ERIC Number: ED465530
Record Type: RIE
Publication Date: 2002-Apr-2
The Resilience of Overgeneralization of Knowledge about Data Representations.
Baker, Ryan Shaun; Corbett, Albert T.; Koedinger, Kenneth R.
Data analysis has become a topic of increasing emphasis within middle school mathematics in the last few years, especially in the recent recommendations by the National Council of Teachers of Mathematics (NCTM 2000). In order to better inform efforts to expand data analysis's role in middle school curricula, we have begun the development of a cognitive model of student thinking in this domain. Proper representation of data is an essential part of the process of data analysis (Larkin and Simon 1987)--therefore, we have focused on modeling how students learn to generate and interpret some of the important and widely-used representations of data, such as histograms and scatterplots. Beyond just choosing more familiar representations, though, students have been observed to attempt to transfer in knowledge about more familiar representations when attempting to interpret or generate a newer representation (Baker, Corbett, and Koedinger 2001). Specifically, this study found that middle school students attempt to apply their extensive prior knowledge of how to generate and interpret standard bar graphs when attempting to generate and interpret scatterplots and histograms (here defined as having an X axis broken into intervals of a quantitative variable, and a Y axis with the frequency of each interval). This attempt has both positive and negative effects. In this paper, we present a study that we conducted to explore the depth of this transfer and to investigate methods for reducing its occurrence in generation, where it is clearly inappropriate. Given the strength of the student desire to choose axes appropriate to a bar graph when generating scatterplots and histograms, we decided to investigate whether there were ways to induce these students to instead draw the correct axes, and if there was further mis-transfer of bar graph knowledge once the students had the correct axes, as the effect in Lehrer et al. suggests. Therefore, we chose the general intervention of drawing the students' attention to the variables, in order to attempt to express each of these factors. (MM)
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Note: Paper presented at the Annual Meeting of the American Educational Research Association (New Orleans, LA, April 1-5, 2002).