# Data

This project was motivated by 5 years of historical data on students success in Calculus I collected by the Math Department.

Starting in Fall 2016 and contingent upon scraping together funding, all teachers in Calculus I embedded a proctored ALEKS PPL assessment as a part of the Calculus I course, typically worth 2 quiz grades.

Starting in Fall 2017, the Math Department began coordination all sections of Calculus I. For us, coordination means all common assessments (homework, quizzes, midterms, final) and common grading of major assessments (midterms and final). All assessments are developed by consensus. Coordination applies to in-person, synchronous on-line and asynchronous courses.

We found the data to be enlightening and motived continued coordination despite its costs. Here are some examples.

The bar graph (linked above) splits 5 semesters of Calculus I students into subsets according to their proctored ALEKS PPL scores at the beginning of the semester. For each subpopulation, the bar indicates the proportion of that population that earned the grades A, B, C or the combined set D,F or W. A grade of W indicates the student withdrew from the course.

It demonstrates that higher proctored ALEKS PPL scores indicate higher percentages of that population passing Calculus I and getting higher grades in Calculus I.

The pie chart (linked above) shows the proctored ALEKS PPL scores for the whole population of Calculus I students for the semesters: Fall 2016, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Spring 2020. They are split according to the course that score would have placed them into at UAF. The ALEKS PPL placement scores at UAF can be found here but they are pretty typical of other colleges and universities.

It demonstrates that over this period, only 40% of enrolled students (ie students who were placed into Calculus via some placement method whether coursework or a math placement score) could place into Calculus in a proctored environment. One-third of students did not achieve scores that would place them into a prerequisite course.

Proctored ALEKS PPL Scores split by Individual Section

This graphic shows the population of students who are high-scoring, medium-scoring, or low-scoring on the proctored ALEKS PPL assessment are not evenly distributed across individual sections of Calculus I. That is, even though roughly 40 % of students were high-scoring, individual instructors will likely experience wide variations in their classroom. In the graphic, it is clear that the person teaching Section A or Section D will have a different classroom dynamic than the person teaching Section Q.

Understanding that different instructors in the same semester will be working with very different populations of students has helped instructors focus on teaching the students they have, meeting the students where they are and working together as a team.

Proctored ALEKS PPL Scores over Time

The graphic illustrates the proportion of proctored ALEKS PPL scores over the ten semesters in which we have had funding to incorporate it into our Calculus I course. The graph indicates that the proportion of high scoring students is decreasing while the proportion of lower-scoring students is increasing. (Updated 30 May 2023)

Comparing Letter Grades in Calculus I: before and after the experiment

In the following graphics, the letters HC stand for the historical cohorts of students (Fall 2017, Spring 2018, Fall 2018, Spring 2019) and EC stands for the experimental cohorts (Fall 2021, Spring 2022, Fall 2023). All HC and EC sections were taught in a tightly coordinated format with a lot of support resources. However, the EC sections had built-in, co-requisite precalculus support and a new, formative, quizzing structure.

A typical co-requisite course in Calculus I would target students with proctored ALEKS PPL scores in the 70's. Students with scores in the 60's would typically be encouraged to enroll in a Precalculus course. Note that both populations of students perform better with the new course structure.

Population of students with proctored ALEKS PPL scores in the ranges: