# Common Core’s Cloudy Vision of College Readiness in Math (by Sandra Stotsky)

Common Core’s egalitarian tentacles are now slithering towards high school diploma requirements. In states that respond to a current prod to “align” their high school graduation requirements in mathematics with the academic level reflected in Common Core’s college-readiness mathematics standards, the mathematics coursework taken by our low-achieving high school students may indeed become stronger. But if such an alignment is not strategically altered, states may be unwittingly reducing other students’ participation in more demanding mathematics curricula and their academic eligibility for undergraduate STEM majors and internationally competitive jobs in mathematics-dependent areas.

Common Core has carefully disguised its road to equally low outcomes for all demographic groups, and many state boards of education may quickly follow up their unexamined adoption of Common Core’s K-12 standards (as well as of Achieve’s science standards) by lowering their high school graduation requirements in the name of alignment, thinking that, once again, they have strengthened their public schools. (I’m willing to credit state board members with good intentions. Not so, Common Core’s and Achieve’s standards writers, who chose not to align their college-readiness or high school standards with international benchmarks.)

The form taken by this egalitarian prod is a four-page report titled *Out of Sync*, whose overt purpose is to indicate whether a state has high school diploma requirements “aligned” with Common Core’s “vision” of college readiness in mathematics.[1] This vision, according to the report, consists of “math in each year of high school” and “substantial content typically taught in Algebra I, Geometry, and Algebra II classes.” The report is careful not to say “most of the content” typically taught in these courses—simply an undefined “substantial” part of it.

**W]hy [should] states whose own mathematics standards were academically stronger than Common Core’s and whose students were high-achieving on the latest Trends in the International Mathematics and Science Survey (TIMSS) need to be aligned with Common Core’s mathematics standards[?]**[/quote]

**How many states are not aligned?**

Results of the report’s analysis: Graduation requirements in only 11 Common Core states meet its definition of alignment. Requirements in 13 other states are only partially aligned, but 22 lack graduation requirements that “match the expectations of the new standards.” Not unreasonably, one might take such a finding to mean that the vast majority of states need to increase graduation requirements. But when Massachusetts, Montana, New Jersey, and Vermont (high achieving states in grade 8 mathematics on the 2011 NAEP) end up in the “not aligned” category, one begins to wonder what matching might mean. Requiring all high school students to take four years of mathematics may sound like an advance for many states, but the other part of the vision puzzles. The report sees alignment when it finds specification of Algebra II in graduation requirements, as indicated by the comments for each state.[2] Yet, many non-aligned but high-achieving states require only a specific number of years of study, or math credits, rather than Algebra II.

So why the insistence on the specification of Algebra II for “alignment” with Common Core? Perhaps it sounds more demanding than the wording used by the majority of states? Perhaps it will look good for students to have colleges and employers think they have taken an Algebra II course after passing a Common Core-based test of college readiness. The unanswered question is: What mathematics are they now prepared for?

**When Algebra II Is Not Algebra II**

The content of a traditional Algebra II course has for many years led directly in most high schools to a trigonometry/analytical geometry or pre-calculus course. Students interested in engineering or science-related careers (or students who wanted to be sure all possible options were open to them in college) were then ready for a calculus course in grade 12 or in their freshman year at a selective college. That is why a requirement to pass an Algebra II course or its equivalent for a college degree led to so many freshman remedial mathematics courses at the post-secondary level. A traditional Algebra II course is difficult and unnecessary for students who are not mathematically ambitious. (For example, see the topics for Algebra II in the 1997 California Mathematics Curriculum Framework or the 2000 Massachusetts Mathematics Curriculum Framework.) That is why Florida and Michigan have removed the Algebra II requirement for a high school diploma.

But an Algebra II course with less demanding content can be passed by much larger numbers, and that is what seems to have driven Common Core’s conception of college readiness, dubbed “Algebra II lite” or “Algebra I plus” by some mathematicians. That is why Jason Zimba, the chief mathematics standards writer for Common Core, told the Massachusetts Board of Elementary and Secondary Education in March 2010 that Common Core’s college-readiness level in mathematics meant readiness for a non-selective college. Similarly, this Board was told on another occasion that passing Common Core’s college-readiness test would indicate readiness for College Algebra.

While College Algebra is a course title that may sound impressive to many parents and state board members, it is a course that many mathematicians consider akin to remedial Algebra II. In other words, completion of Common Core’s Algebra II will make students ready for remedial Algebra II at the college level, but with one huge difference. Students will be entitled to college credit for it.

To be sure, many educators and state board members may see nothing amiss in this scenario for college-interested high school students oriented to the humanities or the arts. But how will a signal be sent to mathematically able students as well as to those with an interest in a mathematics-dependent field that their talents or interests may not be furthered if their teachers’ goal is restricted to getting all students to pass Common Core’s college-readiness test?

Change the Equation’s report will undoubtedly confuse many state board of education members and legislators who do not understand the differences in content between a traditional Algebra II course and Common Core’s Algebra II. How can they understand why they are being advised to align with Common Core’s vision of college readiness in mathematics (“a mathematics sequence through Algebra II or Integrated Math III, plus one more year of math”)[3] when, in many cases, their own graduation requirements already specify Algebra I and Geometry and a third year of mathematics. All that may seem different to them is the requirement of four years of mathematics, instead of three. They do not understand that Common Core’s vision of Algebra II is not the Algebra II course that led to a pre-calculus course (and to a calculus course in college or grade 12).

What they will learn in Out of Sync is that just keeping to the “traditional” sequence won’t do. As the report stresses, “the ‘traditional’ course pathway — Algebra I, Geometry, Algebra II, and further mathematical coursework—might neglect critical Common Core content or mathematical practices if the courses are not re-examined and aligned to the new demands.” Because Appendix A in Common Core’s mathematics standards doesn’t outline the contents of a pre-calculus or, as it was often titled, a trigonometry/analytical geometry course, and because “any pathway would have to include substantial content traditionally taught in Algebra I, geometry, Algebra II, and statistics and probability courses,” there may not be much room in a Common Core-dominated high school mathematics curriculum for a course that leads to the freshman mathematics course in a science- or engineering-oriented undergraduate program.

**Why a Trig Course Matters**

The importance of a trigonometry course should not be underestimated. In a 2003 survey of the mathematics requirements in the 11 colleges of engineering in Massachusetts, department of education staff found that trigonometry was required for admission to 8 of the 11 colleges.[4] Staff also found that a high school chemistry course was required in 9 of the 11. The standards for a high school chemistry course do not appear in Achieve Inc.’s recently released Next Generation Science Standards, now adopted by about a half dozen states. One wonders if their boards of education ever thought to consult their engineering school faculty.

The reduction of the contents of the traditional Algebra II course needs to be understood in the context of the “alignment” of newly released Adult Learning Standards and the standards for the General Education Diploma (GED) with the academic level of Common Core’s future college-readiness tests in mathematics. One should not expect science-related specialists or engineers to come from programs based on those standards, either.

**What a High School Diploma Never Meant**

Few state board of education members seem to have understood that a critical academic distinction was being badly muddled, conceptually and practically, when they adopted Common Core’s standards, which claim to prepare students for credit-bearing college coursework. A state’s own high school standards were created to prepare students for a high school diploma. A general high school diploma never signified readiness for credit-bearing college courses. Students who wanted to enroll in a college took college prep courses and a mathematics sequence that typically went beyond Algebra II and included trigonometry or a pre-calculus course. Successful completion of college prep coursework (or graduation from an exam high school like Boston Latin) was intended to indicate a higher level of academic achievement than that reflected by the general high school diploma.

Nowhere does Change the Equation’s report explain why states whose own mathematics standards were academically stronger than Common Core’s and whose students were high-achieving on the latest Trends in the International Mathematics and Science Survey (TIMSS) need to be aligned with Common Core’s mathematics standards. Why should their high school diplomas indicate readiness for credit-bearing coursework at a non-selective college? Why should their high school mathematics programs ignore those students who might become our future engineers and scientists? This is apparently the grand bargain that over 45 state boards of education bought into without asking engineering and science faculty in their own state’s colleges and universities whether they agreed with Common Core’s or Achieve’s vision of college readiness as expressed in their standards. Instead of aligning with a set of standards that lowers the vision for their high-achieving students in order to raise the vision of their low-achieving students, states should offer two or three different types of high school diplomas to make sure that mathematically ambitious students are not only encouraged but rewarded for their efforts. Several already do.

Notes:

[1]*Out of Sync*: Many Common Core States Have Yet to Define a Common Core-Worthy Diploma. This report was released in June 2013 by the National School Boards Association’s Center for Public Education and Change the Equation, an organization focused on STEM learning. The report compared only state high school graduation requirements in mathematics to Common Core’s high school mathematics standards. It explained that it could not do the same comparison in English because the titles of many English courses (e.g., English I, II, or III) don’t indicate content. Nor do Common Core’s English language arts standards, for the most part. [2] http://changetheequation.org/sites/default/files/MathGraduationRequirements_table.pdf [3] Actually, there is no clear definition of college readiness in Common Core’s mathematics documents and four years of mathematics is only implied in Appendix A, which Common Core states are not required to follow because it was added in mid to late August 2010, after release of the final version of the main document (June 2, 2010). [4] Center for Teaching and Learning. MATHEMATICS AND SCIENCE COURSES REQUIRED OR RECOMMENDED FOR ADMISSION INTO ENGINEERING AND ENGINEERING TECHNOLOGY PROGRAMS AT MASSACHUSETTS INSTITUTIONS OF HIGHER EDUCATION. Massachusetts Department of Education, July 2003. http://www.doe.mass.edu/boe/sac/tech/0703mathsci.pdf

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