Monday, August 1, 2016

MAA Calculus Study: Placement

In November’s column, MAA Calculus Study: A New Initiative, I described a survey that MAA has conducted of practices for and concerns about the precalculus through calculus sequence at departments of mathematics that have graduate programs. The initial summary of the survey results is now available as Progress through Calculus: National Survey Summary, which can also be accessed through the Publications & Reports under Progress through Calculus on the web page Universities were distinguished by whether the highest degree offered in mathematics was a Masters or a PhD.

As I reported in November, placement was the number one issue among mathematics departments when comparing self-evaluation of importance to the program with confidence that the department is doing it well. Figure 1 shows that most PhD-granting departments rely on internally constructed instruments for placement.

Figure 1. Percentage of respondents using specific placement tools for precalculus/calculus.
Respondents could select more than one.
It is discouraging that a majority of Masters-granting departments and almost half of the PhD- granting departments use ACT or SAT scores for placement, instruments that are particularly ill suited to this purpose, even when only used to distinguish between placement into precalculus versus a previous course. It is also discouraging that so few PhD-granting universities use high school grades in determining placement. While not sufficient on their own, the study of Characteristics of Successful Program in College Calculus did reveal that including these grades improved departmental satisfaction with its placement decisions (see [1]). One of the striking results of the survey is that the number of PhD-granting departments using ALEKS increased from 10% in our 2010 survey to 28% in 2015. This may be somewhat misleading because the 2010 question only asked about placement into Calculus I, while the 2015 question asked about placement into precalculus or calculus, but from my own experience, the past several years have seen strong growing interest in and adoption of ALEKS.

Figure 2 shows the overall degree of satisfaction of the department with their placement procedures. Note that the bars above the placement tools represent degree of satisfaction with the entire placement procedure among those institutions that include this particular tool. Thus it does not necessarily reflect the degree of satisfaction with that particular instrument. Nevertheless, this does indicate that there is no single instrument that guarantees satisfaction.

Figure 2. Number of universities (out of 223) using each placement, with degree of
overall satisfaction with placement procedures.
Among all of the surveyed universities, 9% were not satisfied with their placement procedures, and 39% considered them adequate but could be improved. Even though 52% were generally satisfied, we found that there is a lot of churn in placement procedures: 30% of the universities had recently replaced or were currently replacing their placement procedures, and an additional 29% were considering replacing these procedures.

Perhaps the most interesting and potentially alarming result is that only 43% of respondents (45% of PhD-granting departments and 41% of Masters-granting departments) reported that they regularly review adherence to placement recommendations. It is hard to know how well your placement is working if you do not monitor it.

 [1] Hsu, E. and Bressoud, D. 2015. Placement and Student Performance in Calculus I. pages 59–67 in Insights and Recommendations from the MAA National Study of College Calculus, Bressoud, Mesa, and Rasmussen, editors. MAA Notes #84. Washington, DC: MAA Press.