### 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.

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."

Eleven students in physical science summer 2017 were given a pre-assessment consisting of eleven questions which focused on interpreting and generating numeric information in graphic forms.

A pre-assessment on the first day of class indicated that despite strong mathematical preparation, performance was remarkably poor.

The math classes the students had completed are listed in the far right column and include MS 096 Elementary Algebra, MS 100 College Algebra, MS 101 Algebra and Trigonometry, MS 106 Technical Math II, and MS 150 Statistics. In a blog article at that time I argued that mathematics taught in isolation from contexts leads to little to no retention.

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 can provide cognitive hooks on which the students can attach a stronger comprehension of linear mathematical models. Laboratories one, two, four, five, seven, nine, eleven, twelve, and fourteen involve exploring linear relationships between the variables being studied. Non-linear relationships are also generated by some activities in the course.

Although the students used Desmos to obtain the best fit trend line, the students were still working with concrete systems with variables that are related linearly. Laboratory three used Desmos to run a quadratic regression.

The questions asked on the pre-assessment reappeared on the final examination. A twelfth student had joined the course after the first day of class.

Performances were markedly improved for the students from the pre to post-assessment.

Performance on a question-by-question basis were also markedly and significantly improved. The overall average lifted from 36% to 72%.
Although the course does not directly or intentionally teach students to plot points, determine slopes and intercepts (Desmos graphing calculator apps and web site were used to plot data and find linear regressions to the data), the post-assessment 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 in quantitative reasoning.