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Interpreting Patterns and Trends in Data

“The instant I saw the picture my mouth fell open and my pulse began to race. The pattern was unbelievably simpler than those obtained previously (“A” form). Moreover, the black cross of reflections which dominated the picture could arise only from a helical structure.” James D. Watson, The Double Helix, 1968.

The instant Watson saw the pattern on the paper, he immediately had an idea of what it meant.

As a judge at Science Fairs, I have observed that some students make beautiful graphs, but unfortunately, the graphs are wrong. What I mean is that some students either do not use the correct type of line, or worse, they draw the wrong type of graph entirely (e.g., a pie chart instead of a line graph).

How can we help students learn these skills? When I taught science in a grade 7 – 12 school, I realized that it was worth my effort to spend time reinforcing the importance of graphs with my students. The key part of the Alberta curriculum regarding this says that the students shall “interpret patterns and trends in data, and infer and explain relationships among the variables”. That should be a full stop. But the curriculum goes on to say the student should do this by predicting “the value of a variable by interpolating or extrapolating from graphical data”.

Yes, data points are important, but not nearly as important as the shape of the graph that they produce. Like Watson, students need to be able to determine the implied relationship between the variables at a glance from the shape of the graph. Alternately, the students should be able to sketch the shape of the graph that shows the relationship that they wish to describe. In addition, students should be able to sketch the shape of the graph they expect from an experiment. That is a very clear way to show their prediction and therefore their understanding of the problem. After completing the experiment and graphing the actual data, they should be able to determine if their data confirms or refutes their prediction.

At the high school level, there are a limited number of graph shapes that students need to know. From an operational perspective, the manipulated variable is always on the horizontal axis and the responding variable is always on the vertical. The numbers should always get bigger left to right and bottom to top.

I have compiled a gallery of graph sketches that would be useful for students to know.


Trend Graph 1Sketch A) The first sketch shows a situation where, as the manipulated variable increases, the responding variable also increases and at a constant rate.
















Trend Graph 2
Sketch B) The second sketch shows the responding variable decreasing as the manipulated variable increases, still at a constant rate.
















Trend Graph 3Sketch C) Here is a sketch where the responding variable is increasing at an increasing rate as the manipulated variable increases. This is sometimes called an exponential curve.
















Trend Graph 4Sketch D) Many students never contemplate this result. Here is an example where there is no apparent effect of the manipulated variable on the responding variable. There are some interesting variations on this graph which I describe below.



 
















Trend Graph 5
Sketch E) In this example, the responding variable increases as the manipulated variable increases, but only until it reaches a maximum. In some ways, this graph represents a combination of both Sketch A in the first portion, and Sketch D in the last portion. I have seen student experimental designs where they predicted this type of outcome, and sketched it out in advance of collecting data. When that data came back appearing to support only sketch D, the students were then alerted to take more careful measurements at the lower end of the range resulting in verifying their original predictions. Without this level of understanding, a student may miss very critical measurements.






 





Trend Graph 6Sketch F) Similar to Sketch E, this graph combines elements of sketches A and D. This one though has Sketch D in the first and the third portion with Sketch A sandwiched into the middle.



 











Trend Graph 7&8Sketches G and H) These two similar graphs result when the responding variable has an optimal maximum or minimum. These graphs can result from direct data collection such as enzyme activity versus temperature, or they can result from re-graphing rate of increase of the responding variable in Sketch F back to the manipulated variable.



 







Have your students improve their graphing skills through simple sketches that demonstrate their understanding of the relationship between manipulated and responding variables. You can have your students learn more about DNA and the Double Helix by participating in DNA Day on Friday April 20, 2012.

Interpreting Patterns and Trends in Data

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