Mathematical reasoning in teachers’ presentations

This paper presents a study of the opportunities presented to students that allow them to learn different types of mathematical reasoning during teachers’ ordinary task solving presentations. The characteristics of algorithmic and creative reasoning that are seen in the presentations are analyzed. We find that most task solutions are based on available algorithms, often without arguments that justify the reasoning, which may lead to rote learning. The students are given some opportunities to see aspects of creative reasoning, such as reflection and arguments that are anchored in the mathematical properties of the task components, but in relatively modest ways.

► We model the opportunities students have to learn from teachers’ presentations.
► Most presentations are based on applications of available algorithms.
► Some opportunities are given to see creative reasoning, but mainly in modest ways.
► The lack of explicit arguments supporting the reasoning may lead to rote learning.