In spring 2013, the National Center for Education and the Economy (NCEE) issued the results of a research study that analyzed the math and English requirements for community college students entering nine popular occupational fields, including biotechnology, nursing, computer programming, and business. The study addressed the question: "What does it really mean to be college and work ready"? I contributed to the research as the only non-mathematician on the mathematics panel. I will briefly summarize my thoughts relating to the math portion of the study; you can download the full report and reach your own conclusions at http://ncee.org/college-and-work-ready/.
Here are a few provocative lines from the executive summary of the study: "In sum, a substantial part of the high school mathematics that we teach is mathematics that most students do not need, some of what is needed in the first year of community college is not taught in our schools, and the mathematics that is most needed by our community college students is actually elementary and middle school mathematics..." How did NCEE arrive at this strongly-worded conclusion?
To conduct the research, panelists analyzed the math in the first year discipline-specific core courses in the nine occupational fields and also whatever math course was required for each program. In many cases the required math course was taught in the math department, for example, "College Algebra" or "General Math." In some cases, programs had specialized required math courses such as "Math for Nursing" or "Business Math." Courses from seven randomly selected community colleges in seven states were analyzed. For the selected courses, panelists scanned each page of every required textbook, exam, and project looking for math. When we found an example of math, we coded the math content based on the Common Core State Standards for Mathematics, CCSSM.
Chart 1:This summarizes the coding results for core courses for all nine disciplines from the NCEE report (provided with permission). Observe that the math topics most often found were ratios and proportions, expressions and equations at the middle school level, and the three underappreciated domains. The high school level topics were limited and typically involved exponents.
The conclusion that the math "most needed by our community college students is actually elementary and middle school mathematics" is supported by the data the panel collected for all disciplines studied; see for example Chart I. Over and over again we found ratios and proportions, simple algebraic equations, linear relationships, and graphing. (For example, a textbook description of how to prepare a 10% reagent would code to ratios and proportions.) All of these math tools are learned by eighth grade - at least according to the CCSSM. Little content coded to high school math; the exceptions typically were problems requiring exponents. Hence the summary statement that the math students typically study in high school is "mathematics that students do not need."
..."much of what students need to know is not taught." There are three mathematical domains that arose frequently in the discipline core courses, yet were not explicitly found in the CCSSM. These three areas are: complex applications of measurement (e.g.; measurement uncertainty and significant figures), geometric visualization (e.g.; a two-dimensional representation of the internal workings of a carburetor), and schematic diagrams (e.g.; a flow chart for a computer algorithm). Complex applications of measurement are particularly important in biotechnology. I will call these three areas "underappreciated" in traditional math curricula.
When we coded the required math courses taught by math departments in two year colleges, we found that those courses usually devoted considerable time to the same math taught in high schools, including many topics that were seldom, if ever, found in the core occupational courses. These required math courses did sometimes address the three underappreciated areas, but only to a limited extent. Not surprisingly, in contrast to traditional math courses taught in math departments, the math courses specific for occupational programs (e.g.; "Math for Nursing") were closely aligned to the core courses.
While there is much more to the report, the research provides data demonstrating a profound mismatch between the demands of real world occupations and the math generally taught in math departments at the high school and college level. You might be thinking that we already knew this. Nonetheless, it was dramatic, as a panelist, to see the same results roll in over and over again for all nine disciplines.
The first response that people - including the panelists - usually have to this report is that there are reasons to learn math beyond what is required for most careers. In fact, there is passionate resistance to the idea of tying math instruction to the requirements of common careers. People fear that doors will close for students who do not persist in working on the math that leads to calculus. However, I would respond that we do not require students to take music or poetry or French throughout their K-12 studies just in case they might someday become a musician, poet, or travel to France. Rather, we encourage those students who are interested in these topics to pursue their passion with advanced courses, just as we should provide abstract and advanced math for interested students. At first glance it might seem that requiring students to study math that they will never use won't hurt them, even if it is not useful in their careers. However, as the NCEE report notes, requiring math that is extraneous to most students' practical needs becomes an artificial barrier that prevents many people from successfully entering careers in which they might have thrived. Also, the math curriculum as summarized in the CCSSM becomes increasingly abstract as students progress through high school. This leaves limited time for students to develop skill solving real world problems that apply simpler math tools (such as ratios and proportions). A further problem is that in many people's minds "contextual math" equates to "dumbed down" math. Done right, however, a contextual math curriculum that is tied to real world problems can be challenging and thought-provoking and will help all students succeed in life and future careers, whether they become a musician or astrophysicist.
The NCEE report does not specifically advocate program-specific math courses, but this is a requirement that we have found increases student success and confidence. Our biotechnology program requires a course in biotechnology laboratory math specifically aimed at our students' career needs. We require remedial math courses outside of our program only for those few students whose skills are particularly weak in math. In the vast majority of cases our incoming students can perform middle school math - when it looks like it did in their middle school math books. What they cannot do, and must learn in our courses, is how to apply their math tools to real situations in the laboratory.
I think that, as educators in occupational programs, we cannot possibly imagine everything our students will need to know in their future careers. The only thing we can be sure about is that they will need to learn new things throughout their lives. This might mean later taking more math classes. Our responsibility is to prepare students to learn throughout life, not teach them everything, just in case they might need it someday. Let's make math a required tool to succeed in the real world, not a requirement that is a barrier to success.