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El. knyga: Youngsters Solving Mathematical Problems with Technology: The Results and Implications of the Problem@Web Project

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This book contributes to both mathematical problem solving and the communication of mathematics by students, and the role of personal and home technologies in learning beyond school. It does this by reporting on major results and implications of the Problem@Web project that investigated youngsters" mathematical problem solving and, in particular, their use of digital technologies in tackling, and communicating the results of their problem solving, in environments beyond school. The book has two focuses: Mathematical problem solving skills and strategies, forms of representing and expressing mathematical thinking, technological-based solutions; and students and teachers perspectives on mathematics learning, especially school compared to beyond-school mathematics.

Foreword.- Preface.- Mathematical problem-solving with technology: an overview of the Problem@Web project.- Youngsters solving mathematical problems with technology: their experiences.- Perspectives of teachers on youngsters solving mathematical problems with technology.- Theoretical perspectives on youngsters solving mathematical problems with technology.- Digitally expressing conceptual models of geometrical invariance.- Digitally expressing algebraic thinking in quantity variation.- Youngsters solving mathematical problems with technology: findings and implications.- Afterword.

Recenzijos

I enjoyed reading the book and I enjoyed my time solving the problems also by putting myself in young students shoes. I can see the benefit of using these problems as well as the suggested solutions in secondary mathematics problem-solving activities. I am planning to use some of these problems (and suggested solutions)with undergraduate, graduate and teacher students as a trigger for a discussion on problem-solving also with digital environments. (Irene Biza, Research in Mathematics Education, Vol. 19 (3), 2018)









This book is an extensive summary/report of a three year project where schoolchildren were given problems to solve outside the usual classroom problems. this study is invaluable in giving modern mathematical educators insights into adapting modern pedagogical techniques to reflect how young people solve problems. all will find something that they can use to improve the effectiveness of their teaching. (Charles Ashbacher, MAA Reviews, maa.org, May, 2016)

1 Mathematical Problem-Solving with Technology: An Overview of the Problem@Web Project
1(20)
1.1 Introduction
1(1)
1.2 Young People with Technology
2(2)
1.3 Young People's Mathematical Problem-Solving with Technology
4(2)
1.4 The Research Focus
6(2)
1.5 The SUB12 and SUB14 Mathematics Competitions
8(7)
1.6 Methodological Issues
15(2)
1.7 Concluding Comments
17(4)
References
18(3)
2 Youngsters Solving Mathematical Problems with Technology: Their Experiences and Productions
21(34)
2.1 Introduction
21(1)
2.2 The Participants in the Mathematical Competitions SUB12 and SUB14
22(4)
2.3 The Participants and the Use of Digital Technologies
26(3)
2.4 The Participants' Productions with Digital Technologies
29(22)
2.4.1 From the Use of Paper and Pencil to Writing with Word and Excel
29(6)
2.4.2 The Use of Tables
35(4)
2.4.3 The Use of Images and Diagrams
39(5)
2.4.4 The Use of Numerical Software
44(1)
2.4.5 The Use of Geometrical Software
45(6)
2.5 Concluding Comments
51(4)
References
53(2)
3 Perspectives of Teachers on Youngsters Solving Mathematical Problems with Technology
55(28)
3.1 Introduction
55(2)
3.2 The Role of the Teachers in the Mathematical Competitions
57(6)
3.2.1 The Support of the Teachers: From the First Round to the Final
59(3)
3.2.2 The Social Part of the Competitions: The Meeting at the Final
62(1)
3.3 Perspectives of Teachers About the Mathematical Competitions SUB12 and SUB14
63(9)
3.4 Mathematical Communication: An Additional Challenge
72(2)
3.5 The Use of Technology: The Sharing of Experiences Between Teachers and Students
74(5)
3.6 Overview and Conclusion
79(4)
References
80(3)
4 Theoretical Perspectives on Youngsters Solving Mathematical Problems with Technology
83(30)
4.1 The Theoretical Stance
83(2)
4.2 Problem-Solving as Mathematisation
85(3)
4.3 Problem-Solving as Expressing Thinking
88(8)
4.3.1 Expository Discourse in Problem-Solving
90(3)
4.3.2 Technology Used for Expressing Thinking in Problem-Solving
93(3)
4.4 Multiple External Representations
96(2)
4.5 Humans-with-Media and Co-action with Digital Tools
98(8)
4.6 An Outlook
106(7)
References
108(5)
5 Digitally Expressing Conceptual Models of Geometrical Invariance
113(28)
5.1 Main Theoretical Ideas
113(9)
5.1.1 Perceiving Affordances of Digital Tools
114(3)
5.1.2 The Indivisibility Between the Subject and the Context
117(2)
5.1.3 Humans-with-Media Mathematising
119(1)
5.1.4 Mathematisation with Dynamic Geometry Software
120(2)
5.2 Context and Method
122(2)
5.3 Data Analysis
124(14)
5.3.1 The Problem: Building a Flowerbed
124(1)
5.3.2 Zooming in: The Participants' Productions
125(10)
5.3.3 Zooming Out: Comparing and Contrasting
135(3)
5.4 Discussion and Conclusion
138(3)
References
139(2)
6 Digitally Expressing Algebraic Thinking in Quantity Variation
141(32)
6.1 Main Theoretical Ideas
141(6)
6.1.1 Digital Representations in the Spreadsheet
142(2)
6.1.2 Algebraic Thinking
144(1)
6.1.3 Problem-Solving with the Spreadsheet and the Development of Algebraic Thinking
145(1)
6.1.4 Expressing Algebraic Thinking and Co-action with the Spreadsheet
146(1)
6.2 Context and Method
147(2)
6.3 Data Analysis
149(19)
6.3.1 The First Problem: The Treasure of King Edgar
149(11)
6.3.2 The Second Problem: The Opening of the Restaurant "Sombrero Style"
160(8)
6.4 Discussion and Conclusion
168(5)
References
171(2)
7 Digitally Expressing Co-variation in a Motion Problem
173(36)
7.1 Main Theoretical Ideas
173(7)
7.1.1 Co-variation and Modelling Motion
175(3)
7.1.2 Visualisation in Motion Problems
178(2)
7.2 Context and Method
180(2)
7.3 Data Analysis
182(5)
7.3.1 The Experts' Solutions to the Problem
182(4)
7.3.2 Definition of Categories
186(1)
7.4 Analysis of the Students' Solutions to the Problem
187(17)
7.4.1 Conceptual Models Involved in the Participants' Problem-Solving and Expressing
188(3)
7.4.2 Forms of Representation in Students' Digital Productions
191(13)
7.5 Discussion and Conclusion
204(5)
References
207(2)
8 Youngsters Solving Mathematical Problems with Technology: Summary and Implications
209(32)
8.1 Introduction
209(1)
8.2 The Problem@Web Project
210(4)
8.3 The Youngsters Solving Mathematical Problems with Technology
214(4)
8.4 The Perspectives of the Youngsters' Teachers
218(5)
8.5 Theoretical Framework
223(2)
8.6 Digitally Expressing Mathematical Problem-Solving
225(7)
8.6.1 Digitally Expressing Conceptual Models of Geometrical Invariance
226(1)
8.6.2 Digitally Expressing Algebraic Thinking in Quantity Variation
227(3)
8.6.3 Digitally Expressing Co-variation in a Motion Problem
230(2)
8.7 Discussion of the Findings
232(3)
8.8 Implications and Suggestions for Further Research
235(6)
References
237(4)
Afterword 241(4)
About the Authors 245(4)
Index 249
Susana Carreira is an associate professor in the mathematics department of the Faculty of Sciences and Technology at the University of Algarve. Keith Jones is an associate professor in the School of Education at the University of Southampton. Nélia Amado is an assistant professor in the mathematics department of the Faculty of Sciences and Technology at the University of Algarve. Hélia Jacinto is a PhD student at the research unit of the Institute of Education of the University of Lisbon & Jose Saramago Middle School. Sandra Nobre is a PhD student and mathematics teacher, associated with the research unit of the Institute of Education of the University of Lisbon & Schools group of Paula Nogueira, Olhćo, Portugal.
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