Interpreting graphs and building mathematical models

The SC 130 Physical Science final examination included questions which tasked the student with reading data from a graph, interpreting charts, interpreting a mathematical model from data, and plotting data on a graph followed by finding the slope for the data.

These questions sought to examine student learning outcome 1.2 for the course, the ability of the students to generate and work with mathematical models for physical science systems. The questions also sought to provide information on general education program learning outcome 3.2, present and interpret numeric information in graphic forms.

Thirty-four students sat the final examination.

Interpreting graphical information

The students were presented with a time versus distance xy scatter graph as seen below. The graph shows the motion of three different marbles. The marbles are labeled A, B, and C. All three marbles start from a time of 0 seconds and a distance of 0 centimeters.

Students were asked:
  1. Which marble is slowing down?
  2. Which marble is speeding up?
  3. Which marble is moving at a constant speed?
30 of the 34 students answered two and three correctly. All 34 answered number four correctly. The students can infer physical results from data presented in graphical form.

The students were then asked,
  1. What is the speed of marble A between five and nine seconds?
  2. What is the speed of marble B between four and eight seconds?
  3. What is the speed of marble C between five and eight seconds?
28, 24, and 26 students resepctively answered these questions correctly. At least 70% of the students can calculate a slope from data presented in graphical form. Slopes are the basis of the mathematical models in SC 130.

In question eleven he students were asked to determine whether a data set is linear or non-linear.

Extension (cm) Force (gmf)
0 0
3 15
6 30
9 45

11. Section five force: Data was gathered for the extension of an elastic band using a cup and marbles to generate the force. The data in the table is from the experiment. Is the elastic band a linear elastic material?

33 of the 34 students correctly determined that the data is linear. 23 students went on to correctly use Hooke's law to determine Hooke's constant for the system.

For question 28 the students were given data in a table and asked to plot that data on a blank graph. 32 of the 34 students correctly plotted all six data points. The other two students plotted all but one data point correctly. Students can plot data on a graph. 26 of the 34 students (76%) then correctly calculated the slope of the line for their data. The most common error was inverting the slope.

Students who have completed SC 130 physical science can read and interpret graphical information, comprehend the mathematical models implied by data and charts, and  they can plot data generating their own graphs.The SC 130 curriculum supports general education program learning outcome 3.2 and the course student learning outcome 1.2. An assessment on other aspects of the course is available.

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