Mathematical Challenges For All

ISBN-13: 9783031188671 / Angielski / Twarda / 2023 / 587 str.

Roza Leikin

Opis

This book argues that mathematical challenge can be found at any level and at every age and constitutes an essential characteristic of any mathematics classroom aimed at developing the students’ mathematical knowledge and skills. Since each mathematics classroom is heterogeneous with respect to students’ mathematical potential, quality mathematical instruction results from matching the level of mathematical challenge to different students’ potential. Thus, effective integration of mathematical challenge in the instructional process is strongly connected to the equity principle of mathematics education. In the three sections in this volume readers can find diverse views on mathematical challenges in curriculum and instructional design, kinds and variation of mathematically challenging tasks and collections of mathematical problems. Evidence-based analysis is interwoven with theoretical positions expressed by the authors of the chapters. Cognitive, social and affective characteristics of challenging mathematical activities are observed and analyzed. The volume opens new avenues of research in mathematics education, and pose multiple questions about mathematical instruction rich in mathematical challenge for all. The authors invite readers to explore and enjoy mathematical challenges at different levels.   

Spis treści

Section 1: Mathematical challenges in curriculum and instructional design

​Chapter 1: The personalized mathematics inquiry model for developing Cyprus mathematics textbooks

Chapter 2: Advancing the mathematical argumentation of elementary students and prospective teachers through small group discussions of complex mathematical tasks

Chapter 3: Challenging students to develop mathematical reasoning

Chapter 4: Mathematical modelling as a stimulus for curriculum and instructional reform in secondary school mathematics

Chapter 5: Development and stimulation of early core mathematical competencies in young children: results from the Leuven Wis & C° project

Chapter 6: Mathematical challenges in problem posing

Chapter 7: Using dynamic applets for varying mathematical challenge in open mathematical tasks

Chapter 8: Response

Section 2: Kinds and variation of mathematically challenging tasks

Chapter 9: Preparing teachers for mathematical challenge in the classroom through MathTASK teacher education activities

Chapter 10: Visualization a pathway to mathematical challenging tasks

Chapter 11: Mathematical challenge in linking advanced and secondary mathematics

Chapter 12: Challenges in designing and solving technology based tasks

Chapter 13: Challenge in the eyes of the beholder

Chapter 14: Pitching Tasks: Balancing Challenge, Accessibility and Fruitfulness

Chapter 15: Creativity and Challenge: connections between task complexity and insight required for tasks solution

Chapter 16: Response

Section 3: Collections of mathematical problems

Chapter 17: Task design, and the 'Unity of Mathematics’

Chapter 18: The power of modelling problems for learning and teaching mathematics

Chapter 19: Challenge: The essence of the discipline? Or an optional extra?

Chapter 20: Designing chains of problems with different levels of challenge through solving investigation tasks

Chapter 21: In Search of Effectiveness and Meaningfulness

Chapter 22: Ambiguity and Uncertainty in Mathematical Problems

Chapter 23: How mathematical problems are collected by Taiwanese middle school teachers

Chapter 24: Flow and Evolving Complexity

Chapter 25: Response

O autorze

Roza Leikin is a Professor of Mathematics Education and Education of Gifted at the Faculty of Education, University of Haifa. Her research and practice is focuses on mathematically challenging instructional design, associated mathematical tasks and teachers’ professional potential. She is interested in integration of neuro-cognitive research to the field of mathematics education. Dr. Leikin is the Dean of faculty of Education, a member of the Department of Mathematics Education and the Establishing Director of the RANGE Center - the Interdisciplinary Center for the Research and Advancement of Giftedness and Excellence in the University of Haifa. During 2012-2017 she served as the President of MCG – the International Group for Mathematical Creativity and Giftedness (affiliated with ICMI). Dr. Leikin is a Senior Mathematical Editor of the International Journal for Science and Mathematics Education. She has edited 12 volumes related to research in mathematics education and the education of gifted, published more than 150 papers in peer reviewed research journals, books, and refereed conference proceedings.