### Numeric information in graphic forms skills pre 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."

Twenty-five students in physical science spring 2014 were given nine questions which focused on this particular outcome. The preassessment was done on the first day of class.

The students are not unfamiliar with mathematics. The last question asked the highest math class taken by the students. Fifteen of the students had completed college algebra, four had completed post-college algebra courses (two completed algebra and trigonometry, two completed statistics). The remaining six chose not to answer the question on the preassessment.

Despite 19 of the 25 students having completed college algebra, performance on the preassessment was abysmal. Although 14 students could plot xy coordinate pairs, only three students could determine the slope of a line from a graph, only six were able to determine that the y-intercept was zero (the first and third questions in the chart below). The number of students answering a question correctly is shown in the following chart.

The last two questions were non-graphical questions. They presented the students with an equation in the format y = b + mx and asked the students to determine the slope and intercept. Only five identified the slope correctly, only four the intercept. Many students left this and other questions blank.

With nine questions, a perfect paper would have been a score of nine. The highest score was a single score of six. The average was 1.6 and the median was one. Seven students scored zero correct. The distribution of the student scores can be seen in the following box plot.

The score distribution is so low that the lower whisker (the minimum) is also the first quartile - seven zeroes out of 25 students.

The student performance was not just weak, the performance was weaker than the fall term 2013 performance on the same instrument. On five of the nine questions performance fell term-on-term. The sample sizes were nearly identical.

The red bars represent a drop from fall 2013 to spring 2014, the blue bars represent a gain (two questions) or no change (two questions) in the number of students answering correctly.

SC 130 Physical Science is intended 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, 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.

While these questions will be retested at term end, the question that remains unanswered is "downstream" retention. To what extent do students who have taken physical science retain some of these mathematical skills beyond the end of the course.