Lack of retention of basic mathematical knowledge shown in pre-assessment

A pre-assessment of basic mathematical skills was given to eleven students on the first day of summer session 2017 in physical science. On the pre-assessment there were eleven questions that focused on plotting points, slope and intercept of a direct variation, and calculations using a slope and intercept. These are skills that are first developed in eighth grade algebra and in high school algebra I. In the following chart of student performance the math courses listed are:

MS 096 Elementary Algebra
MS 100 College Algebra
MS 101 Algebra and Trigonometry
MS 106 Technical Math II
MS 150 Statistics

The average success rate across all items was 35.5%. From the chart one can see that even with courses such as MS 101 Algebra and Trigonometry and MS 150 Statistics (both with MS 100 College Algebra pre-requisites), the success rate for individual students was poor.

When the success rate is looked at by course, the sample sizes become far too small for significance. Given that caveat, there does not appear to be a clear pattern that completion of higher level courses is correlated to improved performance on the basic mathematics found on the pre-assessment. A few years back Madolehnihmw High School taught their students four years of mathematics including a precalculus course. On the college mathematics placement test, the MHS students actually underperformed students from other high schools who had only completed an algebra I or algebra II course. Although somewhat counter-intuitive, more mathematics does not necessarily yield better performance on lower level material.

Overall, the students showed little retention of what might be arguably some of the most basic skills found in first degree equations - slope, intercept, and calculating value using a slope and intercept. The one skill the students do appear to retain is the ability to plot points on an xy scatter graph when given a data table.

To one degree or another perhaps few people retain algebraic knowledge beyond the bounds of their mathematics courses.  Unless one is using algebra in one's daily life, that knowledge slips away. This appears to leave unanswered the question of "To what end, intent, or purpose is collegiate algebra being taught?" What is it that the students should be taking away from such a class? In this day and age of the denial of scientific facts, questions of truth and perceived reality, mathematics may have an important role to play. Mathematical facts are the least disputable facts. Two plus two really is four in base ten.

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