Abstract
Reading mathematical texts is closely related to the effort of the reader to understand its content; therefore, it is reasonable to consider such reading as a problem-solving activity. In this paper, the Principle of Mathematical Induction was given to secondary education students, and their effort to comprehend the text was examined in order to identify whether significant elements of problem solving are involved. The findings give evidence that while negotiating the content of the text, the students went through Polya’s four phases of problem solving. Moreover, this approach of reading the Principle of Mathematical Induction in the sense of a problem that must be solved seems a promising idea for the conceptual understanding of the notion of mathematical induction.
Highlights
Mamona-Downs and Downs (2005), considering the ‘identity’ of problem solving, raised a series of issues including, among others, the reading of mathematical texts and considered whether this could involve significant elements of problem solving. They acknowledge that ‘reading mathematical text often needs an effort from the reader to understand and assimilate its content’ (p. 386), and this prompted the question of whether it is reasonable to consider such reading as a problem-solving activity
This paper has attempted to show that reading a mathematical text could be considered a problem-solving activity
Students are engaged in reading mathematical texts with content completely unknown to them
Summary
Mamona-Downs and Downs (2005), considering the ‘identity’ of problem solving, raised a series of issues including, among others, the reading of mathematical texts and considered whether this could involve significant elements of problem solving. They acknowledge that ‘reading mathematical text often needs an effort from the reader to understand and assimilate its content’ As Mamona-Downs and Downs (2005) explain, there are three aspects in examining a proof relevant to the issue. The first concerns ‘the locating and examining of the implications occurring in the argument’ The third concerns the extracting of meaning from the exposition in the sense that ‘the reader creates concept images in order to relate the material to intuitively understood schemas’ (p. 397)
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