CA’s misguided Algebra I policy, or “Here we go again”

Recently the California State Board of Education, egged on by the Governator and business bigwigs, decided to require that, starting in three years, all CA 8th graders shall take Algebra I, regardless of their state of prior mathematical knowledge, understanding, or ability. The move was in response to a NCLB-related demand from the US Dept. of Ed to align CA’s 8th testing practices with their curriculum standards. More info can be found here. In this post, I discuss rationales given in favor of the policy, arguments made against it, and my own reasons why I think it is both morally wrong and likely to prove to be a big fat mistake extremely misguided.

A few weeks ago Education Week hosted a “chat” regarding the policy; all quotes given below are taken from this chat. The chat can be accessed here; you’ll have to register, but if you carefully uncheck certain boxes in the process, they won’t burden you with unwanted emails. There were three participants in the chat, responding to pre-screened questions submitted by others. The participants were a representative of business interests from the California Foundation for Commerce and Education (which on its web site claims, interestingly, “The Foundation is strictly non-partisan and non-political, and takes no positions on pending legislation, ballot measures or other policy proposals.”); a senior policy analyst at the Education Commission of the States (which also has strong ties to business in general, and ed-related business in particular); and a member of the Association of California School Administrators. Below, I shall ID the first two of them as “Business guy” and “Policy wonk” respectively.

BACKGROUND INFORMATION

A few numbers to keep in mind, gleaned from the table at the bottom of this report (I took their numbers and did some math to arrive at my numbers):

First we’ll assume that pretty much all CA students take Alg I either during their 8th grade or their 9th grade year. In 2004, only around 24% of them passed the test by NCLB standards (which means gaining a “proficient” or “advanced” score) the first time they attempted Algebra; in 2007, this may have increased slightly, to around 26-27%. Of the students who were 8th graders in 2004, somewhere in the neighborhood of 68,000 (about 14%) of them still had not passed the test by the end of the 11th grade. (All my numbers are only crude estimates because I didn’t start with raw data, and because I can’t even estimate such things as student attrition from year to year, or the number of 9th graders who were repeating algebra rather than taking it for the first time.)

Thus, based on our history, we can estimate that when this policy goes into effect perhaps 25% of California’s students will pass the Algebra I test their first time around (in the 8th grade), 10-15% may never pass it but will stay in school to the bitter end, 50-60% will pass it after multiple attempts, and an unknown number will drop out because they can’t pass it (or believe they can’t or get sick of trying). Hopefully the results will be a bit better than this–but it’s not likely they’ll be hugely better.

Two more pieces of background: First, in California, we are legally required to teach all students “at grade level”, as defined by the state’s curriculum standards. This verges on making it illegal to remediate those who are below grade level; schools, and teachers, do get around this in order to teach students appropriately, but it ain’t easy, and isn’t always particularly successful, in part because they have to work against the system to try to provide students what they need.

Second, 9th grade classes tend to be reasonably-sized because some years ago CA started trying to reduce class sizes, starting with K-2 and 9th grades. However, 8th grade classes tend to be between 35-50 students in many districts. And it will be in those large 8th grade classes that students will all be getting their aglebra, ready or not, unless someone notices that this doesn’t make sense and changes the policy–and provides the funding necessary.

OK, enough background. On to the arguments pro and con.

There seem to be three arguments proferred in favor of the policy: an economic argument (“CA needs more workers with college degrees, CA needs more workers with math skills”); an “equity” argument (“all students should be treated the same; all students need to be aware of what it takes to get into college; students who enter college having taken math beyond Alg II do better in college”); and a “math is just good for you” argument.

The arguments against the policy all appeal to reality in some way, having to do with available resources, unfavorable impacts on other aspects of students’ education, and unfavorable impacts on students who do not succeed in 8th grade algebra.

I will address each of these arguments in turn, using quotes from the Ed Week chat as a springboard.

ARGUMENTS IN FAVOR OF THE POLICY

The economic rationale

Business guy:

We will need highly educated workers throughout the state’s economy. The shift toward service-related industries from manufacturing will increase demand for college-educated workers. Over 40 percent of workers today in the fast-growing services industry have a college degree (a bachelor’s or higher graduate degree). In manufacturing, the share of workers with a college degree is 28 percent. In nearly all major industries the share of workers with a college degree has increased over the past decade. If this trend continues, employment projections suggest that the share of workers with a college degree would need to increase from 30 percent in 2000 to 39 percent in 2020.

The argument seems to be that we need a larger minority of college-educated workers, so everyone should have to take algebra I in the 8th grade.

A couple of things: is everyone with a college degree actually using that degree in their line of work? Probably not. So these facts don’t even clearly establish what the economic need really is for college educated workers, let alone for workers to know more math.

But let’s grant that we need more people with more math knowledge in our increasingly technical economy. Let’s even assume that what we need will be, say, 75% with college degrees, and 40% with significant expertise in math and science. How does this justify “algebra for all”, let alone “algebra for all in the 8th grade”? Clearly, it doesn’t, as a stand-alone argument. So enters

The “equity” rationale:

In brief, this argument amounts to “more students are likely to go to college, and more likely to be successful once there, if they take algebra I in the 8th grade”. Implicit in this argument is that a college degree opens up opportunities for people, that it’s an important way to “move up” socioeconomically. Let’s consider some specifics.

Policy wonk

[Taking Algebra I in 8th grade] allow[s] students to reach the trigonometry, precalculus, calculus that Cliff Adelman’s research indicates a student is significantly more likely to finish high school, enter a four-year institution, and complete a bachelor’s degree within a reasonable amount of time. And the ACT “college readiness benchmark” also notes that students whose high school math coursetaking culminates above Algebra II are much more likely to be ready for College Algebra than those whose coursetaking ends with Algebra II.

Taking more advanced math–and taking math the last two years of high school–will reduce the odds that poor performance on math placement exams will force students to spend precious tuition dollars (and time to degree) on non-credit-bearing courses once they enter college.

Waiting until 9th grade to take algebra reduces the odds that students will complete much coursework beyond Algebra II.

Students who complete Algebra I–as 8th graders or 9th graders–are more likely to complete higher-level math coursework in high school. Students who are in pre-Algebra I in grade 9 may make it to Algebra I, geometry, and Algebra II (course sequence required for admissions to many four-year postsecondary institutions) by the end of grade 12 but then again, may either decide to take their senior year off from math, or may not receive clear messages from their teachers, parents, counselors, others that this is the high school course sequence required by many four-year institutions. The Bridge Project research (Stanford University) makes clear that students who are in college prep/honors tracks get much clearer messages about courses required for college admissions than non-honors track students.

And see also the Adelman and ACT research on the math courses that put students on a trajectory for college success. It’s only after Algebra II that math coursetaking makes a significant impact.

So what research supports is the following: If you take Algebra I in 8th grade and are successful at it, and continue taking more math courses and continue to be successful at them, you are more likely to 1) be properly informed as to the math required for entering college, 2) more likely to enter college, and 3) more likely to be successful in college. All of these desirable outcomes depend on the student both being successful in the first place, and continuing to take math and succeeding in it in the second place.

How this supports forcing everyone into algebra in the 8th grade, regardless of the state of their math knowledge, is beyond me. At best, they’re playing a numbers game: by forcing everyone to take algebra in 8th grade, among those who would otherwise wait until 9th grade to take it, or who would avoid it altogether given the choice, some will succeed, and will go on to do more math and enter college and be successful. Among these, some of them would not have gone to college, or been as successful in college, without the math. So there is some (unknown, but probably small) number of people who will benefit from this policy, and this is taken to justify blindly imposing 8th grade algebra on everyone.

The argument that some will succeed and go on to college who otherwise would not is taken to be an equity argument because historically, and currently, there are significant differences among different demographic groups in regard to math achievement and college entry and completion. Therefore, presumably, if we improve (some number of) students’ success, it will inevitably reduce the demographic gaps.

One problem with this line of reasoning is the numbers: we have no reason to believe that enough students will be positively influenced to significantly reduce the gaps between demographic groups. Another is that it ignores what happens to students who aren’t successful in 8th grade algebra, and the possibility/liklihood that these students will be disproportionately female, black, Hispanic, from poor families, etc. It’s not at all impossible that the policy will increase the inequities, not reduce them. Hence my quotes around “equity” above; the claimed intent is to increase equity, but the refusal to address the realistic probability of widespread negative consequences leads me to believe it’s a specious and cynical argument, and that all the proponents really care about is that the numbers game described above will provide the workers business wants.

You may have noticed that even ceding the “equity”, or perhaps I should say the “college prep”, argument, we still don’t have an adequate rationale for why everyone should take algebra at all, let alone in the 8th grade. After all, no one is claiming everyone will, or even that everyone should, go to college, only that the numbers will and should increase. Further, a lot of college-educated people never need or use algebra vocationally. Thus enters the

“Algebra is good for you” rationale

Business guy

Algebra is about problem solving and critical thinking. Let’s be clear: I’ve never used the quadratic equation in my career as a public policy professional, but learning algebra was probably the first time that I was subjected to disciplined, critical analysis of a problem, and forced to systematically apply rules to solving that problem. This is a gateway to critical thinking, pivotal for success – not only in science and technology and engineering – but in any field that requires disciplined approach to getting the job done. Which is to say, any field that is high skilled and high reward.

Why algebra? Not because – like you or me – they’re going to be solving quadratic equations in their daily life. But because algebra is a gateway to critical thinking, pivotal for success not just in science, engineering and technology, but also because it provides the discipline – maybe the first time in a child’s education – for using rules, critical thinking and analysis to solve problems. It’s the learning process and the skills, not the slope or y-intercept that’s important.

There are several things wrong with this argument.

1) It’s based on the belief that the thinking skills developed in algebra will transfer into other contexts. The research we have on this uniformly indicates that this kind of transfer only happens for the majority of people if it is explicitly taught for–it does not happen spontaneously except for a rather small minority of people. Traditional algebra curricula do not “teach for transfer”, quite the opposite.

2) It assumes that algebra actually teaches critical thinking and problem solving. However, what is tested is precisely rote recollection of algebra skills–factoring polynomials, solving 1 and 2-step linear equations, solving quadratic equations, finding the slope and y-intercept of linear functions, etc. Reasoning, critical thinking, concepts, and problem-solving are not well-represented on the test, and hence not well-represented in the curriculum students encounter. In many instances, what kids experience in math classes in general, and in algebra classes in particular, actually discourages problem solving and any form of independent or critical thinking. This has always been true, and the nature of the California curriculum standards, the tests themselves, and the pressures being put on the adults in the system, are exacerbating this tendency, not ameliorating it.

3) The argument is based on his own personal experience; he’s implicitly assuming that “If it worked for me, it will work for everyone.” I trust the fallacy in that is clear?

4) Again, even if everyone who learns algebra were to derive these general thinking-skills benefit–which is not the case, I repeat, but even if they did, this assumes basic success in learning the algebra in the first place. Which we know not everyone will. So we’re back to justifying a policy to be applied to all because it may be good for some, ignoring the harm it may do to the rest.

5) It’s disingenuous. If what you’re really after is thinking and problem-solving skills, and you want to get at that through math, and you want to do it through content most likely to directly benefit the vast majority of people, basic probability and statistics are a much better candidate for achieving those stated goals. But the real goal is to increase the number of people with the math and science skills to feed hi-tech industry (IMO), and the belief is that algebra for all 8th graders will do it (via the numbers game described above). The “algebra is good for you” argument is being invoked only to make the policy sound more reasonable, virtuous, and palatable.

6) It ignores pedagogical realities. If the first time a child encounters “the discipline . . . for using rules, critical thinking and analysis to solve problems” is in 8th grade–believe me, that child will not learn it in algebra class (at least, not the average algebra class). To avoid making this post the longest in the history of blogging, I’ll have to ask you to trust me on that one–but as math teacher and teacher of teachers for about the past 35 years, I know whereof I speak.

Time to turn to the

ARGUMENTS AGAINST THE POLICY

I can identify five types of arguments agains the policy, four of which are represented in the Ed Week chat, and one of which is my own. All of them appeal to reality in some way (one would think that reality-based thinking would would be a good thing, but apparently it just annoys the proponents of the new policy.) The five types of arguments are: 1) the availability of necessary resources for adequate implementation of the policy; 2) questioning the need or benefits of algebra-for-all; 3) anticipated negative impact on other valued and valuable aspects of education; 4) anticipated negative impact on large numbers of students; and 5) lack of a professional knowledge base adequate for teaching algebra to everyone.

First, resources. This has several parts to it. First, there aren’t enough qualified teachers in California to put a trained math teacher in every 8th grade algebra I classroom. We don’t even have enough trained math teachers for all the 8th grade algebra classes we have now, let alone for the thousands that will have to be added for the new policy. When a questioner raised this point, the Business Guy dismissed this argument with

Don’t get me started. First, if we have a “multitude of unqualified persons currently teaching algebra in 8th grade,” shouldn’t we, um, replace them? That won’t take much in the way of new resources.

To which I reply, “If we had the qualified teachers available, don’t you think we, um, would replace the unqualified ones?” That he assumes this could be readily done, and with minimal expenditure of resources, just demonstrates his ignorance. That he appears to assume this could be easily done, yet hasn’t been, is also insulting. Educators may not be, on average, the smartest people in the world–on average, we’re pretty average, about as smart as the rest of y’all out there–but we’re smart enough to figure out for ourselves that teachers should be qualified to teach their subjects. His flip dismissal simply doesn’t rise to the level of a meaningful response to a serious problem the system already faces that the new policy will only exacerbate.

The second resource-related issue is one acknowledged in the chat: if we are to have any hope of success in teaching algebra to 8th graders, improved teaching must begin long before students begin algebra. No one could make the argument with a straight face that the majority–let alone all–students are well-prepared to learn algebra by the 8th grade. The very tests that NCLB enthusiasts rely upon so heavily would disprove any such claim. This in turn means that the state will need to mount a huge professional development effort with K-7 teachers. Which in turn means a huge infusion of money, and we are in the midst of a budget crisis in this state. As I write, the state has yet to arrive at a budget for the coming year, but given the size of the deficit, cuts to education in general, and professional development programs in particular, are much more likely than any funding increases.

Finally, there is the issue of time (which I count as a resource–it’s often cited as the scarcest resource in education). Even if the $$$ came through to reduce 8th grade algebra classes in every school to reasonable numbers, to attract, train, and hire all the algebra teachers that will be required, and to help K-7 teachers understand how better to prepare students for algebra–three years is insufficient time to make the changes necessary for the policy to succeed. They are setting us–schools, teachers, students alike–up for failure with this time limit. How about a little intelligent scaling-up, a few benchmarks along the way? California is a huge state, and education is a huge and complex enterprise, which means there’s a lot of inertia in the system–not the inertia of stupidity, or unthinking resistance, or laziness (though you’ll find some of that in any human enterprise), but simply the inertia of sheer size and the time frame needed for people to figure out and implement new things. It all takes way more time than they have allowed for in this policy.

On to the second type of argument against the policy. Does everyone really need to know algebra? Highly doubtful. How many people actually use algebra once out of school? Only a minority, though perhaps a large minority–so why force everyone to learn it (even assuming we could get everyone to learn it?) Don’t get me wrong–when students ask “When am I ever gonna use this?”–which they do often–I point out to them that they don’t want to close doors of opportunity for themselves quite this early in their lives. I’m all for getting as many kids to learn algebra as possible, and for encouraging them to stick with it. But algebra is not something one uses in daily life–it is essentially a vocational skill, used in one’s job or pretty much not at all.

This argument is of course an argument against algebra-for-all in general, and as such branches out into a discussion of “Does everyone really need to go to college, and if so why and for what?” and “Does every college-educated person need to have some math at or above the level of algebra?”, which are beyond the scope of this post, so I’ll leave it an turn to the next type of argument oagainst the policy: anticipated negative impact on other valued and valuable aspects of education

There is little doubt that the policy will result in further erosion of other aspects of education: the arts, PE and health, technology courses, vocational courses, even core subjects such as science and history/social studies. We know this because it has already happened just based on the emphasis on reading and math already in the system. The “algebra for all 8th graders” will increase this erosion becasue of the simple fact that so many students are not, and will not be, ready for success in algebra, so additional time will be taken from the 6-hour school day to do more math with them. That’s already happening, too–a lot of 8th and 9th graders are doing math two or three hours every day in the attempt to increase test scores. That time has to come from somewhere, and it comes from the subjects listed above. This is not a good trend–and I say that as a math person, who likes and values math. We need well-rounded educational opportunities, both for the sake of developing well-rounded individuals, but also for the sake of having a well-rounded society. To say nothing of keeping all our future artists, professional athletes, plumbers, journalists, historians, clinical psychologists, etc. in school and give them the best possible shot at becoming artists, athletes, plumbers, journalists, historians, clinical psychologists, etc.

The fourth type of argument agains the policy is that there will be a negative impact on the lives of many students. If you look at our track record, we can predict with confidence that many students will never succeed in passing the test–what happens to them? Do we simply not care, as a society? And even for those who do pass, after repeated attempts–what is the likely impact on them? Some may learn more math, and learn to like math, and go on into math-related careers–but many will simply learn to hate math and become math-avoidant. Do we care about that? If this is a large proportion of students, that will obviate the various rationales for the policy, especially the equity and “math is good for you” arguments. Does that matter?

This is another argument that goes beyond the “algebra in 8th grade” policy to argue against the “algebra for all” policy. However, it can be brought to bear on the “algebra for 8th grade” policy by questioning whether in fact more students will go on to more advanced math by starting algebra in the 8th grade than under a policy based on measuring algebra readiness and having students take it only when they’ve reached some threshold of readiness. This is an empirical question, and we’ll see. But we’ll need more than anecdotes from people who were forced to take algebra in 8th grade and credit that fact with their going on to college and ultimate successful adulthood. We’ll also need to pay attention to stories of people who drop out of school becasue of algebra, or who simply come to hate math and avoid any occupation that requires it, as a result of being forced to take algebra in 8th grade. Will there be more of the former than the latter? The proponents of the policy are banking that the answer will be “yes” (and are OK with ignoring the negative stories). I, on the contrary, think it’s questionable that there will be more positive than negative stories, and I think the negative stories are as important as the positive ones.

Finally, there’s the argument I add to the above based on my expertise as a teacher of math teachers. We don’t in fact have a professional knowledge base adequate to teaching algebra to everyone, especially given the prevailing conditions of large classes of students with diverse math backgrounds (which may range from 3rd grade levels of understanding and skill to mathematically gifted students in the same class). We’ve never, as a society, tried to do this before; there seems to be a naive assumption out there that what has worked with successful math students in the past will work with everyone, given anough time and tutoring, but we have no actual basis for that belief, and good reasons to think it’s simply mistaken. We have cases of success with populations of students not usually successful at algebra (Bob Moses and The Algebra Project spring to mind), but these cases are not using the traditional methods enshrined in the typical algebra text or used in the typical algebra classroom. I believe down to my toes that the vast majority of human beings can learn math, and specifically algebra–way more than do now–but all the evidence indicates that this won’t happen just by doing more of the same. We have some good ideas about how to expand the number of people who “get” math, but no definitive answers for how to make sure everyone “gets” it. We don’t know how to “scale up” from those cases of proven success to widespread success. Nor is the current system hospitible to methods that are known to work with the kids who don’t “get” it using the traditional approach. I guess the policy folks think that if they set the goal, and beat up on us hard enough for failure, we’ll figure it out. But somehow, I don’t think that’s a very smart way of going about it.

As you can see, I think this policy is a terrible idea and will have more negative effects than positive. I think to impose such a policy in the mere hope that some people will as a result progress to college, in sufficent numbers to feed our need for hi-tech workers, and simply ignore the negative impact on others or on our education system as a whole, is immoral. I could go on and spell out what I think would be a good policy, one that would have good potential for achieving desirable outcomes while minimizing negative ones, but this post is already too long, so I’ll just stop here.