Investigating the Complexity of Middle Grade Students' Understandings of Mathematical Constructs : An Example from Graphic Representation / Robert M. Capraro, Gerald Kulm and Mary Margaret Capraro.

This study explored a model for students development of the understandings and skills that are involved in being able to construct graphical representations of data and to interpret these graphs. The study examined four components of prior understanding required for graphic representation that were adapted from a learning map from the Atlas of Science Literacy (American Association for the Advancement of Science, 2001). The components involved knowledge about: (1) coordinate relationships; (2) graphs showing a variety of relationships; (3) reading simple tables; and (4) graphic display. Complete data from 82 sixth graders from the classes of 3 teachers were collected and analyzed using multiple regression, factor analysis, and structural equation modeling (SEM) to examine the nature and alignment of assessment items that could be used to measure these components of prior knowledge. The results indicate that the SEM models reflect significant fits with the Atlas map. While further research with a larger sample will be needed to examine the relationships among the four components and with the target learning goal for graphic representation, the SEM analysis appears to be a promising approach for modeling the construction of student knowledge in specific content areas of mathematics. Six appendixes contain some assessment items and student responses. (Contains 38 references.) (Author/SLD)

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