Proving in the Elementary Mathematics Classroom by Andreas J. Stylianides

By Andreas J. Stylianides

Even supposing proving is center to arithmetic as a sense-making job, it at present has a marginal position in basic study rooms across the world. mixing study with functional views, this booklet addresses what it can take to raise where of proving at uncomplicated school.

The publication makes use of school room episodes from international locations to envision other kinds of proving projects and the proving job they could generate within the hassle-free school room. It examines additional the position of academics in mediating the connection among proving projects and proving task, together with significant mathematical and pedagogical matters that come up for lecturers as they enforce every one form of proving job. as well as its contribution to investigate wisdom, the booklet has vital implications for instructing, curricular assets, and instructor education.

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2003), who analyzed the kinds of reasoning encouraged by the mathematics tasks used in the lessons of the TIMSS 1999 Video Study, including those tasks that involved proofs.  73). They found that such tasks were evident to a substantial degree only in Japanese lessons, in which on average 26% of the tasks per lesson involved proofs and 39% of the lessons included at least one proof. In the Czech Republic, Hong Kong SAR, and Switzerland the corresponding percentages were considerably lower (1, 2, and 3% and 5, 12, and 11%, respectively), while in Australia, the Netherlands, and the United States there were too few instances of proofs to allow the calculation of reliable estimates.

2008; Stylianides & Stylianides, 2014b). , 1996). Notwithstanding the importance of these and other related factors, they are rather generic and can apply potentially to the classroom implementation of a broad range of mathematics tasks. This raises the issue: Do the varying characteristics of the kinds of proving tasks that I described earlier play, or have the potential to play, any specific role in the proving activity that each of these kinds of tasks can generate in the classroom? I propose that the answer to this question is in the affirmative and that different kinds of proving tasks can potentially support qualitatively different proving activities.

This proof for the 4-by-4 square can easily be extended for a square of any size, provided that the action of “sliding” is done in one’s imagination rather than physically. In a project I conducted with 14–15-year-olds in England, the students worked on a variant of the Squares Problem (Stylianides, 2009a; Stylianides & Stylianides, 2014b) and used the idea of a sliding square in their proofs about the number of different 3-by-3 squares in a 60-by-60 square. 1, and they imagined sliding it over to the right, one place at a time, until it reached the upper right side of the 60-by-60 square.

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