California has new ideas about how to teach math, but critics argue it won't work
California has new guidelines for teaching math in public schools. The guidelines propose things like delaying algebra until the 9th grade. And offering classes like data science instead of advancing students toward calculus.
Critics say the math guidelines are flawed to the core.
But America does have a math problem. National student achievement scores are lagging far behind other peer nations.
Today, On Point: How to teach math better.
Brian Conrad, professor of mathematics and the director of undergraduate studies in mathematics at Stanford University. Author of a recent article in The Atlantic, called “California’s Math Misadventure Is About to Go National.”
Adrian Mims, CEO and founder of The Calculus Project.
Rori Abernethy, seventh grade math teacher at James Denman Middle School in San Francisco.
Phil Daro, lead author on the Common Core mathematics standards and consultant with school districts, states and higher education institutions to improve the teaching of mathematics.
MEGHNA CHAKRABARTI: Okay, say you’re given a rudimentary map on a piece of paper, a really simple one, more of a diagram really, and it shows two towns. And lines in between those towns connecting them. So obviously those lines represent roads, and on each road there’s a number, and that number, it means the number of miles on that particular road segment.
Okay, so on this diagram, as you’re looking at it, excuse me, there are several different ways to get from Town A to Town B. And you’re asked, which way is the shortest?
Alright, so map two towns, bunch of lines connecting them. You know how long each line is. Which way is the shortest between Town A and Town B?
Do you think you could answer that question correctly? Honestly, I would actually love to give this problem to you in reality, but I’ll admit it’s a pretty visual problem, right? It would help a lot to actually have the map in front of you. So I’ll just have to trust your answer about whether you could get a problem like that correct or not.
I’m going to guess that most of you said yes, you could answer this, and I really hope that’s true. Because, let’s be honest, it’s a fairly straightforward and easy problem. But the real problem is that large numbers of American 8th graders can’t answer that question correctly.
When they try, they get it wrong. Because that map question, it’s one that I took from a sample of the most recent national assessment of educational progress. It’s the gold standard federal exam given to American students every couple of years. So that problem comes directly from their website. It’s a sample problem for 8th graders.
And this summer, the federal government released test scores from the NAEP, as it’s called, and it revealed that math scores for American 13-year-olds dipped significantly since 2019. Of course, pandemic interruptions to in person schooling had a lot to do with that. But if you take a broader look, there has been a stubborn plateau in math scores for American kids for more than 20 years.
Put another way, the test scores released this summer were the lowest in decades, but the highs were not that much higher. In other words, American kids are not getting better at math. And when compared to peer nations, the United States scores lower than average on math achievement than any other nations in the OECD, or the Organization for Economic Cooperation and Development.
This is one of the reasons why the state, with the largest public-school enrollment in the country, has spent years revising its mathematics framework. In July, California finally adopted its new statewide framework after years of development and controversy. And by the way, the state of California scores in the bottom third of states on that national math assessment.
So earlier drafts of California’s framework sought to reduce math achievement gaps by, quote, “dismantling racism in mathematics instruction,” by, quote, “having teachers develop students’ sociopolitical consciousness.” Early drafts also asserted that students at different levels should be kept together in math classes because differentiated instruction causes, quote, “student fragility and racial animosity.”
Now, that was the controversial part, and much of the language has been removed. But the final adopted framework still contains some very bold changes in how math is proposed to be taught in California’s schools. So we’re going to talk about those changes today, because the question is, will they make math instruction better?
And given California’s size, other states are definitely paying attention. So overall, what is at stake for all American schoolchildren if this nation does not get better at teaching such a fundamental skill. In order to have that conversation, Brian Conrad is joining us. He’s the director of Undergraduate Studies in Mathematics at Stanford University and author of a recent article that appeared in The Atlantic titled “California’s Math Misadventure Is About to Go National.”
Professor Conrad, welcome to you.
BRIAN CONRAD: Glad to be here. Also with us is Dr. Adrian Mims. He’s CEO and founder of The Calculus Project. It’s an organization that seeks to increase the number of Black, Hispanic, and low-income students enrolled in Calculus Honors, AP Calculus, and AP Statistics. Dr. Mims, pleasure to have you here today.
ADRIAN MIMS: Great to be here. Thanks for having me.
CHAKRABARTI: Okay Brian Conrad, let me start with you. The California framework, as you wrote in The Atlantic, is a thousand pages long, right? So certainly, it has to have some good stuff in it, which we’ll talk about in a minute. But overall, do you think it’s a meaningful improvement from those earlier drafts, which I quoted bits from?
CONRAD: It certainly removed quite a few of the concerning parts from the earlier versions, but other concerning features remain.
CHAKRABARTI: Such as?
CONRAD: Such as, it plays both sides of the fence on the issue of 8th grade Algebra 1. Some parts, it says it has value, other parts it advocates against it. And it plays both sides of the fence about advocating that students may take data science classes instead of Algebra 2, for example.
CHAKRABARTI: Okay. Tell me about why you think the importance of when a student can take Algebra 1. Why is that so important?
CONRAD: If a student wants to be prepared for quantitative degrees at college and to be admitted to perhaps more selective universities, either way, they need to be ready to learn calculus in college.
And for some students, if they can learn calculus in high school, it opens up more opportunities, summer internships and so on earlier in college, other course options and so forth. So to have more students be ready to access greater quantitative opportunities while they’re in college, access to calculus in high school is very valuable.
And to reach that without having to double up or compress classes, you need Algebra 1 in eighth grade.
CHAKRABARTI: Okay. Adrian Mims, tell me more about that. You’ve dedicated your professional life to helping kids who might be typically seen as not being the high achievers, to show that they can be those high achievers.
Tell me about your view of Algebra 1, 8th grade, 9th grade.
MIMS: We work on making sure that students are taking algebra in the eighth grade, because if they’re taking algebra in the eighth grade, they’re on a trajectory to taking calculus their senior year, and I totally agree with Dr. Conrad. And when I worked in Orange County public schools, which is Orlando, Florida we launched The Calculus Project there and they wanted seventh graders to take algebra.
And so that was our goal there, because the superintendent at the time, Dr. Barbara Jenkins, wanted students to take AP Calc BC, and so that was very audacious and very ambitious, and it was tough the first year, but we have really good data when we started focusing on algebra in the seventh grade, so it can be done. But it really takes a lot of training, preparation, a lot of support of the teachers, and you definitely need to involve the parents.
CHAKRABARTI: Okay, I want to talk in a few minutes about that support and preparation that’s at the heart of The Calculus Project, but Brian Conrad, okay, so for the both of you, mathematics instructions expert, say that children should have the option or the ability to take Algebra 1 in 8th grade, point taken.
The data science class, what’s the problem with that?
CONRAD: So data science, so first of all, I should say, so data science is a kind of hybrid of topics from math, statistics, and computer science. And of course, it opens up many great career opportunities. And I don’t have any concerns with the existence of such classes.
The big concern, which has been shared in an open letter signed by more than 425 quantitative experts across many fields in California colleges and universities, is that there’s this idea going around. That if you don’t take Algebra 2 in high school, and instead you take one of these data science classes, the most popular of which tend to have very light math content, that you’re still on the trajectory for many options in college.
And the true paradox and the irony of the whole thing is that data science relies crucially on calculus. So telling somebody to take data science and not Algebra 2, which is what part of the CMF does advocate, and has been popping up in other places, will actually be an off ramp from any realistic aspect access to such degrees in college. And the high paying careers that follow from that.
CHAKRABARTI: But tell me more about that I’m not quite sure I get why that would be the off ramp.
CONRAD: Okay. So the point is that although it is true that calculus was invented by Newton to solve problems in physics. It’s really the mathematics of optimization. And problems and data science, artificial intelligence and so on involve solving optimization problems, minimizing error and so forth in large numbers of variables.
And so to do that, you need to have the mathematical skills associated with calculus, and that requires learning Algebra 2 in high school. If you’re going to get the relevant math background by early college, which you need to complete that four-year degree, we want a four-year college degree in data science to be worth more than a Google analytics certificate, for example, in terms of job security and salary.
And so you need that Algebra 2 skill from high school. If you take data science as an elective, like high school economics. No problem, but it’s been advocated in various places that this is a more equitable course, or it’s more engaging, as if usual math can’t be taught in an engaging way, which of course is not true. And as I said, it sends out this messaging that it’s somehow more relevant.
It’s absolutely the case that a lot of math content in the high schools may be taught in a way that doesn’t show the contemporary relevance, but that’s because the teachers haven’t been given material with which they can show students, like trigonometry shows up in video game design or certain parts of algebra under like cryptography and so forth.
And if they just gave them that kind of material, then students could see the value in the usual content, which remains the foundation for all quantitative work at the college level, data science included.
CHAKRABARTI: Okay. Adrian Mims, we have just a minute until our first break. We can talk about the data science angle more. But what I want to hear just at least the beginnings of your thoughts on, when I read those NAEP scores, they were for 8th graders. So we were talking about students who were already struggling even before they’re thinking about taking algebra, geometry, trig, or calculus. Could you just briefly describe in a few seconds, what you think the core problem is and how we teach math in this country.
I’ll let you answer more when we come back, but I wanted to let you start here for a second.
MIMS: (LAUGHS) Wow. That’s a big, long answer. I’ll make it very succinct. I think it’s bigger than just looking at curriculum alone. We have to look at teacher training, teacher preparation, and make sure that teachers are ready to go into the classroom and work collaboratively with students and their parents. And I’ll add more later.
This article was originally published on WBUR.org.
Copyright 2023 NPR. To see more, visit https://www.npr.org.