The posing and solving of problems from discrete domains and mathematics teachers in training
Main Article Content
Keywords
Problem Posing, Problem Solving, Grounded Theory, Discrete Domains.
Abstract
This paper reports the findings of a research with a qualitative approach and a grounded theory design, focused on answering the question, how are the strategies manifested by a group of mathematics teachers in training when they pose and solve problems from situations in discrete domains? A series of learning sequences and a semi-structured interview were designed and implemented as data sources. The findings show how the tasks proposed in the learning sequences made it possible for each participant to build relationships, make assertions, generalize from these assertions, and use examples and counterexamples as a form of proof. The way in which the students solved the problems when new demands were imposed on the solutions of the linear diophantine equation of the form ax + by = c and the way in which they subsequently used them to pose new problems and propose real life situations as contexts to formulate new problems is also highlighted. As a result, the core of the theory was constructed, characterized as a flow of actions and interactions between the strategies of conjecturing, generalizing, testing and posing problems. Finally, this led to the conclusion that problem posing is immersed in problem solving from the proposed context and that students are a good source for problem posing.
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