### 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 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 fall 2013, I gave a nine question pre-assessment in August 2013 and then included the same material on the final examination in December 2013.

The nine questions focused on calculating the slope and y-intercepts of lines on a graph, determining the units of the slope, writing the y = mx+b form of the line, reading the slope and intercept from a y = a + bx formatted linear equation, and plotting coordinates on an xy scatter graph. Nineteen of the 26 students tested had completed a one hundred level math course prior to taking SC 130 Physical Science.Three students had completed only developmental pre-collegiate mathematics courses. Four students did not answer this question.

Given that the students have worked with slope-intercept form equations either in high school, developmental, or collegiate mathematics, the exceptionally weak pretest performance term after term is probably surprising to those who have not explored how little students retain after a course ends. SC 130 Physical Science has as one of its intents the placing of the mathematics into less abstract contexts. The concept is that the laboratory systems and data might provide cognitive hooks on which the students can attach a stronger comprehension of linear mathematical models.

Laboratories one, two, three, five, seven, nine, eleven, twelve, and fourteen involved linear relationships between the variables being studied. Laboratories four and six generated non-linear relationships. Although the students use spreadsheets to obtain the best fit trend line, the students were still working with concrete systems with variables that are related linearly.

Fall 2013 three questions had been added to the pretest and post-test. The following chart, for purposes of multi-term comparison, only includes the six questions that have appeared on every pretest and post-test since summer 2012. Twenty-six students took the pretest and post-test

On the fall 2013 pretest the median was a score of one - a single question of the six answered correctly.
On the post-test the median was four correct out of six.

On the pretest five students answered all six questions incorrectly - five scores of zero.
On the post-test no student obtained a score of zero.

On the pretest only one student scored higher than a two, and that was a single student with a score of three.
On the post-test seven students answered all six questions correctly.

This term featured three additional questions. When these questions are included, the pretest and post-test score distributions still show a strong improvement.

Again, the pretest has a lower whisker that reaches down to a score of zero, with an upper whisker at five correct out of nine. The post-test box plot shows no score below three correct and the upper whisker extending to nine correct. The course has strongly lifted performance on these questions. This lift is all the more fascinating to this author because the course does not intentionally nor directly attempt to teach this material. The course generates slopes and intercepts, the material uses linear relationships, but this material is never specifically taught.

While the above distributions focus on the overall number correct, the overall score, the number answering each individual question also improved.

The improvement from the pre-assessment to the post-assessment this fall can be seen in the item analysis 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 improvement varied by question, all questions showed improvement in performance. One of the largest gains was in the ability to calculate the slope of a line on a graph.

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.

Allston and Gyrone measuring apparent depth.