Designing High-Impact "Writing-to-Learn" Math Assignments for Killer Courses.

The body of literature on a Writing-to-Learn (WTL) approach in math courses offers up a variety of assignment types from which to choose. However, few of these articles provide empirical evidence on the ways these writing assignments contribute to students' learning. This mixed-methods study, conducted at the University of New Mexico, a Hispanic-Serving Institution, examines the effect of WTL assignments on students' success in two "killer courses": a Survey of Math class for non-STEM majors and a Calculus I class for STEM majors. While the quantitative results did not prove statistically significant, the qualitative results suggest that high-impact assignments are those that ask students to focus on procedural knowledge, or analyzing the process, rather than simply solving for the right answer. At the start of the 2013 academic year, the University of New Mexico (UNM), a "very high research" Hispanic-Serving Institution (HSI), published internally a list of undergraduate "killer courses" offered in the fall 2012 semester. These killer courses, which often serve as the "gateway" to the major in that subject, are known, as the moniker suggests, to "'kill' a student's GPA, motivation, academic progress, scholarship eligibility and interest in remaining in college" (Barefoot, 2013). The anecdotal causes for these effects include students' lack of academic preparation in a subject (especially mathematics), a lack of placement procedures for a class, (large) class size, and a lack of early feedback to students (Barefoot, 2013). At UNM, the "killer course" designation was given to those aggregated sections of a particular course with a total fail rate of 20% or higher, where failing is a grade of Cor below. Seventy-nine courses at UNM made the list in fall 2012, with STEM (science, technology, engineering, and math) courses making up 33% of these. Among the killer STEM courses, 42% were math classes (or 11% of all killer courses). Students' difficulty in the STEM courses at UNM reflects a larger trend as seen in the nationwide attrition of STEM students (see Chen & Soldner, 2014). Of particular concern is the high dropout rate or switching out of STEM majors by women and minority students, as illustrated in the 2010 U.S. Commission on Civil Rights briefing report "Encouraging Minority Students to Pursue Science, Technology, Engineering and Math Careers".[1] Recently Cristyn had co-developed a new first-year Stretch/Studio composition curriculum[2] that focused on providing students with additional in-class support on their writing assignments. The new curriculum resulted in the elimination of "remedial" writing courses at UNM and increased student pass rates that exceed those of the traditional composition courses offered. Following this experience, Cristyn became interested in the possible intersectionality between "killer courses," as a framework for identifying courses where students could use more support, and writing, as a tool for increasing students' success. "Writingintensive courses" are recognized by the Association of American Colleges and Universities as one of 10 high-impact practices with a positive effect on student engagement (Kuh, 2008). Therefore, Cristyn was interested in investigating the effects of a "writing-to-learn" (WTL) approach in killer courses across the Elder and Champine 2 curriculum. Of particular importance was the dramatic, positive effect that such an "educationally purposeful" activity could have, as reported by Kuh (2008), on the GPA and retention rate of minority students in their first and second year, respectively (pp. 18-19), as UNM's beginning freshmen class profile most recently reported in fall 2015 was 52% Hispanic (Office of Institutional Analytics, 2015). As mathematics is one of the leading "killer course" subjects at UNM, it seemed like a good place to start. UNM does not have a formal Writing Across the Curriculum program beyond the individual, isolated efforts of faculty and graduate students on campus. Therefore, independently, Cristyn teamed up with Karen, a full-time lecturer with more than 20 years of experience teaching math courses that span the curriculum. For this collaborative, IRB-approved research project, our main objective became that of assessing the effectiveness of Math writing assignments on students' learning. In fall 2014, we began a pilot study with MATH 129: Survey of Math, a class for non-majors. Karen was already incorporating two writing assignments of her own into the course, and the curriculum was one which we thought we might have the greatest influence on since Karen is the program coordinator for the course. Also, while not officially designated a "killer course" in the traditional sense, as the only way to "fail" MATH 129 is to withdraw from it[3], the course is one where Karen often sees students repeatedly re-enroll as they attempt to earn a C or better to satisfy the university's core curriculum requirements. Following our fall 2014 pilot study during which we tested new and revised writing assignments, student surveys, and focus group questions, we continued our research in spring 2015 with MATH 129 and included an additional course in our investigation that Karen would also be teaching that semester: MATH 162: Calculus I. MATH 162 is a designated "killer course" for STEM majors with an aggregated fail rate in fall 2012 of 41.6% across sections. With the course instructor a controlled variable, we wanted to evaluate the possible effect of writing assignments on students' learning in MATH 129, an un-official killer math course for non-STEM majors, and MATH 162, a designated "killer" and required course for STEM majors. We expected to find that the non-math majors would respond more positively than the STEM majors to the writing assignments and that the assignments would contribute more to non-math majors' learning, as we thought the non-math majors, who are largely enrolled in humanities courses, would be more familiar with writing assignments as a form of learning and assessment. On the other hand, STEM majors, we predicted, would perhaps be more familiar with solving numerical problems as a form of developing and assessing their knowledge about math concepts and, therefore, less amenable to writing assignments related to math as a tool for learning and assessment. A Review of WTL Math Assignments As we prepared to collaborate on the design of writing assignments for Karen's two math classes and assess their impact on students' learning, we reviewed a number of existing articles that describe the kinds of WTL assignments that might be used in a college math course. We began with "Writing to Learn Mathematics," in which Russek (1998) describes a range of writing assignments for use across the math curriculum. For example, in the course Theory & Methods of Mathematics, as described by Russek, students learning about mathematics education respond to prompts such as "What is Mathematics?" or "What Makes an Effective Math Teacher?" (pp. 36-37). In an introductory algebra class, students solve for a weekly "math trick," explaining in a couple of paragraphs why it works. Or in Algebra Part I, students write a "mathography" in which they describe their feelings about and experiences with math. Other courses Russek describes require students to solve mini-research problems and submit an end-of-semester portfolio. For a "service" or "core" course similar to MATH 129, Crisman (2008) describes asking students to write a three-page essay on a "historical mathematician." Crannell et al. (2004) provide a range of problem-based written assignments for use in Survey of Math to Calculus courses. For these assignments, students receive problems written in the form of letters from a well-defined (yet fictional) character and then offer responses that include the solution and an explanation of the solution "in precise mathematical prose" (p. 3). High-Impact "Writing-to-Learn" Math Assignments 3 An example of a math assignment for STEM majors comes from Goodman (2005), who asks his calculus students to write to a friend or family member a one-page, weekly letter in which the student summarizes two or three main concepts or issues discussed in class that week and comments on any aspects the student is struggling to understand. Parker and Mattison (2010) describe in detail asking math majors and minors to write a math course textbook on proofs for their peers. And most recently in "Transfer and the Transformation of Writing Pedagogies in a Mathematics Course," Bryant, Lape, and Schaefer (2014) promote the genre of proof writing as a way to transform mathematics instruction through writing. As demonstrated by the examples above, the body of literature on WTL in math offers up quite a range of assignment types to choose from, including those that require students to write about math in historical terms, others that ask students to define mathematical concepts, and still others that ask students to articulate their process as they solve mathematical equations. The authors often offered anecdotal evidence regarding the positive ways that students responded to the assignments. However, very few articles offered empirical evidence on which and how these writing assignments contributed to students' learning. Nor did they specifically address increasing students' success within a "killer course" framework. Therefore, with this study, we seek to add to the above body of literature with an empirical examination of whether and which kinds of writing assignments impact students' learning in a math class for majors and a math class for non-majors and to what effect within a killer course context. Using what Haswell (2005) calls "RAD" research—that which is repeatable, aggregable, and data-drive—the main research questions driving this study are as follows: 1. Do students perceive that writing assignments contribute to their learning of course content? 2. Does the scaf