Assessment of graphing, plotting, calculating slopes

In order to generate and comprehend the mathematical models that live at the core of physical science systems, students have to be familiar with the xy coordinate system, plotting points, graphing lines, calculating and understanding slopes of lines.

Eight questions that focused on graphing skills and which were tested on the first test summer 2011 were presented to the SC 130 Physical Science students fall 2011 on the first quiz of the term. The skills tested focus on student learning outcome 1.2 on the outline.

Twenty-nine of thirty-two students sat quiz one fall 2011. Data from the first test summer 2011 and the first quiz fall 2011 is presented in the table. Percentages are the percent of students answering the item correctly. Summer 2011 the sample size was fifteen students.

Question topic Su 11 Fall 11 Δ%
calculate slope from line on graph 0.67 0.52 -0.15
density as equal to slope 0.47 0.38 -0.09
infer effect of density 0.67 0.66 -0.01
calculate density from measurements 0.53 0.34 -0.19
calculate mass from density and volume 0.67 0.83 0.16
plot data on graph 1.00 0.72 -0.28
draw line through data points 0.93 0.72 -0.21
calculate slope from line on graph 0.73 0.55 -0.18

Overall performance this fall was lower than seen at the start of the summer term. Success rates for these questions do not exist for prior terms, suggesting an academically weaker class than seen this past summer.

Given a line on a graph only half of the students (15) could calculate the slope. Although laboratory one had focused on slope as density, only 11 of these 15 correctly understand that the slope is the density of the material which was graphed.

Given, however, just numbers to directly plug into a given formula, 83% made the essentially arithmetic calculation correctly.

Somewhat concerning was that eight students were unable to plot tabular data correctly on a supplied xy scattergraph - there was only a 72% success rate on this item. Of the 21 students who plotted the data correctly, only sixteen could then calculate the slope. This echoes the first item - only half of the students can calculate a slope from a graph, even when given the formula for slope on the quiz itself.

There is no math pre-requisite for SC 130 Physical Science, nor is there any intention to introduce one. The course includes the intention to teach math through science. That said, the students are usually either in MS 100 College Algebra, or have finished that class, or are eligible to take the course. This often means that they have completed MS 099 Intermediate Algebra. In other words, graphing and plotting should not be unfamiliar mathematical terrain. The data, however, suggests otherwise.

The data above suggests that I will have work more carefully early on in the term to connect together physical concepts with mathematical models, and ensure that the math itself does not become a barrier to comprehension.

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