What Student Graphs Reveal:

Using Data from the Olympic Games to Assess Expertise and Misconceptions

Knowing how to graph real-world data is important in an "information age" society. Dealing with inherent inconsistencies and uncertainties while providing a pictorial representation of data is telling--expertise and misconceptions are both revealed. This article reveals some of the responses students typically provide to graphing Olympic Games and offers suggestions for their meaning.

My high school students graph data from the Olympic Games as an initial assessment. I use the information from the initial assessment to determine  expected understanding to keep "surprises" a minimum. Their responses are scale-scored based upon the level of understanding they appear to contain. I provide them a data table clipped from the World Almanac and Book of Facts along with a few prompts. The problem begins as follows:

Graph the data and use it to predict the winning times for the next Olympic Games and for the year 2064.  Describe your graph and include a discussion of the "reasonableness" of the winning times.

Men's 400 Meter Run

Year	Winning Time (seconds)
1896	54.2
1900	49.4
1904	49.2
1908	50.0
1912	48.2
1920	49.6
1924	47.6
1928	47.8
1932	46.2
1936	46.5
1948	46.2
1952	45.9
1956	46.7
1960	44.9
1964	45.1
1968	43.86
1972	44.66
1976	44.26
1980	44.60
1984	44.27
1988	43.87
1992	43.50
1996	43.49
2000	43.84

Sample data table from the  Almanac

There are several revealing outcomes students produce. The main characteristics that inform me of students' level of understanding fall into the following categories:

• Making a bar-graph rather than a scatter-plot. Students interpret the data as categorical (showing counts in unrelated groups) rather than ratio (where there is a scaled relationship between movement along the x-axis).
• Neglecting the "gaps" in the 4-year sequences when the Olympic Games were not held. Also suggestive of a categorical interpretation but not quite as serious when displayed as a bar-graph.
• Making a scatter-plot but connecting dot-to-dot rather than attempting some form or "best fit curve." Students graphing this way probably see data as absolute values rather than containing inherent variability. Real-world data is never exact and is only as good as the accuracy (the correctness of the data) and precision (to how many decimal places the data can be reported) of the measurement system allowsÑsomething most students still need to understand.
• Not using the graph to predict future outcomes. Student answers show no connection to the graph and most likely represent a relatively blind guess.
• Applying a linear interpretation to the data. Students predict an entirely unreasonable winning time for the 2064 games and justify it with "people just keep getting faster" without realizing the times over the last several games have not changed significantly. The x-axis should have been extended out to the year 2064 to demonstrate both understanding how to graph this kind of data and using the graph to predict.

The Olympic Games are now be held every even-numbered year--the Winter Games in 1994, 1998, etc. and the Summer games in 1996, 2000, etc. They provide a wealth of opportunities for students to develop and extend their mathematical understanding. Searching for trends while looking at events historically allows students to model data, make predictions, and check for reasonableness. They practice communication, reasoning, and problem solving while they explore connections within and outside mathematics.

Richard T. Edgerton, Ph.D.

Seattle Public Schools

rtedgerton@seattleschools.org

Reference

World Almanac and Book of Facts. New York: World Almanac Books. Published yearly.