*Context*: You teach subjects and concepts based on the analysis and interpretation of experimental data. Students will understand and remember the concepts better if they study and analyze the data. A chart or graph can present complex information succinctly, and in a form that students are likely to encounter in lab activities, other courses, and the workplace.

φφφ

*Problem & Forces*: **Students must understand and be able to identify relationships based on experimental data. **However, students often lack the skills, experience, or time. Thus, teachers may be reluctant to use activities or assignments where students must perform such tasks.

φφφ

*Solution & Consequences*: **Therefore, use a chart or graph as the model for **EIA (Explore, Invent, Apply) Learning Cycles. Questions will guide students to *explore* the chart or graph and notice things that an expert would see, and then to *invent* their own understanding of the concept, which they then *apply*. This takes longer than a lecture or reading on the concepts, but students will understand the concepts better and be better able to apply them in the future. This practice with information processing and critical thinking will help students develop skills to work more effectively with a Chart or Graph in the future.

*Discussion*: The chart or graph can use real or simulated data. **Models with Authentic Data **may appeal to students, but may also contain complexities, noise, or outliers that can distract students. **Models with Synthetic Data** give more control to the activity author to adjust variability, construct special cases, and so forth. Use *directed* questions to *explore* the model and notice what an expert would notice (e.g. axes, scales, legends). Use *convergent *questions to *explore* further and *invent* their own insights and understanding of key concepts. Use *convergent* and *divergent* questions to *apply* the concepts in other contexts.

Figure: Sample Models - Charts or Graphs.

*Examples*: The figure above shows a histogram (left) and a scatter plot (right) fitted with a straight line. Note that both are clearly labeled (e.g. axes and scales) and avoid potentially distracting information.

*Typical DCV (Directed, Convergent, Divergent) Questions*:

- D:
*What information is shown on each axis? What units are used?*

Prompts students to examine the axes, which some might not do otherwise. - D:
*What is the range (min & max) of values on each axis?**How many data sets are shown?*

Prompts students to examine the data and legend, etc. - C:
*Which points might be considered outliers?*Prompts students to look at the distribution of values. - C:
*Describe the general shape of the data*(e.g. linear, quadratic, exponential, logarithmic). - C:
*Draw a best fit line through the data and estimate its slope*. - C:
*Predict how this graph would look if .*Prompts students to apply

the current concept to a modified context. - V:
*What factors might have contributed to the outliers?*Prompts students to consider sources of error. - V:
*Where have you a similar relationship before?*Prompts students to relate this to another context.

*Author*: Clif Kussmaul

*Publication*: C Kussmaul. 2016. Patterns in classroom activities for Process Oriented Guided Inquiry Learning (POGIL). *HILLSIDE Proc. of Conf. on Pattern Lang. of Prog. *23 (October 2016).