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ERIC Number: EJ940843
Record Type: Journal
Publication Date: 2011-Sep
Pages: 11
Abstractor: As Provided
Reference Count: 0
ISSN: ISSN-0732-3123
Fifth Graders' Additive and Multiplicative Reasoning: Establishing Connections across Conceptual Fields Using a Graph
Caddle, Mary C.; Brizuela, Barbara M.
Journal of Mathematical Behavior, v30 n3 p224-234 Sep 2011
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. (Contains 3 tables and 2 figures.)
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Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education; Grade 5
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A