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2. 40 Years of CMESG/Les 40 Ans du GCEDM. 40th Anniversary Issue of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques
- Author
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Canadian Mathematics Education Study Group (CMESG), Liljedahl, Peter, Allan, Darien, Chapman, Olive, Gourdeau, Frédéric, Lajoie, Caroline, Oesterle, Susan, Simmt, Elaine, Taylor, Peter, Liljedahl, Peter, Allan, Darien, Chapman, Olive, Gourdeau, Frédéric, Lajoie, Caroline, Oesterle, Susan, Simmt, Elaine, Taylor, Peter, and Canadian Mathematics Education Study Group (CMESG)
- Abstract
This special issue of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) Proceedings looks at CMESG/GCEDM's collective history, reflects on where the group has been, and who the members have become as an organization. Through a selection of excerpts from past proceedings, the editors have stitched together a partial history of CMESG/GCEDM's time as an organization. This serves not only as a summary of the collective history, but also serves as an introduction to the activities of CMESG/GCEDM through the first 40 years. The pieces selected for inclusion in this special issue stand as signposts along CMESG/GCEDM's history--as exemplifications of what CMESG/GCEDM is as an organization as well as the activities of CMESG/GCEDM at annual meetings. Crafted introductions to each piece articulate the ways in which that piece exemplifies the valued aspects of CMESG/GCEDM. Following an introduction to the special issue (Peter Liljedahl) [Written in English and French], a foreword (Peter Taylor) [Written in English and French], a Preface to the 1977 CMESG Proceedings (Albert Coleman, Bill Higginson, and David Wheeler), and The Origins and Activities of CMESG (David Wheeler), this issue contains the following papers: (1) Mathematics Education Research in Canada: A Prospective View (Tom Kieren); (2) Innovations in Teacher Education Programmes (Claude Gaulin); (3) The Objectives of Mathematics Education (Albert Coleman); (4) Confessions of an Accidental Theorist (Alan Schoenfeld); (5) The Role of Epistemology in the Analysis of Teaching/Learning Relationships In Mathematics Education (Michèle Artigue); (6) Alive Mathematical Reasoning (David Henderson); (7) Toward a Practice-Based Theory of Mathematical Knowledge for Teaching (Deborah Loewenberg Ball and Hyman Bass); (8) Mathematics as Medicine (Edward Doolittle); (9) Old and New Mathematical Ideas from Africa: Challenges for Reflection (Paulus Gerdes); (10) The Role of Proof in Post-Secondary Education (William Byers and Harvey Gerber); (11) From Theory To Observational Data (And Back Again) (Carolyn Kieran and Jo Towers); (12) Where Is The Mathematics? (John Mason and Eric Muller); (13) The Arithmetic/Algebra Interface: Implications For Primary And Secondary Mathematics = Articulation Arithmétique/Algèbre: implications pour l'enseignement des mathématiques au primaire et au secondaire (Nadine Bednarz and Lesley) [Written in English and French]; (14) Images Of Undergraduate Mathematics (Miroslav Lovric and David Poole); (15) A Mathematics Curriculum Manifesto (Walter Whiteley and Brent Davis); (16) Learner Generated Examples (Nathalie Sinclair, Anne Watson, and Rina Zazkis); (17) Étude des pratiques d'enseignement (Jamie Pyper, Hassane Squalli, and Laurent Theis) [Written in English and French]; (18) Mathematics of Planet Earth 2013: Education and Communication = Mathématiques de la planète terre 2013: formation et communication (Doug Franks, Kathleen Pineau, and Walter Whiteley); (19) Indigenous Ways of Knowing in Mathematics (Lisa Lunney Borden and Florence Glanfield); (20) The Commonsense of Teaching (David Wheeler); (21) A Historical Perspective on Mathematics Education Research in Canada: The Emergence of a Community (Carolyn Kieran); (22) Lessons from the Past, Questions for the Future: Méditation sur thème impose (Roberta Mura) [Written in French]; (23) Building Thinking Classrooms: Conditions for Problem Solving (Peter Liljedahl); (24) Where Do I Want Students' Attention? And What Can I Do to Affect Their Attention? (David Hewitt); and (25) Measuring the Impact of a Mentor Program (A. J. Dawson). Individual papers contain references.
- Published
- 2016
3. The Spontaneous Emergence of Elementary Number-Theoretic Concepts and Techniques in Interaction with Computing Technology
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Kieran, Carolyn and Guzman, Jose
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We present in this paper five case studies of instrumental genesis of number-theoretic concepts and techniques involving multiples, divisors, and numerical decomposition. The pupils, who were 12 to 15 years old, used the multi-line screen display of the graphing calculator to explore numerical tasks related to the "Five steps to zero" problem. The paper begins with a mathematical task analysis of various techniques that could be used to determine divisibility by 9. Findings show that the use of the technological tool permits students of this age to spontaneously develop variants of these techniques within tasks that simultaneously afford the co-emergence of related conceptual notions. (Contains 3 footnotes and 6 figures.) [Additional support for the research described in this paper was provided by CONACYT of Mexico. For complete proceedings, see ED500858.]
- Published
- 2003
4. Making Change Can Be Hard: Some Penniless Thoughts on Those 'Damn Kids These Days…'
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Chernoff, Egan J.
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Constantly on the lookout for Canadian mathematics education matters, because if Canadian mathematics education matters then Canadian mathematics education matters, three young university bookstore employees, university students, unable to make proper change when I handed them a five dollar bill for a sticker I was purchasing for my laptop, absolutely crushed my spirit. As they say though, it is not what happens to you, rather it is how you react to what happened to you. As such, rising from what I am now calling "the sticker incident," this article is a many part investigation into the oft-heard phrase "Damn kids these days cannot make change without a calculator." Under examination: the subtraction skills of a particular subset of adult employees not often asked to prove their arithmetic resolve; detailing a personal mistake I made while making change in a big spot; recounting a retelling of a mistake that has haunted someone for many years; detailing which particular customers cashiers need to be worried about when making change (old men with coin purses); wonderings as to why stories about making change do not reflect our now penniless country; and, a brief look at the future responsibilities of cashless immigrants. With this particular matter now in the rearview mirror, I am back in the wild looking for other Canadian mathematics education matters. Stay tuned.
- Published
- 2022
- Full Text
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5. Proceedings of the 2007 Annual Meeting of the Canadian Mathematics Education Study Group = Actes de la Rencontre Annuelle 2007 du Groupe Canadien d'Etude en Didactique des Mathematiques (31st, Fredricton, New Brunswick, Canada, Jun 8-12, 2007)
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Canadian Mathematics Education Study Group (CMESG) and Liljedahl, Peter
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This submission contains the Proceedings of the 2007 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of New Brunswick in Fredricton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc sessions and a panel discussion. Papers include: (1) Understanding Abstraction in Mathematics Education: Meaning, Language, Gesture, and the Human Brain (Rafael Nunez); (2) Mathematics Departments, New Faculty, and the Future of Collegiate Mathematics (T. Christine Stevens); (3) Outreach in Mathematics--Activities, Engagement, & Reflection (Veronique Hussin and Eric Muller); (4) Geometry, Space, and Technology: Challenges for Teachers and Students (Shelley Hunter, Donna Kotsopoulos, and Walter Whiteley); (5) The Design and Implementation of Learning Situations (Anna McQuillan, Fernando Hitt, and Luis Radford); (6) The Multifaceted Role of Feedback in the Teaching and Learning of Mathematics (Jerome Proulx and Florence Glanfield); (7) Mathematics Educational Neuroscience: Origins, Activities, and New Opportunities (Stephen R. Campbell); (8) Communicating the Excitement and Beauty of Mathematics (Malgorzata Dubiel); (9) Conception et experimentation de situations didactiques au prescolaire/primaire / Design and Experimentation of Didactical Situations in Kindergarten and Elementary School (Jacinthe Giroux) [Written in French]; (10) Cabri 3D: An Environment for Purposeful Mathematical Activity? (Kate Mackrell); (11) Equity and Opportunities to Learn in Cooperative Mathematical Work (Indigo Esmond); (12) (Elargir les) Connaissances mathematiques des enseignants de mathematiques du secondaire: une etude sur la formation continue / (Enlarging) Secondary-Level Mathematics Teachers' Mathematical Knowledge: An Investigation of Professional Development (Jerome Proulx) [Presented in both French and English]; (13) Un paradigme d'experimentation au laboratoire de sciences pour l'identification et l'optimisation statistique d'un modele algebrique par interaction visuo-graphique (Georges Touma) [Written in French]; (14) What Factors Influence Understanding of Written Arithmetic Problems? (Dominic Voyer); (15) Probabilities / Probabilites (Egan Chernoff and Annie Savard); (16) First Steps toward an Archeology of Gesture in Graphing (Susan Gerofsky); (17) Function Modelling Using Secondary Data from Statistics Canada's E-STAT Database (Jennifer Hall); (18) Explanation and Proof in Mathematics and Mathematics Education (Gilla Hanna, Ella Kaye, and Riaz Saloojee); (19) Exploring Our Embodied Knowing of the Gauss-Bonnet Theorem: Barn-Raising and Endo-Pentakis-Icosi-Dodecahedron (Eva Knoll); (20) Mathematical Biography (John Grant McLoughlin); (21) This Is Mathematics; This Isn't Mathematics; But That... I'm Not So Certain About: The Possible "Emancipation" of Secondary School Mathematics from the Bonds of "Real" Mathematics (Craig Newell); and (22) What Courses Could or Should Mathematics Departments Offer to Graduate Programs in Mathematics Education? (France Caron, Morris Orzech, and Elaine Simmt). Appended are: (1) Working Groups at Each Annual Meeting; (2) Plenary Lecture at Each Annual Meeting; and (3) Proceedings of Annual Meetings. Individual papers contain references, figures, and tables. [Abstract modified to meet ERIC guidelines. For the 2006 proceedings, see ED529562.]
- Published
- 2008
6. Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 2
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International Group for the Psychology of Mathematics Education., Novotna, Jarmila, Moraova, Hana, Kratka, Magdalena, and Stehlikova, Nad'a
- Abstract
This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr and Dri: (1) The Odds of Understanding the Law of Large Numbers: A Design for Grounding Intuitive Probability in Combinatorial Analysis (Dor Abrahamson and Rose M. Cendak); (2) Imaginary-Symbolic Relations, Pedagogic Resources and the Constitution of Mathematics for Teaching in In-Service Mathematics Teacher Education (Jill Adler and Zain Davis); (3) Relationship between Pre-Service Mathematics Teachers' Teaching and Learning Beliefs and Their Practices (Hatice Akkoc and Feral Ogan-Bekiroglu); (4) Teachers' Awareness of Dimensions of Variation: A Mathematics Intervention Project (Thabit Al-Murani); (5) The Student Teacher and the Others: Multimembership on the Process of Introducing Technology in the Classroom (Nelia Amado and Susana Carreira); (6) Improving Student Teachers' Understanding of Fractions (Solange Amorim Amato); (7) Autodidactic Learning of Probabilistic Concepts through Games (Miriam Amit and Irma Jan); (8) Graduate Students' Processes in Generating Examples of Mathematical Objects (Samuele Antonini); (9) Reasoning in an Absurd World: Difficulties with Proof by Contradiction (Samuele Antonini and Maria Alessandra Mariotti); (10) Will Penelope Choose Another Bridegroom? Looking for an Answer through Signs (Ferdinando Arzarello, Luciana Bazzini, Francesca Ferrara, Ornella Robutti, Cristina Sabena, and Bruna Villa); (11) Motivation and Perceptions of Classroom Culture in Mathematics of Students across Grades 5 to 7 (Chryso Athanasiou and George N. Philippou); (12) Deductive Reasoning: Different Conceptions and Approaches (Michal Ayalon and Ruhama Even); (13) The Tendency to Use Intuitive Rules among Students with Different Piagetian Cognitive Levels (Reuven Babai); (14) Coming to Appreciate the Pedagogical Uses of CAS (Lynda Ball and Kaye Stacey); (15) Students' Conceptions of "m" and "c": How to Tune a Linear Function (Caroline Bardini and Kaye Stacey); (16) A Contradiction between Pedagogical Content Knowledge and Teaching Indications (Ibrahim Bayazit and Eddie Gray); (17) Identifying and Supporting Mathematical Conjectures through the Use of Dynamic Software (David Benitez Mojica and Manuel Santos Trigo); (18) Students Constructing Representations for Outcomes of Experiments (Palma Benko and Carolyn A. Maher); (19) Logarithms: Snapshots from Two Tasks (Tanya Berezovski and Rina Zazkis); (20) Trying to Reach the Limit--The Role of Algebra in Mathematical Reasoning (Christer Bergsten); (21) Semiotic Sequence Analysis--Constructing Epistemic Types Empirically (Angelika Bikner-Ahsbahs); (22) Service Teaching: Mathematical Education of Students of Client Departments (Erhan Bingolbali, John Monaghan, and Tom Roper); (23) Students' Thinking about the Tangent Line (Irene Biza, Constantinos Christou, and Theodossios Zachariades); (24) Habermas' Theory of Rationality as a Comprehensive Frame for Conjecturing and Proving in School (Paulo Boero); (25) Extending Students' Understanding of Decimal Numbers via Realistic Mathematical Modeling and Problem Posing (Cinzia Bonotto); (26) Different Media, Different Types of Collective Work in Online Continuing Teacher Education: Would You Pass the Pen, Please? (Marcelo C. Borba and Rubia B. A. Zulatto); (27) Reformulating "Mathematical Modelling" in the Framework of the Anthropological Theory of Didactics (Marianna Bosch, Fco. Javier Garcia, Josep Gascon, and Luisa Ruiz Higueras); (28) Students' Impressions of the Value of Games for the Learning of Mathematics (Leicha A. Bragg); (29) The Transition from Arithmetic to Algebra: To Reason, Explain, Argue, Generalize and Justify (Trygve Breiteig and Barbro Grevholm); (30) Resisting Reform Pedagogy: Teacher and Learner Contributions (Karin Brodie); (31) Manifestations of Affordances of a Technology-Rich Teaching and Learning Environment (TRTLE) (Jill P. Brown); (32) Types of Representations of the Number Line in Textbooks (Alicia Bruno and Noemi Cabrera); (33) Educational Neuroscience: New Horizons for Research in Mathematics Education (Stephen R. Campbell); (34) Variability in a Probability Context: Developing Pre-Service Teachers' Understanding (Daniel L. Canada); (35) Implementing a Reform-Oriented Mathematics Syllabus: A Survey of Secondary Teachers (Michael Cavanagh); (36) Student's Modelling with a Lattice of Conceptions in the Domain of Linear Equations and Inequations (Hamid Chaachoua, Marilena Bittar, and Jean-Francois Nicaud); (37) Using Reading and Coloring to Enhance Incomplete Prover's Performance in Geometry Proof (Ying-Hao Cheng and Fou-Lai Lin); (38) Aspects of Teachers' Pedagogical Content Knowledge for Decimals (Helen Chick, Monica Baker, Thuy Pham, and Hui Cheng); (39) Collaborative Action Research on Implementing Inquiry-Based Instruction in an Eighth Grade Mathematics Class: An Alternative Mode for Mathematics Teacher Professional Development (Erh-Tsung Chin, Yung-Chi Lin, Yann-Tyng Ko, Chi-Tung Chien, and Hsiao-Lin Tuan); (40) Routine and Novel Mathematical Solutions: Central-Cognitive or Peripheral-Affective Participation in Mathematics Learning (Mei-Shiu Chiu); (41) The Role of Self-Generated Problem Posing in Mathematics Exploration (Victor V. Cifarelli and Jinfa Cai); (42) A Longitudinal Study of Children's Mental Computation Strategies (Barbara Clarke, Doug M. Clarke, and Marj Horne); (43) Assessing Fraction Understanding Using Task-Based Interviews (Doug M. Clarke, Michal Sukenik, Anne Roche, and Annie Mitchell); (44) Evaluation of a Teaching Concept for the Development of Problem Solving Competences in Connection with Self-Regulation (Christina Collet and Regina Bruder); (45) Developing Probability Thinking in Primary School: A Case Study on the Constructive Role of Natural Language in Classroom Discussions (Valeria Consogno, Teresa Gazzolo, and Paulo Boero); (46) Collaboration with Teachers to Improve Mathematics Learning: Pedagogy at Three Levels (Tom J. Cooper, Annette R. Baturo, and Edlyn J. Grant); (47) "Aim High--Beat Yourself": Effective Mathematics Teaching in a Remote Indigenous Community (Tom J. Cooper, Annette R. Baturo, Elizabeth Warren, and Edlyn J. Grant); (48) Development of Children's Understanding of Length, Area, and Volume Measurement Principles (Margaret Curry, Michael Mitchelmore, and Lynne Outhred; (49) Mathematics-for-Teaching: The Cases of Multiplication and Division (Brent Davis, Elaine Simmt, and Dennis Sumara); (50) Generative Concept Images (Gary E. Davis and Catherine A. Pearn); (51) Developmental Assessment of Data Handling Performance Age 7-14 (Pauline Davis, Maria Pampaka, Julian Williams, and Lawrence Wo); (52) The Effect of Different Teaching Tools in Overcoming the Impact of the Intuitive Rules (Eleni Deliyianni, Eleni Michael, and Demetra Pitta-Pantazi); (53) Investigating Social and Individual Aspects in Teacher's Approaches to Problem Solving (Fien Depaepe, Erik De Corte, and Lieven Verschaffel); (54) Maths Avoidance and the Choice of University (Pietro Di Martino and Francesca Morselli); (55) Primary Students' Reasoning about Diagrams: The Building Blocks of Matrix Knowledge (Carmel M. Diezmann); (56) Integrating Errors into Developmental Assessment: "Time" for Ages 8-13 (Brian Doig, Julian Williams, Lawrence Wo, and Maria Pampaka); (57) Vygotsky's Everyday Concepts/Scientific Concepts Dialectics in School Context: A Case Study (Nadia Douek); (58) Creating Mathematical Models with Structures (Katherine Doyle); (59) Mechanisms for Consolidating Knowledge Constructs (Tommy Dreyfus, Nurit Hadas, Rina Hershkowitz, and Baruch Schwarz); and (60) Reconciling Factorizations Made with CAS and with Paper-and-Pencil: The Power of Confronting Two Media (Paul Drijvers, Carolyn Kieran, Andre Boileau, Fernando Hitt, Denis Tanguay, Luis Saldanha, and Jose Guzman). (Individual papers contain references.)
- Published
- 2006
7. Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group = Actes de la Rencontre Annuelle 2002 du Groupe Canadien d'Etude en Didactique des Mathematiques (26th, Kingston, Ontario, Canada, May 24-28, 2002)
- Author
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Canadian Mathematics Education Study Group (CMESG), Simmt, Elaine, and Davis, Brent
- Abstract
This submission contains the Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Queen's University in Kingston, Ontario. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc and special anniversary sessions. Papers include: (1) Toward a Practice-Based Theory of Mathematical Knowledge for Teaching (Deborah Ball and Hyman Bass); (2) The Experimental Mathematician: The Pleasure of Discovery and the Role of Proof (Jon Borwein); (3) Mathematics and the Arts (Susan Gerofsky, Nathalie Sinclair, and Brent Davis); (4) Philosophy for Children and Mathematics (Richard Pallascio and Elaine Simmt); (5) The Arithmetic/Algebra Interface: Implications for Primary and Secondary Mathematics / Articulation arithmetique/algebre: Implications pour l'enseignement des mathematiques au primaire et au secondaire (Nadine Bednarz and Lesley Lee); (6) Mathematics, the Written and the Drawn (David Pimm and Nick Jackiw); (7) Des cours de mathematiques pour les futurs (et actuels) maitres au secondaire / Types and Characteristics Desired of Courses in Mathematics Programs for Future (and In-Service) Teachers (Walter Whiteley, Peter Taylor, and Harry White) [Presented in both French and English]; (8) High School Mathematics Teachers' Perspectives of Mathematical Word Problems (Olive Chapman); (9) What are Critical Online Experiences for Mathematics Teachers and Students? (George Gadanidis); (10) Socioeconomic Gradients in Mathematics Achievement: Findings for Canada from the Third International Mathematics and Science Study (George Frempong); (11) Light and Shadows (in) Knowing Mathematics and Science (Kathleen Nolan); (12) Supporting Student Efforts to Learn with Understanding: An Investigation of the Use of "JavaSketchpad" Sketches in the Secondary Geometry Classroom (Margaret P. Sinclair); (13) Conceptualizing Limit in Calculus (Why is It Still a Problem?) (Allan Brown); (14) Amplifying Mathematical Intelligence Using Web-Based Interactive Activities (George Gadanidis); (15) Grades 5-6 Teachers' Algebra Teaching Beliefs and Practices (George Gadanidis); (16) Researching the Effect of Interactive Applets in Mathematics Teaching (George Gadanidis); (17) Creativity and the Psychology of Mathematical Invention (Peter Liljedahl); (18) Logical Reasoning and Mathematical Games (Ralph Mason and Janelle McFeetors); (19) Collective Mathematical Thinking (Immaculate Namukasa); (20) Proofs and Refutations on the Web: Mathematics Environments for Grades 7 & 8 (Geoffrey Roulet); (21) Being in a Mathematical Place: Immersion in Mathematical Investigation (David Wagner); (22) Reflections on 25 Years with CMESG (Eric Muller); (23) Reflexions d'un mathematicien sur le GCEDM (Frederic Gourdeau) [Written in French]; (24) A Historical Perspective on Mathematics Education Research in Canada: The Emergence of a Community (Carolyn Kieran); (25) Lessons from the Past, Questions for the Future (Brent Davis); and (26) Lessons from the Past, Questions for the Future: meditation sur theme impose (Roberta Mura) [Written in French]. Appended are: (1) Working Groups at Each Annual Meeting; (2) Plenary Lectures at Each Annual Meeting; and (3) Proceedings of Annual Meetings. Individual papers contain references, figures, and tables. [Abstract modified to meet ERIC guidelines. For the 2001 proceedings, see ED472094.]
- Published
- 2003
8. Divisibility and Multiplicative Structure of Natural Numbers: Preservice Teachers' Understanding.
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Simon Fraser Univ., Burnaby (British Columbia). Faculty of Education., Zazkis, Rina, and Campbell, Stephen
- Abstract
This study contributes to a growing body of research on the development of elementary teacher's content knowledge of mathematics. Individual clinical interviews were conducted with preservice elementary teachers (N=21) enrolled in a professional development course called "Foundations of Mathematics for Teachers." An instrument that allowed for the flexibility to probe and clarify participant understandings of elementary number theoretical concepts was employed. Questions were designed to clarify participants' understandings of procedures and concepts relating to divisibility and to investigate their abilities to make connections and inferences from them. A constructivist-oriented phenomenological analysis of reflective abstraction was adapted as a framework for interpreting data acquired in the interviews. Data analysis supports the general claim that teacher's content knowledge is "weak" and teacher's conceptual understanding is "insufficient" at times to teach arithmetic even in the elementary grades. Results provide a preliminary basis of a descriptive theory for the development of mental constructions involving elementary numbers concepts, their properties and relationships. An illustration of the model used to guide analysis and excerpts from the interviews are included. (Contains 16 references.) (LL)
- Published
- 1994
9. Grade 11 Students' Interconnected Use of Conceptual Knowledge, Procedural Skills, and Strategic Competence in Algebra: A Mixed Method Study of Error Analysis
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Egodawatte, Gunawardena and Stoilescu, Dorian
- Abstract
The purpose of this mixed-method study was to investigate grade 11 university/college stream mathematics students' difficulties in applying conceptual knowledge, procedural skills, strategic competence, and algebraic thinking in solving routine (instructional) algebraic problems. A standardized algebra test was administered to thirty randomly selected grade 11 students in an urban school in Ontario, Canada. Ten students were later interviewed. In this paper, we discuss the solutions and interviews of five students. The results showed that the majority of university/college stream mathematics students were in the transition stage from arithmetic to algebra. Another prominent feature of these students' problem solving process was their overuse of procedures without being able to critically evaluate whether these procedures would work or not. They also demonstrated lack of "relational," "application," and "structural" abilities when solving instructional problems. We emphasize that, in order to be successful, all components of problem solving (procedural work, local focus, strategic skills, and algebraic reasoning) should work together in a coherent manner, as the main learning challenge in problem solving remains keeping cohesion between its multiple interconnected components. Therefore, it is necessary that to show them the arithmetic-algebraic connection in problem solving and to facilitate them to systematically check their answers in the context of a general strategy.
- Published
- 2015
10. How the Relational Paradigm Can Transform the Teaching and Learning of Mathematics: Experiment in Quebec
- Author
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Polotskaia, Elena
- Abstract
The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical work in this field has not yet been fully recognised by the larger international community. In this article, I use Davydov's vision of mathematics as the study of quantitative relationships--the vision underlying the relational paradigm in teaching and learning of mathematics. I use the example of one research project to demonstrate how the relational paradigm changes and reforms teaching practices. I discuss the teaching approach, developed within this paradigm, as well as the learning outcomes demonstrating the transformative power of Davydov's ideas.
- Published
- 2017
11. The Role of Children's Diagrams and Pictures in Their Solution of Complex Arithmetic Problems.
- Author
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Biron, Diane and Bednarz, Nadine
- Abstract
This research was concerned with the clarification of the role that the external representation process (e.g. drawing) plays in children's solving of complex arithmetic problems. Fourteen children in the 10- to 12-year-old age range were asked to represent and solve five complex arithmetic problems (three with temporal organization of data, two with spatial organization). The analysis of the representation process in relation to problem solving revealed that: (1) the older children had more ability to represent and to illustrate the relations between the data of the problem; and (2) discursive representation (reformulation of the problem by the child) seemed easier in the problems that called into play a temporal organization. The significance of these results for research in the area of problem solving in the teaching of mathematics is discussed. (Author/YP)
- Published
- 1989
12. Coaxing Children.
- Author
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Southern Illinois Univ., Edwardsville., Bates, John, and O'Brien, Thomas C.
- Abstract
This text is a verbatim transcription of an interview with John Bates, a former math coordinator for Metro-Toronto schools, and the Director of Inner City Education, Toronto, Canada. (The interview was conducted by Thomas C. O'Brien under the auspices of the Teachers' Center Project of Southern Illinois University at Edwardsville.) Much of the interview focuses on three math activities for elementary school students that are designed to enhance the flexibility and creativity of students while they acquire basic math skills. Math activities discussed include (1) graphic frames for learning arithmetical operations, (2) a quadrant game utilizing rule-governed allocations of symbols to different areas to develop categorization skills, and (3) rule-constrained colored block manipulation activities that involve sequential transformation from symmetrical arrangement through non-symmetrical arrangement and a return to the original symmetry. Additionally, some remarks are made about language arts activities designed to personalize, and thereby motivate, young children's involvement in reading and writing. The use of note-boxes for a student mail system and the entry of students' stories in bound book form into the school library (including reader feedback to the student author) are described. (Author/RH)
- Published
- 1982
13. Fuzzy set theory based methodology for the analysis of measurement uncertainties in river discharge and stage.
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Shrestha, Rajesh R. and Simonovic, Slobodan P.
- Subjects
FUZZY sets ,STREAM measurements ,ARITHMETIC ,QUALITY control ,RIVERS - Abstract
Copyright of Canadian Journal of Civil Engineering is the property of Canadian Science Publishing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2010
- Full Text
- View/download PDF
14. PERFORMANCE IN MATHEMATICAL PROBLEM SOLVING AS A FUNCTION OF COMPREHENSION AND ARITHMETIC SKILLS.
- Author
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Voyer, Dominic
- Subjects
PROBLEM solving in children ,STUDY & teaching of arithmetic in primary schools ,MATHEMATICAL analysis ,COMPREHENSION in children ,FRENCH-speaking countries ,PROBLEM solving ability testing - Abstract
Many factors influence a student's performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils' real-world knowledge, which support the construction of a 'situation model'. In this study, we examine some factors related to the pupil or to the word problem itself, which may influence the comprehension process, and we assess the effects of the situation model on pupils' problem solving performance. The sample is composed of 750 pupils of grade 6 elementary school. They were selected from 35 classes in 17 Francophone schools located in the province of Quebec, Canada. For this study, 3 arithmetic problems were developed. Each problem was written in 4 different versions, to allow the manipulation of the type of information included in the problem statement. Each pupil was asked to solve 3 problems of the same version and to complete a task that allowed us to evaluate the construction of a situation model. Our results show that pupils with weaker arithmetic skills construct different representations, based on the information presented in the problem. Also, pupils who give greater importance to situational information in a problem have greater success in solving the problem. The situation model influences pupils' problem solving performance, but this influence depends on the type of information included in the problem statement, as well as on the arithmetic skills of each individual pupil. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
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