Common Core and “Who Needs Algebra?”

Published by MrHonner on

Every so often, some variant of the question “Is Algebra Necessary?” comes to the fore in our national conversation on math education.

As I’ve written before, conversations like this don’t bother me.  I love math and I love teaching math, but I think the underlying questions here, “How much math, and what math, should everyone be required to know?”, are legitimate and worthy of serious consideration.  The mere fact that it keeps coming up suggests we don’t have great answers to these questions, or even great explanations as to why things are the way they are.

So I’m always interested in pieces like NPR’s “Who Needs Algebra?”, which describes how colleges around the country are trying to address the problems created by algebra requirements.  According to NPR, nearly 50% of community college students fail to graduate because they can not pass a required algebra course.  For this reason, algebra is often called a gatekeeper course, as it prevents access to the credential of a college degree.

As the piece notes, colleges are doing some interesting and innovative things to try to get students around the algebra requirement.  One particular approach, developed by the Community College Pathways initiative, offers statistics and quantitative reasoning courses that “largely skip over abstract algebraic formulas and go directly to math concepts that students will use and find engaging”.  The piece speaks positively about this new approach, which I think has merit and deserves attention.

But I can’t help but wonder how this fits in with the Common Core standards initiative.  The Common Core state math standards mandate a substantial amount of algebra in junior high and high school.  In many cases, this is the same algebra that colleges are attempting to circumvent in order to increase graduation rates.  How can mandatory algebra in high school be reconciled with optional algebra in college?

I think about Common Core, too, when I read about the great work Cornell professor Steven Strogatz is doing in “teaching math to people who think they hate it“.  Strogatz, both a renowned mathematician and teacher, is implementing a curriculum based on Westfield State University’s Discovering the Art of Mathematics, and is finding great success reaching math-averse liberal arts students with its activity- and inquiry-based approach.  But can this type of course, that excites and engages students in authentic mathematics while eschewing the typical trappings of a traditional algebra curriculum, be reconciled with the mandatory algebra standards set forth in the Common Core?  [Strogatz shared some of his informed opinions about math education in his Math Horizons interview last year.]

I don’t believe these various positions are completely incompatible, but I do see a fundamental conflict here.  After all, if a reasonable argument can be made that “Not everyone needs algebra”, then mandating algebra for everyone seems likely to create as many problems as it attempts to solve.

Categories: Teaching


Hao · October 22, 2014 at 11:57 am

I agree that “not everyone needs algebra”, but at the same time I also believe that “most people can benefit from knowing some basic algebra”. There are some generally useful problem-solving principles in an Algebra 1 course that could be emphasized a bit more (i.e., manipulating the problem from the goal to constrain the possible solutions), but thinking about it a bit more, probably it is not necessary to require mastery of quadratic equations – linear equations show up fairly often in everyday life (scaling quantities up and down, comments captcha here, etc.), but I don’t think I’ve ever had to apply the quadratic equation outside of math courses. Instead, it might be useful to focus more on general principles (e.g., fundamental theorem of algebra, computer methods for finding solutions), so that students have enough context to be able to search the internet for appropriate methods when dealing with new problems.

    MrHonner · October 22, 2014 at 5:14 pm

    You are advocating for a reasonable, flexible, but vague approach. The questions that the Common Core initiative force us to answer are very specific. For instance, must everyone learn to “Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines” (CCSS.MATH.CONTENT.HSA.SSE.B.3.B)?

      Hao · October 23, 2014 at 10:23 pm

      Yeah, I guess I was vague. I’m not really sure what should or should not be included on something like common core. Personally, I just feel like it is that important to require students to be able to accomplish a specific task like “complete the square”. I don’t think anyone actually uses something like that in practice, so I’m not sure what mastery of it demonstrates other than the implicit “has mastered completing the square”.

      I do think there is potential to teach the more general lesson of transforming a problem into a form with a known solution, but it’s not clear to me how to test something like that. I think there is also the possibility of turning away students who might otherwise like math by giving them the impression that it’s simply a bunch of procedures for solving very specific kinds of problems. (and in the case of completing the square, a method that can simply be generalized into the quadratic formula)

Kenneth Tilton · October 22, 2014 at 12:03 pm

“How can mandatory algebra in high school be reconciled with optional algebra in college?”

Oooh! Oooh! *raises hand* The whole idea of Common Core is to fix the fact that colleges are being forced to back off it as a requirement. So in X years after CC works its wonders colleges will be able to start requiring algebra again.

No, I do not think it will work.

Some students try five times to pass Algebra at the college level before giving up, and from what I can see of CC nothing is going to change that. If anything they will lose more students with their focus on deep understanding (great for the apt students, tough on others who do better if just allowed to learn the procedures).

btw, I am headed for the annual AMATYC conference next month where they will vote on a position paper favoring dropping the algebra requirement for non-STEM majors.

First Latin, now Algebra…

    MrHonner · October 22, 2014 at 5:48 pm

    I’m not sure that’s the “whole idea” of Common Core, but I’m sure that’s how it’s been promoted to college instructors.

    I spoke at the most recent NYSMATC conference and was a bit surprised at how comfortable attendees were with the notion that Common Core would substantially address the remediation issue. Those I spoke with, however, were not very familiar with the pre-CCSS standards in New York.

Dave Marain · October 22, 2014 at 12:38 pm

First of all requiring an in-depth conceptual understanding of algebra for all students shows complete insensitivity to special needs students and their longsuffering teachers and parents. Sure just modify the curriculum for them. Go ahead. Show me exactly what that looks like and those who are pontificating the loudest come with me on the front lines of these classrooms and put your money where your mouth us.

Now for the rest…
Students should be expected to struggle much more than has been required of them for the past 3 decades. I’ve supported Common Core long before that name was coined because I believed not having uniform standards across the states was unethical and promotes inequalities for our children. That belief is unwavering. However I’ve never believed all children should be subjected to a deluge of high-stakes assessments from the age of 8 or 9. Particularly when it takes 5-10 years for any new curriculum to “set”. Particularly when teachers need extensive preservice and in service training. Particularly when full released versions of these assessments have not yet been made public.

The rush to assess is purely politically driven and our leaders should be ashamed of themselves. In the name of accountability our children are needless guinea pigs. That us unconscionable. Sone of our best teachers are frustrated to the point that they might walk away from the profession they love. And that would be a real tragedy. The efficacy of the Core is dependent on our classroom leaders. If we lose the best of the best, we will all lose. Wake up before it’s too late. Sadly that time may have passed…

    MrHonner · October 22, 2014 at 5:56 pm

    I agree with many of the complaints you make here. Most people who support the standards categorize these kinds of complaints as implementation issues, in an attempt to separate them from the standards themselves. Personally, I find it difficult to untangle these issues enough to evaluate them independently.

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