کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
360828 1436028 2011 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Fifth graders’ additive and multiplicative reasoning: Establishing connections across conceptual fields using a graph
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Fifth graders’ additive and multiplicative reasoning: Establishing connections across conceptual fields using a graph
چکیده انگلیسی

This paper looks at 21 fifth grade students as they discuss a linear graph in the Cartesian plane. The problem presented to students depicted a graph showing distance as a function of elapsed time for a person walking at a constant rate of 5 miles/h. The question asked students to consider how many more hours, after having already walked 4 h, would be required to reach 35 miles. To answer this question, the students needed to extend the graph that was presented, either mentally or on paper, as the axes did not go up to 7 h or 35 miles. They also needed to be able to consider not only the total number of hours to reach 35 miles, but also the interval of time after 4 h. The purpose of this paper is to consider the student responses from the viewpoint of multiplicative and additive reasoning, and specifically within Vergnaud's framework of multiplicative and additive conceptual fields and scalar and functional approaches to linear relationships (Vergnaud, 1994). The analysis shows that: some student answers cannot be classified as either scalar or functional; some students combined several kinds of approaches in their explanations; and that the representation of the problem using a graph may have facilitated responses that are different from those typically found when the representation presented is a function table.


► We look at students as they discuss a graph of distance as a function of time.
► We examine whether the students use additive or multiplicative reasoning, or both.
► We find that some students combine more than one type of reasoning.
► We discuss how the graphical representation may affect the type of reasoning used.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: The Journal of Mathematical Behavior - Volume 30, Issue 3, September 2011, Pages 224–234
نویسندگان
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