Categorizing Precalculus Final Grades by Campus and SAT/Placement Test Score

Nathan Rush, Research Analyst
Office of Institutional Research
Becker College
 

The following data visualization was created as part of a departmental review (mathematics) at Becker College. Becker operates two campuses, and while some programs and courses are exclusive to one or the other, many general education courses have sections on both. It was observed that final grade distributions differed considerably between the campuses for sections of Precalculus (PC) – students with strong preparation were failing or withdrawing on one campus, while low-scoring students received As and Bs on the other. Institutional Research was asked to create a visual that represented several pieces of information about each student, including final course grade, campus where they took Precalculus, and the method through which they placed into the course.

We decided that a pair of bubble charts, created in Microsoft Excel, would meet our needs – a single chart for both campuses was too crowded and difficult to understand. The size of the bubbles corresponds to the number of students with the same final course grade (X-axis) and method of placement (Y-axis). Students at Becker can enter PC with a minimum ACT/SAT math score, minimum Accuplacer® score, or by completing a lower level math course, such as College Algebra. The chart is arranged as a 2 x 2 matrix, with the X-axis crossing the Y at the minimum SAT math score for placement into PC; passing and failing grades are divided by the Y-axis. A secondary Y-axis is used for Accuplacer® scores, also with the minimum score accepted for PC placement at the origin. In order for Excel to fully display bubbles at the edges of the chart, each axis extends beyond the minimum and maximum values of the data.

Arranging the chart into a 2 x 2 matrix allowed us to categorize students into one of four groups, depending on what led them to PC (test scores or previous coursework) and their final grade. High Achievers (Quadrant I) are what one would expect: students with high placement scores who earned high PC grades, while the Overachievers (Quadrant IV) are low-placing students who finish PC with a low (but passing) grade. The most challenging part of creating this visualization was ensuring that when a bubble from one series overlapped with another bubble, it did not obscure too much data. A combination of reordering the series, switching colors, and tweaking transparency mostly addressed this problem.

One final consideration: What to do about two bubbles representing the same number of students, identical placement scores and final grades, but different methods of placement? This came up in two situations. Bubbles representing two placement methods were manually “split” using half-moon shapes representing the two colors. As for the instance of three students from each of the three placement methods earning the same final grade, we used a different color (orange) and an explanation to draw attention to this bubble.

Organizing and displaying the data in this manner made it easier for the Institutional Research department and Academic Affairs to compare the difference in grade distribution on each campus, as well as to qualify our discussions based on the relationship between placement (as a proxy for student preparation) and final course grade. . 

 

Distribution of Precalculus final grades by SAT/ACT/Accuplacer Algebra score
or previous coursework*: Leicester campus only (N=63)

bubble1.jpg
 

 *ACT Math scores (11-36) have been converted, and Accuplacer scores (20-120) have been converted and scaled based on placement threshold to SAT scores for inclusion. Of 192 matriculated student registrations in Precalculus over five terms (fall 2011 – fall 2013), 181 (94%) had either an Accuplacer Algebra or SAT/ACT score on file.

 


 

Distribution of Precalculus final grades by SAT/ACT/Accuplacer Algebra score
or previous coursework*: Worcester campus only (N=118)
  
bubble2.jpg
 

 *ACT Math scores (11-36) have been converted, and Accuplacer scores (20-120) have been converted and scaled based on placement threshold to SAT scores for inclusion. Of 192 matriculated student registrations in Precalculus over five terms (fall 2011 – fall 2013), 181 (94%) had either an Accuplacer Algebra or SAT/ACT score on file.  

 

 

 

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Total Comments: 4
 
Betsy posted on 11/13/2014 10:36 AM
The general idea works very well and shows the stark difference between the two campuses. This I hoped has raised some questions about the underachievers in particular who are withdrawing from the course in the Worcester campus. I'm wondering if I'm too much drawn to what seems to be an exceptional group of 3 students represented in the peach-colored circle. Though Excel might not let you do it, visually it might be better to fudge the grades slightly, or perhaps to allow a wider field for withdrawals that might allow bubbles to be placed side-by-side.
Reuben posted on 11/13/2014 3:29 PM
I commonly display pass rates by ACT scores (or other placement scores) and think that it's one of the best ways to look at the relationship between cut-offs, placement, and student success. I'm glad to see that at least some other institutions are using similar data to look at student outcomes. Nice work!
Norma posted on 11/14/2014 9:06 AM
I think this is a very good use of bubble charts. It clearly brings into focus the differences between the distributions on the two campuses and their relationships to the placement criteria.
Rachel posted on 11/17/2014 9:51 AM
I think this is a great use of bubble charts. The consistent color shades for the bubbles across campuses (light colors for SAT/ACT, dark colors for ACCU_AL) made the charts easier to compare. I think it would be interesting to recreate a similar chart using the institutions Cumulative GPA. In past work, I have found that GPA (current institution and not so much HS) is a better predictor of course performance than SAT or ACT math scores. The limitation of this, however, would be that not all students would have a cumulative GPA if Precalculus is taken in their first semester. Great work!