In a response to my recent post concerning NCEE’s study of the expectations of the nation’s community colleges for incoming freshman, Andy Zuckerman wrote the following:
I have great respect for Marc Tucker. He looks for evidence and weighs it carefully, and is not an ideologue. Nonetheless, there seems to be a conflict between Marc's firm support for the Common Core standards and the findings of this study. The common core math standards prescribe the content of Algebra I and Algebra II for all students, while Marc concludes from this recent study about college readiness that what is normally taught in h.s. mathematics is not needed in community colleges. The NCEE report says that "the policy of requiring a passing score on an Algebra II exam for high school graduation simply cannot be justified." What are the implications for the common core state standards for mathematics? Do they need to be revised? How does Marc square his support for these standards -- arguing against people like Diane Ravitch -- with the findings and recommendations of the NCEE study suggesting that the standards are not well connected to what so many young people need to succeed in community college?
What our research showed is that the content of the typical College Mathematics course in the community colleges we studied included most or all of the topics typically associated with Algebra I, plus a few topics in Geometry and Statistics, what one could reasonably call Algebra one-and-a-quarter. These courses usually represented the most demanding math that community college freshman were asked to do in their first year program. One clearly does not have to master Algebra II in order to study Algebra I, so it was obvious to our mathematics panel that high school students headed for community colleges do not need to take Algebra II to be successful in community college.
We also observed that the point of taking Algebra II is to prepare oneself for the rest of the courses that culminate in the calculus. But fewer than five percent of the American workforce uses the calculus in their work. It did not make sense to us or to our advisors to require all high school students to take Algebra II if fewer than five percent would ever need to know the calculus.
That, however, did not mean, as some have suggested, that we recommended lowering the mathematics standards in our schools. The contrary is true. Any subject in mathematics can be studied at a rudimentary level or a much more sophisticated level. It turns out that what our first year community college students really need is fairly complex understanding of middle school mathematics, but all they actually have is a rudimentary understanding of middle school mathematics. Our panel thought that they needed to spend more time in school studying middle school mathematics so they could get the depth of understanding of that subject that they would need to go on in mathematics in high school and beyond.
All of which begs the question as to what kind of mathematics our students should be studying in high school. Our panel was clear on this point. Some students, including many who will go on to STEM careers, should study Algebra II and beyond, including, if possible, calculus. But many others, going on to other sorts of careers, should study the advanced mathematics that is appropriate for the kind of work they will do. Homebuilders, surveyors and navigators might need geometry and trigonometry, whereas those going into industrial production or public health might want to pursue statistics and probability. We argued not for lowering the standards but for creating pathways through advanced mathematics in high school that make sense in terms of the kind of mathematics that may be most useful to students when they leave school and enter the workforce.
Andy asked in particular how this recommendation and line of thinking relates to the Common Core State Standards for mathematics. Phil Daro headed the team that wrote the Common Core standards for mathematics. He also co-chaired our panel on mathematics for our community college study. I asked Phil to comment on Andy’s question. Here is what he had to say:
“The Common Core State Standards (CCSS) set goals. A distinction is made in the High School Standards for Mathematics between “college ready” and STEM. A "+" is marked next to standards for STEM-intending students. The + standards go beyond the CCSS definition of college ready. Most of the + standards are traditionally part of Algebra II. Thus, CCSS definition of college ready covers fewer topics than traditional Algebra II; the CCSS is more focused. Nonetheless, it is true that the CCSS are more demanding than the NCEE study found was necessary for success in existing 2-year Community College programs and the CCSS focus is more mathematical and less pragmatic.
“In writing the CCSS, we were charged with articulating one set of standards for all students that would be sufficient preparation for 4-year college programs. It was an assumed principle that this was what all students needed. We were constrained by this principle of a single standard; we could not customize different standards for different students with different destinations. The principle behind this is social justice, but it has a cost. One could argue that it would be better to have the common standards end earlier, and specialized standards start sooner. Indeed, my own view is that there should be two mathematics pathways to college readiness that split after grade 9: one for students with STEM ambitions and one for students with other ambitions. There are always social justice risks associated with different pathways, but these can be mitigated by making both pathways qualify for college admission without remediation and by replacing placement with student choice based on prerequisite qualifications.
“Progress on making the intersection of K-12 with the higher education and career systems more rational for students requires all systems to collaborate. When K-12 writes standards for itself, it has to accept current college policies as conditions to be met. We would all have to sit down together and revise all our policies together to get bigger changes than we were able to produce in the CCSS. Of course, the CCSS should be revised, but on a sensible cycle. It takes time for states, districts, schools and teachers to absorb and put into practice a set of standards. Worldwide, 10 years is a common cycle. I hope the CCSS are revised on a cycle like that, and I hope we learn in the meanwhile. The NCEE report is part of that learning.”
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