Realizing the problem-solving phases of Pólya in classroom practice

When teaching mathematical problem-solving is mentioned, the name of Pólya György inevitably comes to mind. Many problem-solving lessons are planned using Pólya's steps and helping questions, and teachers often rely on his heuristics even if their application happens unconsciously. In this article, we would like to examine how the two phases, Making a plan and Looking back, can be realized in a secondary school mathematics lesson. A case study was designed to observe and analyse a lesson delivered using cooperative work.

Subject Classification: 97B10, 97C70, 97D40, 97D50

Looking back on Pólya’s teaching of problem solving

This article is a personal reflection on Pólya's work on problem solving, supported by a re-reading of some of his books and viewing his film Let Us Teach Guessing. Pólya's work has had lasting impact on the goals of school mathematics, especially in establishing solving problems (including non-routine problems) as a major goal and in establishing the elements of how to teach for problem solving. His work demonstrated the importance of choosing rich problems for students to explore, equipping them with some heuristic strategies and metacognitive awareness of the problem solving process, and promoting 'looking back' as a way of learning from the problem solving experience. The ideas are all still influential. What has changed most is the nature of classrooms, with the subsequent appreciation of a supporting yet challenging classroom where students work collaboratively and play an active role in classroom discussion.

Subject Classification: 97D50, 97A30

Pólya’s influence on (my) research

In this article, I outline the influence of George Pólya's work on research in different areas and especially on mathematics education, namely heuristics and models of the problem-solving process. On a more personal note, I will go into some details regarding Pólya's influence on my own work in mathematical problem solving with a focus on the research project for my PhD thesis.

Subject Classification: 97xxx

What can we learn from Tamás Varga’s work regarding the arithmetic-algebra transition?

Tamás Varga’s Complex Mathematics Education program plays an important role in Hungarian mathematics education. In this program, attention is given to the continuous “movement” between concrete and abstract levels. In the process of transition from arithmetic to algebra, the learner moves from a concrete level to a more abstract level. In our research, we aim to track the transition process from arithmetic to algebra by studying the 5-8-grader textbooks and teacher manuals edited under Tamás Varga's supervision. For this, we use the appearance of “working backward” and “use an equation” heuristic strategies in the examined textbooks and manuals, which play a central role in the mentioned process.

Subject Classification: 97-01, 97-03, 97D50