### Pre-assessment on graphical mathematics skills among physical science students

A pre-assessment in mathematics skills was administered to 18 students in SC 130 Physical Science on the first day of class. The students were unaware of the pre-assessment and thus were taking the pre-assessment without any preparation. The 18 students had all completed MS 100 College Algebra, MS 101 Algebra and Trigonometry, or MS 150 Statistics. The level of the mathematics on the pre-assessment was material found in high school algebra one.

Although the strong majority of the students who reported taking a mathematics course reported having had a college level mathematics course, overall performance on the pre-assessment was weak.

Calculations of slope and intercept were unusually low against historic performance levels. Students showed skill only in plotting points. Note that students did better on calculating a y-value given an x-value and calculating an x-value given a y-value than they did on the preceding slope and intercept questions. As these questions were for the same data, this result might seem puzzling. The key to understanding this is to look at the pre-assessment. The latter two problems could be solved by using ratios in lieu of linear equations, rather simple 2:1 ratios for each.

The pre-assessment performance this year was the weakest seen in a fall or spring term for SC 130. This pre-assessment provides some insight to student performance on general education program learning outcome 3.2 at the college. The learning outcomes states that students will be able to present and interpret numeric information in graphic forms. As this is considered to be a general skill that the students carry with them beyond any particular term, the performance is perhaps disappointing.

One reaction might be to call for more mathematics courses, but this might miss the key point. These students completed college algebra or higher. These math skills were fundamental prerequisites to the courses that these students have already passed. To do more of the same and expect a different outcome is unrealistic. The solution is not more of what did not work.

While I do not have solutions, I concur with Edward Frenkel, "What if you had to take an art class in which you were taught only how to paint a fence, but were never shown the paintings of van Gogh or Picasso? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry." Students do not walk out of mathematics courses excited about the field of mathematics. Many, if not most, students are happy to have their math requirements in their academic rear view mirror. The curriculum focuses on algorithmic solutions to artificial problems (yes, even the "real world applications" problems are contrived) that can be solved today by algebraic software such as Photomath or Desmos.

I realize that teachers claim students must master these algorithms to understand the math, but I do not have to know how to build a car engine to drive a car. In other words, I have never thought that the inability to factor and solve a quadratic algebraically by hand is a barrier to understanding that the solutions occur where the graph crosses the x-axis.

Mathematics courses are not teaching retained knowledge and they do little to excite students about the field of mathematics. New approaches, curricula, and tactics which integrate the technologies now available ought to be explored.

*Highest math class taken*

Although the strong majority of the students who reported taking a mathematics course reported having had a college level mathematics course, overall performance on the pre-assessment was weak.

*Performance by item on the pre-assessment n = 18*

Calculations of slope and intercept were unusually low against historic performance levels. Students showed skill only in plotting points. Note that students did better on calculating a y-value given an x-value and calculating an x-value given a y-value than they did on the preceding slope and intercept questions. As these questions were for the same data, this result might seem puzzling. The key to understanding this is to look at the pre-assessment. The latter two problems could be solved by using ratios in lieu of linear equations, rather simple 2:1 ratios for each.

*Performance on pre-assessments (Kosrae campus summer 2018 is not in overall mean)*

The pre-assessment performance this year was the weakest seen in a fall or spring term for SC 130. This pre-assessment provides some insight to student performance on general education program learning outcome 3.2 at the college. The learning outcomes states that students will be able to present and interpret numeric information in graphic forms. As this is considered to be a general skill that the students carry with them beyond any particular term, the performance is perhaps disappointing.

One reaction might be to call for more mathematics courses, but this might miss the key point. These students completed college algebra or higher. These math skills were fundamental prerequisites to the courses that these students have already passed. To do more of the same and expect a different outcome is unrealistic. The solution is not more of what did not work.

While I do not have solutions, I concur with Edward Frenkel, "What if you had to take an art class in which you were taught only how to paint a fence, but were never shown the paintings of van Gogh or Picasso? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry." Students do not walk out of mathematics courses excited about the field of mathematics. Many, if not most, students are happy to have their math requirements in their academic rear view mirror. The curriculum focuses on algorithmic solutions to artificial problems (yes, even the "real world applications" problems are contrived) that can be solved today by algebraic software such as Photomath or Desmos.

I realize that teachers claim students must master these algorithms to understand the math, but I do not have to know how to build a car engine to drive a car. In other words, I have never thought that the inability to factor and solve a quadratic algebraically by hand is a barrier to understanding that the solutions occur where the graph crosses the x-axis.

Mathematics courses are not teaching retained knowledge and they do little to excite students about the field of mathematics. New approaches, curricula, and tactics which integrate the technologies now available ought to be explored.

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