### 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.

Cutting soap to make a new volume versus mass measurement

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."

Twenty-three of the thirty students enrolled in physical science fall 2017 were present the first day. These 23 students completed a pre-assessment consisting of eleven questions which focused on interpreting and generating numeric information in graphic forms. The pre-assessment graph interpretation and data interpretation both use direct linear relationships with a y-intercept of zero - arguably the easiest form of relationship to work with in algebra.

The students have a more than sufficient mathematical background to handle the pre-assessment. The pre-assessment questions are early high school algebra one level questions. Twenty-two students have either taken MS 100 College Algebra, MS 101 Algebra and Trigonometry, or MS 150 Statistics. One student had taken MS 106 Technical Mathematics as their highest math course. The students should be able to easily answer a strong majority, if not all, of the questions.

In general student performance was generally weak. The average was 5.26 questions (48%)  answered correctly with a median of 4.5 of 11 questions answered correctly. Not coincidentally, this poor performance is essentially identical in average to the performance seen a year ago in August 2016. The answer is not more math classes: to continue to repeat the same thing that did not work in the past is one definition of insanity. More math will not fix these weaknesses seen year after year. These poor performances are consistently repeatable.

Recording data using Desmos

My own personal take on this is that mathematics does not provide the concrete systems upon which the mind can built the cognitive hooks and framework necessary for the abstract mathematical knowledge. Pure algebraic mathematics as a separate subject does not produce long term learning and comprehension. And, no, the "real world word problems" in each section of a math text do not constitute concrete systems for building the needed cognitive structures. The problem is not a failure of instruction but of the inability of mathematics taught in isolation as a vehicle for teaching quantitative and mathematical thinking.

Obtaining a linear regression in Desmos

Over the years some have suggested that a course such as physical science should have a math pre-requisite. I have long argued that the other way around is the approach that should be taken: mathematics should have a physical science pre-requisite. Or other courses in which mathematics is deployed. If mathematics should be taught at all, mathematics should be taught after the mathematics has been learned in other courses.

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.

Working with Desmos in the computer laboratory, plotting linear density data

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 are still working with concrete systems with variables that are related linearly.

The students do not "work problem one to thirty even" but rather focus on a single relationship each week, one equation in each laboratory. An equation that has a physical meaning and interpretation, with parts that also have real world meanings. A volume versus mass slope greater than one gram per cubic centimeter leads to soap sinking, less than one gram per cubic centimeter and the soap floats. The slope of the relationship tells the students what the soap will do when placed in water. One equation is studied in detail.

Mathematics should be taught in context on an "as needed" basis, a "just in time" deliver that ensures the learner is both in need of that piece of mathematics and has a use for that mathematics.

Alternatively one might consider quantitative reasoning courses that de-emphasize the working of multiple problems each with "cute math twists and tricks" and focus on specific quantitative solutions in context.

Although fall term 2016 is only just beginning, historically performance improves markedly from the pre-assessment to the post-assessment. Whether students then retain this knowledge through to graduation, or beyond, remains an open question.