**Connecting Current Mathematical Problem Solving Research Findings with
Curriculum Proposals and Teaching Practices**

**Manuel SANTOS-TRIGO**

#### Centre for Research and Advanced Studies

Cinvestav-IPN

Mexico

Published in The Mathematician Educator, 2023, Vol 4, No. 2, pp 109-124.

### Abstract

Mathematical problem solving is a prominent perspective for students to understand concepts and to apply mathematical knowledge. Indeed, problem formulation and looking for different ways to solve problems are crucial activities in the development of mathematics. Furthermore, understanding and characterizing what the process of posing and solving mathematical problems entails have been part of the research agenda in mathematics education. What are the important research findings in the problem solving domain and how can they be used in teaching practices? To address this question, three intertwined themes are discussed: seminal conceptual frameworks to characterize problem solving approaches; inquiring methods to problematize students’ problem solving activities; and the influence of tasks or problems used in research to frame curricula and mathematical instruction. Throughout the presentation of these themes, teachers’ and students’ use of digital affordances is analyzed to discuss what ways of reasoning emerge in approaching and solving mathematical tasks. In this context, students’ processes to transform the tools in instruments to explore concepts and to solve problems becomes essential for teachers to structure and implement problem solving activities.

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