scholarly journals Teacher Interventions for Advancing Students’ Mathematical Understanding

2020 ◽  
Vol 10 (6) ◽  
pp. 164
Author(s):  
Xiangquan Yao ◽  
Azita Manouchehri
Keyword(s):  
Mathematical Thinking ◽  
Dynamic Geometry ◽  
Mathematical Understanding ◽  
Dynamic Geometry Environment ◽  
School Students ◽  
Geometric Transformations ◽  
Teacher Interventions ◽  
Teacher Researcher ◽  
Dynamic Growth ◽  
Support Students

The relationship between teacher interventions and students’ mathematical thinking has been the subject of inquiry for quite some time. Using the Pirie–Kieren theory for dynamic growth in mathematical understanding, this study documents teacher interventions that support students’ growth toward developing a general understanding of a mathematical idea in a designed learning environment. By studying the interactions of seven middle school students and the teacher-researcher working on a two-week unit on geometric transformations within a dynamic geometry environment, this study identified nine major categories of teacher interventions that support and extend students’ investigations of mathematical ideas around geometric transformations. The typology of teacher interventions reported in this study provides a cognition-based framework for teacher moves that extend and advance students’ mathematical understanding.

scholarly journals Hybrid-dynamic objects: DGS environments and conceptual transformations

2019 ◽  
Vol 1 (1) ◽  
pp. 31
Author(s):  
Stavroula Patsiomitou
Keyword(s):  
Mathematical Thinking ◽  
Dynamic Geometry ◽  
Research Process ◽  
Dynamic Geometry Environment ◽  
Theoretical Perspectives ◽  
Dynamic Objects ◽  
Dynamic Hybrid ◽  
Geometric Processes ◽  
Theoretical Considerations ◽  
Didactics Of Mathematics

A few theoretical perspectives have been taken under consideration the meaning of an object as the result of a process in mathematical thinking. Building on their work, I shall investigate the meaning of ‘object’ in a dynamic geometry environment. Using the recently introduced notions of dynamic-hybrid objects, diagrams and sections which complement our understanding of geometric processes and concepts as we perform actions in the dynamic software, I shall explain what could be considered to be a ‘procept-in-action’. Finally, a few examples will be analyzed through the lenses of hybrid and dynamic objects in terms of how I designed them. A few snapshots of the research process will be presented to reinforce the theoretical considerations. My aim is to contribute to the field of the Didactics of Mathematics using ICT in relation to students’ cognitive development

scholarly journals Generalizing-Promoting Actions: How Classroom Collaborations Can Support Students' Mathematical Generalizations

2011 ◽  
Vol 42 (4) ◽  
pp. 308-345 ◽  
Author(s):  
Amy B. Ellis
Keyword(s):  
Middle School Students ◽  
Quadratic Growth ◽  
Mathematical Activity ◽  
School Students ◽  
Growth Functions ◽  
Interaction Processes ◽  
Teachers And Students ◽  
Teacher Researcher ◽  
Support Students ◽  
Socially Situated

Generalization is a critical component of mathematical activity and has garnered increased attention in school mathematics at all levels. This study documents the multiple interrelated processes that support productive generalizing in classroom settings. By studying the situated actions of 6 middle school students and their teacher–researcher working on a 3–week unit on quadratic growth functions that can be represented by y = ax2, the study identified 7 major categories of generalizingpromoting actions. These actions represent how teachers and students can act in interaction with other agents to foster students' generalizing activities. Two classroom episodes are presented that identify cyclical interaction processes that promoted the development and refinement of generalizations. The results highlight generalization as a dynamic, socially situated process that can evolve through collaborative acts.

The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment

2021 ◽  
pp. 073563312097993
Author(s):  
Zhihao Cui ◽  
Oi-Lam Ng
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Computational Thinking ◽  
Programming Environment ◽  
Primary School Students ◽  
School Students ◽  
Mathematical Concepts ◽  
Block Based

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation.

scholarly journals Creativity as a function of problem-solving expertise: posing new problems through investigations

ZDM ◽  
2021 ◽  
Author(s):  
Haim Elgrably ◽  
Roza Leikin
Keyword(s):  
Problem Solving ◽  
Dynamic Geometry ◽  
Problem Posing ◽  
Dynamic Geometry Environment ◽  
Mathematics Majors ◽  
Individual Interviews ◽  
University Mathematics ◽  
Domain Specific ◽  
Mathematics Test ◽  
Different Types

AbstractThis study was inspired by the following question: how is mathematical creativity connected to different kinds of expertise in mathematics? Basing our work on arguments about the domain-specific nature of expertise and creativity, we looked at how participants from two groups with two different types of expertise performed in problem-posing-through-investigations (PPI) in a dynamic geometry environment (DGE). The first type of expertise—MO—involved being a candidate or a member of the Israeli International Mathematical Olympiad team. The second type—MM—was comprised of mathematics majors who excelled in university mathematics. We conducted individual interviews with eight MO participants who were asked to perform PPI in geometry, without previous experience in performing a task of this kind. Eleven MMs tackled the same PPI task during a mathematics test at the end of a 52-h course that integrated PPI. To characterize connections between creativity and expertise, we analyzed participants’ performance on the PPI tasks according to proof skills (i.e., auxiliary constructions, the complexity of posed tasks, and correctness of their proofs) and creativity components (i.e., fluency, flexibility and originality of the discovered properties). Our findings demonstrate significant differences between PPI by MO participants and by MM participants as reflected in the more creative performance and more successful proving processes demonstrated by MO participants. We argue that problem posing and problem solving are inseparable when MO experts are engaged in PPI.

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