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“Basic skills” math taught contextually is rare – but more effective, finds this study.

Wiseley, W. C. (2011) Effective basic skills instruction: The case for contextualized developmental math. Policy Brief, 11-1.

College-going rates in the U.S. are higher than ever. In response to the needs of a more highly credentialed workforce, nearly half of all 18- to 24-year-olds who complete high school enroll in a degree-granting postsecondary institution, up from only about one-third in 1967. However, the increased importance of postsecondary education comes at a price: not only is higher education tuition expensive, the increased access to it has led to a wider population of entering college students whose high school education has left them deficient in basic reading, writing, or math skills.

These students typically play catchup in non-credit "developmental" (or "remedial") courses, having been assigned to these courses by a skills test. Developmental education is a massive undertaking: nationwide, roughly 2.5 million students per year, and almost 30% of incoming college students, enroll in developmental education courses. A 2008 study amusingly titled Diploma to Nowhere estimates the cost of developmental education at about $2 billion per year in community colleges and an additional $500 million in 4-year universities. Worse yet, students who take these non-credit courses in college are less likely to graduate: Massachusetts 4-year colleges have the highest graduation rate in the nation for remedial students, but it’s only 51%. The graduation rate for developmental students at community colleges, where more students are assigned to sequences of non-credit courses spanning two or more semesters, is much lower still: in Massachusetts only 10.3% have earned their associate’s degree after three years.

Basic skills math courses are frequently taught as just that: basic math, devoid of context and nearly identical in form and pedagogy to the middle- and high-school math courses whose content they mimic. One can hardly blame the instructors that teach them, as many of them have long experience as K-12 math teachers. But developmental math students owe their circumstances to an unproductive experience with the same kind of teaching. For many students, the developmental math experience in college amounts to the worst kind of high school déjà vu. The stigma of feeling “sent back to high school” is for some students insurmountable.

But that trend may be changing as more basic skills math classes are finding new life in context. A joint statement issued by Complete College America, The Charles A. Dana Center, and others makes the assertion that

With its one-size-fits-all curriculum, remedial education does not provide solid academic preparation for the programs of study most students pursue. As a result, remedial education too often serves as a filter — which sorts students out of college — rather than as a funnel — guiding them into a program of study.

The report cites a 2012 working paper by the National Bureau on Economic Research which finds that on the whole, students are not picking up the skills they truly need for college success in their developmental courses, because those courses tend to focus on isolated skills rather than connective reasoning.

This brings us (at last) to W. Charles Wiseley’s policy brief, written for Policy Analysis for California Education (PACE) at Stanford University. In it, Wiseley analyzes developmental math course offerings across California’s 110-school community college system, and carefully classifies each as being either a traditional, narrowly focused course (e.g. Beginning Algebra) or a contextual course (e.g. Business Math). Both tracks of developmental courses address the same mathematical reasoning outcomes, from pre-algebra through intermediate algebra content, and should therefore be considered preparatory for college-level mathematics.

The results are striking. The contextual students passed their developmental course at much higher rates (86% vs 59%) and passed credit-bearing college courses that same semester at higher rates (93% vs 75%). Students who passed contextual basic skills math were 70% more likely to pass credit-bearing courses in the following semester. While they were substantially less likely to attempt transfer-level courses in the following semester – likely because many were enrolled in terminal vocational certificate programs – those that did were more than twice as likely to pass that course as their traditionally-trained counterparts.

Success in contextual courses is also more inclusive. Compared to their counterparts and controlling for other demographic and socioeconomic factors, black students were 2.6 times as likely to pass contextual basic skills math than traditional; Native American and other nonwhite students 33% more likely; and Hispanic students 27% more likely. (Interestingly, there is a small negative effect among Asian students, who are 12% less likely to pass the contextual version than the traditional. White students saw no significant difference.) Given that students in racial and ethnic minority groups enroll in developmental coursework at disproportionately high rates, contextualization of these courses seems to be a socially just pedagogy.

This tells me that context has two effects. Tying math skills to vocational contexts supplies a necessity for learning that increases student engagement and receptivity to learning. It also enfranchises students’ informal quantitative reasoning abilities: especially when it comes to pre- and beginning-algebra content, students are more successful at solving contextual story problems than the equivalent context-free algebra problem. Not only does context give students a reason to learn and to care, it also permits them to access problem-solving abilities from their rich contextual lives.

Unfortunately, the study sample is fairly small since contextual pre-algebra level courses were (and are) incredibly scarce. Students in traditional courses outnumbered students in contextual courses 40 to 1. Furthermore, there was no ability in the study to correlate student success in common successor courses: for instance, it is not clear whether contextually trained students and traditionally trained students would perform differently in the same college-level course (e.g. College Algebra or Calculus for Business). The overall pass rates in the credit-bearing and transfer-level courses these students took were not contrasted, but it is in my opinion likely that some of the contextual students’ higher success is owed to higher overall pass rates in the credit-bearing courses their contextualized programs offer compared to traditional credit-bearing courses like precalculus.

Still, the study is eye-opening for all the reasons listed above. The more contextual a student’s development of basic skills, the more likely they are to succeed in developing and retaining those skills through the context important to their field. Contextual basic-skills training may be, for students beginning college at a math skill disadvantage, the best hope for (inclusively!) building their numeracy.