By Andreas J. Stylianides
Even if proving is middle to arithmetic as a sense-making task, it presently has a marginal position in undemanding study rooms across the world. mixing examine with functional views, this ebook addresses what it is going to take to raise where of proving at hassle-free school.
The publication makes use of school room episodes from nations to check other kinds of proving initiatives and the proving task they could generate within the easy school room. It examines additional the function of academics in mediating the connection among proving initiatives 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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Extra info for Proving in the Elementary Mathematics Classroom
Example text
In the following chapters I propose and study a categorization of proving tasks that elementary teachers can use in their classrooms in order to create productive opportunities for their students to engage in proving. In particular, I explore the interplay between different kinds of proving tasks and the proving activity that tasks of each kind might help generate in the classroom, while also considering the role of teachers in implementing the tasks and in supporting their students’ work. Given the issues that I discussed earlier in relation to the four factors that might have contributed to the marginal place of proving in elementary classrooms today, the work reported in the book can have important implications for elevating that place.
1. ” The third characteristic emerges from the realization that the conditions of a proving task are usually, or can be, subject to different assumptions by students (Herbst & Brach, 2006), with different legitimate assumptions having the potential to give rise to different solution paths and thus variant proving activities (Fawcett, 1938; Stylianides, 2007a). At a basic level, there may be an unintentional ambiguity in the conditions of a proving task due to an oversight in its design or phrasing.
Carpenter, Fennema, & Franke, 1996; Fischbein, Deri, Nello, & Marino, 1985; Haylock, 2014). Indeed, the overemphasis of typical classroom instruction on certain kinds of arithmetic tasks that promote certain meanings of the basic operations creates a cognitive obstacle to students learning other meanings. , 1985). Making an analogy to the area of proving, I argue that a broad-based and deep understanding of proving requires that students engage in different kinds of proving tasks so that they benefit from the complementary nature and learning affordances of those tasks.