Why “Algebra” should be a dirty word

(I’ll warn you from the outset that this is one of my big personal crusades. It’s also been a shift in thinking for me over the past few years, so if I revisit this topic in a few months, I’ll probably say something different.)

(Also, I’ll preemptively warn you that I’m gonna go way overboard on parenthetical asides, even more so than usual. Enough preamble.)

Quick!

Name every English course you took in high school.

Name every Math course you took in high school.

(I’d suggest you do the same for your college career, but I imagine the example is much less illustrative because of differences due to major requirements, distribution requirements, etc.)

Unless your high school went the entirely uncreative route of naming English courses by year (English 9, Sophomore English, or something like that), I don’t know that I’d be able to guess what you said about your English courses.

But math? I’d be willing to bet that you took a course called Geometry and at least one (probably two) titled Algebra – Algebra 1 and/or Algebra 2 or some variation upon the same. Why are math courses so uniform? Are math teachers and program coordinators just that uncreative? Goodness no! We are just either lazy or unnaturally beholden to tradition. We cling to Algebra and to Geometry as the key anchors of high school math. And those remain critical areas to develop. But they are two of the five (six if you include the Modeling theme) conceptual categories within CCSS. And I would even argue that way are not the two most critical when it comes either to future mathematical work or the most relevant career-readiness applications.

To make matters worse, for a good two decades, if not longer, we’ve been touting Algebra Readiness as a key indicator for student success in K-5 mathematics. But what is Algebra Readiness? Why is Algebra the goal? It seems to me that “Algebra Readiness” has long been a proxy for higher-order reasoning. Success in Algebra 1 is something administrators look towards as a measure of math growth. Putting aside for a moment that, even with the same standards to guide us, different teachers and different districts and different programs may have different conceptions of what Algebra is.

Some of the biggest outcry in reaction to the rollout of the CCSSM was that the standards had “moved Algebra 1 out of the middle school.” First of all, Algebra 1 is a social construct. What the standards had done is made more rigorous the foundations of what is now high school algebra. The shifts in the standards have made high school Algebra 1 a more rigorous course than it was before. What I learned as Algebra 1 is still very much in the middle school curriculum, it’s just that administrators can’t get away with claiming their students are above-level by labeling a middle school course with what has been generally accepted as a high school course name.

(The real driving force behind wanting to push Algebra 1 into the middle school may be a desire to offer AP Calculus in high school, which is tricky if we are locked into the mindset of Algebra 1 – Geometry – Algebra 2 – PreCalculus – Calculus, but shoehorning Calculus into high school and increasing rates of AP participation has merely led to substandard Calculus instruction in high school and a majority of high school “Calculus” students being forced to retake calculus in college, potentially discouraging otherwise prospective STEM majors from persisting, but that’s a topic for much deeper research. And who’s to say that calculus should be the goal in the first place? But again, I’m getting well ahead of myself. Another time.)

Algebra is a stepping stone on the route towards Calculus and rigorous development of mathematics, which is not inherently part of college and career readiness. CCR is a much broader goal than the traditional pre-engineering pathway, but the standards are still too constrained by past traditions.

Interestingly (back on the topic of Geometry for a minute; I’ll dig deeper into this another time) the common core standards represent a major departure in Geometric teaching from the traditions of the last couple of thousand years, wit a move from a regurgitation of Euclid to a transformation-based approach. Algebra in the common core, however, is not a tremendous departure from what’s found in “First Book in Algebra,” a 1920 I found kicking around the office.

Now don’t get me wrong. Algebra is a key skill. Algebraic reasoning is something we need to instill in our students. Success in high-school math courses, especially first courses, as Algebra 1 often is. But we don’t need to dedicate half of high school math instructional time to Algebra any more. It goes beyond a cosmetic issue. We need to do more than rename these courses – we need to rethink the structure and nature of high school math. We need to re-purpose high school math to serve 21st century students and their learning needs.

Unfortunately, the CCSSM Appendix A has become something of a bible outlining what high school courses should look like, and the dominant model in Appendix A is an Algebra 1 – Geometry – Algebra 2 pathway. Since PARCC and Smarter Balanced have followed that lead, we may be stuck with Algebra for now. Maybe the Integrated pathway will catch on. Maybe some other innovative pathways will gain traction as more and more districts experiment with their curricula. But hopefully sooner or later, Appendix A will fall out of favor as the proof of concept it was intended to be rather than the be-all-and-end-all it has turned into.

 

There is no such thing as Common Core Mathematics

As it stands today, I think the biggest failure of the Common Core standards in general has been around the public messaging around the standards. The public dialogue around Common Core has been shaped by its opponents and detractors, which may have been inevitable given the decentralized nature of education policy in this country. Nowhere has this been more evident than on social media, the technology era’s iteration of talk radio, serving as an echo chamber where every voice can be heard (which is good), but every voice is given equal volume (which can be not so good). Facebook, Twitter and the like serve as echo chambers that seem to have served only to entrench people into their prior opinions, and, as there is no central force behind positive messaging on behalf of the Common Core standards, the discussion is dominated by those who find fault with the standards, due, in large part, to a misunderstanding of what the standards are.

In college, I had the pleasure of seeing Stephen Jay Gould speak on evolution. For a bit of context, he was giving a general talk open to all students at a small liberal arts college in New England. At the close of the talk, Gould was asked something along the lines of “What do you say to those who don’t believe in evolution?” His response has stuck with me some fifteen years, and while I may not remember it word-for-word, the gist of it was “What do you mean you don’t believe in evolution, that’s like saying you don’t believe in breathing. Evolution is a fact.” I bring this up because my attitude to Common Core detractors is much the same.

When parents say that they don’t want their children to learn the Common Core Standards, my first reaction is much along the lines of Gould’s. To say that you don’t want your child to learn the Common Core is to say that you don’t want your child to read literature, to learn to count, add and multiply, to communicate through writing and speaking, and to make sense of problems and persevere in solving them. Standards are still a relatively new thing in this country. The parents and politicians who are up in arms over the standards often fundamentally misunderstand what the standards are. They are not an agenda, but an educational promise of what teachers dedicate their careers to deliver upon. Many – or I dare say most – parents today went through school before standards took hold. The Common Core Standards are the first time that standards have hit the radar for the general population at the national level, so now is the time for education leaders to make clear what standards are and why they are key to guiding student learning. The research behind the standards movement is strong, but very much unknown outside the academic and educational fields.

There is no such thing as Common Core Math. The Common Core is not New Math – it is nothing like New Math – but my impression is that most parents, politicians and, sadly, even some teachers see it as this generation’s New Math. Where New Math sought to expand the scope of students’ exposure to math, the Common Core standards do not represent a major change to what students need to learn as compared to past standards. (There may be a few new concepts brought into the fold, but if anything, the Common Core has trimmed out some of the fat from the traditional school math curriculum. But that’s a topic for another day.) The Common Core standards serve to drive students to a deeper and more coherent understanding of essential math understandings.

The big problem on this front has been the way that textbook publishers have sought to address the Common Core standards. Within months of the standards’ publication, there were textbooks claiming to be Common Core aligned. It took a while for a wave of textbooks that have been genuinely built from the Common Core standards and progressions, but even those textbooks are rarely without their faults. So many of the standards in the elementary grades focus on getting students to construct meaning of the mathematics they are working on. The standards seek to have students develop strategies, often mental strategies, to add and subtract, and later multiply and divide, yet some textbooks try to train students to reach those mental strategies and understandings through rote practice and direct instruction. These are best accessed through instructional techniques that textbooks can rarely capture. The problem is not the Common Core standards themselves, but with how some authors have tried to shoehorn the standards into their texts’ instructional frameworks. (Again, a topic for another day, but textbooks are just as guilty of holding on to vestigial content that has long since outlived its usefulness, but this is also a small concern I have with the secondary Common Core standards.)

Common Core Math is just math. It has a different focus from prior school mathematics. It promotes deeper understanding of mathematics. It prepares students better for advanced work in STEM fields than prior programs of standards. It is a first step towards mitigating the mile-wide and inch-deep approach to mathematics expectations in the US, but increasing the rigor of those expectations is only the first step towards transforming math education. Better preparation of teachers, better instructional materials and a better focus on measurement of learning aside from high-stakes assessment are the missing pieces that will help the Common Core standards deliver on their promise, but the standards themselves need a few more champions to promote their upside and potential.

In the beginning …

First things first —

I am a big fan of the Common Core State Standards in Mathematics, both in principle and execution. The movement towards standards has finally matured to a point that the CCSSM represent a strong, workable foundation for K–12 mathematics, and, while the apparatus to successfully deliver on the standards for our students’ success is still in a formative stage, the standards themselves serve as a starting point.

Note that my viewpoint is particular to the Standards themselves, irrespective of the politics behind their creation and adoption, and likewise separate from the high-stakes, technology-driven assessments attached to them in most, if not all, states. I’ll speak to my views on those issues as they arise.

(My opinion on the CCSS in ELA is much less informed, but I expect to have more to say as I start to dig in a bit more.)

With all that preamble out of the way, what’s the point of this blog in the first place? More than anything else, it’s a place for me to collect my ever-fleeting thoughts on the standards. Beyond that, I hope it will begin to serve as a platform for further discussion and reflection on the standards and on my random thoughts.

A little background on me can be found on the About Me link. I promise to be opinionated and I hope to be at least mildly controversial. My thoughts on the standards are my own and not those of the schools or districts I work in or have worked in, though my particular experience is bound to be somewhat implicit in my views.

While I reserve the right to moderate comments that are abusive or do not otherwise contribute to the discussion, I do not intend to censor others’ viewpoints or opinions.

I welcome your questions and constructive feedback and I look forward to the discussion.