1. Students’ Difficulties & Misconceptions Reema Alnizami Apr. 27, 2011

2. Center as a summary “When learning about averages, students often struggle with the idea of how one number can represent many numbers” (Mason & Shifflett, 2009, p. 247)

3. Categorical vs. Numerical “One can calculate the mean only with quantitative variables. The median can be found with quantitative variables and with categorical variables for which a clear ordering exists among the categories. The mode applies to all categorical variables but is only useful with some quantitative variables” (Rossman & Chance P. 71).

4. Hair color Example: if we were interested in the typical/standard hair color in this room, “since no numerical order is possible, the concept of median does not apply” (Lappan et al. 1988, p. 24). Mode is a better center in this case.

5. Mean “The students appear that they face difficulties in comprehension of mean and show a tendency to calculate the algorithm so that they resolve statistical problems” (Michalis & Tsaliki, 2010, p. 3) “when students are asked to find the “center” of a set of data, they most often choose the mean regardless of the context.” (p.2)

6. Use of Bar Graph Some students inappropriate use of a bar graph with numerical data. A bar graph represents frequencies of categorical data. However, if in rare cases we care about the frequencies of numerical data, the bar graph can be used.

7. References Lappan, G. (1988). Research into practice: Teaching statistics: mean, median, and mode. Arithmetic Teacher, 35(7), 25-26. Rossman, A. J. & Chance, B. L. (2001). Workshop statistics: Discovery with data. Emeryville, CA: Key College. Michalis, C., & Tsaliki, C. (2010). Elementary school students’ understanding of concept of arithmetic mean. International Association of Statistical Education. Mason, J., & Shifflett, E. (2009). Generating meaning for range, mode, median, and mean. Teaching Children Mathematics, 16(4), 246-252.