Embedded Mathematics Remediation Using the Math you Need,When you Need it: A 21 st –Century Solution to an Age–Old Problem

Introductory science courses are gateways for potential science majors to discover the field as well as avenues for general education students to gain scientific knowledge and literacy skills essential for full participation in today's world. All too often, however, the quantitative component of introductory science courses is a major barrier due to students’ variable and often weak mathematical preparation as well as their difficulty in applying the mathematics they do know. Requiring students to complete prerequisite mathematics courses may not solve the problem because, as Gavriel Salomon and David N. Perkins pointed out in their 1989 Educational Psychologist article, a mismatch between the content of math courses and the mathematics used in science hinders the transfer of learning. Even in courses with a mathematics prerequisite, science faculty find themselves spending precious course time teaching basic mathematics. Further, although faculty understand how mathematics is applied in their fields, they less often understand how to effectively teach this to students. Therefore, finding effective ways to remediate required mathematical skills is key to broadening access and student success in introductory science courses.

Providing students with access to high–quality, online content for course–specific mathematics remediation is one new and promising approach that can be used by faculty in a variety of disciplines. For students in introductory geoscience courses (e.g., geology, earth science), The Math You Need, When You Need It (TMYN) (http://serc.carleton.edu/mathyouneed/index.html) is a set of online mathematics tutorials containing quantitative topics applied to geoscience problems that, on a national survey, geoscience faculty ranked as important in their introductory courses. For the past five years, the tutorials have been used extensively by geoscience faculty in both two– and four–year undergraduate institutions and studied for their effectiveness in engaging and remediating students’ mathematical skills. Lessons learned suggest the positive benefit of an embedded approach to mathematics remediation and underscore the crucial role that faculty play in promoting student engagement in asynchronous, online learning.

Program Development

TMYN began as a collaboration between a geoscience faculty member and a mathematics faculty member in the late 1990s. Together, they puzzled over local data the geologist collected that revealed mathematics was a barrier to success in physical geology (Geology 101). The data showed that even students who completed precalculus struggled when asked to apply basic mathematics concepts, such as rearranging equations or unit conversions, to geoscience contexts. Recognizing that no single prerequisite mathematics course covered the required content, the two faculty members created a one–credit course they affectionately called Mathpatch.

The philosophy behind the course was to teach students the exact mathematics they needed for Geology 101—using a just–in–time approach that emphasized geoscience contexts similar to those that students would see in a lab or lecture. In theory, the approach would increase students’ transfer of mathematics to geoscience and, as a result, reduce the need for the instructor to spend class time teaching mathematics. Mathpatch, taught by the mathematics instructor, ran concurrently with Geology 101 and met twice per week, face–to–face, for the first half of the course. While Mathpatch was initially voluntary, early promising results led to students being required to enroll in and pay for the course based on their performance on a skills test given on the first day of Geology 101.

At about this same time (late 1990s/early 2000s), geoscience faculty across the United States were coalescing efforts to reinsert quantitative content that had been stripped from their introductory courses and textbooks in the preceding decades. According to an article by Cathryn A. Manduca, Eric Baer, Greg Hancock, R. Heather Macdonald, Sam Patterson, Mary Savina, and Jennifer Wenner, this loss of quantitative content had led students to view these courses as non–math–related, as epitomized by such undesirable monikers as “rocks for jocks.” Leveraging the movement to reincorporate quantitative content, Mathpatch blossomed into a national project titled The Math You Need, When You Need It, comprising a suite of eight online modules available to any geoscience faculty members interested in supporting students in applying mathematics in their courses. TMYN modules include unit conversions, rearranging equations, graphing, slopes, rates, density, hypsometric curve, and trigonometry. The modules can be used in any order, and each includes an instructor resource page.

As the modules were piloted, several factors emerged as key to securing high levels of student engagement and learning. First, to facilitate usability, the modules have a parallel structure: an explanation page that introduces the quantitative concept, a set of practice problems with worked answers, and a post–module quiz. Each page of the module adheres to major web design principles such as those Richard E. Mayer outlines in his 2001 book, Multimedia Learning; these principles aim to reduce cognitive load and maximize information processing. Another pattern that emerged from the pilots was higher and sustained levels of student engagement in courses where remediation modules were embedded in a course rather than packaged as a stand–alone course as in the original Mathpatch. For students, the embedded approach removes mental, fiscal, and temporal barriers created by co–requisite courses.

Additionally, completion and success rates were higher when faculty gave direct instruction on how to navigate the modules, and when faculty made explicit connections between TMYN modules and course topics. Together, these instructional practices increased students’ expectation that they could successfully complete the modules and their perception that the modules were useful and relevant to their success in the course, which in turn bolstered student motivation to engage with the modules—just as we hoped for, based on the findings of researchers like Allan Wigfield and Jacquelynne S. Eccles, who examined expectancy and motivation in their 2000 Contemporary Educational Psychology article.

Assessment

Since 2010, TMYN modules have been used nationwide by more than 20 geoscience faculty and 1,600 students in both two– and four–year institutions. In a typical course, instructors assign four to five modules. The modules are intended to support the learning of quantitative skills used in geoscience courses in a way that students find helpful without spending classroom time. Students complete a pretest prior to using the modules and a posttest upon completion. The tests are equivalent in content and difficulty and provide both a baseline measure of students’ skills and a measure of learning gains. In addition, after completing each module, students take a post–module quiz that includes two questions to rate students’ perception of the module's helpfulness and difficulty, using a forced–response Likert scale. Lastly, instructors using TMYN complete a questionnaire at the end of the course that provides targeted feedback about the modules’ effectiveness. Together, these measures are analyzed to assess the impact of TMYN on student learning.

Student engagement in the modules is high, with 80 percent (n = 1,348) of students completing all or all but one of the assigned modules. More than a third (35 percent) of the courses using TMYN have module completion rates of 90 percent or greater. Pre– to posttest gains are also high. Across courses using TMYN, the mean pretest score was 59 percent, with individual courses ranging from 41 to 75 percent while the average posttest score was 76 percent (minimum of 60 percent to maximum of 89 percent). Learning gains occurred even among students with high pretest scores. To be sure, students scoring below the course mean on the pretest showed the greatest improvement (43 percentage–point gain). However, even among students scoring greater than one standard deviation above the class mean on the pretest, a majority (58 percent) showed positive pre–to–posttest gains, with a mean gain of 23 percentage points. This finding has led to the recommendation that faculty assign embedded remediation to all students, leveling the playing field while not stigmatizing students with lower levels of mathematical preparation.

Upon completing the modules, students report that the modules are helpful and have the right amount of difficulty to be appropriately challenging but not overwhelming. Faculty implementers report that students who used the modules arrive prepared to apply mathematical skills to quantitative exercises in lab and class, freeing up more class time for science instruction. Taken together, data show that the modules provide effective remediation of quantitative skills and concepts for students, enabling faculty to maintain or increase the quantitative content in their courses.

Implementation Challenges and Strategies to Address Them

Embedded remediation delivered in a just–in–time fashion can be adapted to disciplines beyond geoscience and need not require a major grant for development. The Internet is replete with open–access resources, such as Khan Academy videos, that provide instruction on concepts and skills for science, statistics, and economics. Further, embedded remediation need not be limited to teaching quantitative skills. Faculty in writing–intensive disciplines can help their students by developing remediation modules that teach students how to create citations and references or how to structure a thesis or develop an argument. In the absence of readily available open–source materials, faculty can create customized remediation modules fairly easily and inexpensively using available technology developed to support online learning such as Camtasia or other lecture–capturing software. Regardless of the source, it is recommended that faculty seek out instructional design staff to help review and configure the remediation modules for maximum student usability and, ideally, to test and evaluate their effectiveness.

Even the best–quality modules, however, will require faculty efforts to secure student buy–in. A “build–it–and–they–will–come” approach will likely be met with disappointment as students, for a variety of reasons, frequently do not take advantage of available out–of–class resources, or they limit their use to cramming for exams. Faculty wishing to secure student buy–in should consider lessons learned from faculty who have successfully used TMYN: (1) devote a small amount of class time to explaining how to access and use the remediation modules, (2) design and configure the modules with a parallel structure so that completion requires only a modest amount of time, and (3) build students’ perceptions of relevance and usefulness by referencing module content as related topics arise in class. Faculty who take these steps are likely to experience a handsome payoff in terms of student engagement and learning!