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E-raamat: Algebra Structure Sense Development amongst Diverse Learners: Theoretical and Empirical Insights to Support In-Person and Remote Learning [Taylor & Francis e-raamat]

Edited by (National Polytechnic Institute, Mexico)
  • Formaat: 176 pages, 6 Tables, black and white; 9 Line drawings, black and white; 25 Halftones, black and white; 34 Illustrations, black and white
  • Sari: Routledge Research in STEM Education
  • Ilmumisaeg: 03-Jun-2022
  • Kirjastus: Routledge
  • ISBN-13: 9781003197867
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  • Taylor & Francis e-raamat
  • Hind: 161,57 €*
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Algebra Structure Sense Development amongst Diverse Learners: Theoretical and Empirical Insights to Support In-Person and Remote LearningSuurem pilt
  • Formaat: 176 pages, 6 Tables, black and white; 9 Line drawings, black and white; 25 Halftones, black and white; 34 Illustrations, black and white
  • Sari: Routledge Research in STEM Education
  • Ilmumisaeg: 03-Jun-2022
  • Kirjastus: Routledge
  • ISBN-13: 9781003197867
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003197867
"This volume emphasizes the role of effective curriculum design, teaching materials, and pedagogy to foster algebra structure sense at different educational levels. Positing algebra structure sense as fundamental to developing students' broader mathematical maturity and advanced thinking, this text reviews conceptual, historical, cognitive, and semiotic factors which influence the acquisition of algebra structure sense. It provides empirical evidence to demonstrate the feasibility of linking algebra structure sense to technological tools and promoting it amongst diverse learners. Didactic approaches include the use of adaptive digital environments, gamification, diagnostic and monitoring tools, as well as exercises and algebraic sequences of varied complexity. Advocating for a focus on both intuitive and formal knowledge, this volume will be of interest to students, scholars, and researchers with an interest in educational research, as well as mathematics education and numeracy"--

This volume emphasizes the role of effective curriculum design, teaching materials, and pedagogy to foster algebra structure sense at different educational levels.

List of Tables
viii
List of Figures
ix
List of Contributors
xi
Foreword xv
Preface xx
Acknowledgements xxii
1 Algebra Structure Sense: Conceptual Approaches and Elements for Its Development
1(19)
Teresa Rojano
Introduction
1(1)
The Objects of Symbolic Algebra
2(3)
Internal Order and Awareness of the Structure
5(4)
Algebra Structure Sense Development
9(2)
Technology, a Gateway to the Development of ASS
11(3)
The Importance of ASS in Advanced Mathematical Thinking
14(1)
Connection to Upcoming
Chapters
15(2)
References
17(3)
2 Ideas of Structure in the History of Algebra and Its Teaching
20(15)
Luis Puig
Problems, Equations, Structures
20(3)
Algebraic Features in Old Babylonian Problem Solving
23(3)
Building a Language for Algebraic Problem Solving: A Rough Overview and Some Snapshots
26(7)
References
33(2)
3 Structure Sense at Early Ages: The Case of Equivalence of Numerical Expressions and Equalities
35(32)
Carolyn Kieran
Cesar Martinez-Hernandez
Introduction
35(1)
On Mathematical Equivalence
36(1)
On Structure, Structuring, and Structure Sense
37(3)
On Prior Research in This Area
40(2)
On the Research Study: Methodology
42(2)
On the Research Study: Results
44(14)
Discussion
58(5)
Concluding Remarks
63(1)
References
64(3)
4 Developing Structure Sense with Digital Technologies: Introducing the MEx Platform
67(21)
Valentina Munoz-Porras
Ulises Xolocotzin
Introduction
67(1)
Teaching and Learning Algebra with Digital Technologies
68(8)
Design Principles for Supporting Structure Sense
76(3)
Designing Interactions with Algebraic Foundations: The MEx Platform
79(6)
Conclusion
85(1)
References
86(2)
5 Transformational Algebra, Structure Sense, and Notes on a Semiotic Interpretation
88(20)
Armando Solares-Rojas
Teresa Rojano
A Semiotic Explanation of the Development of ASS
88(1)
Development of ASS, Leveling-Up Design and Task Types
89(2)
Development of ASS: The Study with the Expression Machine
91(2)
Francisco, Lulu, and MEx Tasks
93(10)
Algebra Structure Sense in MEx: Notes on a Semiotic Interpretation
103(1)
Revisiting the Notion of Algebra Structure Sense
104(2)
References
106(2)
6 Students' Justification Strategies on the Correctness and Equivalence of Computer-Based Algebraic Expressions
108(33)
Eirini Geraniou
Manolis Mavrikis
Introduction
108(2)
Theoretical Background
110(4)
The eXpresser Microworld and Activities
114(4)
Methodology
118(4)
Justification Strategies
122(10)
Discussion
132(4)
Acknowledgements
136(1)
References
137(4)
7 The Importance of Algebra Structure Sense for the Teaching and Learning of Mathematics
141(17)
Teresa Rojano
Santiago Palmas
Introduction
141(1)
Transformative Algebra and the Presence of Structural Aspects in the Curriculum
142(4)
ASS and Transformational Algebra in Post-Secondary School Topics
146(3)
ASS in Advanced Mathematics Topics
149(2)
Transformative Algebra and ASS
151(1)
ASS in Teaching Algebraic Syntax
152(3)
References
155(3)
8 On the Connection of Structure Sense in Mathematics and Who Sees and Transforms It: Internal Structure, Visual Salience, and Transformative Algebra
158(12)
Teresa Rojano
Introduction
158(1)
Intrinsic Structure of Mathematical Objects: The Case of Symbolic Algebra
158(4)
Signification and Manipulation of Algebraic Objects
162(2)
Structure Sense in Other Contexts and Sign Systems
164(3)
Creation of Textual Spaces for Development of Structure Sense
167(3)
References 170(2)
Index 172
Teresa Rojano is Professor in the Department of Mathematics Education, Center of Research and Advanced Studies (Cinvestav) of the National Polytechnic Institute, Mexico.
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