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Conference Paper

• A comparative study of a computer programming and a textbook approach in teaching the concept of variable

The purpose of this study was to investigate whether there were significant differences in understanding the concept of variable and in attitudes toward mathematics among sixth-grade students (n=89) who use a Logo graphics approach, students who used a textbook-based approach, and students who received no instruction on the concept of variable. The Test of Logical Thinking (TOLT), Comprehensive Test of Basic Skills (CTBS), and Robustness Semantic Differential (RSD) were administered as pretreatment measures. The Understanding of the Concept of Variable Instrument (UCVI) was administered immediately and three weeks after the experiment ceased. Although the results indicated there was no significant difference between computer and textbook-based groups with respect to understanding the concept of variable immediately after treatment, there was a significant difference (p &lt; .01) between the two groups with respect to long-term retention (three weeks after treatment ceased). There were significant positive correlations between CTBS and TOLT scores and UCVI scores.

• The role of an evaluation exercise in the resolution of misconceptions of probability

The differential effect of two activity-based instructional treatments on subjects' concepts of probability was investigated. The concepts of interest were a classical/frequentist interpretation of probability and three misconceptions cited in the literature: law of averages, law of small numbers and availability. All subjects completed a workbook which presented a long-run frequency interpretation of probability. After completion of the workbook, subjects participated in a probability-matching activity where the task was to predict correctly the outcomes for 100 coin tosses of a fair coin. Half the subjects ( the No-Evaluation group) recorded only the outcome of each toss but not their guess. After the 100 tosses, No-Evaluation subjects were presented statements which pointed out congruities between the observed outcomes and the theory presented in the workbook. Evaluation subjects recorded both their guess and the outcome of each toss. In addition to the same statements presented to the No-Evaluation subjects, Evaluation subjects were asked questions which pointed out incongruitities between their recorded data and the three misconceptions. Evaluation subjects showed an increase in classical/frequentist responses from pretest to posttest. In contrast, No-Evaluation subjects showed an increase in law of averages responses with a consequent decrease in classical/ frequentist responses. These findings support the idea that misconceptions formed before or during instruction can be reinforced by experience with stochastic phenomena since subjects may be biased to attend information which confirms the misconceptions.

• Changing conceptions of statistics: A problem area for teacher education

Content 1. Changing conceptions of statistics 2. Meta-knowledge as part of teachers professional knowledge 2.1 The relevance of meta-knowledge 2.2 Meta-knowledge for teachers 3. Elements of teacher knowledge about developments related to Exploratory Data Analysis 3.1 Data and their context 3.2 Activity of data analysis 3.3 Graphs 4. Concluding remarks References