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Analyzing Students' Works with Quantitative and Qualitative Graphs Using Two Frameworks of Covariational Reasoning  

Park, JongHee (Graduate School, Korea National University of Education)
Shin, Jaehong (Korea National University of Education)
Lee, Soo Jin (Korea National University of Education)
Ma, Minyoung (Graduate School, Korea National University of Education)
Publication Information
Journal of Educational Research in Mathematics / v.27, no.1, 2017 , pp. 23-49 More about this Journal
Abstract
This study examined two current learning models for covariational reasoning(Carlson et al.(2002), Thompson, & Carlson(2017)), applied the models to teaching two $9^{th}$ grade students, and analyzed the results according to the types of graphs(a quantitative graph or qualitative graph). Results showed that the model of Thompson and Carlson(2017) was more useful than that of Carlson et al.(2002) in figuring out the students' levels in their quantitative graphing activities. Applying Carlson et al.(2002)'s model made it possible to classify levels of the students in their qualitative graphs. The results of this study suggest that not only quantitative understanding but also qualitative understanding is important in investigating students' covariational reasoning levels. The model of Thompson and Carlson(2017) reveals more various aspects in exploring students' levels of quantitative understanding, and the model of Carlson et al.(2002) revealing more of qualitative understanding.
Keywords
function; covariational reasoning; rate of change; graph;
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