Mathematical misconceptions in graphing and central tendency among sixth grade and undergraduate students

Abstract

The problem addressed by this study was that of the possible presence of similar mathematical misconceptions between both 6th grade and undergraduate students. Also, if these misconceptions do exist, the question thus arises whether or not the students, teachers, and administrators are aware of such inaccuracies in their teaching and/or learning. The rationale for such a study is the ever-presence of standardized testing and the accountability that this type of assessment theoretically ensures. Seventy-nine 6th grade students were assessed in the spring semester of 2001 with a question, referred to as Vet Club, which asked the students to construct a graph from a given set of data and then analyze the data in terms of central tendencies and "typical" information. Also, during the spring semester of 2002, 147 elementary education undergraduates were given a test to gauge their knowledge of various mathematical concepts, including graph construction, central tendencies, and "typical" data. The result of this study found that there are in fact similar mathematical misconceptions between both 6th grade and undergraduate students. Specifically, using intervals or unequal distances between values on a graph, assigning a category to one of the axes, and employing an intuitive notion to the concept of central tendency. The 6th graders TAAS test scores, however, do not reveal similar findings. This was evident when the regression analysis exposed that the TAAS scores could not be sufficiently predicted by the Vet Club data. If the TAAS test did adequately assess student knowledge of graphing and central tendency, then the students who harbored the 3 aforementioned misconceptions should not have succeeded on the probability and statistics objective. This was not the case, however, and the students, teachers, and administrators have been led to believe that successful and appropriate teaching and learning has occurred in the 6th grade classroom.