Abstract
Current views in the teaching and learning of data handling suggest that learners should create graphs of data they collect themselves and not just use textbook data. It is presumed real-world data creates an ideal environment for learners to tap from their pool of stored knowledge and demonstrate their meta-representational competences. Although prior knowledge is acknowledged as a critical resource out of which expertise is constructed, empirical evidence shows that new levels of mathematical thinking do not always build logically and consistently on previous experience. This suggests that researchers should analyse this resource in more detail in order to understand where prior knowledge could be supportive and where it could be problematic in the process of learning. This article analyses Grade 11 learners’meta-representational competences when constructing bar graphs. The basic premise was that by examining the process of graph construction and how learners respond to a variety of stages thereof, it was possible to create a description of a graphical frame or a knowledge representation structure that was stored in the learner’s memory. Errors could then be described and explained in terms of the inadequacies of the frame, that is: ‘Is the learner making good use of the stored prior knowledge?’ A total of 43 learners were observed over a week in a classroom environment whilst they attempted to draw graphs for data they had collected for a mathematics project. Four units of analysis are used to focus on how learners created a frequency table, axes, bars and the overall representativeness of the graph vis-à-vis the data. Results show that learners had an inadequate graphical frame as they drew a graph that had elements of a value bar graph, distribution bar graph and a histogram all representing the same data set. This inability to distinguish between these graphs and the types of data they represent implies that learners were likely to face difficulties with measures of centre and variability which are interpreted differently across these three graphs but are foundational in all statistical thinking.
Highlights
Instructional focus in the statistics classroom has been on learners’ construction of various graphs with the instruction being didactic in nature but with little attention being given to the analysis of reasons why the graphs were constructed that way in the first place (Friel, Curcio & Bright, 2001)
A recommendation that is consistent with current views of ‘data handling’ that goes beyond ‘statistics’ is put forth by Shah and Hoeffner (2002), who suggest that research on learners’ abilities to construct graphs, and how this relates to their ability to comprehend graphs, was relevant for project-based activities in which learners create graphs of data that they collect for themselves
From the discussion that took place during the process of making a frequency table for the collected data, it is evident the learners brought the knowledge of tallying from the ‘previous teacher’
Summary
Instructional focus in the statistics classroom has been on learners’ construction of various graphs with the instruction being didactic in nature but with little attention being given to the analysis of reasons why the graphs were constructed that way in the first place (Friel, Curcio & Bright, 2001). The article aims to tease out evidence of the knowledge representation structures that were stored in the learners’ memory and the extent to which this pool of knowledge was (in)adequate as a resource for bar graph construction Given this objective, it is doubtful whether one could discuss adequacy, productivity or effectiveness in graph construction without making references to conventions that guide us in validating our concept of adequate, truth, correctness and accuracy in such mathematical activities. In a histogram the counting of a particular data point at the midpoint of intervals is supported by Cooper and Shore (2010), who argue that at times we may want to read the trend of the distribution We can achieve this by creating a histograph or frequency polygon from a histogram. The analysis focused on the extent to which learners’ representations were consistent with or in violation of these conventions
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