What This Means for Instruction

Here are some tips to help educators planning instruction in data analysis:

• Teach students to examine shape and spread and to look at distribution in a number of ways for insights about data (Shaughnessy et al., 1999).
• Use these strategies to promote statistical reasoning:
1. Provide students with opportunities to work with real data.
2. Include regular written and oral communication.
3. Invite students to discuss and compare different solutions.
4. Use technology for complex calculations and constructions.
5. Use high-quality software programs that simulate data processes to enable students to observe the results in changes in sample size, differences in various data representations and how various measures of central tendency may provide different interpretations of the data.
6. Confront common misconceptions and faulty reasoning by asking students to make predictions and validate these predictions with results.
7. Build on and connect students' real-world experiences and prior knowledge with developing statistical knowledge (Garfield & Gal, 1999).
• Use these instructional suggestions (from a meta-analysis of research by Friel, Curcio, & Bright, 2001) to help students develop understanding of graphs:
• Grades K-2: Emphasize representations such as simple tables, objects graphs and bar graphs, that can help students tally responses. Use objects or pictures before using abstract representations, such as line plots or graphs.
• Grades 3-5: Develop notions of scale by creating pictures graphs in which one picture shows a number other than one. Introduce data with spread and variation in stem plots.
• Grades 6-8: Introduce complex data sets shown in graphs with scaled intervals and scaled frequencies. Introduce histograms, box plots and line graphs. Encourage students to compare data sets.
• Challenge common misconceptions among students. For example, provide multiple graphical representations of a situation to address the common misconception that a graph will provide a realistic visual image of the given situation (Swan, 1985).
• Design instruction to address the three properties of mean with which students have particular difficulty (Bright & Hoeffner in Owens, 1993):
1. that the sum of the deviations from the average is zero
2. that zero has an impact on mean
3. that the mean is not necessarily part of the data but is a representation of the data