This Black Hills State University project builds on previously successful efforts to decrease attrition in pre-STEM mathematics courses and positions the university to investigate those variables in the teaching and learning process that are most influential in successful remediation within a developmental mathematics sequence. The goal is to determine what works in learning developmental mathematics by analyzing the results obtained after restructuring basic and intermediate algebra courses at Black Hills State University. Beneficial applications are translatable to all STEM disciplines, and especially to projects serving underrepresented students. This potential is underscored and expected as there already have been increases in student success achieved by the program in key pre-university level mathematics courses.
The purpose of the project was to establish a multi-tiered system of supports (MTSS) model to address the disturbing failure rates of college students placed in remedial mathematics. Results demonstrated improved student outcomes in passing basic and intermediate algebra, college algebra, and the mathematics subtest of the Collegiate Assessment of Academic Proficiencies (CAAP) examination. Consequently, completing these general education mathematics requirements makes graduating with a college degree possible for under-prepared college students. Intellectual Merit Enrollments in remedial math courses are estimated to average 28% of freshman at universities and 60% at community colleges across the country. As alarming, only 25% of these students pass the required coursework. The expertise of the project team from educational psychology and mathematics offered a practical, research-based solution for institutions with liberal admission standards and limited resources to meet the learning needs of students placed in remedial mathematics. Ultimately, the project results contribute to the knowledgebase in mathematics education, educational psychology, and developmental education. Broader Impact Investigators consistently report disproportionality by ethnicity, socio-economic status, and language proficiency in developmental mathematics programs in community college and university settings. Without success in basic and intermediate algebra, efforts to retain underrepresented students are irrelevant since completing college algebra is a core graduation requirement for many degrees. Furthermore, this project promoted the use of instructional methods grounded in scientifically-based research. Our findings confirmed the effectiveness of explicit instruction with adult learners who needed direct teaching methods to learn fluency with numbers and the procedural knowledge necessary to achieve conceptual understanding. As importantly, changes in course structure, instruction, and student engagement in learning established within our multi-tiered system of supports model show promise in improved retention and graduation rates for underrepresented and disadvantaged groups without adding significant resources beyond what is available at most institutions. Significant Outcomes 1. Identified, developed, revised, and validated four student attribute measures to assess math anxiety, academic motivation, math confidence, and math usefulness in college students enrolled in basic and intermediate algebra to determine effects on passing developmental mathematics coursework, passing college algebra, and passing the mathematics subtest of the CAAP required to graduate. The Math Confidence Scale - Revised measured fluency with numbers, pre-algebra/algebra, and geometry/abstract reasoning, while the Math Anxiety Scale - Revised (Bai, 2010) measured the impact of positive and negative feelings toward mathematics on student success. The Math Usefulness Scale - Revised measured personal, family, achievement, career, and social factors contributing to passing general education mathematics required to graduate, while the Academic Motivation Scale - Revised measured intrinsic motivation, amotivation, and extrinsic motivation to attain a college degree. The contribution of the attribute measures (variance accounted for) to the grade in basic and intermediate algebra was relatively small (5%), while the contribution of the attributes to the mathematics subtest of the CAAP increased significantly (12%). Of the 805 students involved in the project, 108 of those took the attribute measures twice. Moderate effect size changes (Cohen, 1992) were noted on the MAS-R (negative affect), MCS-R (geometry/abstract reasoning), MUS-R (social), and the AMS-R (intrinsic motivation) factors, while a large effect was noted on the MCS-R (pre-algebra, algebra). 2. Established a multi-tiered system of supports with adult learners placed in developmental mathematics courses utilizing evidence-based practices adapted from the National Math Advisory Panel (2008), Institute for Educational Sciences guidebooks, and related cognitive-behavioral psychology literature. Re-structured the semester to accommodate an additional block of instructional time (Tier III) to re-teach students who failed a unit exam was essential to implementing the MTSS model. MTSS model implementation was dependent upon instructor commitment to use scientifically-based research from the education sciences; in particular, explicit instruction to directly teach fluency with numbers, procedural knowledge, and conceptual understanding for under-prepared students to master learning outcomes. 3. In an effort to evaluate the impact of the MTSS model components, basic and intermediate algebra grades were regressed upon the independent variables within the model (N = 805). R2 and effect sizes (Cohen, 1992) were computed for each independent variable. Power analysis (Cohen, 1992; power = .80) allowed identification of moderate and large effects at the .01 level. The results yielded large effects for the two formative assessments (homework & quizzes), attendance, Tier III, and explicit instruction. Moderate effects were associated with having a math mentor in class, as well as traditional instruction. Pass rates nearly doubled within both basic and intermediate algebra during the course of the study. To date, 291 of the 805 students (36%) in the sample have successfully completed college algebra; while 125 have gone on to pass the mathematics subtest of the Collegiate Assessment of Academic Proficiencies. Finally, perceptions of students and instructors corroborated how the MTSS model components supported passing basic and intermediate algebra throughout the two year project.
