# 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

Sandra Stotsky has the qualifications to comment on the ELA standards, but not the mathematics standards.

Posted on behalf of Sandra Stotsky: In

a recent Wall Street Journal

op-ed, two mathematicians said Common Core’s ELA standards were rigorous.

No one said they had no qualifications to make any comment at all.

Perhaps you could respond substantively to the blog, instead of making an ad

hominem remark. – Sandra Stotsky

Here’s something from Bill McCallum, one of the chief authors of the Common Core. I hope he’s sufficiently credentialed for your taste.

“McCallum, a math professor at the University of Arizona … said that the overall standards would not be too high, certainly not in comparison other nations, including East Asia, where math education excels.”

The highest PLD level 5 (“Distinguished”) for PARCC only means that a student will be successful in a college algebra course. Their lower college readiness PLD level means that only 75 percent of the students would pass an average college algebra test. PARCC specifically does not address STEM requirements, and this starts in the lowest grades. In spite of all of the talk of critical thinking and understanding, CCSS does NOT provide a path for STEM readiness. The seemingly higher Algebra II Lite requirement at the top end is NOT supported by any higher expectations in K-6. Any talk of “fluency” is superficial, and specifically NOT at a STEM level.

ACT at least calibrates their readiness level to somewhere in the (equivalent) ACT 17 range. Parents at least have some idea of what an ACT score of 17 means. However, for PARCC, parents might see that although little Suzie is getting “distinguished” ratings throughout K-6, she will end up on the math track to nowhere by 7th grade.

I don’t see CCSS changing most high schools, which will still be driven by AP classes. AP Calculus even keeps integrated math curricula a little bit honest in high schools. Many parents know that state tests provide no proper feedback, even in K-6. In high school, college readiness is driven by honors and AP classes. College Prep was the highest level when I was in high school, but most people (kids and parents) know that CP is now the new “General”, or community college track. Skip CCSS. Just use Accuplacer.

CCSS is about spending a lot of money for minimal improvements. Life will go on the same for many kids and parents. They will continue to ignore the state tests.

The biggest problem with CCSS in math is that it never dealt properly with the low expectations in K-6. When I was young, I was able to get to calculus with no help from my parents. Nowadays, schools send home notes telling parents to practice math facts. (I find that astonishing.) My (AIME-level) son would never have gotten to calculus without my specific help with mastery of basic skills. All of the talk of critical thinking and understanding in K-6 is just cover for low expectations. How can schools increase the range of abilities with full inclusion and then expect to achieve better results using some sort of magic dust like differentiated instruction or Everyday Math’s “trust the spiral”.

Over 10 years ago, I distinctly remember thinking about all of the things I did not like about my “traditional” math education. Then I found out that our schools were using MathLand. I was dumbfounded. They got it completely wrong. I wanted more mathematical understanding and context. What MathLand gave was low expectations and silliness. What many K-6 educational pedagogues want is NOT mathematical understanding, but active group learning in class where the teacher is the guide-on-the-side. They think that the process will get the job done. They think that all they need to provide is engagement and motivation. That is not enough. My son’s fifth grade EM teacher had to stop trusting the spiral because bright kids still did not know the times table. Putting the onus of learning on students may sound like one is preparing them to be life-long learners, but it’s really a copout.

When I was young, the range of abilities was smaller and the expectations were higher. If kids did not meet those expectations, they had to go to summer school, or worse, stay back a year. This put pressure on the kids, their parents, and even the teachers. Nowadays, schools “pump” kids along because they don’t want schools to be big “filters”. They don’t deal with the problems and then kids are hit with the big math filter that typically happens in 7th grade at pre-algebra. There is little that can be done at that point without help from home or from tutors. Schools trust the spiral and pump kids along until the problems seem like they belong to the student, parents, and society – and many kids will believe that they are just not good in math. Then these kids are stuck in a nightmare “Groundhog Day” high school math cycle that repeatedly tries to get them to recover from bad K-6 math. How many years does it take to learn algebra so that you can pass a college algebra course with a 75 percent probability? This leads many educators to blame IQ instead of bad math curricula. “How many adults really need algebra?” This is a horrible thing to ask. And then CCSS guarantees that this will be the case because it specifically does not provide a proper curriculum path for STEM.

CCSS institutionalized low expectations. That’s clearly visible with ACT’s and PARCC’s low college readiness levels. Only the CollegeBoard, with it’s Pre-AP program, seems to be driving STEM requirements into lower grades, but I think even that ends at 6th grade. Our high school math requirements drove out the bad CMP math from our middle schools, but it hit a brick pedagogical fairyland wall at 6th grade. I don’t know why, but K-6 educational thought seems to drive all of the talk in eduland. Never mind that that there are so many high school teachers using textbooks, nightly homework, and direct teaching who are carrying the load and really preparing students for college.