Preassessment, Gen Ed 3.2 numeric information in graphic forms, and math placement
An anonymous preassessment briefly looked at some of the graphical mathematical skills the students have in my fall 2025 courses. The preassessment also asked a few basic linear calculations. The preassessment was sent via a link in an email to the 137 students in my courses for fall 2025. The survey was completed anonymously, remotely, and unsupervised. 36 students responded to the preassessment.
The students were in both mathematical and non-mathematical courses.
The survey asked some math course background questions, and then presented the following questions. The survey included images for graphical questions.
- Which of the points is at the coordinate (3,1)?
- What is the slope of the line on the graph? Enter the slope as a decimal value.
- What is the y-intercept of the line on the graph?
- Which line on the graph matches the data in the time versus distance table?
- If a person is running at 2.58 meters per second, how far will they go in 3600 seconds? Do not include the units in your response.
- Julien Alfred from the Caribbean island nation of Saint Lucia ran 100 meters in 10.72 seconds to win a gold medal in the 2024 Paris Olympics. Using that data, what was her speed in meters per second? Round your answer to two decimal places. Do not include the units in your answer.
- A line passes through (8, 11) with a slope of ⅝ (five eighths or 0.625 in decimal form). What is the y-intercept?
The item analysis indicates relative strength in correctly identifying a coordinate on a graph and the y-intercept for a direct relationship with a y-intercept of zero. Performance was weaker on other questions, with identifying the correct line from tabular data being the weakest performance.
Performance on a similar instrument nine years ago was extremely weak.
2012 results
This level of performance was typical from 2012 through to at least 2019, with some areas of specific improvement by 2019. The overall success rate was 28% in 2012.
2019 results
Average success rate 2017-2019
By 2022 performance had improved across all of the questions, with the overall average rising to a 71% success rate. The sample size, however, was small. Of 18 students who were sent the preassessment, 12 responded.
This term the average was a 68% success rate for 36 students in four courses, an average well in line with the 71% performance in 2022.
The average success rates based on the self-reported highest math class has to be viewed with a strong caveat on the underlying sample sizes.
The top performance seen for MS 101 is for only two students. Of the courses, only MS 100 College algebra has anything close to a meaningful sample size.
SC 130 Physical Science
The original intent of the preassessment over a decade ago was to provide information on mathematical skills of the students enrolled in SC 130 Physical Science.
The number of respondents who are physical science this term was 18. The physical science course primarily encounters systems modeled by linear equations, students who have had high school algebra I should be able to grasp the mathematical models. Equations are generated by data from Desmos, simplifying the process of determining the best fit trend line for the data.
The overall success rate was 60% with strengths and weaknesses echoing those seen in the larger sample of all courses.
The first laboratory of the term had the students measuring the volume and mass of different sized rectangular chunks of soap. This forms a linear relationship with a slope equal to the density of the soap.
Week two opened with the relationship of time versus distance for a RipStik caster board ridden at a constant velocity across 30 meters of sidewalk. The slope is the linear velocity of the RipStik.
The students then walked 30 meters taking split times every three meters and graphing their results to obtain their walking speed. At the end of this session students had seen three different linear systems, including two involving velocities.
The laboratory the second week would involve measuring three different speeds: slow, medium, and fast. The students were asked to draw what they thought a graph would look like for these three speeds.
Click to enlarge
A sample of their predictions is seen above. Two students realized that since velocity (speed) is slope, the slope would increase. The rest of the students had a variety of different predictions. At the lower right, for example, is a prediction that the lower coordinate is a slow speed, the middle coordinate is a medium speed, and the upper coordinate is a fast speed. Other papers display other predictions. This goes to the one of the implicit skills underneath general education learning outcome 3.2, that students will be able to "Present and interpret numeric information in graphic forms."
The physical science class then did an experiment to measure an object moving at three different constant velocities, using Desmos to display the results. The velocities were in meters per second.
One of the intents of SC 130 Physical science is to address general education learning outcome 3.2 throughout the term.
Placement thoughts
The college recently shifted from an entrance test to a placement test as part of a change to open enrollment. During this process I was assisting new freshmen with their course selection. Two of the new freshmen I worked with had taken Algebra I, Geometry, Algebra II, and Precalculus at a high school with a reasonably strong academic reputation. One reported having an A in Precalculus, the other reported having a B in Precalculus. The student with the A in Precalculus placed into MS 096. The student with the B in Precalculus placed into MS 095. MS 095 means a year and half of developmental math before reaching college algebra. This reinforced my own confirmation bias as to the lack of validity of mathematics placement test, especially for students who have completed high school mathematics courses.
High stakes, single event tests are known in the education field to be problematic. Transcripts and grades are, in most cases, the far more reliable measure of what courses a student can potentially succeed in. The placement test in use is home grown and has not been evaluated for reliability, validity, or predictive power. A student has one bad day, they are deeply under-placed. A student gets lucky on the multiple choice, and they over-place.
Transcripts involve more work than simply using a set of scores in a spreadsheet from a placement test, work that is necessary to properly and appropriately place students. The college already has transcripts for all admissions. This is a process that can be done with some effort.
There should be a starting place for this conversation at the college. The preassessment results attempted to inform that conversation starter. The number of new freshmen in the sample was too small to obtain placement patterns.
The proposed discussion starter is seen above in the tinting of the cells. The numeric values are not related to the tinting, there are two students who took the survey and indicated that they were freshmen and who remembered their mathematics placement. Both had taken precalculus, one placed into MS 100, the other placed into MS 101. They were not asked to self-report their grades in their high school course on the preassessment.
The tinting is a proposed starting point for placements by transcript.
The green tint is where an incoming freshman with an A or B in the highest math class displayed on the left would be placed.
The pink tint would be the placement of the incoming freshman with a C in their highest math class taken.
The orange tint would be a D in their highest math class.
Transcripts would obviously be used, not a self-reporting system. As per current practice, placement into MS 101 would include the option to take MS 150 Statistics. The table would also need to be expanded to handle MS 104 and MS 106, along with PH/MS 109.
This article would be remiss if a recent mathematics curriculum working group effort was left unmentioned. That group appeared poised to recommend a way to compress or reduce the number of developmental mathematics courses. As no changes ensued, the above chart presumes that the status quo mathematics curriculum is retained. This is intended as a starting place for a discussion among the mathematics faculty about a shift from using a placement test to using transcripts to place students in mathematics.
The placement-by-transcript system would also need provisions for moving a student to another course early in the term if necessary. This is an area known to have complexities because of differences in the credit and contact hours between collegiate and developmental courses, along with student class schedule impacts.
Ideally, follow-on research into the success rates of students placed by transcript should be done, but any such study would have to be measured against the success rates of students placed by the current placement test system.
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