# Ep 25. Understanding math reform ideology with Tom Loveless

This transcript was created with speech-to-text software. It was reviewed before posting but may contain errors. Credit to Jazmin Boisclair.

You can listen to the episode here: Chalk & Talk Podcast.

Ep 25. Understanding math reform ideology with Tom Loveless

[00:00:00] Anna Stokke: Welcome to Chalk and Talk, a podcast about education and math. I'm Anna Stokke, a math professor, and your host.

You are listening to episode 25 of Chalk and Talk. My guest in this episode is Dr. Tom Loveless. Tom is an expert in education policy, and he knows a lot about the history of math education in North America. I wanted to have someone come on the show to talk about the origins of current math teaching philosophies, and Tom is the ideal person for that.

He even served on the National Math Advisory Panel. For those unfamiliar, The National Math Advisory Panel is akin to the National Reading Panel. It consisted of a group of experts commissioned by the U. S. government to summarize the best research available on how to teach math. Their 2008 report offered excellent concrete recommendations, but sadly, it doesn't seem to have had much of an impact on math education policy in the U. S. or Canada.

You can find a link to the report on the resource page. In the episode, Tom and I discussed that report, including its recommendations on conceptual understanding and procedural fluency. We discussed the history of the math wars, and whether some of the popular ideas about teaching math, like providing rich tasks, or teaching through open-ended problems, are really new ideas or not.

We talk about the influential 1989 NCTM standards, that stands for National Council of Teachers of Mathematics, and their global impact on math education. I asked Tom for his opinion on the California Math Framework and whether its recommendations are aligned with those in the National Math Advisory Panel report.

We also discussed the importance of memorizing math facts and a whole lot more. This episode is a must-listen for anyone who teaches math, as well as parents and policymakers. Now, without further ado, let's get started.

I am excited to be joined by Dr. Tom Loveless today. And he is joining me from California. He is an education researcher and former senior fellow at the Brookings Institution. He has a Ph.D. in Curriculum and Instruction with an emphasis on policy. Prior to getting his Ph.D., he was a classroom teacher. He was also a professor at Harvard University's College of John F. Kennedy School of Government, where he taught education policy courses.

He's an author of several books, he has written numerous educational policy documents, and he has written many articles for the public in publications such as Education Week. And he was a member of the National Math Advisory Panel, which we will hear more about today.

Welcome, Tom. Welcome to my podcast.

[00:03:10] Tom Loveless: Well, thank you for having me.

[00:03:12] Anna Stokke: So I just read your book, Between the State and the Schoolhouse: Understanding the Failure of Common Core. So, you know a lot about the history of education policy and the various math wars and how that's played out. I'd like to talk a bit about some of the history of math education in North America, reform math, the math wars, and how we got to where we are today.

So, we could go back to the 60s, or even further, but I think I'd like to start with 1989. So, there's an organization based out of the United States called the National Council of Teachers of Mathematics, or the NCTM. They've been highly influential on the direction of K-12 math education in the U. S., and that generally spills over to Canada, so here's why I'm starting with 1989.

[00:04:02] Tom Loveless: Think that's a good, place.

[00:04:04] Anna Stokke: In 1989, the NCTM launched a campaign to change the content and the teaching of mathematics. They published a document called "Curriculum and Evaluation Standards for School Mathematics." And my understanding is that that document was highly influential and perhaps the beginning of the math wars can be traced back to the reforms stipulated. in that document.

So these NCTM standards, they de-emphasized memorization of number facts and procedural skills, disparaged standard algorithms, and teaching by telling. They encouraged the use of calculators, even in primary school, and promoted discovery learning. You can correct me if I'm wrong on this or if I'm missing anything. So what prompted the NCTM to publish this document?

[00:04:52] Tom Loveless: Well, in the 1980s, there was another document that came out in the United States called A Nation at Risk, and that really catalyzed a reform movement throughout the United States, including a push for standards. And so along comes in CTM when people were beginning to clamour by the end of the decade for standards along comes in CTM and says, “We have some standards,” and they offered a complete revision of K through 12 mathematics, especially actually in primary grades and in early secondary grades, what we call middle school in the United States.

So that's basically where it came from.

[00:05:38] Anna Stokke: And so why did the NCTM standards disparage basic skills and standard algorithms and teaching by telling?

[00:05:49] Tom Loveless: Now we go back before 1989, that is a mainstay of progressive education. Progressive educators have complained about the teaching of mathematics for at least a century, goes back to the 1920s, and NCTM is a very progressive organization in terms of believing in progressive principles.

I'll just give you one little taste of it. The word arithmetic, which had been really the primary duty of elementary K through six teachers, the teaching of arithmetic, the word arithmetic almost wasn't even mentioned in the ‘89 NCTM standards. And when it was talked about by NCTM leaders, it was done so disparagingly.

Like for instance there's a speech that was given by an NCTM president. I think it was 1995, you can find it on the internet still, and arithmetic is referred to as shopkeeper arithmetic. And that term does two things. First of all, it says it's old-fashioned, you don't need to do that anymore, we have calculators and things that can do all that for us.

And so, this whole idea of something being out of fashion, not needed anymore, really was one of the major points of contention that later led to the math wars in the 1990s.

[00:07:17] Anna Stokke: What was the impact after they published this document? What happened?

[00:07:22] Tom Loveless: Well, one of the ways in which there was impact was in the National Assessment of Educational Progress, known as NAEP. It's also called the, referred to as the National Report Card in the United States. And NAEP gives a reading test and a math test. The NAEP math standards, the NAEP math framework, use the NCTM standards for the way in which it organized and presented mathematics for assessment.

And so, for example, there are five strands of learning that are recommended in the NCTM ‘89 standards, NAEP adopted all those five strands and NAEP reports five different scores and it also reports a composite score. So it was influential among policy leaders, especially leaders in Washington. The states, which have much more power over curriculum than the federal government of the United States, they use the NCTM standards as a template for the development of their own standards.

I mentioned that whole push for standards and accountability in the 1980s, well in the 1990s it actually started happening on the state level. You had states developing tests, holding schools accountable. And for the most part, they used, at least in the beginning of the 1990s, they used the NCTM standards as their kind of guiding light.

[00:08:54] Anna Stokke: So, first of all, these weren't really new ideas as you just kind of explained, like this sort of thing had been, you know, a mainstay, as you said, of progressive education for, many years. Now my understanding is that based on these NCTM standards, several programs were developed.

The one I kind of remember people always talking about was TERC. Does that ring a bell?

[00:09:17] Tom Loveless: Yes.

[00:09:17] Anna Stokke: Everyday math? Is that one?

[00:09:20] Tom Loveless: Everyday math is another one, yes. Everyday math came from the University of Chicago math project, and TERC came from Boston.

[00:09:28] Anna Stokke: So, my understanding is that there was public backlash. Parents were upset, they couldn't understand the math their kids were doing, kids probably weren't learning that well and there's a lot of criticism from mathematicians.

The programs were, often described by critics as “fuzzy math.” There were open letters at the time by prominent mathematicians, they were published and calling out the programs and, you know, and parent advocacy groups were formed. So, some people refer to this as the math wars, these differing perspectives.

So can you say a bit about that? Like what were the two sides of the math wars saying and how did things play out at that point?

[00:10:11] Tom Loveless: And by the way, the two sides that I'm going to mention, and they go by shorthanded terms of progressives on the one hand and then traditionalists on the other, like I said, they go back to the 1920s. They've been arguing about how to teach math and how to teach reading as well for at least a century.

And it continues today, actually, the argument between those two camps. The alliance between parents and mathematicians was really, truly different, though. That was unique, and that kind of bubbled up in the 1990s. You had a group of parents in California, they founded a website called “Mathematically Correct.”

And it was a terrific website that documented all of these grievances against the math programs and published some of the most, you know, the silly problems that kids were getting and, and that kind of thing. And mathematicians really formed an alliance with parents. And by mathematicians, I don't mean math educators.

Math educators are, they are in NCTM. but mathematicians, actual mathematicians, and math departments, they formed an alliance with parents and it became a very powerful alliance, at least in two states, California and Massachusetts, where the NCTM-backed standards were thrown out and discarded.

And then a group of mathematicians in California, there were four mathematicians from Stanford who were instrumental in developing a new set of standards. And the same thing happened in Massachusetts where a new set of standards was developed. And again, it was influenced very heavily by mathematicians in that state.

[00:12:02] Anna Stokke: A lot of the controversy you mentioned was in California and we're kind of seeing that again today, right? So, why California? Why does California often seem to be the center of these debates?

[00:12:16] Tom Loveless: I think it's historical. Historically, it goes back to the way education is structured in California, the way public education is structured. Historically in California, districts and schools have tremendous power except for curriculum. And things like standards and selecting textbooks.

California has had state-adopted textbooks. So the state actually says, here are the books that you use. And it used to be mandated. Now it's just suggestions, “Here are the books we recommend.” But, for a very long time, going back to the 19th century, shortly after California became a state in the 1850s, it adopted state textbook adoption. That became the law of the state.

So, California has always had a very important role for the state to play in curriculum. And that's not true in other states. In the state of Massachusetts, for example, districts decide They decide what they're going to use, with some state guidance, but it's only guidance and it can be rejected. In the state of Illinois, they even allow schools to select textbooks, separate textbooks.

You can have schools just a few miles apart that have different textbooks. So, each state in the United States differs in the state role. And in California, because it's been a state role to pick textbooks and by the way to assess students, the California assessment program started in the early 1970s, long before other states were doing much assessment.

All those things, because they're at the state level, are very political, they're debated, public hearings are held, and that's why these controversies often start in California.

[00:14:13] Anna Stokke: And I just want to mention too that those 1989 NCTM standards also impacted math curricula in Canada. And I've researched that shift. So here in Canada, we started to see the impact in the 90s. So de-emphasizing of times table memorization, more emphasis on multiple strategies, disparaging practice as drill and kill, and then in many provinces like mine, doubling down in around 2006 or so. So it certainly spilled into Canada and we still see the impact today, I think.

[00:14:49] Tom Loveless: Oh, yes. And it was worldwide. So, these reform movements, both the math reform movement and in the United States it was in CTM math. I just call it reform math, and it was a worldwide phenomenon. It happened in, in countries throughout Europe, it even happened in Asia where mathematics has a completely different, more revered status than it does in the United States.

So it happened worldwide.

[00:15:18] Anna Stokke: And I just want to read something from an article that you sent me that you wrote. This is a 1997 article, and it's a great article called "The Second Great Math Rebellion," October 15th, 1997. This is a quote from the article. “We've been through this before. In the 1960s, the curriculum known as the new math was rooted from classrooms by angry parents and teachers. Parents didn't recognize the mathematics that children were bringing home from school, and teachers found it almost impossible to instruct students on the strange new topics recommended by reformers.”

So, there's nothing new. This is, it's the same idea. And I think you would find articles today that said the same thing about the math that's being taught in schools today.

[00:16:07] Tom Loveless: Yes. I edited a book, it was published by Brookings in 2001 called The Great Curriculum Debate, and half the chapters were devoted to mathematics and half were devoted to reading. And it was about the 1990s arguments that went on over both of those subjects.

But I wrote the introductory chapter and I started with some quotes from John Dewey back in 1901. I think they, the quotes were from, and it was going on then. When I hear people complain about these huge debates or wars or whatever you want to call them, they went on a hundred years ago. They're going to, be going on a hundred years from now. These are long-time things.

[00:16:49] Anna Stokke: Definitely. And there's nothing new about teaching by open-ended problems and, rich tasks, discovery learning. They just bring it back under a new name.

[00:17:00] Tom Loveless: Yes.

[00:17:01] Anna Stokke: You mentioned 1997, the California State Board of Education adopted a new set of math standards, which were written with the help of four Stanford mathematicians.

So how did that happen?

[00:17:14] Tom Loveless: Well, the state of California didn't like the fact that when the first state NAEP scores came out, again, that's often referred to as the National Report Card, it's the first time that states were broken out before just a national score was reported or sometimes some regional scores, but California scored terribly in both math and reading on this NAEP assessment.

And the legislature got very concerned and appointed task groups to take a look at the standards and the curriculum in the state. There was a distrust of educational bureaucrats who might work in the State Department of Education to be in charge of the writing of new standards.

So they just, the State Board turned over this new project to these Stanford professors.

[00:18:08] Anna Stokke: Wow. that's got to be kind of unprecedented. Is that right?

[00:18:12] Tom Loveless: Yes, very unique.

[00:18:14] Anna Stokke: So what was the response? How did that play out? Did it go well?

[00:18:19] Tom Loveless: It's hard to say. I mean, there was a mixed response. The people who were rebelling in the 1990s, the parents and mathematicians, they were quite pleased. However, the whole progressive agenda in both math and in reading, and it spills over into science and social studies too, they have their own groups like this

Progressive educators are very influential. Most teachers are trained under those principles. And so I think the response of teachers in the classroom was, “Oh, we'll just cope with this,” and they didn't necessarily follow. I mean, I think standards are a very weak instrument to change what goes on in classrooms.

You really have to convince local educators, “Here's a better way of doing things, and we have evidence that kids will learn more if you do it this way, instead of the way you've been doing it.” And to use any kind of state policy as an instrument to change what schools do, it just doesn't work.

[00:19:29] Anna Stokke: I've actually looked at that set of standards from 1997. and I thought it was really great. I would be very happy if we had that, what I call a curriculum here in my province. But it sounds like maybe they didn't have buy-in necessarily from all the players like the teachers. Is that what you were saying?

[00:19:50] Tom Loveless: Yeah, I mean, you're not going to take people who believe in open-ended tasks, for example, or who believe in mathematical mindsets and suddenly get them to, “no, you should be” for example, “you should make kids memorize basic facts. That's a good idea.” They've been trained that's a bad idea. So to get to get teachers to see that that's a good idea or that learning standard algorithms to the point of automaticity where you don't have to stop and think, “Now, what do I do now,” that that's a good idea, well, they've been trained that that's not a good idea. So, it's hard to affect change that goes against what teachers are used to doing.

[00:20:41] Anna Stokke: How long were those, that set of standards from 1997, how long was that set of standards used?

[00:20:49] Tom Loveless: Until Common Core. Common Core was released in 2010.

[00:20:54] Anna Stokke: So, let's talk about the National Math Advisory Panel. That's another report that I've read very closely. So, can you discuss the National Math Advisory Panel, listeners might not know what it was, why it was established and what exactly it did.

So, can you tell us a little bit about that?

[00:21:14] Tom Loveless: Yeah, it was created by executive order of the president of the United States George W. Bush in 2006. And we, the panel immediately went to work. The panel, I think had 22 members, somewhere in that area. Immediately went to work and then released a report in 2008. The basic objective of the panel, and it was modelled after an earlier panel in reading, earlier in the decade, around 2001 there was a national reading panel.

The objective of the panel was to summarize the best research that we had. And by that, I mean, essentially, either experimental or quasi-experimental studies of how kids learn, what they should be learning in preparation for algebra. So, in other words, what they should be learning in K through seventh or eighth grade.

And then a definition also of “what is an algebra course?” What does a real algebra course, Algebra One course, what topics does it teach? So that was the, that was the basic thrust of the panel. We met for two years, all over the country, held public hearings and released the report in 2008.

[00:22:34] Anna Stokke: So, what were the qualifications of the people on that committee?

[00:22:38] Tom Loveless: Each brought different qualifications. I'm not a mathematician, nor am I a math educator. I'm a policy analyst, so that was kind of my role. There were cognitive psychologists on the committee, there were math educators, including the president of NCTM at the time, Skip Fennell.

That pretty much covered it. So, math educators, there were mathematicians on the panel, which a lot of panels historically have been dominated by math educators and have not included mathematicians and they really have different training and totally different views on mathematical topics.

And there was one classroom teacher on the panel also, Vern Williams.

[00:23:21] Anna Stokke: But the panel did, they collected a lot of opinions from teachers of algebra, though. Isn’t that right?

[00:23:28] Tom Loveless: Yes, I was the chair of that task force actually. So, and all the way along, I insisted that we do some kind of survey of algebra teachers. You know, we need to hear from the field. This is an algebra-focused project and we need to hear from the field of teachers about what are the obstacles they face. You know, and I think that was very enlightening, and especially for some of the weaknesses of the math reform movement I think it was enlightening.

For example, tracking and ability grouping has been disparaged for a very long time by progressive education educators. And, and yet, the algebra teachers identified as one of their biggest obstacles the vast array of abilities and preparation of their students that they face on day one.

It's very hard to teach linear equations at the same time you're teaching addition of two-digit numbers or subtraction with borrowing. This is just impossible. It can't be done. And so, teachers listed the heterogeneity of the preparation of their students as one obstacle.

They listed other obstacles, such as the quality of instructional materials they were getting, which is what we call curriculum. The survey was really important.

[00:24:52] Anna Stokke: I seem to recall that the panel looked at something like 16,000 research articles, but you had standards for which ones actually were considered. And I mean, this kind of ties into an earlier episode, I had, “Red Flags in Education Research,” because a lot of education research actually isn't that well done, and some studies are good studies and some are not at all, right?

So the committee then went through those and determined which sort of met the standard to be included. When making recommendations, is that correct?

[00:25:28] Tom Loveless: Yes, that's exactly right. There were, in fact, there was actually, we subdivided, as I said, into these different task forces and subcommittees and subgroups. There was a group that was just dedicated to standards of evidence. And we were influenced by the What Works Clearinghouse in the United States because it has standards of evidence and also by the standards of evidence that the National Reading Panel earlier in the decade had adopted.

And so, we gave more prominence and more weight to experimental work and quasi-experimental work that had a comparison group that had objective measures of student outcomes and that focused on achievement as opposed to other outcomes.

[00:26:14] Anna Stokke: And my impression was that the National Math Advisory Panel was formed almost to settle some of these debates. So, for instance, there’s sometimes an idea that conceptual understanding is more important than procedural skills or that they're at odds with each other, but to quote the report, “Debates regarding the relative importance of conceptual knowledge, procedural skills, and the commitment of addition, subtraction, multiplication, and division facts to long-term memory are misguided. These capabilities are mutually supportive, each facilitating learning of the others.”

And the report also addressed automatic recall of basic facts and standard algorithms. So, another quote, “Computational facility with whole number operations rests on the automatic recall of addition and related subtraction facts and of multiplication and related division facts. It requires fluency with the standard algorithms for addition, subtraction, multiplication, and division. Fluent use of the algorithms not only depends on the automatic recall of number facts but also reinforces it.” And I do encourage listeners to take a look at the report.

It also lists benchmarks for the most critical topics to cover in grades 3 to 8, and by what grade level students should be proficient with each topic, so it's really helpful.

[00:27:45] Tom Loveless: And basically, the idea was that in grades one through four or kindergarten through four that students would learn whole number arithmetic. And so the four operations with whole numbers would be the main job of grades one through four. And in grades five through eight, it would be rational numbers.

So fractions, decimals, percents and how to manipulate fractions, decimals, and percents. And you mentioned the false dichotomy, and the panel report really did emphasize, it's actually more than a dichotomy, it's a trichotomy. It's, it's three things, and that is computation skills, conceptual understanding, and problem-solving as the third.

And all three of these can be developed simultaneously, they're mutually reinforcing. And so that's the best that we know about teaching kids mathematics, that all three of those things need to be included.

[00:28:45] Anna Stokke: Exactly. So, it's really quite a good document. And with the idea being that we want students to be prepared for algebra because algebra is kind of the gateway to higher-level math. I mean, these days we have, we now have people trying to claim that algebra isn't important and that's just lunacy, right?

So, but in any case, I mean, if we can at least stick with the, the idea, which is fairly clear to me that we have to think about preparing students for algebra. If they're to have any hope of continuing on in higher-level math, the idea of the recommendations in the National Math Advisory Panel's report is how do you prepare students for algebra?

[00:29:28] Tom Loveless: That's right. I'm going to hold this up to you since you'll be able to see it, but here's the report. It's fairly slim. It's not huge and you can download it. You can also download, and this is much different in size, these are the reports of the task force. It's like Oxford Dictionary, it's massive, but you can go through and find different aspects of the report laid out and elaborated in the reports of the task groups.

[00:30:00] Anna Stokke: Tom, about that big document you have there, I'd love to look at it, but I have a question, and maybe you'll refuse to answer it, maybe not, but I've always wondered about the Kamii and Dominick article that claims standard algorithms are harmful and how the National Math Advisory Panel rated the quality of that research. Can you comment on that?

[00:30:23] Tom Loveless: I won’t answer that in terms of any specific.

[00:30:27] Anna Stokke: Okay, okay. Fair enough, fair enough, but I do have a podcast episode where we discuss that article.

[00:30:34] Tom Loveless: Did you read Steven Leinwand's op-ed in Education Week, which appeared right around the time of the one that I sent to you that I wrote? He called it abuse to pencil, paper, arithmetic, he called it a form of abuse, actually because we don't need to be computing like that anymore.

We have little calculators that can do it.

[00:30:55] Anna Stokke: Right. And that's a, that's a ridiculous assertion. I mean, we're talking about doing math using pencil and paper. How could that be abuse? It just doesn't make any sense. But in any case, I have a great podcast discussion about standard algorithms with Ben Solomon. So people can go back and listen to that one if they want to. It's called “Red Flags in Education Research with Ben Solomon.”

So my next question is, how was the National Math Advisory Panel's report used? Did the NCTM incorporate any of the report's recommendations into their guidance?

[00:31:31] Tom Loveless: No, and the report in general, just collected dust on bookshelves. I mean, the report, it's pretty disappointing how the report was received. A publication of the American AERA, the American Educational Research Association called "Educational Researcher," shortly after the National Math Panel report came out, devoted an entire issue to the National Math Panel.

There was not one article that was supportive of the National Math Panel report. They were all critical. Jo Boaler wrote an article for it. They were all critical of the National Math Panel's findings.

[00:32:14] Anna Stokke: I mean, that's really depressing. The entire point of the panel was to bring people together, to bring experts together, to review the best evidence for how to teach children math and this was ignored.

[00:32:27] Tom Loveless: Yeah, but if I can add one thing, and this will, this will be a little more conciliatory towards the other side, and obviously I do have a point of view in this, I mentioned Skip Fennell was on the committee and he, on the panel, and he was president of the NCTM at the time. Under Skip Fennell, the NCTM published, I think, the best document they've published in a hundred years, and it was called the "Focal Points" and it came out, I think, in 2006. The National Math Panel did refer to the focal points.

So the influence actually went a little bit in the other direction because we praise the focal points. The focal points were great, the focal points essentially presented this idea of okay, we're telling teachers to teach all these things in third grade. What are the really important things that kids need to know?

You know, what are the critical things that kids need to know in mathematics in third grade? And they did that for each of the grades. So that was an important development on the part of NCTM. And in my view, they haven't published anything like it since. And they certainly didn't before that either.

There's this whole idea of, you know, if we just get people in the room with opposing points of view, we can compromise and come up with a document that represents that compromise. And again, I'm skeptical of that endeavour. I don't think it quite works that way.

[00:33:58] Anna Stokke: I also think that compromising between good instruction and bad instruction, why would you do that?

[00:34:05] Tom Loveless: It doesn't get you anywhere.

[00:34:07] Anna Stokke: You should use good instruction, and you can't compromise between things like, “Well, I think that children should be prepared for algebra and I think that algebra isn't important.

You can't compromise between things like that. When there's one thing that's clearly correct and backed by evidence, that's the thing you have to go with. So, I mean, these are complicated issues, but yes, it's very unfortunate the way things played out there.

[00:34:33] Tom Loveless: You're quite right. So, you either, you either believe children need to memorize basic facts, the addition, subtraction, multiplication and division facts, or you don't, or you, you know, you just don't think they're very important to know by heart. You know, to the point of automaticity and there, there really is no kind of middle ground there.

[00:34:57] Anna Stokke: No, there, there isn't. It's just like, you should teach children to read using phonics. There's evidence that this is the case. If there are some people out there who refuse to believe that, we should not cave to them because they're wrong.

There are similar issues in mathematics. I just don't think they've received quite as much attention. Right.

[00:35:18] Tom Loveless: They haven't. You're right.

[00:35:19] Anna Stokke: So let's talk about Common Core. what precipitated that? Why was there the need to develop the Common Core State Standards?

[00:35:30] Tom Loveless: Well, I mentioned two states that kind of went their own way and rejected NCTM standards, California and Massachusetts. Every state, in a way, went its own route, defined mathematics and reading, and the objectives that go, you know, under those two subjects in their own way. And so people started complaining about, you know, we have 50 sets of standards.

We have 50 states, and so we have 50 sets of standards. We have 50 different tests to measure where the kids are learning those standards and this should be, we don't need that. We should just have one set of standards. Let's agree on a set of standards, make it a national set of standards. United States has a very mobile population, people move around a lot.

And the complaint was, you know, you have kids moving from state to state and suddenly they're getting the same thing over and over again sometimes. So that was the impetus for Common Core.

[00:36:33] Anna Stokke: So how many states use Common Core?

[00:36:37] Tom Loveless: Well, originally. Over 45 states signed on to the project, so almost all of the states. There were, there were five holdouts that said, no, we're not interested in that, 45 states signed on. After the Common Core was written and adopted by the states, they started falling away.

And eventually, particularly in the red states, the Republican-dominated states of the United States, there were, again, parent rebellions against the Common Core, there were people coming on television and on the internet circulating really absurd, mathematics problems, and Common Core just got a bad reputation.

States began saying, “Well, we don't want that anymore,” and adopted their own standards. Today, it's somewhere between 18 and 25 states that still use Common Core. But let me say why that number is so fuzzy, is you had states that said we're rejecting Common Core, we want nothing to do with it anymore and we're going to write new standards.

And then they would just tinker, just make trivial changes in the Common Core standards and say, “Okay, here are our brand new non-Common Core standards.” And they looked basically the same as Common Core.

[00:38:02] Anna Stokke: In your book, you mentioned that Common Core emphasizes that conceptual understanding, procedural skill or fluency, and applications should be pursued with equal intensity. But you also point out that no one involved with writing Common Core could ever provide evidence for this. So can you elaborate on that a bit?

[00:38:25] Tom Loveless: That comes out of the National Math Panel. National Math Panel said all three of those things are mutually reinforcing. What the Math Panel didn't say is you should, you should teach them with equal intensity or anything like that. We honestly don't know if you should teach them with equal intensity.

My own view as a school teacher, former school teacher is you should not. I always taught, I began with computation. So I would begin with, you know, here's how you add fractions. You make sure they have a common denominator and you add the numerators and then I would explain why it works that way. You know, why is it that fractions can be added together that way?

And then maybe towards the end, once kids had mastered the computation of fractions, and once they understood why it worked the way it works, then we could take fractions and solve problems with them. Very often today what you get, and this was one of the arguments of the California Math Framework, very often today you get people who want to start with the problems.

Give kids a rich task and have them struggle productively. Productive struggle is one of the terms that's used. And have them figure out how they would solve this problem. Well, how would you solve it? How would you solve it? And how would this third kid solve it? And then they talk about that, and they decide the best way of solving it.

To me, that's a very inefficient way of teaching. But that's one of the ways in which all three of the ideas, computation skills, conceptual understanding, and problem-solving, devote where one-third and one third and one third of time is devoted to them. And that's not necessarily going to bring about better learning.

[00:40:25] Anna Stokke: And you make a good point about the productive struggle. As you say, it's inefficient, but I also think it's just not a great way to teach. It's probably better to teach students how to solve problems and then give them problems to work on.

[00:40:41] Tom Loveless: Yeah, so they don't struggle. I mean, the objective should be for students not to be struggling. And so you help explain things in a manner so that they understand it. So they have that understanding and then they don't struggle. They'll struggle enough.

You know, just learning is not that easy all the time. So they'll struggle enough without teachers kind of engineering productive struggle. It's unnecessary.

[00:41:06] Anna Stokke: It's common sense, really, from my point of view and, coming at this from outside of education, a lot of it's been really surprising to me, or it was surprising. At this point, I probably wouldn't be surprised by too much anymore. But like, I remember a while back we saw a tweet and this was from a math consultant in our province.

And tweet was it was a quote from this math education celebrity and the quote was “Teach less clearly.” And we, we thought it was a joke, like, who would give this, advice? Like, that's literally the worst advice you could give someone about how to teach.

[00:41:46] Tom Loveless: I know, I've been reading some history of the progressive versus traditionalist battles. And there was a movement in the 1930s, it just fascinated me. Talk about just crazy. It was called the incidental movement. And in math, it was called incidental mathematics. And what it was based on was math educators discovered that kids who were really good at math, that they used math a lot in their kind of daily life.

And they thought about math a lot. And so there was a group of math reformers, progressives who came up with the idea that the way to get kids really good at math was not to teach it because kids would pick it up in their incidental living of life and master it in a way that was more, more sure to hold than if they were taught it by teachers.

And one of the traditionalists wrote this great article and he said something like, “Let me get this straight. You're saying the best way for kids to learn is not to teach the subject? You want them to learn. That makes absolutely no sense whatsoever.”

And that's why, again, to get back to this idea, science isn't going to fix this and research won't fix this. This is more like a religious disagreement. A lot of this is, are people taking things on faith. And so it's, it's more or less something that it can't be compromised and it, it can't be fixed.

And so you, you need to enter the world of ideas and debate and discuss, you know, as we see happening all the time with math standards and math instruction.

[00:43:34] Anna Stokke: Okay, so you think the answer is more debate and more discussion.

[00:43:37] Tom Loveless: Yes.

[00:43:38] Anna Stokke: You don't think sort of like a top-down approach works.

[00:43:42] Tom Loveless: No. It never works. And, I think there's a section in my book where I say, even if I wrote the standards and agreed with every word of them, they would have no effect. They'd have very, well, I didn't say no effect, but very little effect. And the reason is the people you convince are already doing it the way you want them to do it.

They're already doing it and the people who just aren't going to do it the way you want them to do it, you don't have the tools to force them to do it. So no, you're not going to affect change through any kind of top-down policies.

[00:44:23] Anna Stokke: Okay, so let's fast forward. We've sort of set the scene. I'm going to ask some questions now about the California Math Framework. So I discussed the CMF on previous episodes with Jelani Nelson and Brian Conrad. It's probably the most controversial K to 12 math education document in North America in recent years.

To remind listeners, the Common Core State Standards lay out what students are supposed to learn in California, and the CMF provides guidance for teachers and school districts on how to teach the standards. So, the first version of the most recent CMF was released to the public in 2020. There was a lot of backlash, both from the public and from STEM leaders, and Brian Conrad identified citation misrepresentations throughout the document.

It was revised several times, but many would say there are still serious issues with the CMF. So, for more information on that, listeners can consult Brian Conrad's public comments on that final approved version, and I will include a link to his commentary on the resource page. Now, nonetheless, it was adopted by the California State Board of Education in July 2023.

[00:45:48] Tom Loveless: Yes.

[00:45:49] Anna Stokke: So my question does the CMF cite the National Math Advisory Panel's report? Is it aligned with the recommendations of that report?

[00:45:59] Tom Loveless: No. I don't recall it being cited. I'd be surprised if it's cited. If it is cited, it might be cited as a don't do this kind of thing, as a counter example, but let's just say it's, it's, it's not prominent in the California Math Framework. It really, it comes from a whole different idea.

[00:46:21] Anna Stokke: It's interesting because I read parts of the California Math Framework, and I was quite shocked because the parts about algorithms that seem to be almost back to what we saw in 1989, so promoting invented strategies and things like that, the work cited were very old, like from way before the National Math Advisory Panel.

And it seemed to even go against the things that the National Math Advisory Panel had recommended. Now, this to me seems absurd because the National Math Advisory Panel came together, they looked at all the research and they made recommendations based on the best available research available, right?

Now you have the CMF in 2023 making recommendations that are quite, in my opinion, regressive. Does that, sort of ring true to you as well?

[00:47:17] Tom Loveless: Well, you're preaching, preaching to the choir here. I wrote a critique of the California Math Framework that was published in Education Next, and I wrote about elementary math because everybody else was talking about high school, and I thought they had that pretty well covered in post-algebra courses that kids would be taking in high school.

So I wrote about the elementary grades, and, and I wrote about basic facts and knowing basic facts from memory. Which are in Common Core, but the California math framework, every time it mentions the word memory, it does it in disparaging way. Talking about, fluency no longer involves speed and whereas fluency traditionally has been defined as both quick and accurate, including in NCTM documents before the California Math Framework.

But the California Math Framework, really the way it envisions elementary math, K through six mathematics, it disparages basic facts and it disparages the learning of algorithms, especially with any level of automaticity.

[00:48:31] Anna Stokke: So, I wanted to ask about. The times table outcome. What does it say about times tables in the state standards?

[00:48:40] Tom Loveless: It says students will know basic facts through single digit times, single-digit arithmetic, meaning multiplication through nine times nine by the end of third grade, and it says from memory. Now it didn't use the word memorize, it used this weird phrase from memory and that's what the standards call for.

I don't think, however, that any of the Common Core aligned tests actually test to see whether kids have that skill or not. It's something I think it's been shuffled aside. By a lot of teachers in Common Core states where at the end of third grade, the kids don't know their times tables and they're supposed to know them according to Common Core, but no one is holding textbooks or teachers accountable for actually teaching it.

[00:49:37] Anna Stokke: I want to say a couple of things about times tables. So first of all, a plug for times tables. It's really important that children memorize their times tables. If they don't, it will hold them back later on, right? So I've talked a lot about working memory on the podcast and you really need to be using that working memory for solving more complex problems. You don't want kids getting hung up on their times tables.

[00:49:58] Tom Loveless: That's right.

[00:49:59] Anna Stokke: And the next thing I want to say is about language and definitions. So you mentioned that the phrasing in the Common Core State Standards is, students should know the basic facts from memory. To me, that would mean they have to memorize their times tables, so they should know them automatically or instantaneously.

But if there is one thing I've learned about math education, it's that people will play around with the language and definitions. So for example, sometimes people use the word fluency, that students should be fluent with number facts. And I thought, okay, fluency must mean you have to have memorized your times tables and be able to say them automatically.

And I was surprised to find out that some people think fluency means something like you should be able to say that six times seven is 42 after, you know, 30 seconds. And you should be able to do it in three different ways. So I agree with you. We may think that from memory means know them instantaneously, but it's hard to say if that's what everyone intends for that phrase to mean.

[00:51:03] Tom Loveless: Right.

[00:51:04] Anna Stokke: So, what I'm wondering is with the CMF written the way it is, with some disparaging comments about time tests and maybe not encouraging memorization of times tables, could this cause that particular outcome in the standards to be ignored?

[00:51:25] Tom Loveless: Yes, I think the phrasing has a lot to do with how it was ignored or why it was ignored. And this whole idea of alternative strategies. One, for example, counting. If you know 7 times 6 equals 42 and you're asked, what is 7 times 7? The person who knows it's 42, 7 times 6, will just count 7 more and get to 49.

Well, if you can memorize 7 times 6 equals 42, you can easily memorize 7 times 7 equals 49. You don't have to use counting on, which is a, for one thing, it's just prone to error. You can count wrong, it's unreliable. And as you said, you don't want to use working memory with all this counting on and alternative strategies, drawing figures and boxes and doing all that when these are facts that people have memorized for centuries, there's no reason why kids today can't memorize them.

And kids enjoy memorizing basic facts. It's not a chore like many people portray. It can be a game kids enjoy, and they can do it quickly. It doesn't have to cause math anxiety. And I think the research on math anxiety is quite weak when it comes to memorizing basic facts, it just doesn't happen that way. There's really no, no reason to do this halfway. Kids should know their basic facts to me and all four operations with single digits.

[00:53:00] Anna Stokke: The other thing I wanted to ask you about in, in terms of research. So I understand you're quite familiar with What Works Clearinghouse.

And What Works Clearinghouse has these wonderful guides and pretty much every cognitive psychologist or psychologist I've had on the podcast has recommended these wonderful guides from the Institute of Educational Sciences, which I think is associated with What Works Clearinghouse on how to teach math.

[00:53:32] Tom Loveless: Yeah, What Works is under IES. It's part of IES. IES is the larger governmental body.

[00:53:41] Anna Stokke: Okay, got it. And my understanding is that those practice guides are similar to like the National Math Advisory Panel. They look at the best available research and come up with recommendations for how to teach and in what we're talking about, how to teach math. And they'll say if this is - there is a strong, you know, it's strong, there's a lot of research supporting this particular thing.

As an example, timed activities, it actually has a strong research base. This aids with fluency, yet the CMF even went against that. In fact, recommended against timed activities without any valid research to back that claim up.

So you've even mentioned that the CMF actually didn't cite these guides from What Works Clearinghouse. Why would CMF ignore these guides from What Works Clearinghouse?

[00:54:40] Tom Loveless: My own theory, and it's only that, is they had to ignore them because had they paid any attention to the practice guides, it would've simply undermined and everything that they were going to write in the California Math Framework.

So the California Math Framework had a set of it had an agenda before it did any research, and the research was investigated to come up with documentation of why these recommendations were good, not the other way around, which is the scientific way of doing it, where you examine research first and then from that research, you distill it into a set of clear recommendations. The research followed, it didn't lead in the of the California math framework.

[00:55:34] Anna Stokke: It sounds like it's basically ideology.

[00:55:37] Tom Loveless: Basically, yes. And there were, I think there were a hundred over a hundred studies in the practice guides, and I went through the California Math Framework and only found one that was cited out of over a hundred studies. And the importance of that is, you mentioned earlier the National Math Panel, the practice guides that I examined in mathematics, and there were four or five of them, they all were released after the National Math Panel Report.

So this is new research or newer research than the National Math Panel had access to. And even with this research, which is very public, but it was either experimental or quasi-experimental studies that were examined. It was not mentioned in the California Math Framework.

[00:56:28] Anna Stokke: It's unbelievable.

[00:56:29] Tom Loveless: Yes.

[00:56:30] Anna Stokke: So let's talk a bit about detracking, so I'm wondering if you can talk about the failed detracking experiment a little bit in San Francisco, and in particular about the equity implications.

[00:56:45] Tom Loveless: Well, San Francisco had a very interesting policy when it came to algebra in eighth grade. I mentioned the California standards that were in place that were written by the four mathematicians and then they were in place for about a decade. Those standards urged eighth grade being the grade in which Algebra One would be taken statewide by virtually all students.

And it rewarded schools in terms of the accountability system for having more kids in Algebra One. So San Francisco went, they adopted a policy of algebra for all. Algebra was mandatory for every student. Then when Common Core was adopted, they switched gears and said, “Now we're going to have, now we're going to have algebra for no one.”

So they banned everyone from taking algebra. And the key commonality of those two policies is San Francisco sought to have everyone take the same math course. That was their definition of equity. And what was discovered, I think, from the San Francisco experience is once you do that and you try to force everybody to take the same math course in 8th, 9th, and 10th grades, the people who can work around that are parents and families that have a lot of wealth, that have means.

If you have the money, you can go out and buy on the private market, you can buy an algebra course, you can buy a tutor, hire a tutor, and you can get credit for Algebra One simply by taking it outside of the school system.

The kids who rely on the school system are working-class kids. And, and kids from impoverished households, they rely on the schools to teach them algebra. And so if you have a very bright eighth grader, who's ready for algebra and has mastered rational numbers and has mastered whole number arithmetic, that, kid is ready for algebra.

And only the parents and only the families that had the money to be able to go out or perhaps even leave the school system altogether and to go to private schools. Those are the families that were able to get what their kids needed.

So it's counter-equity, is what it is.

[00:59:08] Anna Stokke: Yes. And I think they found that out in San Francisco that this didn't work, right? And so now they're, they're stepping back from it.

[00:59:16] Tom Loveless: Correct. They're now going to going to allow some eighth-grade algebra. It was even on the ballot in San Francisco, it continues to be argued about, but the school system, I think for the most part, the district has admitted defeat and is going to allow students to take algebra. Not this year, it's like a year or two off.

[00:59:35] Anna Stokke: Just out of curiosity, you know a lot about policy. So is there actual research on tracking versus detracking, just generally?

[00:59:46] Tom Loveless: There's a lot of research on tracking. And again, that's, that extends back to the 1920s, even, even back to World War I before the 1920s, there's not as much good research on detracking. And I think the way to think about it is, you know, one of the, one of the pitfalls of tracking, just like actually a whole bunch of things in education, they can be used well, these are tools that can be used well, or they can be used poorly.

And one of the pitfalls of tracking are inequities, where you go into a school and you say, “show me your high track,” and you go into the high track classroom and you see predominantly see a lot of White and Asian faces and then you say, “Let me see your low track class,” and you go walk into that room and you see a lot of Black or Hispanic kids attending those classes.

That's a legitimate concern. And I think there's a good way of addressing it and there's a bad way of address addressing it. The bad way of addressing it is doing exactly what San Francisco did and said, “Well, we just, we're going to fix this by insisting everyone take the same thing.” That doesn't work very well.

The good way of addressing it is difficult. It's hard. And that is prepare more Black and Hispanic kids so they can take algebra successfully in eighth grade. Make sure they learn all the things that they need to learn in K through eight so they're ready for an algebra course. But harder to do.

[01:01:23] Anna Stokke: Don't you think that some of those other things that we talked about that are going on in K to 8 might be contributing to these gaps in the first place? So, for instance, like, the multiple representations. You mentioned this in the book, I'm not sure if it's written into Common Core, but it's quite common here in Canada that students are supposed to do things in multiple ways.

They're supposed to learn many different algorithms, no algorithms better than another. And this takes an awful lot of time, it's confusing. In fact, that's one of the things a lot of teachers have written to me, particularly about that thing, that they're required to be teaching things in multiple ways, multiple strategies and so the kids actually aren't learning any efficient strategy well, because they don't have enough time to practice.

So a lot of these things maybe that are embedded into Common Core that you're seeing in the CMF that, dictate what happens in K to eight, they're probably exacerbating those gaps, right?

Because the same thing's going to happen. the parents who can are going to make sure that they get their kids extra tutoring, or they're going to teach them themselves and then those kids will just go continue to excel.

[01:02:44] Tom Loveless: No, I think that's exactly right. And you mentioned multiple representations. There, there's another aspect to kind of modern mathematics that I think is another problem. And it's, it's there in Common Core, and that is the idea that kids need to explain their answers all the time in writing.

And this gets back to the emphasis on conceptual understanding. Let's say you take children for whom English is not their first language, And now you're asking them to explain how it is they arrived at a particular answer. This is an effort to monitor their conceptual understanding.

And actually what it does is bring in language and their proficiency with language into their mathematics performance. And that's unfair to kids whose first language is not English. You know, they're learning conversational English, they're not learning mathematical English, and it's unfair for them to have that demand placed on them.

I wrote a book on tracking in the 1990s, and I visited a school very near the border, south of San Diego, and very near the border. And this school had, it had several algebra classes, which was really cool. And the teacher was fantastic, and one class were all Spanish-speaking kids taking algebra.

And it may have even been seventh grade. So, it was not even eighth grade, I think it was pretty sure it was seventh grade. And the teacher told me, she said, “These kids are so outstanding at mathematics.” She said most of them, for one thing, they had come from private schools in Mexico that had taught algebra very early in the progression of grades.

And for some children, they have a strength in math that they don't have in language. And so to shift the mathematical burden to make it a language based burden is to me, in my mind, it's just unfair. And I don't think, I don't think it helps kids.

[01:04:51] Anna Stokke: You mentioned kids for which English is a second language. Just this morning, you know, I had tweeted something out about the math scores in Ontario, because only 50 percent of students, grade six students are actually hitting though.

The standard where they're deemed proficient in math and someone from the Ontario Dyslexia Association replied to me and said, “Well, look at these questions, they're so language-based. If a student is struggling with reading now, they can't do the math problem.”

We do have to learn to do word problems and work with word problems, but I think that some of the word problems are so convoluted, it's really disadvantaging kids who struggle with the language piece.

[01:05:36] Tom Loveless: Yes.

[01:05:38] Anna Stokke: You've seen many of the math reform ideas tried and failed in the 1990s. What ideas in the CMF actually give you the greatest concerns?

[01:05:48] Tom Loveless: I think the disparagement of memorization, of practice, because practice is very important in math in learning math, the kind of debasement of explicit instruction where teachers stand in front of a room and explain how things work, and as we've mentioned earlier in this podcast the whole treatment of memorization and of retrieval, you know, you need to know things quickly and it comes to basic facts so that you can free up the resources of the mind of working memory to work on more complex mathematics.

[01:06:29] Anna Stokke: So final question. Do you see any hope for policies in the future that might improve math achievement and actually maybe take research evidence into consideration?

[01:06:41] Tom Loveless: I think policy probably again is not the instrument to affect change. By that, I mean, you can't mandate from the top and expect classrooms simply to change on a dime. That doesn't happen that way. However, that being said, what leaders and policymakers can be doing is supporting research because we need more research with a lot of these topics and also deploying resources in such a way that, for instance, kids who have fallen years behind get tutoring so that they can catch up.

Also, the teachers can be supplied with good materials that have been field tested. You know, if we started thinking of curriculum materials the way we think of pharmaceuticals where we always have field trials and there are safety protocols that are put into place to make sure that any drug that we pop into our mouth, any pill we pop into our mouth, that it's not going to kill us and that it has the intended effect.

We need to make sure that our curriculum materials also have that. And we are so far away from that very few of the books that are recommended by states in either reading or math have been field tested or field evaluated, you know, with good, solid randomized trials, and we need more of those.

If those things happen then I'm optimistic, and I am optimistic. I think we're headed in that direction, and we do more of it today than we did when I started in this business in the seventies.

[01:08:24] Anna Stokke: Okay, well, that sounds promising. So we'll end on that high note. So thank you so much for coming on my podcast and sharing all your knowledge and expertise and discussing the history piece with me. It's been really great. I've learned a lot. Thank you so much.

[01:08:41] Tom Loveless: Thank you. I enjoyed it.

[01:08:42] Anna Stokke: More in just a moment. As always, we've included a resource page for this episode that has links to articles and books mentioned in the episode, including a link to the National Math Advisory Panel Report. I'll have another great episode coming out on May 3rd.

If you enjoy this podcast, please consider showing your support by leaving a five-star review on Spotify or Apple Podcasts. Chalk and Talk is produced by me, Anna Stokke, transcript and resource page by Jazmin Boisclair, social media images by Nicole Maylem Gutierrez.

Subscribe on your favourite podcast app to get new episodes delivered as they become available. You can follow me on X for notifications or check out my website, annastokke.com, for more information. This podcast received funding through a University of Winnipeg Knowledge Mobilization and Community Impact grant funded through the Anthony Swaity Knowledge Impact Fund.