of Grade-11 Students through Science Technology Engineering and Mathematics (STEM Education) in the Study of Stoichiometry

    ERIC Educational Resources Information Center

    Chonkaew, Patcharee; Sukhummek, Boonnak; Faikhamta, Chatree

    2016-01-01

    The purpose of this study was to investigate the analytical thinking abilities and attitudes towards science learning of grade-11 students through science, technology, engineering, and mathematics (STEM) education integrated with a problem-based learning in the study of stoichiometry. The research tools consisted of a pre- and post-analytical…

  7. Participation in Advanced Mathematics: Do Expectation and Influence of Students, Peers, Teachers, and Parents Matter?

    PubMed

    Ma, Xin

    2001-01-01

    Using six waves of data (Grades 7 through 12) from the Longitudinal Study of American Youth (LSAY), this study investigated the effects of expectation and influence of students, peers, teachers, and parents on participation in advanced mathematics. Results of survival analysis indicated a significant decline in participation rate in the transition from Grades 11 to 12. Students with higher future expectation were more likely to participate in advanced mathematics. Peer influence and teacher expectation did not have strong effects, and the effect of student future expectation was independent of peer and teacher effects. The effect of parent expectation and parent college plan for children were strong, and in their presence, the effect of student future expectation declined. Mathematics achievement and attitude toward mathematics were the most important factors affecting participation in advanced mathematics. With control over achievement and attitude, (a) the effect of student future expectation declined, (b) the effects of peer influence and teacher expectation disappeared, and (c) the effects of parent expectation and parent college plan for children were reduced. Copyright 2001 Academic Press.

  8. Which Advanced Mathematics Courses Influence ACT Score? A State Level Analysis of the Iowa Class of 2012

    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…

  9. Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Student's Text.

    ERIC Educational Resources Information Center

    Stanford Univ., CA. School Mathematics Study Group.

    This text is the first 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. The first chapter, devoted to organizing geometric knowledge, deals with the distinction…

  10. Mathematical Modelling and Tuberculosis: Advances in Diagnostics and Novel Therapies

    PubMed Central

    Zwerling, Alice; Shrestha, Sourya; Dowdy, David W.

    2015-01-01

    As novel diagnostics, therapies, and algorithms are developed to improve case finding, diagnosis, and clinical management of patients with TB, policymakers must make difficult decisions and choose among multiple new technologies while operating under heavy resource constrained settings. Mathematical modelling can provide helpful insight by describing the types of interventions likely to maximize impact on the population level and highlighting those gaps in our current knowledge that are most important for making such assessments. This review discusses the major contributions of TB transmission models in general, namely, the ability to improve our understanding of the epidemiology of TB. We focus particularly on those elements that are important to appropriately understand the role of TB diagnosis and treatment (i.e., what elements of better diagnosis or treatment are likely to have greatest population-level impact) and yet remain poorly understood at present. It is essential for modellers, decision-makers, and epidemiologists alike to recognize these outstanding gaps in knowledge and understand their potential influence on model projections that may guide critical policy choices (e.g., investment and scale-up decisions). PMID:26556559

  11. Advancing K-8 Teachers' STEM Education for Teaching Interdisciplinary Science and Mathematics with Technologies

    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)…

  12. Factors Influencing Women's Decisions to Enroll in Advanced Mathematics Courses. Final Report.

    ERIC Educational Resources Information Center

    Stallings, Jane; Robertson, Anne

    This study was designed to identify the factors that relate to the decisions of females in secondary education to elect or decline advanced instruction in mathematics. The final sample included 91 classrooms in 11 high schools, with the focus of the investigation upon 489 students in 22 geometry classes. The findings indicate that the most…

  13. Science and Mathematics Advanced Placement Exams: Growth and Achievement over Time

    ERIC Educational Resources Information Center

    Judson, Eugene

    2017-01-01

    Rapid growth of Advanced Placement (AP) exams in the last 2 decades has been paralleled by national enthusiasm to promote availability and rigor of science, technology, engineering, and mathematics (STEM). Trends were examined in STEM AP to evaluate and compare growth and achievement. Analysis included individual STEM subjects and disaggregation…

  14. Technologies That Facilitate the Study of Advanced Mathematics by Students Who Are Blind: Teachers' Perspectives

    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…

  15. Using Tree-Ring Data to Develop Critical Scientific and Mathematical Thinking Skills in Undergraduate Students

    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

  16. Applying Systems Thinking via Systemigrams(TM) for Defining the Body of Knowledge and Curriculum to Advance Systems Engineering (BKCASE) Project

    DTIC Science & Technology

    2010-01-01

    Systems thinking is commonly accepted as the backbone of a successful systems engineering approach. As such, the Body of Knowledge and Curriculum to...Advance Systems Engineering (BKCASE) team chose to leverage a systems thinking based tool called Systemitool, to describe our project to the vast

  17. 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…

  18. Advancing precollege science and mathematics education in San Diego County. Progress report, March 1, 1995--June 30, 1996

    SciTech Connect

    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.

  19. The Impact of a Teacher Education Culture-Based Project on Identity as a Mathematically Thinking Teacher

    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…

  20. A Study of Students' Conceptual, Procedural Knowledge, Logical Thinking and Creativity during the First Year of Tertiary Mathematics

    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…

  1. Assessing Children's Multiplicative Thinking

    ERIC Educational Resources Information Center

    Hurst, Chris; Hurrell, Derek

    2016-01-01

    Multiplicative thinking is a "big idea" of mathematics that underpins much of the mathematics learned beyond the early primary school years. This paper reports on a current study that utilises an interview tool and a written quiz to gather data about children's multiplicative thinking. The development of the tools and some of the…

  2. "I Think I Can, but I'm Afraid to Try": The Role of Self-Efficacy Beliefs and Mathematics Anxiety in Mathematics Problem-Solving Efficiency

    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…

  3. Building an advanced climate model: Program plan for the CHAMMP (Computer Hardware, Advanced Mathematics, and Model Physics) Climate Modeling Program

    SciTech Connect

    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.

  4. Mathematics Underground

    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…

  5. Mathematics.

    ERIC Educational Resources Information Center

    Costellano, Janet; Scaffa, Matthew

    The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…

  6. Interfacing theories of program with theories of evaluation for advancing evaluation practice: Reductionism, systems thinking, and pragmatic synthesis.

    PubMed

    Chen, Huey T

    2016-12-01

    Theories of program and theories of evaluation form the foundation of program evaluation theories. Theories of program reflect assumptions on how to conceptualize an intervention program for evaluation purposes, while theories of evaluation reflect assumptions on how to design useful evaluation. These two types of theories are related, but often discussed separately. This paper attempts to use three theoretical perspectives (reductionism, systems thinking, and pragmatic synthesis) to interface them and discuss the implications for evaluation practice. Reductionism proposes that an intervention program can be broken into crucial components for rigorous analyses; systems thinking view an intervention program as dynamic and complex, requiring a holistic examination. In spite of their contributions, reductionism and systems thinking represent the extreme ends of a theoretical spectrum; many real-world programs, however, may fall in the middle. Pragmatic synthesis is being developed to serve these moderate- complexity programs. These three theoretical perspectives have their own strengths and challenges. Knowledge on these three perspectives and their evaluation implications can provide a better guide for designing fruitful evaluations, improving the quality of evaluation practice, informing potential areas for developing cutting-edge evaluation approaches, and contributing to advancing program evaluation toward a mature applied science.

  7. Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5. Series in Essential Understandings

    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…

  8. The Role of JRME in Advancing Learning and Teaching Elementary School Mathematics.

    ERIC Educational Resources Information Center

    Battista, Michael T.; Larson, Carol Novillis

    1994-01-01

    Focuses on the contribution of the "Journal for Research in Mathematics Education" to the view of learning and teaching elementary school mathematics embodied in current curricular recommendations for school mathematics. (23 references) (MKR)

  9. A Course in Modern Mathematical Physics

    NASA Astrophysics Data System (ADS)

    Szekeres, Peter

    2005-01-01

    Presenting an introduction to the mathematics of modern physics for advanced undergraduate and graduate students, this textbook introduces the reader to modern mathematical thinking within a physics context. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book also includes exercises and proofed examples to test the students' understanding of the various concepts, as well as to extend the text's themes.

  10. An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service.

    PubMed

    Shamsan, Zaid Ahmed; Al-Hetar, Abdulaziz M

    2016-01-01

    Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum.

  11. An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service

    PubMed Central

    Al-hetar, Abdulaziz M.

    2016-01-01

    Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum. PMID:27855216

  12. Adaptability: Time to Start Thinking about Thinking

    DTIC Science & Technology

    2015-05-21

    Adaptability : Time to Start Thinking about Thinking A Monograph by MAJ Cassandra S. Crosby United States Army School of Advanced Military...Monograph 3. DATES COVERED (From - To) June 2014 - May 2015 4. TITLE AND SUBTITLE Adaptability : Time to Start Thinking about Thinking 5a...understanding of adaptability and the conditions required to achieve it. Developing adaptive leaders is one of the Chief of Staff of the US Army’s top

  13. Thinking Like a Mathematician

    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…

  14. 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.

  15. Proceedings of the diffuse intrinsic pontine glioma (DIPG) Toronto Think Tank: advancing basic and translational research and cooperation in DIPG.

    PubMed

    Bartels, Ute; Hawkins, Cynthia; Vézina, Gilbert; Kun, Larry; Souweidane, Mark; Bouffet, Eric

    2011-10-01

    Diffuse intrinsic pontine glioma (DIPG) nearly exclusively affects children. The prognosis of DIPGs has remained grim despite more than three decades of clinical research and numerous clinical trials. More than 90% of the children with DIPG will succumb within 2 years of diagnosis. The tumor's incidence is still undefined, but data suggest 100-150 affected children annually in the US. The single proven effective treatment modality in DIPG remains radiation therapy. For the majority of patients however this treatment is only of transient effectiveness. Recent breakthroughs in the understanding of the molecular biology of DIPG have raised new hope and opened new avenues for therapeutic options. The advancement of basic and translational research and cooperation was the objective of the Toronto Think Tank, as new approaches are urgently needed.

  16. Strategic Alliance to Advanced Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level

    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…

  17. Integration of Technology, Curriculum, and Professional Development for Advancing Middle School Mathematics: Three Large-Scale Studies

    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,…

  18. Technologies Used in the Study of Advanced Mathematics by Students Who Are Visually Impaired in Classrooms: Teachers' Perspectives

    ERIC Educational Resources Information Center

    DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.

    2015-01-01

    Introduction: This research examined the perspectives of teachers of students who are visually impaired regarding the use and effectiveness of high-tech assistive technology purported to assist visually impaired students in advanced mathematics. Methods: The data for this study were collected via a mixed-methods online survey distributed through…

  19. Mathematics Teachers' Development, Exploration, and Advancement of Technological Pedagogical Content Knowledge in the Teaching and Learning of Algebra

    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…

  20. Equal Educational Opportunity and Nondiscrimination for Girls in Advanced Mathematics, Science, and Technology Education: Federal Enforcement of Title IX. Equal Educational Opportunity Project Series, Volume V.

    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…

  1. Levels of line graph question interpretation with intermediate elementary students of varying scientific and mathematical knowledge and ability: A think aloud study

    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

  2. Thinking about Learning in Mathematics: Understanding Why and How Teachers Support the Development of Self-Regulated Learners

    ERIC Educational Resources Information Center

    Kelley, Julie B.

    2015-01-01

    Self-regulated learning is an elaborate metacognitive process consisting of an individual's awareness of the thought process, flexibility in one's approach to problem solving, and motivation to persist through obstacles until a goal has been met. Strategies and instructional practices used to develop mathematically proficient thinkers also develop…

  3. Exploration of Mathematics Problem Solving Process Based on the Thinking Level of Students in Junior High School

    ERIC Educational Resources Information Center

    Rahman, Abdul; Ahmar, Ansari Saleh

    2016-01-01

    Several studies suggest that most students are not in the same level of development (Slavin, 2008). From concrete operation level to formal operation level, students experience lateness in the transition phase. Consequently, students feel difficulty in solving mathematics problems. Method research is a qualitatively descriptive-explorative…

  4. Fostering the Development of Logico-Mathematical Thinking in a Card Game at Ages 5-6

    ERIC Educational Resources Information Center

    Kamii, Constance; Kato, Yasuhiko

    2005-01-01

    A class of 14 kindergartners in Japan was videotaped while playing a card game in groups of three involving the placement of cards in numerical order. The children were followed up in first grade, and it was found that development in one area of logico-mathematical knowledge (for example, the making of temporal relationships) stimulates…

  5. Undergraduate Mathematics Majors' Writing Performance Producing Proofs and Counterexamples about Continuous Functions

    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…

  6. Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication

    ERIC Educational Resources Information Center

    Kaya, Defne; Aydin, Hasan

    2016-01-01

    Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…

  7. 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…

  8. Doctoral Research in Educational Leadership: Expectations for Those Thinking about an Advanced Degree

    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…

  9. 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…

  10. Advancing the application of systems thinking in health: understanding the dynamics of neonatal mortality in Uganda

    PubMed Central

    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

  11. CONFERENCE NOTE: International Workshop on Advanced Mathematical Tools in Metrology, Villa Gualino, Torino, Italy, 20 22 October 1993

    NASA Astrophysics Data System (ADS)

    1993-01-01

    Preliminary Programme The three-day programme features approximately twenty-five invited contributions. Participants may present a poster on the topic "Applications for Industrial Measurements", concerning applied mathematics, software development and computer-based measurements. 20 October Two plenary talks on mathematical methods and metrological applications "Numerical Methods and Modelling" Partial differential equations and integral equations Methods of identification and validation Algorithms for approximation Geometrical shape determination of industrial solids Round Table 21 October "Data Analysis" Spectral analysis and wavelets Calibration of precision instrumentation Comparison measurement of standards Statistical methods in metrology Robust estimation and outliers Applications of the bootstrap method Round Table 22 October (in cooperation with SIMAI and ASP) "Applications for Industrial Measurements" Data acquisition Measurement software, standard computational modules and their validation Round Table Industrial presentations Discussion of poster presentations Conclusions Lecturers Mathematicians from the international metrological community; mathematicians from Italian universities (Politecnico of Torino, Milano, Università di Genova, Milano, Padova, Roma, Trento); scientists and mathematicians from national standards institutes and the Italian National Research Council. The workshop will be of interest to people in universities, research centres and industry who are involved in measurement and need advanced mathematical tools to solve their problems, and to those who work in the development of these mathematical tools. Metrology is concerned with measurement at the highest level of precision. Advances in metrology depend on many factors: improvements in scientific and technical knowledge, instrumentation quality, better use of advanced mathematical tools and the development of new tools. In some countries, metrological institutions have a tradition of

  12. 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…

  13. Biologic Treatments for Sports Injuries II Think Tank—Current Concepts, Future Research, and Barriers to Advancement, Part 3

    PubMed Central

    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

  14. Computational thinking and thinking about computing

    PubMed Central

    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

  15. 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…

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

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  17. 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…

  18. Avoiding Misinterpretations of Piaget and Vygotsky: Mathematical Teaching without Learning, Learning without Teaching, or Helpful Learning-Path Teaching?

    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…

  19. Thinking is believing.

    PubMed

    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.

  20. Advanced High School Biology in an Era of Rapid Change: A Summary of the Biology Panel Report from the NRC Committee on Programs for Advanced Study of Mathematics and Science in American High Schools

    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,…

  1. Tracing the Construction of Mathematical Activity with an Advanced Graphing Calculator to Understand the Roles of Technology Developers, Teachers and Students

    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…

  2. 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.

  3. Thinking about Thinking.

    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.…

  4. 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…

  5. Factors Associated with the Selection of Advanced Academic Mathematics Courses by Girls in High School.

    ERIC Educational Resources Information Center

    Haven, Elizabeth W.

    This study sought to identify factors that motivate girls to complete a four-year sequence of academic mathematics. Forty variables involving community, family, school and personal factors were measured and analyzed by a MANOVA for correlations with two criterion variables. The first criterion was a classification of schools on the basis of the…

  6. 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…

  7. Advanced Mathematics Online: Assessing Particularities in the Online Delivery of a Second Linear Algebra Course

    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…

  8. Who Can Know Mathematics?

    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…

  9. Examination of the Computational Thinking Skills of Students

    ERIC Educational Resources Information Center

    Korucu, Agah Tugrul; Gencturk, Abdullah Tarik; Gundogdu, Mustafa Mucahit

    2017-01-01

    Computational thinking is generally considered as a kind of analytical way of thinking. According to Wings (2008) it shares with mathematical thinking, engineering thinking and scientific thinking in the general ways in which we may use for solving a problem, designing and evaluating complex systems or understanding computability and intelligence…

  10. Recent advances in mathematical modeling of nitrous oxides emissions from wastewater treatment processes.

    PubMed

    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.

  11. Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

    PubMed

    Schaid, Daniel J

    2010-01-01

    Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1].

  12. Siegfried the Dragonslayer Meets the Web: Using Digital Media for Developing Historical Awareness and Advanced Language and Critical Thinking Skills

    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…

  13. Book Mathematics--Part 1

    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,…

  14. High School Mathematics Teachers' Perspectives on the Purposes of Mathematical Proof in School Mathematics

    ERIC Educational Resources Information Center

    Dickerson, David S.; Doerr, Helen M.

    2014-01-01

    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…

  15. Developing a Plan to Support Mathematics Students with Advanced Placement Potential at Indian River High School

    ERIC Educational Resources Information Center

    Timmons, Sara J.

    2009-01-01

    One of the many goals of schools is to have each student reach his/her fullest potential. One way schools challenge the accelerated learners is through the advanced placement (AP) program. Many able students at Indian River High School (IRHS) are choosing to enroll in college prep math courses instead of enrolling in honors and AP math. When…

  16. Mathematics Meets Literature.

    ERIC Educational Resources Information Center

    Goos, Merrilyn

    2000-01-01

    Presents an activity using the familiar fairy tale "Cinderella" to provide the context for stimulating mathematical thinking about a real life problem. Makes use of graphing calculator technology to investigate the relationship between shoe sizes and shoe lengths. (ASK)

  17. 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…

  18. Characteristics and Impact of the Further Mathematics Knowledge Networks: Analysis of an English Professional Development Initiative on the Teaching of Advanced Mathematics

    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…

  19. Thinking about Thinking.

    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.…

  20. The Effects of Schema-Based Instruction on the Proportional Thinking of Students with Mathematics Difficulties with and without Reading Difficulties

    ERIC Educational Resources Information Center

    Jitendra, Asha K.; Dupuis, Danielle N.; Star, Jon R.; Rodriguez, Michael C.

    2016-01-01

    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…

  1. How can mathematical models advance tuberculosis control in high HIV prevalence settings?

    PubMed

    Houben, R M G J; Dowdy, D W; Vassall, A; Cohen, T; Nicol, M P; Granich, R M; Shea, J E; Eckhoff, P; Dye, C; Kimerling, M E; White, R G

    2014-05-01

    Existing approaches to tuberculosis (TB) control have been no more than partially successful in areas with high human immunodeficiency virus (HIV) prevalence. In the context of increasingly constrained resources, mathematical modelling can augment understanding and support policy for implementing those strategies that are most likely to bring public health and economic benefits. In this paper, we present an overview of past and recent contributions of TB modelling in this key area, and suggest a way forward through a modelling research agenda that supports a more effective response to the TB-HIV epidemic, based on expert discussions at a meeting convened by the TB Modelling and Analysis Consortium. The research agenda identified high-priority areas for future modelling efforts, including 1) the difficult diagnosis and high mortality of TB-HIV; 2) the high risk of disease progression; 3) TB health systems in high HIV prevalence settings; 4) uncertainty in the natural progression of TB-HIV; and 5) combined interventions for TB-HIV. Efficient and rapid progress towards completion of this modelling agenda will require co-ordination between the modelling community and key stakeholders, including advocates, health policy makers, donors and national or regional finance officials. A continuing dialogue will ensure that new results are effectively communicated and new policy-relevant questions are addressed swiftly.

  2. 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…

  3. 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…

  4. Third Millennium Mathematics.

    ERIC Educational Resources Information Center

    Fluellen, Jerry

    This paper describes a mathematics-centered thematic unit for 5th graders which organizes all the topics in the Houghton Mifflin Mathematics Program by combining critical thinking and whole language frameworks to help students retain, understand, and make active use of knowledge within and across domains. The unit connects inquiry, goals, critical…

  5. 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…

  6. Assessing Advanced High School and Undergraduate Students' Thinking Skills: The Chemistry--From the Nanoscale to Microelectronics Module

    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…

  7. 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…

  8. 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…

  9. Thinking unleashed.

    PubMed

    Condon, Barbara Backer

    2012-07-01

    As the nursing profession continues to expand, the tendency to think based on the medical model also seems to be increasing. The thinking that is currently taught in nursing curricula is well known as critical thinking. However, over the years, the numerous attempts to revise and redefine critical thinking indicate awareness, by educators and members of the profession, of its limitations. The author of this column discusses some of these limitations, while proposing a more open and transparent way of thinking for nurses based upon humanbecoming ontology involving the emerging now, the resurrection of listening and silence, and contemplative thought.

  10. 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…

  11. Thinking Is Literacy, Literacy Thinking

    ERIC Educational Resources Information Center

    Roberts, Terry; Billings, Laura

    2008-01-01

    Recognizing the profound relationship between thinking and language, the authors have developed the traditional Paideia seminar into a literacy cycle of instruction that involves students in reading, speaking, listening, writing, and thinking. As staff members of the National Paideia Center, they have observed that learning to think requires…

  12. "The Blue Table Means You Don't Have a Clue": The Persistence of Fixed-Ability Thinking and Practices in Primary Mathematics in English Schools

    ERIC Educational Resources Information Center

    Marks, Rachel

    2013-01-01

    The use of structured ability grouping is increasing in English primary schools and is regularly seen in primary mathematics classrooms. Ability is a normalised discourse with beliefs that some individuals are "born to do maths" permeating society and infiltrating school practices. In this article, observation and interview data…

  13. Thinking ahead – the need for early Advance Care Planning for people on haemodialysis: A qualitative interview study

    PubMed Central

    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

  14. Thinking Conics

    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…

  15. Advancing Earth Systems Thinking and Problem Based Learning in the Classroom: Insights From ESSEA Course Graduates in Kentucky

    NASA Astrophysics Data System (ADS)

    Siewers, F. D.; Crowder, M. E.

    2008-12-01

    Western Kentucky University has been an active member of the Earth System Science Education Alliance (ESSEA) since 2003 and has offered the high school ESSEA course a total of four times during that period. Twenty-six individuals from across Kentucky successfully passed the course and at least half of those individuals are currently involved in K-12 science education. Preliminary communications with course graduates indicate that Earth System Science (ESS) concepts and content knowledge advanced in the high school ESSEA course have been incorporated into the science curricula of several Kentucky schools. Several teachers and schools have also enthusiastically adopted Problem Based Learning (PBL), the pedagogical foundation of the high school ESSEA course. This presentation will highlight the insights and experience of ESSEA course graduates working to incorporate ESS and PBL into their courses and science curricula. Particular attention will focus on those factors - both positive and negative - that teachers feel most influence the advance of ESS education and PBL in Kentucky schools.

  16. Mathematical Visualization

    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…

  17. Biologic Treatments for Sports Injuries II Think Tank-Current Concepts, Future Research, and Barriers to Advancement, Part 3: Articular Cartilage.

    PubMed

    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.

  18. Exploring Metacognition in Preservice Teachers: Problem Solving Processes in Elementary Mathematics

    ERIC Educational Resources Information Center

    Sparkman, Dana; Harris, Kymberly

    2009-01-01

    In Principles and Standards for School Mathematics (2000), the (U.S.) National Council of Teachers of Mathematics recommended that students communicate their mathematical thinking in a logical manner, and use the language of mathematics to express their thinking accurately and logically. Students should not only learn mathematics content, but…

  19. Thinking creatively is thinking critically.

    PubMed

    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.

  20. Critical thinking.

    PubMed

    Price, A; Price, B

    1996-05-01

    Critical thinking is a process applied to midwifery theory, research and experience. It is a positive activity, responsive to context, drawing on negative and positive triggers and emotions to suggest ways of acting in future. Practice-based and reflective midwifery assignments should reflect the midwifery goals of critical thinking. This may require adjustments in assessment criteria and a questioning of standard academic conventions.

  1. Thinking Strategically.

    ERIC Educational Resources Information Center

    Jeffress, Conway

    2000-01-01

    Asserts that community college leaders must think strategically and understand the difference between what is important and immediate, and what is strategic and essential to the long-term survival of a college. States that thinking strategically aligns decision-making and actions with the core purpose of the college; produces core competencies in…

  2. 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…

  3. Analyzing Preservice Mathematics Teachers' Professional Noticing

    ERIC Educational Resources Information Center

    Amador, Julie M.; Carter, Ingrid; Hudson, Rick A.

    2016-01-01

    Recent research in mathematics education has highlighted the importance of teachers' abilities to professionally notice students' thinking. This study examined what preservice teachers professionally notice during lesson study to further describe their attention to students' mathematical thinking, their interpretations about students' reasoning,…

  4. How We Think We Think

    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…

  5. The reality of Mathematics

    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.

  6. 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…

  7. 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…

  8. 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…

  9. Sliding into Multiplicative Thinking: The Power of the "Marvellous Multiplier"

    ERIC Educational Resources Information Center

    Hurst, Chris; Hurrell, Derek

    2016-01-01

    Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…

  10. Understanding Probabilistic Thinking: The Legacy of Efraim Fischbein.

    ERIC Educational Resources Information Center

    Greer, Brian

    2001-01-01

    Honors the contribution of Efraim Fischbein to the study and analysis of probabilistic thinking. Summarizes Fischbein's early work, then focuses on the role of intuition in mathematical and scientific thinking; the development of probabilistic thinking; and the influence of instruction on that development. (Author/MM)

  11. Systems thinking.

    PubMed

    Cabrera, Derek; Colosi, Laura; Lobdell, Claire

    2008-08-01

    Evaluation is one of many fields where "systems thinking" is popular and is said to hold great promise. However, there is disagreement about what constitutes systems thinking. Its meaning is ambiguous, and systems scholars have made diverse and divergent attempts to describe it. Alternative origins include: von Bertalanffy, Aristotle, Lao Tsu or multiple aperiodic "waves." Some scholars describe it as synonymous with systems sciences (i.e., nonlinear dynamics, complexity, chaos). Others view it as taxonomy-a laundry list of systems approaches. Within so much noise, it is often difficult for evaluators to find the systems thinking signal. Recent work in systems thinking describes it as an emergent property of four simple conceptual patterns (rules). For an evaluator to become a "systems thinker", he or she need not spend years learning many methods or nonlinear sciences. Instead, with some practice, one can learn to apply these four simple rules to existing evaluation knowledge with transformative results.

  12. Love thinking.

    PubMed

    Pinch, Adela

    2008-01-01

    This essay places Coventry Patmore's The Angel in the House in the context of Victorian explorations of the act of thinking about a beloved other. It centers on two short "Preludes" from the poem--"The Kiss" and "Love Thinking"--which raise questions about the relationship of love to knowledge. Reading Patmore's poem in this way makes it possible to recognize "The Kiss" as the crucial source for a much more serious poem about thinking, kissing, and sleeping: George Meredith's Modern Love. Through its relation to Meredith's poem and to other texts, as well as to Patmore's theory of poetic meter, "The Kiss" opens onto serious concerns about whether thinking about the one you love is constitutive of--or destructive to--intimacy.

  13. 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…

  14. 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)

  15. Advanced theoretical and experimental studies in automatic control and information systems. [including mathematical programming and game theory

    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.

  16. Advancing Fourth-Grade Students' Understanding of Arithmetic Properties with Instruction That Promotes Mathematical Argumentation

    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…

  17. The Impact of Advanced Geometry and Measurement Curriculum Units on the Mathematics Achievement of First-Grade Students

    ERIC Educational Resources Information Center

    Gavin, M. Katherine; Casa, Tutita M.; Firmender, Janine M.; Carroll, Susan R.

    2013-01-01

    The goal of Project M2 was to develop and field-test challenging geometry and measurement units for K-2 students. The units were developed using recommendations from gifted, mathematics, and early childhood education. This article reports on achievement results for students in Grade 1 at 12 diverse sites in four states using the Iowa Tests of…

  18. Trends in Advanced Mathematics and Science Course Taking and Achievement among ACT-Tested High School Students: 1987-1996.

    ERIC Educational Resources Information Center

    McLure, Gail T.; Sun, Anji; Valiga, Michael J.

    This study investigated changes between 1987 and 1996 in the proportions of ACT-tested students taking or planning to take high school mathematics and science courses prior to high school graduation. The changes in course-taking patterns among racial/ethnic and gender subgroups were also compared. The seven courses studied were Algebra II,…

  19. Two Meanings of Algorithmic Mathematics.

    ERIC Educational Resources Information Center

    Maurer, Stephen B.

    1984-01-01

    Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

  20. 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.

  1. Mathematical Perspectives

    SciTech Connect

    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.

  2. Mathematical Pattern Hunters

    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…

  3. Functioning Mathematically: 2

    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…

  4. 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…

  5. Cultivating strategic thinking skills.

    PubMed

    Shirey, Maria R

    2012-06-01

    This department highlights change management strategies that may be successful in strategically planning and executing organizational change initiatives. With the goal of presenting practical approaches helpful to nurse leaders advancing organizational change, content includes evidence-based projects, tools, and resources that mobilize and sustain organizational change initiatives. In this article, the author presents an overview of strategic leadership and offers approaches for cultivating strategic thinking skills.

  6. Integrating science, mathematics, and environmental education: Resources and guidelines

    NASA Astrophysics Data System (ADS)

    Lorson, Mark V.; Heimlich, Joe E.; Wagner, Sigrid

    1993-06-01

    The integration of mathematics, science, and environmental education permits the students to gain from all three areas simultaneously. Science encompasses the art of questioning, investigating, hypothesizing, and discovering. Mathematics is the language that provides clarity, objectivity, and understanding. Many of the major contemporary issues involve societal issues stemming from advancements in science (Wiebe, Ecklund, & Hillen, 1986). Problem solving, creative mathematics and science thinking, core knowledge, decision making, and environmental training are all available in one time period in a properly conceived and directed activity. Teachers, too, are more interested when using methods and concepts more familiar to them. By increasing awareness and making a more effective use of classroom time we may get closer to producing the informed citizen needed for today’s world.

  7. A Taxonomy of Software for Mathematics Instruction

    ERIC Educational Resources Information Center

    Kurz, Terri L.; Middleton, James A.; Yanik, H. Bahadir

    2005-01-01

    The potential to use mathematics software to enhance student thinking and development is discussed and a taxonomy of software categories is outlined in this paper. Briefly, there are five categories of tool-based mathematics software that can be used fruitfully in a mathematics curriculum: (a) review and practice, (b) general, (c) specific, (d)…

  8. Evolutionary thinking

    PubMed Central

    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

  9. Mathematical Modeling in the Undergraduate Curriculum

    ERIC Educational Resources Information Center

    Toews, Carl

    2012-01-01

    Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

  10. Biologic Treatments for Sports Injuries II Think Tank-Current Concepts, Future Research, and Barriers to Advancement, Part 1: Biologics Overview, Ligament Injury, Tendinopathy.

    PubMed

    LaPrade, Robert F; Geeslin, Andrew G; Murray, Iain R; Musahl, Volker; Zlotnicki, Jason P; Petrigliano, Frank; Mann, Barton J

    2016-12-01

    Biologic therapies, including stem cells, platelet-rich plasma, growth factors, and other biologically active adjuncts, have recently received increased attention in the basic science and clinical literature. At the 2015 AOSSM Biologics II Think Tank held in Colorado Springs, Colorado, a group of orthopaedic surgeons, basic scientists, veterinarians, and other investigators gathered to review the state of the science for biologics and barriers to implementation of biologics for the treatment of sports medicine injuries. This series of current concepts reviews reports the summary of the scientific presentations, roundtable discussions, and recommendations from this think tank.

  11. How Middle Grade Teachers Think about Algebraic Reasoning

    ERIC Educational Resources Information Center

    Glassmeyer, David; Edwards, Belinda

    2016-01-01

    Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathematics, yet little is known about how middle school mathematics teachers think about algebraic reasoning. In this article we describe a research project examining how algebraic reasoning was considered by grades 6, 7, or 8 mathematics teachers in a…

  12. Think green.

    PubMed

    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.

  13. Think Earth.

    ERIC Educational Resources Information Center

    Niedermeyer, Fred; Ice, Kay

    1992-01-01

    Describes a series of environmental education instructional units for grades K-6 developed by the Think Earth Consortium that cover topics such as conservation, pollution control, and waste reduction. Provides testimony from one sixth-grade teacher that field tested the second-grade unit. (MDH)

  14. Visual Thinking.

    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…

  15. Teaching Thinking

    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…

  16. 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…

  17. The Psychosocial Factors Contributing to the Underrepresentation of African American Males in Advanced High School Mathematics Courses

    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…

  18. The materiality of mathematics: presenting mathematics at the blackboard.

    PubMed

    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.

  19. High school mathematics teachers' perspectives on the purposes of mathematical proof in school mathematics

    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.

  20. Research Area 3 - Mathematical Sciences: Multiscale Modeling of the Mechanics of Advanced Energetic Materials Relevant to Detonation Prediction

    DTIC Science & Technology

    2015-08-24

    new energetic materials with enhanced energy release rates and reduced sensitivity to unintentional detonation . The following results have been...Mechanics of Advanced Energetic Materials Relevant to Detonation Prediction The views, opinions and/or findings contained in this report are those of the...modeling, molecular simulations, detonation prediction REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR/MONITOR’S

  1. 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)…

  2. 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…

  3. Computational physics and applied mathematics capability review June 8-10, 2010 (Advance materials to committee members)

    SciTech Connect

    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

  4. 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…

  5. 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…

  6. 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)

  7. 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…

  8. Intuition and Analytical Thinking in Mathematics Education.

    ERIC Educational Resources Information Center

    Fischbein, Efraim

    1983-01-01

    Discussed are the concepts of intuition, the general properties of an intuitive knowledge, and the classification of intuitions as problem solving of affirmative. An example of intuition using multiplication and division is described in some detail. (MNS)

  9. STEM Thinking!

    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…

  10. 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…

  11. Proportion in Middle-School Mathematics: It's Everywhere

    ERIC Educational Resources Information Center

    Shield, Mal; Dole, Shelley

    2008-01-01

    Proportional thinking is the mathematical basis of a wide range of topics in the middle-school mathematics curriculum. While the concept is obvious in the traditionally-named ratio and proportion sections, proportional thinking is also the key to such diverse topics as rate, gradient of a linear function, similarity, trigonometry and percentage,…

  12. How Problem Solving Can Develop an Algebraic Perspective of Mathematics

    ERIC Educational Resources Information Center

    Windsor, Will

    2011-01-01

    SProblem solving has a long and successful history in mathematics education and is valued by many teachers as a way to engage and facilitate learning within their classrooms. The potential benefit for using problem solving in the development of algebraic thinking is that "it may broaden and develop students' mathematical thinking beyond the…

  13. What Makes Critical Thinking Critical for Adult ESL Students

    ERIC Educational Resources Information Center

    Miekley, Joshua P.

    2014-01-01

    Critical-thinking skills help to prepare adult education students for a successful transition to college degree programs and for job advancement. Yet fostering critical thinking poses a challenge to ESL instructors. Brookfield (2012) provides a way forward for adult educators when he explains that the crux of critical thinking is to discover one's…

  14. Credit Card Mathematics

    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.…

  15. On three forms of thinking: magical thinking, dream thinking, and transformative thinking.

    PubMed

    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.

  16. Effects of Experiential Learning Approach on Students' Mathematical Creativity among Secondary School Students of Kericho East Sub-County, Kenya

    ERIC Educational Resources Information Center

    Chesimet, M. C.; Githua, B. N.; Ng'eno, J. K.

    2016-01-01

    Mathematics is a subject which seeks to understand patterns that permeate both the world around us and the mind within us. There are many ways of thinking and the kind of thinking one learns in mathematics is an ability to handle abstraction and solve problems that require knowledge of mathematics. Mathematical creativity is essential for…

  17. An Inside Track: Fostering Mathematical Practices

    ERIC Educational Resources Information Center

    Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia

    2015-01-01

    Classroom teachers may not initially consider games as opportunities for students to engage in deep mathematical thinking. However, this article reveals how a second grade veteran teacher used Attribute Trains, a game adapted from NCTM Illuminations, to foster his students' thinking related to key ideas within the Standards for Mathematical…

  18. 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)

  19. 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.

  20. Listening for Disciplinary Differences in Faculty Goals for Effective Thinking.

    ERIC Educational Resources Information Center

    Eljamal, Melissa B.; Sharp, Sally; Stark, Joan S.; Arnold, Gertrude L.; Lowther, Malcolm A.

    1998-01-01

    Describes a study that examines the extent to which effective thinking skills are incorporated in faculty teaching goals across nine academic disciplines--mathematics, the sciences, and humanities. Indicates that effective thinking skills are included in all faculty goal statements except for those in the romance languages. (3 tables and 33…

  1. 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…

  2. Appreciating mathematical structure for all

    NASA Astrophysics Data System (ADS)

    Mason, John; Stephens, Max; Watson, Anne

    2009-07-01

    We take mathematical structure to mean the identification of general properties which are instantiated in particular situations as relationships between elements or subsets of elements of a set. Because we take the view that appreciating structure is powerfully productive, attention to structure should be an essential part of mathematical teaching and learning. This is not to be confused with teaching children mathematical structure. We observe that children from quite early ages are able to appreciate structure to a greater extent than some authors have imagined. Initiating students to appreciate structure implies, of course, that their appreciation of it needs to be cultivated in order to deepen and to become more mature. We first consider some recent research that supports this view and then go on to argue that unless students are encouraged to attend to structure and to engage in structural thinking they will be blocked from thinking productively and deeply about mathematics. We provide several illustrative cases in which structural thinking helps to bridge the mythical chasm between conceptual and procedural approaches to teaching and learning mathematics. Finally we place our proposals in the context of how several writers in the past have attempted to explore the importance of structure in mathematics teaching and learning.

  3. 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…

  4. The Effect of Teacher Certification and Task Level on Mathematics Achievement.

    ERIC Educational Resources Information Center

    Mandeville, Garrett K.; Liu, Qiduan

    1997-01-01

    This study examined the interaction effect of teachers' mathematics preparation and the thinking level of mathematics problems on student performance. Achievement scores of students whose teachers differed on level of mathematics preparation indicated that students performed better on higher level thinking tasks when teachers had advanced…

  5. 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'…

  6. 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…

  7. Thinking Algebraically across the Elementary School Curriculum

    ERIC Educational Resources Information Center

    Soares, June; Blanton, Maria L.; Kaput, James J.

    2006-01-01

    With testing and accountability on everyone's mind, teachers are looking for creative ways to teach "all" subjects. Literacy is on the top of the list for testing, so it seems to get top priority. But how can teachers make sure that mathematics, especially a crucial area such as algebraic thinking, is a priority as well? Integrating subject matter…

  8. Algebraic Thinking through Koch Snowflake Constructions

    ERIC Educational Resources Information Center

    Ghosh, Jonaki B.

    2016-01-01

    Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…

  9. 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 …

  10. 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…

  11. 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…

  12. Highlights from TIMSS and TIMSS Advanced 2015: Mathematics and Science Achievement of U.S. Students in Grades 4 and 8 and in Advanced Courses at the End of High School in an International Context. NCES 2017-002

    ERIC Educational Resources Information Center

    Stephens, Maria; Landeros, Katherine; Perkins, Robert; Tang, Judy H.

    2016-01-01

    The Trends in International Mathematics and Science Study (TIMSS) 2015 is the sixth administration of this international comparative study since 1995 when first administered. TIMSS is used to compare over time the mathematics and science knowledge and skills of fourth- and eighth-graders. TIMSS is designed to align broadly with mathematics and…

  13. 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…

  14. 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…

  15. 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…

  16. Small-Group Assessment Methods in Mathematics.

    ERIC Educational Resources Information Center

    Berry, John; Nyman, Melvin A.

    2002-01-01

    Discusses a team-oriented formal testing method used in a mathematical modeling course taught during the Alma College intensive spring term. Asks the question, If a collaborative teaching method is used, how does one assess students' acquisition of problem-solving and mathematical-thinking skills? (Author/MM)

  17. 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…

  18. 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…

  19. Mathematical and Scientific Knowledge: An Overview.

    ERIC Educational Resources Information Center

    Resnick, Lauren B.; Gelman, Rochel

    Most of the research on mathematical and scientific thinking has been concerned with uncovering knowledge structures and reasoning processes in people of different levels of competence. How these structures and processes are acquired has only recently become a major concern. Thus, some of the major research on mathematical and scientific thinking…

  20. 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…

  1. Canadian Mathematics Education Study Group = Groupe Canadien d'etude en didactique des mathematiques. Proceedings of the Annual Meeting (22nd, Vancouver, British Columbia, Canada, May 29-June 2, 1998).

    ERIC Educational Resources Information Center

    Pothier, Yvonne M., Ed.

    This proceedings includes the following papers: (1) "Structure of Attention in Teaching Mathematics" (John Mason); (2) "Communicating Mathematics or Mathematics Storytelling" (Kathy Heinrich); (3) "Assessing Mathematical Thinking" (Florence Glanfield and Pat Rogers); (4) "From Theory to Observational Data (and…

  2. Examining the Use of Video to Support Preservice Elementary Teachers' Noticing of Children's Thinking

    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…

  3. 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…

  4. Developing Mathematical Habits of Mind

    ERIC Educational Resources Information Center

    Mark, June; Cuoco, Al; Goldenberg, E. Paul; Sword, Sarah

    2010-01-01

    "Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

  5. 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…

  6. Alternative Thinking.

    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)

  7. Symbols and the Bifurcation between Procedural and Conceptual Thinking.

    ERIC Educational Resources Information Center

    Tall, David; Gray, Eddie; Bin Ali, Maselan; Crowley, Lillie; DeMarois, Phil; McGowen, Mercedes; Pitta, Demetra; Pinto, Marcia; Thomas, Michael; Yusof, Yudariah

    Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this presentation, the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and…

  8. Mathematics, Anyone?

    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…

  9. Critical Thinking Skills.

    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…

  10. Thinking-in-Concert

    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…

  11. Design thinking.

    PubMed

    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.

  12. 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…

  13. 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…

  14. Constructing Meanings of Mathematical Registers Using Metaphorical Reasoning and Models

    ERIC Educational Resources Information Center

    Lai, Mun Yee

    2013-01-01

    Current debates about successful mathematics pedagogy suggest that mathematical learning and problem solving can be enhanced by using metaphors as they provide students with a tool for thinking. But assisting pre-service teachers to understand the importance of careful and accurate explanations for mathematical concepts remains an issue. This…

  15. The Effects of an Educational Video Game on Mathematical Engagement

    ERIC Educational Resources Information Center

    Chang, Mido; Evans, Michael A.; Kim, Sunha; Norton, Anderson; Deater-Deckard, Kirby; Samur, Yavuz

    2016-01-01

    In an effort to maximizing success in mathematics, our research team implemented an educational video game in fifth grade mathematics classrooms in five schools in the Eastern US. The educational game was developed by our multi-disciplinary research team to achieve a hypothetical learning trajectory of mathematical thinking of 5th grade students.…

  16. The Use of Tablet and Related Technologies in Mathematics Teaching

    ERIC Educational Resources Information Center

    Galligan, Linda; Loch, Birgit; McDonald, Christine; Taylor, Janet A.

    2010-01-01

    According to "Standards of Excellence in Teaching Mathematics in Australian Schools," excellent teachers of mathematics need to create "an environment that maximises students' learning opportunities"; so that they can encourage self-directed learning, "model mathematical thinking and reasoning," and provide…

  17. 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…

  18. 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

  19. Putting Research into Practice in the Elementary Grades: Readings from Journals of the National Council of Teachers of Mathematics.

    ERIC Educational Resources Information Center

    Chambers, Donald L., Ed.

    This book describes children's mathematical thinking to guide and support teachers in their reflection upon student thinking and teaching and learning. It is organized into five parts: (1) reasoning, student thinking, and invented strategies independent of the mathematics content domain which addresses the role of discourse in helping students…

  20. Analogy, higher order thinking, and education.

    PubMed

    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.

  1. Changes in Elementary Mathematics Teachers' Understanding of Cognitive Demand: When Adapting, Creating, and Using Mathematical Performance Tasks

    ERIC Educational Resources Information Center

    Jamieson, Thad Spencer

    2015-01-01

    The use of mathematics performance tasks can provide a window into how a student is applying mathematics to various situations, how they are reasoning mathematically and how they are applying conceptual knowledge through problem solving and critical thinking. The purpose of this study was to investigate, according to the elementary mathematics…

  2. Basic mathematical cognition.

    PubMed

    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.

  3. 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…

  4. 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…

  5. 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…

  6. Exploring reflective thinking in nursing practice.

    PubMed

    Teekman, B

    2000-05-01

    While it is claimed in the nursing literature that reflective thinking is the approach par excellence for learning and advancing the art and practice of nursing, few empirical studies have been undertaken in this area to date. Sense-Making, a qualitative research method, was utilized to obtain and analyse data from interviews with 10 registered nurses in order to study reflective thinking in actual nursing practice. Ten non-routine nursing situations were analysed for the presence of reflective thinking. Time-line interviews of the events resulted in a total of 59 micro-moments, each of which was explored in terms of the thinking processes utilized to make sense of the situation as well as the focus of their thought. 'Pre-perceptions' played an important part in how the respondents perceived their situation. Reflective thinking was extensively manifest, especially in moments of doubt and perplexity, and consisted of such cognitive activities as comparing and contrasting phenomena, recognizing patterns, categorizing perceptions, framing, and self-questioning in order to create meaning and understanding. Self-questioning was identified as a significant process within reflective thinking. By exploring and analysing the type of questions respondents were asking themselves, the study uncovered three hierarchical levels of reflective thinking. Respondents most often engaged in reflective thinking-for-action which centred on the here and now in order to act. Reflective thinking-for-evaluation focused on creating wholeness and contributed to the realization of multiple perceptions and multiple responses. Reflective thinking-for-critical-inquiry could not be demonstrated in the study sample. The findings of this study resulted in the development of a model of reflective thinking, which is discussed in terms of the implications for learning in nursing practice.

  7. Psychoticism and thinking.

    PubMed

    Woody, E; Claridge, G

    1977-09-01

    In view of evidence linking psychosis with high creative ability, an attempt was made to evaluate the relationship between thinking abilities and personality traits. Tests of divergent thinking and convergent thinking were administered, along with the Eysencks' Personality Questionnaire, to 100 university students. The hypothesis that 'psychoticism' is related to divergent thinking was strongly confirmed. The hypothesis that psychoticism would be related inversely to speed in a convergent-thinking task was rejected. No evidence was found for any relationship between extraversion--introversion or neuroticism--stability and either thinking style.

  8. Biologic Treatments for Sports Injuries II Think Tank-Current Concepts, Future Research, and Barriers to Advancement, Part 2: Rotator Cuff.

    PubMed

    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.

  9. Mathematic Terminology.

    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)

  10. Mathematical Geology.

    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)

  11. Mathematics disorder

    MedlinePlus

    ... 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 ...

  12. 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,…

  13. The Changing Curriculum: Mathematics.

    ERIC Educational Resources Information Center

    Davis, Robert B.

    In this 1967 booklet, influences of technology, the non-achiever and the culturally disadvantaged, and the revolt against formalism are discussed in relation to the modern mathematics curriculum. Some projects and school programs described include PLATO, the Nuffield Project, the Nova School Program, Advanced Placement Program, and teacher…

  14. Rainforest Mathematics

    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…

  15. What Are Think Tanks Thinking about?

    ERIC Educational Resources Information Center

    Yates, Eleanor Lee

    2000-01-01

    Explores: "What type of people do think tanks attract?"; "How do think tanks operate and how are they funded?"; "Are they prone to compromise their research integrity?"; and "Are they focusing enough attention on the critical issue of minorities and higher education?" Discusses efforts of concern to African…

  16. What Do Teachers Think about Thinking Skills?

    ERIC Educational Resources Information Center

    Baumfield, Vivienne; Oberski, Iddo

    1998-01-01

    A case study of three programs in British secondary schools (Somerset Thinking Skills, Instrumental Enrichment, and Philosophy for Children) affirmed the difficulty arising from the lack of immediate concrete outcomes from thinking-skills lessons. Teachers' perceptions had a significant influence on effective implementation of these programs. (SK)

  17. 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…

  18. 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…

  19. 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…

  20. Effective Thinking Outdoors.

    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…

  1. Art and Thinking Skills.

    ERIC Educational Resources Information Center

    McCoubrey, Sharon

    1994-01-01

    This theme issue reviews and confirms the connection between thinking skills and art education. Articles offer possible teaching approaches and specific lesson plans dealing with thinking skills. The issue includes: (1) "Editor's View" (Sharon McCoubrey); (2) "Critical and Creative Thinking and Making Art" (Carol Fineberg); (3)…

  2. Beyond Critical Thinking.

    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)

  3. Critical thinking dispositions among newly graduated nurses

    PubMed Central

    Wangensteen, Sigrid; Johansson, Inger S; Björkström, Monica E; Nordström, Gun

    2010-01-01

    wangensteen s., johansson i.s., björkström m.e. & nordström g. (2010) Critical thinking dispositions among newly graduated nurses. Journal of Advanced Nursing66(10), 2170–2181. Aim The aim of the study was to describe critical thinking dispositions among newly graduated nurses in Norway, and to study whether background data had any impact on critical thinking dispositions. Background Competence in critical thinking is one of the expectations of nursing education. Critical thinkers are described as well-informed, inquisitive, open-minded and orderly in complex matters. Critical thinking competence has thus been designated as an outcome for judging the quality of nursing education programmes and for the development of clinical judgement. The ability to think critically is also described as reducing the research–practice gap and fostering evidence-based nursing. Methods A cross-sectional descriptive study was performed. The data were collected between October 2006 and April 2007 using the California Critical Thinking Disposition Inventory. The response rate was 33% (n= 618). Pearson’s chi-square tests were used to analyse the data. Results Nearly 80% of the respondents reported a positive disposition towards critical thinking. The highest mean score was on the Inquisitiveness subscale and the lowest on the Truth-seeking subscale. A statistically significant higher proportion of nurses with high critical thinking scores were found among those older than 30 years, those with university education prior to nursing education, and those working in community health care. Conclusion Nurse leaders and nurse teachers should encourage and nurture critical thinking among newly graduated nurses and nursing students. The low Truth-seeking scores found may be a result of traditional teaching strategies in nursing education and might indicate a need for more student-active learning models. PMID:20384637

  4. 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…

  5. Affecting Critical Thinking through Speech.

    ERIC Educational Resources Information Center

    O'Keefe, Virginia P.

    Intended for teachers, this booklet shows how spoken language can affect student thinking and presents strategies for teaching critical thinking skills. The first section discusses the theoretical and research bases for promoting critical thinking through speech, defines critical thinking, explores critical thinking as abstract thinking, and tells…

  6. 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.

  7. Mathematics Majors' Beliefs about Proof Reading

    ERIC Educational Resources Information Center

    Weber, Keith; Mejia-Ramos, Juan Pablo

    2014-01-01

    We argue that mathematics majors learn little from the proofs they read in their advanced mathematics courses because these students and their teachers have different perceptions about students' responsibilities when reading a mathematical proof. We used observations from a qualitative study where 28 undergraduates were observed evaluating…

  8. 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…

  9. Gender and Inquiry: An Investigation into Identifying and Defining the Role of Inquiry in Higher-Order Thinking.

    ERIC Educational Resources Information Center

    Kelly, Catherine A.

    1999-01-01

    Investigated boys' and girls' perceptions of mathematical and scientific higher-order thinking, ways to identify higher order thinking's occurrence, and inquiry methods for developing it in elementary students and preservice teachers. Results indicated that both genders had similar perceptions about inquiry and approaches to higher-order thinking.…

  10. Theoretical Mathematics

    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.

  11. 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…

  12. 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…

  13. 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…

  14. Creative Construction of Mathematics and Science Concepts in Early Childhood.

    ERIC Educational Resources Information Center

    Gallenstein, Nancy L.

    Noting that effective teaching models that emphasize critical thinking in mathematics and science are used less often in early childhood classrooms than in those for older students, this book provides early childhood educators with an explanation of teaching models that promote 3- to 8-year-olds critical thinking, problem solving, decision making,…

  15. 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…

  16. 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…

  17. Experimental Mathematics and Mathematical Physics

    SciTech Connect

    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.

  18. Six Thinking Hats: Argumentativeness and Response to Thinking Model.

    ERIC Educational Resources Information Center

    Carl, Walter John, III

    A study presents a perceptual model of thinking called the "Six Thinking Hats" and argumentativeness as a predictor of response to the model. The "Six Thinking Hats" model creates six artificial contexts for thinking, corresponding to the primary thought modes of objective, subjective, critical, and creative thinking, within a…

  19. Mathematics Scrapbook

    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…

  20. Mathematics Education.

    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…

  1. Technical Mathematics.

    ERIC Educational Resources Information Center

    Flannery, Carol A.

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

  2. Why Mathematics?

    ERIC Educational Resources Information Center

    McClellan, Kathryn T.

    Why mathematics should be learned is discussed. Its role as an important active force in the development of our civilization, and as the most useful subject taught in our schools, next to English, is noted. The primary objective of all mathematics work is to help man study nature, and some practical achievements of this connection are noted.…

  3. Mathematical Literacy

    ERIC Educational Resources Information Center

    Martin, Hope

    2007-01-01

    "Mathematical literacy" implies that a person is able to reason, analyze, formulate, and solve problems in a real-world setting. Mathematically literate individuals are informed citizens and intelligent consumers. They have the ability to interpret and analyze the vast amount of information they are inundated with daily in newspapers, on…

  4. Recent advances in mathematical criminology. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

    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].

  5. Thinking about thinking - thinking about measurement: a Rasch analysis of recursive thinking.

    PubMed

    Müller, Ulrich; Overton, Willis F

    2010-01-01

    Two studies were conducted to examine the dimensionality and hierarchical organization of a measure of recursive thinking. In Study 1, Rasch analysis supported the claim that the recursive thinking task measures a single underlying dimension. Item difficulty, however, appeared to be influenced not only by level of embeddedness but also by syntactic features. In Study 2, this hypothesis was tested by adding new items to the recursive thinking measure. Rasch analysis of the modified recursive thinking task produced evidence for the undimensionality and segmentation. However, Study 2 did not support the idea that syntactic features influence item difficulty.

  6. Thinking styles and emotions.

    PubMed

    Zhang, Li-Fang

    2008-09-01

    This study aimed to explore the relationship between thinking styles and emotions among university students in Hong Kong. Participants were 99 2nd-year students (23 men and 76 women) who responded to the Thinking Styles Inventory-Revised (TSI-R), based on R. J. Sternberg's (1988) theory of mental self-government, and to the Iowa Managing Emotions Inventory (IMEI), based on A. Chickering's (1969) theory of psychosocial development. Results indicated not only that thinking styles were associated with emotions but also that thinking styles had predictive power for emotions beyond age. The author discusses implications of these findings for faculty members and student-development educators.

  7. 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…

  8. 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…

  9. 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…

  10. 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.…

  11. 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…

  12. 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…

  13. 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…

  14. Debunking Myths about the Standards for Mathematical Practice

    ERIC Educational Resources Information Center

    Mateas, Victor

    2016-01-01

    The adoption of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) has caused a shift in the expectations for student learning, with implications for teaching. It has also introduced a new kind of standard focused on the way that students think about content in the form of the Standards for Mathematical Practice (SMP). The SMP…

  15. The Berlin-White Integrated Science and Mathematics Model.

    ERIC Educational Resources Information Center

    Berlin, Donna F.; White, Arthur L.

    1994-01-01

    Discusses six aspects of the Berlin-White Integrated Science and Mathematics Model developed to address the need for a definition of the integration of science and mathematics education. These aspects are ways of learning; ways of knowing; process and thinking skills; content knowledge; attitudes and perceptions; and teaching strategies. (MKR)

  16. A Dynamic Theory of Mathematical Understanding: Some Features and Implications.

    ERIC Educational Resources Information Center

    Pirie, Susan; Kieren, Thomas

    Given the current and widespread practical interest in mathematical understanding, particularly with respect to higher order thinking skills, curriculum reform advocates in many countries cite the need for teaching mathematics with understanding. However, the characterization of understanding in ways that highlight its growth, as well as the…

  17. The Characteristics of the Growth of Mathematical Understanding.

    ERIC Educational Resources Information Center

    Kieren, T. E.; Pirie, S. E. B.

    Given the current and widespread practical interest in mathematical understanding, particularly with respect to higher order thinking skills, curriculum reform advocates in many countries cite the need for teaching mathematics with understanding. However, the characterization of understanding in ways that highlight its growth, as well as the…

  18. Investigating Preservice Mathematics Teachers' Manipulative Material Design Processes

    ERIC Educational Resources Information Center

    Sandir, Hakan

    2016-01-01

    Students use concrete manipulatives to form an imperative affiliation between conceptual and procedural knowledge (Balka, 1993). Hence, it is necessary to design specific mathematics manipulatives that focus on different mathematical concepts. Preservice teachers need to know how to make and use manipulatives that stimulate students' thinking as…

  19. 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…

  20. A Tree at Bedtime Investigation: Connecting Mathematics, Science, and Literature

    ERIC Educational Resources Information Center

    Kieff, Judith

    2006-01-01

    Activities that promote "active thinking" help children learn mathematics and science by allowing them to work at forming relationships, making connections, and integrating concepts and procedures. Dynamic and exciting children's books invite and motivate children to learn mathematics and science by responding to stories, characters, and their…

  1. 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…

  2. Mathematiques 14-24 (Mathematics 14-24).

    ERIC Educational Resources Information Center

    Alberta Learning, Edmonton.

    To set goals and make informed choices, students need an array of thinking and problem-solving skills. Fundamental to this is an understanding of mathematical techniques and processes that will enable them to apply the basic skills necessary to address everyday mathematical situations, as well as acquire higher order skills in logical analysis and…

  3. 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…

  4. 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…

  5. Building a Case for Blocks as Kindergarten Mathematics Learning Tools

    ERIC Educational Resources Information Center

    Kinzer, Cathy; Gerhardt, Kacie; Coca, Nicole

    2016-01-01

    Kindergarteners need access to blocks as thinking tools to develop, model, test, and articulate their mathematical ideas. In the current educational landscape, resources such as blocks are being pushed to the side and being replaced by procedural worksheets and academic "seat time" in order to address standards. Mathematics research…

  6. Investigations in Mathematics Education. Volume 16, Number 3.

    ERIC Educational Resources Information Center

    Suydam, Marilyn N., Ed.; Kasten, Margaret L., Ed.

    1983-01-01

    An editorial comment on the computer and the mathematics educator is included first. Then, abstracts and comments are presented for 11 articles. Studies included focus on mental addition, problem solving by sixth graders, mathematics anxiety, tutoring, direct instruction, a bilingual program, thinking strategies for multiplication basic facts,…

  7. 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…

  8. 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…

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

    ERIC Educational Resources Information Center

    Tasova, Halil Ibrahim; Delice, Ali

    2012-01-01

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

  10. Developing Robust Forms of Pre-Service Teachers' Pedagogical Content Knowledge through Culturally Responsive Mathematics Teaching Analysis

    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 children's…

  11. It Makes You Think

    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…

  12. Thinking inside the Box

    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…

  13. Systems Thinking and Counterinsurgencies

    DTIC Science & Technology

    2007-12-01

    This article presents the essentials of a successful counterinsurgency strategy by applying a technique known as systems thinking .1 The fundamentals...unexpected ways, and how to measure progress in achieving the ends of the strategy. Systems thinking has proven successful in other contexts at explaining

  14. An Hypothesis on Thinking

    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.…

  15. Thinking in Orienteering.

    ERIC Educational Resources Information Center

    Johansen, Bjorn Tore

    1997-01-01

    A think-aloud technique, in which 20 orienteers verbalized their exact thoughts during orienteering, was used to examine the phenomenon of cognition during orienteering. Results indicate that orienteering is experienced as a task to be accomplished, a physical movement, and a dynamic process, and that thinking involves attuning perceptions to…

  16. Rural Thinking Skills Catalog.

    ERIC Educational Resources Information Center

    Kruse, Janice

    This catalog aims to help educators locate materials which will assist them in effectively teaching thinking skills. Research for Better Schools (RBS) serves as the lead educational laboratory for the Department of Education's national project on thinking skills. A total of 248 resources, including pamphlets, documents of activities, computer…

  17. All Our Students Thinking

    ERIC Educational Resources Information Center

    Noddings, Nel

    2008-01-01

    Critical thinking is the sort of mental activity that uses facts to plan, order, and work toward an end; seeks meaning or an explanation; is self-reflective; and uses reason to question claims and make judgments. Any subject--be it physics, algebra, or auto repair--can promote critical thinking as long as teachers teach the subject matter in…

  18. 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…

  19. Reading is Thinking.

    ERIC Educational Resources Information Center

    Winkeljohann, Rosemary

    1979-01-01

    The focus article in this newsletter contains a discussion of the theory of reading as a thinking process and offers practical suggestions for implementing instruction in teaching reading as a thinking process. The section on theory is based on observations of the reading process as perceived by psycholinguists such as Frank Smith and Kenneth…

  20. Kaleidoscopic Thinking for Creativity.

    ERIC Educational Resources Information Center

    Petrini, Catherine M., Ed.

    1991-01-01

    The most successful companies must be flexible and rapidly adaptable. This requires creative management and creative teamwork. Like a kaleidoscope, creative thinking is the ability to rearrange pieces to form a new reality, to see connections, and to think on a global scale. (SK)

  1. Vitalistic thinking in adults.

    PubMed

    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.

  2. Rethinking Critical Thinking

    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…

  3. 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…

  4. Blue Ocean Thinking

    ERIC Educational Resources Information Center

    Orem, Donna

    2016-01-01

    This article describes a concept called the "blue ocean thinking strategy," developed by W. Chan Kim and Renée Mauborgne, professors at INSEAD, an international graduate school of business in France. The "blue ocean" thinking strategy considers opportunities to create new markets for services, rather than focusing solely on…

  5. Practical systems thinking

    NASA Astrophysics Data System (ADS)

    Konkarikoski, K.; Ritala, R.; Ihalainen, H.

    2010-07-01

    System is a dynamic and complex whole, interacting as a structured functional unit. Systems thinking provides tools for understanding a such system structure and its dynamic behavior. Practical systems thinking course teaches first year bachelor students basics about systems and how open problem can be formulated to system task.

  6. 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…

  7. Learning to Think Spatially in an Undergraduate Interdisciplinary Computational Design Context: A Case Study

    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…

  8. 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…

  9. 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…

  10. Thinking in Patterns to Solve Multiplication, Division, and Fraction Problems in Second Grade

    ERIC Educational Resources Information Center

    Stokes, Patricia D.

    2016-01-01

    Experts think in patterns and structures using the specific "language" of their domains. For mathematicians, these patterns and structures are represented by numbers, symbols and their relationships (Stokes, 2014a). To determine whether elementary students in the United States could learn to think in mathematical patterns to solve…

  11. 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…

  12. Thinking about "Rich" Tasks

    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…

  13. About critical thinking.

    PubMed

    Hynes, Patricia; Bennett, Jocelyn

    2004-01-01

    Although a universally accepted definition of critical thinking has yet to be determined, there is much discussion in the literature about its meaning and, in particular, how it can be expressed in professional nursing practice. The simultaneous use of related terms such as reflective thinking, problem solving and clinical decision-making contributes to the lack of clarity around exactly what critical thinking is and, subsequently, how it can be taught and evaluated in the clinical setting. The purpose of this article is to provide an overview of the various components of critical thinking and to discuss barriers, facilitators and strategies that can enhance nurses' attainment of this core competency. Few would argue that registered nurses today must be able to think critically in order to effectively communicate a nursing perspective that reflects a meaningful clinical grasp and preparedness to act.

  14. Mathematical Geology.

    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)

  15. Dynamic Boolean Mathematics

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  16. 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…

  17. Fostering Multiplicative Thinking Using Array-Based Materials

    ERIC Educational Resources Information Center

    Young-Loveridge, Jenny

    2005-01-01

    If the goal is to promote mathematical thinking and help children become flexible problem solvers, then it is important to show students multiple representations of a problem. Because it is important to help students develop both counting-based and collections-based conceptions of number, teachers should be showing students both number line…

  18. Problem Solving through Critical Thinking, Grades 5-8.

    ERIC Educational Resources Information Center

    Edwards, Ronald R.; Cook, Wanda D.

    This book was written to provide the teacher with a collection of problems that address the Standards set forth by the National Council of Teachers of Mathematics (NCTM). The primary goal of this book is to help develop these skills for middle school and junior high school students through the application of critical reading and critical thinking.…

  19. 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…

  20. Thinking backwards can inform concerns about 'incomplete' data.

    PubMed

    Grose, Margaret J

    2014-10-01

    Ecologists often feel that they need complete data before they are able to advise or make decisions. Thinking backwards, an idea from mathematics, suggests that we need to focus on the desired outcome to tell us which way to go for practical solutions for our ecological ambitions.