### 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, "Students will be able to present and interpret numeric information in graphic forms," which in turn serves an institutional learning outcome for quantitative reasoning: "Students will be able to reason and solve quantitative problems from a wide array of authentic contexts and everyday life situations; comprehend and can create sophisticated arguments supported by quantitative evidence and can clearly communicate those arguments in a variety of formats."

Thirteen of fourteen students in physical science summer 2014 were given ten questions which focused on interpreting and generating numeric information in graphic forms. Specifically, the pre-assessment focused on xy scatter graphs and linear trend lines. The pre-assessment was done on the first day of class and included 13 of the 15 students in the course. Two students added the class after the first day of class when the pre-assessment was given.

 Maria-Asunsion and Ursula work on a volume versus mass relationship
SC 130 Physical Science is designed to address these mathematical weaknesses. The course 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, four, five, seven, nine, eleven, twelve, and fourteen involve linear relationships between the variables being studied. Non-linear relationships are also generated by some activities in the course. 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.

The first ten questions of the final examination were either exactly identical to questions on the pre-assessment, or the questions were conceptually identical with changes only in the values. As measured by the number of questions answered correctly, performance was markedly improved on the post-assessment.

On the pre-assessment (n = 13) no student did better than correctly answering six of ten questions, and that was only one student. On the post-assessment (n = 15) ten of the students correctly answered six or more questions.

Note that hand plotting of the (x,y) coordinates slipped on the post-assessment. All students plotted three of the four coordinates correctly. Three of the fifteen students plotted the last coordinate incorrectly, (0.045, 90). Thus these three students can plot points but may have become careless with the last coordinate.

The other nine concepts saw strong  improvements in success rates, but no question was answered corrently by all fifteen students on the post-assessment. Even after a full term of working with linear regressions and xy scattergraphs, there remain a few students who do not master the concepts.

The smallest success rates were seen for using an equation of a line to predict x or y values when the student is given a y or x value. Based on my fourteen years of teaching statistics, using equations to calculate predicted values is often a challenge for students here at the college.

Although the course does not directly or intentionally teach students to plot points, determine slopes and intercepts (spreadsheets are used to plot data and find linear regressions to the data), the post-assessment (with problems solved using only a calculator, not a spreadsheet) indicates that the students have improved their capabilities in these areas. Physical science provides concrete cognitive hooks in the form of physical systems the students can see and manipulate. Physical science provides a framework, a structure, that organizes and makes meaningful abstract mathematical concepts.

The course continues to positively impact program learning outcomes as well as institutional learning outcomes on quantitative reasoning.