Numeric information in graphic forms skills pre-post assessment

Underneath the focus on physical systems, SC 130 Physical Science is built on a foundation of connecting physical systems to their mathematical models and communicating the results in writing. Laboratory exercises lead to the writing up of a full laboratory report that is marked for content, syntax, grammar, vocabulary, organization, and cohesion.

The majority of the laboratories investigate systems that involve a linear mathematical relationship. Reports include xy scatter graphs, best fit linear trend lines, slope, and y-intercept analysis. The course outline includes the learning outcome, "Students will generate mathematical models for physical science systems."  This serves a general education program learning outcome, "Present and interpret numeric information in graphic forms."

As a way of measuring progress against these two learning outcomes summer 2013, I give a six question pre-assessment and then included the same material on the final examination.

The six questions focus on finding the slope of a line on a graph, the y-intercept, the y = mx+b form of the line, and plotting coordinates on an xy scatter graph. Note that all of the students this summer had completed MS 100 College Algebra prior to taking SC 130 Physical Science, so these questions should be trivial, especially as the y-intercept is zero for the two slopes calculated.

Given that the students have all completed MS 100 College Algebra, term after term the students do surprisingly poorly on the pre-assessment. This summer was no exception. Of eleven students present for the pre-assessment, four obtained zero correct, six obtained a score of two correct, and one managed to answer two questions correctly.

Laboratories one, two, three, four, five, seven, nine, eleven, twelve, and fourteen involved linear relationships between the variables being studied. Every week at least one laboratory had a linear regression. Although the students use spreadsheets to obtain the best fit trend line, the students are still working with concrete systems with variables that are related linearly.

On the same six questions at term end performance was significantly improved. Although three of the thirteen students who took the post-assessment obtained only three correct and two obtained only four correct, three students answered five of six questions correctly and five students answered all six questions correctly. The pre-assessment and post-assessment score distributions for this summer and the prior three terms is seen in the chart above. Each and every term performance improves markedly on these questions.

The improvement from the pre-assessment to the post-assessment this summer can also be seen in the item analysis based chart above. The left end of the line is the number of students answering that question correctly on the pre-assessment, the left end of the line is the number of students answering the same question correctly on the post-assessment. Although students still show evidence of difficulty writing the full equation in y = mx + b format, all of the students were able to plot coordinates and calculate the slope of the line by the end of the term.

Physical science can be a powerful vehicle for providing a stronger and deeper understanding of linear equations, a way to make mathematics more approachable and comprehensible. The redesign I implemented in 2007 to focus on mathematics and writing skills while delivering physical science processes and concepts does not cover the breadth of material that a "traditional" physical science course typically attempts to tackle. The students, however, gain a deeper understanding of the mathematics that is at the core of physical science. As physicist Freeman Dyson noted:

"For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created... ...equations are quite miraculous in a certain way. I mean, the fact that nature talks mathematics, I find it miraculous. I mean, I spent my early days calculating very, very precisely how electrons ought to behave. Well, then somebody went into the laboratory and the electron knew the answer. The electron somehow knew it had to resonate at that frequency which I calculated. So that, to me, is something at the basic level we don't understand. Why is nature mathematical? But there's no doubt it's true. And, of course, that was the basis of Einstein's faith. I mean, Einstein talked that mathematical language and found out that nature obeyed his equations, too."

Although difficult to measure, my hope is that the students also can now see that nature talks mathematics, and that there is a beauty in the mathematical nature of the universe. A beauty that is often at the core of the attraction of science for scientists. If my students have glimpsed this, then I have succeeded.
Risenta and Rose Ann discussing whether their pulley data makes sense based on the underlying linear relationship expected for this system.

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