Thinking About Mathematical Thinking

PsycCRITIQUES ◽  
2010 ◽  
Vol 55 (23) ◽  
Author(s):  
Gordon Pitz
Keyword(s):  
Mathematical Thinking

Review of Mathematical Thinking and Problem Solving.

1996 ◽  
Vol 41 (1) ◽  
pp. 80-80
Author(s):  
Daniel Stalder ◽  
Shubhangi Stalder
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking

Exploring the Implementation of Early Math Assessments in Kindergarten Classrooms: A Research-Practice Collaboration

2020 ◽  
Author(s):  
Jennifer McDonald ◽  
Rebecca Merkley ◽  
Jacqueline Mickle ◽  
Lisa Collimore ◽  
Daniel Ansari
Keyword(s):  
Mathematical Thinking ◽  
Math Education ◽  
Kindergarten Students ◽  
First Year ◽  
Research Practice ◽  
Early Numeracy ◽  
Future Directions ◽  
Collaborative Project ◽  
Practice Gap ◽  
Second Year

Research in cognitive development has highlighted that early numeracy skills are associated with later math achievement, suggesting that these skills should be targeted in early math education. Here we tested whether tools used by researchers to assess mathematical thinking could be useful in the classroom. This paper describes a collaborative project between cognitive scientists and school board researchers/educators implementing numeracy screeners with kindergarten students over the course of three school years. The Give-A-Number task (Wynn, 1990) was used with first-year kindergarten students and the Numeracy Screener [BLINDED] with second-year kindergarten students. Results indicated that educators (N = 59) found the tools feasible to implement and helpful for exploring their students’ thinking and targeting instruction. The Educators’ feedback also helped inform improvements to the implementation of the tools and future directions for both the schools and the researchers. This work emphasizes the importance of transdisciplinary collaboration to address the research-practice gap.

Category Theory and Foundations

2018 ◽  
Author(s):  
Michael Ernst
Keyword(s):  
Category Theory ◽  
Mathematical Thinking ◽  
Mathematical Practice ◽  
Foundations Of Mathematics ◽  
Ongoing Debate ◽  
Technical Adequacy ◽  
Theoretical Foundations

In the foundations of mathematics there has been an ongoing debate about whether categorical foundations can replace set-theoretical foundations. The primary goal of this chapter is to provide a condensed summary of that debate. It addresses the two primary points of contention: technical adequacy and autonomy. Finally, it calls attention to a neglected feature of the debate, the claim that categorical foundations are more natural and readily useable, and how deeper investigation of that claim could prove fruitful for our understanding of mathematical thinking and mathematical practice.

Programming and mathematical thinking

ACM Inroads ◽  
2014 ◽  
Vol 5 (1) ◽  
pp. 35-36 ◽  
Author(s):  
Peter B. Henderson ◽  
Allan M. Stavely
Keyword(s):  
Mathematical Thinking

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 Mathematical Thinking Styles—The Advantage of Analytic Thinkers When Learning Mathematics

2021 ◽  
Vol 11 (6) ◽  
pp. 289
Author(s):  
Jaime Huincahue ◽  
Rita Borromeo-Ferri ◽  
Pamela Reyes-Santander ◽  
Viviana Garrido-Véliz
Keyword(s):  
Mathematical Thinking ◽  
Quantitative Approach ◽  
Mathematical Tasks ◽  
Thinking Styles ◽  
Mathematical Performance ◽  
Test Instrument ◽  
Analytical Thinking ◽  
Learning Mathematics ◽  
Valid Test ◽  
Insight Into

School is a space where learning mathematics should be accompanied by the student’s preferences; however, its valuation in the classroom is not necessarily the same. From a quantitative approach, we ask from the mathematical thinking styles (MTS) theory about the correlations between preferences of certain MTS and mathematical performance. For this, a valid test instrument and a sample of 275 16-year-old Chilean students were used to gain insight into their preferences, beliefs and emotions when solving mathematical tasks and when learning mathematics. The results show, among other things, a clear positive correlation between mathematical performance and analytical thinking style, and also evidence the correlation between self-efficacy, analytical thinking and grades. It is concluded that students who prefer the analytical style are more advantageous in school, since the evaluation processes have a higher valuation of analytic mathematical thinking.

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