# Manual Proof and Proving in Mathematics Education: The 19th ICMI Study: 15 (New ICMI Study Series)

Research on the teaching and learning of proof: Taking stock and moving forward. Cai Ed. Proof and argumentation in mathematics education research. Boero Eds. Rotterdam, The Netherlands: Sense Publishers. Secondary students' proof constructions in mathematics: the role of written vs. Review of Education, 7 1 , Context and Implications Document for "Secondary students' proof constructions in mathematics: the role of written vs. Li, H. An examination of the role of the teacher and students during a problem-based learning intervention: lessons learned from a study in a Taiwanese primary mathematics classroom.

Interactive Learning Environments, 26 1 , Demosthenous, E. La matematica e la sua didattica , 26 1 , Diamond, A.

## Andreas Stylianides : Faculty of Education

Personal epistemologies of statisticians in academia: An exploratory study. Statistics Education Research Journal, 16 2 , Research-based interventions in the area of proof: The past, the present, and the future. The role of instructional engineering in reducing the uncertainties of ambitious teaching. Cognition and Instruction , 32 4 , The Journal of Mathematical Behavior, 33, McCrory, R.

International Journal of Educational Research, 64, Notices of the American Mathematical Society, 61 3 , Note: This article was translated into Chinese and was published in Mathematical Advances in Translation , vol. International Journal of Science and Mathematics Education, 11 6 , Seeking research-grounded solutions to problems of practice: Classroom-based interventions in mathematics education.

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Roberts, N. A type of parental involvement with an isomorphic effect on urban children's mathematics, reading, science, and social studies achievement at kindergarten entry. Urban Education, 46 3 , Towards a comprehensive knowledge package for teaching proof: A focus on the misconception that empirical arguments are proofs. Pythagoras, 32 1 , Art. Can a proof and a counterexample coexist? Students' conceptions about the relationship between proof and refutation. Research in Mathematics Education, 12 1 , Mathematics for teaching: A form of applied mathematics.

Teaching and Teacher Education, 26 , Proof constructions and evaluations. Educational Studies in Mathematics, 72, Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education , 40 , Learning about the nature of argument in mathematical and scientific contexts. Mediterranean Journal for Research in Mathematics Education, 8 1 , Understanding and describing mathematical knowledge for teaching: Knowledge about proof for engaging students in the activity of proving.

- Proof and Proving in Mathematics Education;
- La Habana, la Patagonia y el Tribar (Spanish Edition);
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- Gila Hanna (Author of Explanation And Proof In Mathematics).
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- Proof, proving, and teacher-student interaction: theories and contexts.
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Journal of Mathematics Teacher Education, 11, Proof in school mathematics: Insights from psychological research into students' ability for deductive reasoning. Mathematical Thinking and Learning, 10, Studying the classroom implementation of tasks: High-level mathematical tasks embedded in "real-life" contexts. Teaching and Teacher Education, 24, Proof and proving in school mathematics.

Journal for Research in Mathematics Education, 38, The notion of proof in the context of elementary school mathematics. Educational Studies in Mathematics, 65 , Introducing young children to the role of assumptions in proving.

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Mathematical Thinking and Learning, 9 , Preservice teachers' knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10, Learning mathematics with understanding: A critical consideration of the Learning Principle in the Principles and Standards for School Mathematics. The Mathematics Enthusiast, 4 1 , Validation of solutions of construction problems in Dynamic Geometry Environments. Technology, Knowledge and Learning, 10, Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts.

Educational Studies in Mathematics, 55 , Siedel, H. Hanna, Gila. Record type: Book Section. Abstract This chapter focuses on the role of the teacher in teaching proof and proving in the mathematics classroom.

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Available under License Other. Download kB. More information Published date: September Additional Information: The pagination of this author's version is almost identical to the published version. Keywords: pedagogy, curriculum, teaching, learning, mathematics, geometric, geometrical, deductive reasoning, proof, proving, school, national curriculum, euclid, euclidean, classroom, student, teacher, interaction, socio-mathematical norms, variation, instructional exchange, theory, theories, variation theory, teaching with variation.

DOI: doi Date deposited: 03 May Last modified: 06 Jun Experiential learning: Experience as the source of learning and development. Utrecht: PME. Kwong, K.

An analysis of geometry in the junior secondary school grade mathematics textbooks from England, Hong Kong and Chinese Taipei Unpublished doctoral dissertation. Lakatos, I. What does a mathematical proof prove? Currie Eds. Cambridge: Cambridge University Press. Larvor, B. Authoritarian versus authoritative teaching: Polya and Lakatos. Leron, U. Generic proving: Reflections on scope and method. For the Learning of Mathematics, 33 3 , 24— Leung, I.

International Journal for Mathematics Teaching and Learning, 17 3. Levav-Waynberg, A. The role of multiple solution tasks in developing knowledge and creativity in geometry. The Journal of Mathematical Behavior, 31, 73— Malerstein, A. American Journal of Psychotherapy, 33 1 , — Mayring, P. Qualitative Inhaltsanalyse.

Forum Qualitative Sozialforschung. On-line Journal, 1 2. Nardi, E. Reflections on visualization in mathematics and in mathematics education. Dreyfus Eds. Dordrecht: Springer. Natsheh, I. Exploring the potential role of visual reasoning tasks among inexperienced solvers. Niss, M. Papastavridis Eds. Competencies and mathematical learning. Ideas and Inspiration for the development of mathematics teaching and learning in Denmark English ed. Ojose, B. The Mathematics Educator, 18 1 , 26— Poon, K. A study of geometric understanding via logical reasoning in Hong Kong.

Reid, D. Pre-formal, formal, and formulaic proving.

## Mathematics education

Rowland, T. Journal of Mathematics Teacher Education, 8, — The Mathematics Educator, 10 1 , — Schwarz, B. Stewart, P. Investigating the relationship between visual imagery, metacognition and mathematics pedagogical content knowledge. Journal of the International Society for Teacher Education, 18 1 , 26— Tatto, M. Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries. Amsterdam: IEA.