Preparing Students in Developmental Math for College and Beyond: An Assessment of Student Understandings

• In Event: 75.031 - Deepening Our Understanding of Student Mathematics Knowledge in Community Colleges

Abstract

The principal goal of developmental (i.e., remedial) coursework is to prepare students for college-level classes. This requires that students retain skills and knowledge and apply them to novel situations. Existing research on developmental mathematics has focused largely on the challenges students face (e.g., Grubb, 2012) and efforts to improve their completion and persistence (e.g., Rutschow & Schneider, 2011). This study extends this work by exploring student learning in their developmental coursework. Specifically, what are students’ understandings and misunderstandings of key math concepts relative to the learning objectives of their developmental math courses? How do students perform on college-level tasks that draw on those learning objectives?

Students are sampled from two community colleges that recently redesigned their developmental mathematics sequence into standalone modules. An 18-item written assessment was developed in consultation with course faculty members to be aligned with learning objectives of three high-enrollment modules covering fractions, decimals, percents, proportions, and linear equations. Two test items were designed to approximate tasks that students would be asked to complete in introductory college-level accounting and biology courses. Participating students also complete a background questionnaire that includes self-efficacy ratings, and students’ instructors are asked to rate participants on parallel items about mathematical and academic skills. A subsample of students are asked to describe their problem-solving processes in an audio-recorded interview lasting approximately one hour as they solve a series of mathematical problems targeting the same learning objectives. The authors have analyzed preliminary pilot data collected in Spring 2014 from 27 students (8 in interview subsample). This paper will also include analyses of data collected from a larger sample in Fall 2014 (expected n = 250).

The written assessment was scored according to a scoring guide for a maximum possible assessment score of 36. Based on preliminary results from the pilot sample, student scores ranged from 7 to 31 with a mean of 17.6 and a standard deviation of 5.4. On average, student scored most strongly on items related to proportions, ratios, and percents (average item score = 1.29 out of 2) and least strongly on items related to expressions, linear equations, and inequalities (average item score = 0.67 out of 2). There was a significant, positive relationship between test scores and both student self-ratings (corr = 0.45) and teacher ratings of students (corr = 0.40).

We combine data from the written assessment and student interviews to build a picture of student understandings and misunderstandings across course learning objectives. We find that students lacked understanding about how numbers expressed as percents relate to fractions and decimals, suggesting a lack of retention and application of knowledge across modules. They struggled to correctly represent percents visually or to convert percents that presented more complicated challenges than their typical procedures account for (e.g. numbers less than 1%). Planned analyses include additional triangulation of error patterns across college-level tasks and interview data. Findings have implications for enhancing curriculum and instruction in developmental mathematics to prepare students for success in a range of college-level courses.

Authors

• Susan Bickerstaff, Teachers College, Columbia University

• Madeline Joy Trimble, Teachers College, Columbia University