UCLA’s Prof. James Stigler on Teaching & Learning Math

[00:00:18] Charlie: Hi, everybody, and welcome to this week’s edition of the Learning Curve. My name is Charlie Chieppo. I’m a guest co-host this week.

[00:00:28] Charlie: And then along with me this week is Professor Albert Cheng a professor at the University of Arkansas. So, professor Cheng, thank you for being here. And why don’t you tell our listeners a little bit about you.

[00:00:40] Albert: Yeah, it’s great to be with you, Charlie, and be back here on the show. I guess I was on, what, a few weeks ago? Yes. As a guest, but I guess I get to guest host with you. But yeah, for the listeners who don’t know me, I’m a professor at the University of Arkansas. My background’s in education policy and run the classical education [00:01:00] research lab. And hence I was here a couple weeks ago talking to you, Charlie, about classical education. I’m looking forward to what’s on tap today.

[00:01:08] Charlie: Well, you know, the surest proof that you pass the audition is when they have you come back to be the guest co-host.

[00:01:14] Albert: Well yeah, I guess so. I hope I deliver here.

[00:01:17] Charlie: All right. Well, we’re going to jump right into our stories of the week. I think I’m going to go first.

[00:01:25] Charlie: My story this week is about the American Legislative Exchange Council, or ALEC’s Index of State Education Freedom. And this was based on funding and financing for school choice programs, charter schools, homeschooling, virtual schools, and open enrollment policies. It’s not based on student performance.

[00:01:45] Charlie: So, Massachusetts, where I live, got an F at tying with Rhode Island for dead last. Unfortunately, Massachusetts is also looking more and more like Rhode Island in terms of performance. In the 10 years before [00:02:00] the pandemic, Massachusetts NAEP scores fell more than all but 17 states in math and all but more than 14 states in English.

[00:02:09] Charlie: So, you know, I’m not sure I’d necessarily want to get an A in this because I don’t think it’s as simple as, more choice equals better schools. But next to no choice clearly is not the answer. I talked about those falling that falling performance in Massachusetts prior to the pandemic.

[00:02:26] Charlie: Well, of course, then came the pandemic which plummeted Massachusetts scores to a 30-year low. And, you know, in the year or two since then, they have barely budged. So, the summary of the Education Freedom Index reads that the pandemic sparked a national realization that the current one size fits all public education system doesn’t work for too many students. and I think that the reality there is simple — that public education came into households during the pandemic and a whole lot of parents didn’t like what they saw.

[00:02:58] Charlie: So, I think you know, the fallout [00:03:00] from that. Continues to unfold and I’m not exactly sure where it’s going to go, but I think it’s going to be very interesting to watch.

[00:03:06] Albert: Yeah, fascinating. Charlie. Any chance you remember what Arkansas got?

[00:03:12] Charlie: Well, I can check. I know Florida was number one. Okay, check and see where Arkansas came in. Yeah.

[00:03:18] Albert: Well, you know, as I mean, listeners might know that in Arkansas, he recently passed a major ed reform bill that includes a universal education freedom account program.

[00:03:27] Charlie: So that was my story two weeks ago. Oh yeah. Yeah. That’s right. Yeah. Yeah. So, there you go.

[00:03:33] Albert: So I’ve got a story too. And this one’s on music education. So, there was actually an opinion piece a couple of days ago by Sammy Miller. And I actually, I didn’t know who he was. But his bio on, on the opinion piece that he’s a Grammy. Nominated drummer and founder of a music education company and they actually checked out his music which is pretty cool actually.

[00:03:54] Albert: So, listeners, you ought to look up Sammy Miller and the Congregation. It’s I mean I was playing it in my office just before we’re recording this so he’s has a I think an intriguing opinion piece about the state of music education. And you know, he begins with this observation that he’s never met an adult.

[00:04:12] Albert: Who’s thankful to have quit music, right? But on the other hand, he’s met a bunch of adults who had regrets for quitting. And first of all, I don’t know if I brought my parents into this podcast last time I was here, but that made me think of my mom. So I got publicly acknowledged that my mom was right. They made me play the piano and they fought with my resistance for many years, always saying that you’ll thank me later, and I gotta say, like, Mom, you were right. Thank you for not letting me quit. Yeah, yeah. But what Sammy is saying in his piece is you know, he’s made some observations about music education you know, how we might reform that or improve that.

[00:04:51] Albert: And one of the observations he makes struck me as I just, let me just read this part of his piece. So, he writes educators lament that as with other courses, band can frequently fall prey to teaching to the test, in this case, teaching to the holiday concert, a class that by definition is meant to be a creative endeavor, winds up emphasizing rigid reading and rote memorization in service of a single performance.

[00:05:18] Albert: You know, that struck me. I never kind of thought through how music education can become narrowed like some parts of our curriculum. if music education is all about the single performance. Yeah, I think I agree with Sammy that something is lost. You know, I, I just kind of think to my, my own music education that, granted, I guess it was imperfect, but, you know, certainly one of the driving.

[00:05:40] Albert: Yeah. My motivation for that was, hey, it looks good on, on college applications. And so, you know, you learn an instrument just to have that to pad your resume, so to speak. And you know, I think as a young kid, I kind of got lost in that somehow. And then that kind of sucked out the enjoyment of music.

[00:05:56] Albert: And you know, now without that kind of pressure, like I totally enjoy [00:06:00] it. Playing piano and just doing it for its own sake and really enjoying it with other people. I think, you know, one of the things that Sammy says in his article is that music is supposed to be a language. It’s something you do with other people it’s something you know, like you practice language together, you share, you speak with each other, you memorize phrases together read together, and, so, you know, he’s kind of advocating for music education to, take that view to be some kind of common pursuit he writes that, you know, ask any dad rock weekend band or church ensemble how it, how it experiences music, And the performers are likely to tell you it’s not a chore, but a way of building community.

[00:06:35] Albert: And I don’t know, I think there’s something to that. I don’t know how music teachers can practically pull this off. But I do think that reorienting ourselves to think of music education in those ways might do some good. It might be helpful.

[00:06:47] Charlie: Yeah, I think that’s right. And as I listen to you, to describe this, it also makes me think, you know, you see all those articles and things about how the similarities between music and math, you know, in terms of [00:07:00] what it uses in your brain.

[00:07:01] Charlie: I mean, I wonder if it’s knowingly or unwittingly helps you along the way to with the day job, who knows?

[00:07:07] Albert: Yeah, yeah. I think there’s something to that. I mean, I’m pretty sure I. See the world in a weird way that are a unique way, actually, just because, my music background that I’m not even cognizant of.

[00:07:18] Albert: So, I mean, it’d be great to riff on the sound of music, you know, if all our kids could see the hills are alive with the sound of music and make fun of us even more.

[00:07:27] Charlie: Yeah, all right. Well, coming up after the break, we have UCLA professor Jim Stigler talking about teaching and learning in math.

[00:07:57] Charlie: James Stigler is Distinguished Professor of Psychology at UCLA. His research focuses on teaching and learning, especially in mathematics and statistics, and its intersection with culture and technology. He’s co-author of two popular books, The Teaching Gap with James Hiebert and The Learning Gap with Harold Stevenson.

[00:08:15] Charlie: He was director of TIMSS Video Studies and co-founder of two educational technology startups, Lesson Lab and Zaption, and the nonprofit CourseKata.org. He received his AB from Brown University and PhD in developmental psychology from the University of Michigan. Welcome, Professor Stigler.

[00:08:34] Charlie: Going back to 1957 and Sputnik through to 1983 in A Nation at Risk American K-12 education has really struggled with its performance in math and science. I’m certainly an example of that. Would you briefly share with our listeners how and why American education has this struggling factor in the basis of STEM?

[00:08:57] Jim: Well, first of all, one thing [00:09:00] I’m constantly reminded of is there’s no single factor. Education is a complex system, so it includes curriculum, teaching and learning, culture, students, curriculum, materials. I mean, there’s so much involved in education, and we do have a tendency to try to zero in on the one factor or variable we think is most important, but I don’t see it that way.

[00:09:24] Jim: So, I think there are a number of things that have stood out to me over the years. First of all, I think even from the earliest you know, TIMSS work back in the ‘90s, this whole idea of the mile-wide, inch-deep curriculum, I think is very important. You know, we study more topics in our math curriculum than in almost any other country in the world.

[00:09:46] Jim: If you look at our textbooks, they’re thick and they’re heavy and they’re filled with stuff. If you go to Japan, the textbooks are, very, very thin and they don’t include as many topics. But what they do is give teachers and [00:10:00] students the opportunity to go deeply and more conceptually into the topics of math.

[00:10:06] Jim: And I think that that’s very important. As long as we think we have to cover all these topics, it means we’re covering them in a superficial way, which means we’re not learning them in a very deep way, which means we’re The learning doesn’t stick because if we don’t really learn with understanding that the learning tends to degrade over time.

[00:10:25] Jim: So other things, I think that have held us back. One that increasingly I think is important is we have sort of a cultural theory of what learning should look like. And I, I think of it as like, the mastery of the bits, and this is especially true in this age when we’re using technology to do more teaching.

[00:10:47] Jim: We have this idea that we can take math or any other subject matter and divide it up into 300 different little bits of things you need to learn. And then we basically teach it as a memorization class where we say, All right, we did that one. Let’s check it off and go to the next one. Go to the next one.

[00:11:03] Jim: The problem is You can learn all the pieces of math, but if you can’t connect them together and bring them to bear on a novel problem, you really haven’t learned much that’s useful at all. And I think that’s a problem. I think that students, for example, see math as a memorization task and work we’ve done in community colleges.

[00:11:25] Jim: For example, when we ask students, you know why they’re in the community. Remedial math classes that they had to take because they couldn’t place into college level math, they attribute it to not being able to remember all the steps and yet if you talk to a mathematician, they’ll tell you one of the reasons they love math is you don’t have to memorize anything. So it’s a real disconnect between what experts think and what the students think.

[00:11:53] Charlie: When you talked about the curriculum being an inch deep and a mile wide. Is it your sense that that’s somehow [00:12:00] because we simply can’t agree on what to cut out? Or is there a feeling that that’s a better way?

[00:12:09] Jim: Well, I think it’s both of those things. First of all, I think there’s way too much emphasis on what we cover in the math curriculum anyway. And what I always am reminding my students of is what I call the 80/20 rule, 20 percent might be the policy, but 80 percent is the implementation.

[00:12:26] Jim: So regardless of what people put in the books or put in the policies, very different things are happening in classrooms. So, but that said, I think one of the other things happening is we don’t have good models of what it looks like to teach. Deeply with understanding. So, if you reduce the number of topics in the curriculum, I think a lot of teachers aren’t sure. Are you supposed to do instead of covering all those different topics?

[00:12:56] Charlie: Right, right. Interesting. Well, teaching at UCLA, you’ve seen and written extensively about a wide variety of math students from all over the world. The best of whom were likely from countries like China, Japan, Germany, Russia, and India. Could you compare the level of academic preparation in math? of international students to that of their American peers what are some of the countries that you think are the most effective at teaching math?

[00:13:19] Jim: I do want to say that I — my recent work is not in international comparisons and my insights about international students come mostly from my interactions with students at UCLA. But based on my you know, what I’ve read and also my informal interactions, I would say most countries are more effective than the U. S. at teaching math. And I think that’s also findings from the most recent international studies. But it’s not that they know higher level math. It’s that they have deeper sort of intuitions about basic quantitative concepts.

[00:13:55] Jim: For example, in my class at UCLA, which is a highly selected school there are many students who are struggling with ideas like proportionality, you know, if I ask them, oh, you have so many males and so many females and so many of the females smoke and so many of the males smoke. And I say, what two numbers would you divide to get the proportion of males who smoke.

[00:14:20] Jim: I have a certain percentage of my students who aren’t sure what two numbers to divide. So, it’s not that they don’t know calculus. It’s that they don’t know middle school math, and I think that’s what I see is the big difference.

[00:14:33] Charlie: That’s interesting. When you say that, I think I was saying before that I’m kind of the opposite. I can do any of that arithmetic stuff in my head, but I really struggle with the other stuff probably because I wasn’t paying enough attention as I grew older. But anyway, that’s a fascinating observation.

[00:14:50] Jim: We do a terrible job teaching more advanced math. And, I’ve been doing a lot of work recently in high schools and high school math is just terrible. We kill curiosity about math, algebra and geometry in high school, and I think that’s probably what you’re talking about that led you to, you are feeling like you can’t understand those subjects, right?

[00:15:14] Charlie:  No, that’s it. Well, I’m glad I’m not alone. At least you’re not alone. All right. Okay. So for many decades there have been international comparisons in K through 12 education, often measured by standardized tests. I saw in your biography that you had spent some time involved with Tims trends in international mathematics and science study. And there’s also the professional program for international student assessment. Would you talk about these international tests? What do they reveal about teaching and learning math across the globe?

[00:15:47] Jim: Yeah, like I say, I haven’t been involved recently in this, but we’ve been doing this work for a long time. And first of all, we do terribly as a nation. And that’s Our standing internationally hasn’t really changed in decades, so it’s not like we go up and we go down and so on.

[00:16:06] Jim: It’s that we usually rank near the bottom of the industrialized nations on these tests. But the other point I want to make is that the tests really are excellent. Americans, and I’m an American too, but we tend to look for a reason why this doesn’t matter. So, a lot of people say things like, well, those tests don’t measure creativity.

[00:16:30] Jim: We’re very creative, or they don’t measure problem solving. They’re just measuring rote skills that of course they’re good at in other countries. But that is totally not true. The tests are excellent. They measure all kinds of math skills, but also concepts and problem solving. So I think we need to stop trying to explain things away and realize we literally have not figured out yet, as a nation, how to teach math effectively.

[00:16:57] Jim: And I think that goes pretty much from elementary school all the way through higher education, frankly.

[00:17:03] Charlie: Well, that’s a very interesting point. Okay. as high-quality state standards in California and Massachusetts have since been replaced uh, were being developed in the late 1990s, the math wars were raging across American K through 12 education. Could you talk about the two sides of the math wars and that whole phenomenon of the math wars, what its impact was on teaching and learning from your point of view?

[00:17:28] Jim: Well, I’ve tried my whole career to stay out of the math wars, but I mean, well, first of all, I would say, I think the math wars are largely irrelevant to what actually happens in classrooms. Just because of what I was talking about before. So people can argue about, oh, what courses people have to take. What is the content of those courses? But none of that really matters. Teachers have to teach the students they have. And heroically, they figure out, you know, how to get by.

[00:18:00] Jim: But these math wars don’t really decide much of anything, in my opinion. I think instead, we should be focusing on what students actually learn. And the whole math wars discussion would be very different if we did that. So, for example, if. Some professors who are vehemently arguing that all students should be learning calculus in high school, go to high school and teach calculus to current students, and then we can talk about what all students should learn.

[00:18:28] Jim: I mean, I think there’s a huge disconnect between these policy arguments, which are very heated. And what’s actually happening in the classroom. I mean, the same thing is true about pedagogy. You know, people have these huge arguments about oh, we should teach using more discovery learning or oh, we should teach using more direct instruction.

[00:18:48] Jim: But all the research that I’ve done and read suggest that you need both of those things in a classroom, and that’s what higher achieving countries do, like Japan, Czech Republic, the Netherlands. These countries include both time for students to really grapple with problems, struggle, try to solve them on their own, and also include direct instruction, explicit connections of problems to deep mathematical concepts.

[00:19:18] Jim: So, anybody who’s arguing Just one side or the other. I think that’s largely irrelevant, and we should all be holding ourselves accountable for students actually learning deeply with understanding.

[00:19:30] Charlie: Well, having listened to what you’ve had to say so far, I have a sense that Professor Cheng, being a math professor, probably has got a lot to ask you. So I’m going to turn it over to him now.

[00:19:41] Albert: Yeah, well, I mean, not, yeah, and not a math professor but, math major as an undergrad, and I, oh, sorry. No, all good, but I the things about that I, I do miss, you know, and so, yeah, it’s great to be here with you, Dr. Stigler, and, and, learning a lot here, and it’s just reminding me a lot of I taught high school as well before I, what I’m doing right now.

[00:19:59] Albert: But you know, just to follow up on that last question you know, not to push you into the math wars, but you know, you mentioned that like a lot of these foreign countries you know, have certain practices of teaching and learning. whether it’s just direct instruction, whether it’s teaching basic computational skills, repetition, or discovery. So, why is it that our schools struggle to implement the approaches that other countries take? You know, why is it so, so hard to reform things?

[00:20:24] Jim: Well, I think it’s because teaching and learning are both cultural activities. So, in Japan, you can be a teacher and you can pose a really hard problem that nobody in the class knows how to solve and say, see if you can make progress and the students will get to work and may spend 20, 30 minutes just struggling without even finding a solution.

[00:20:48] Jim: If you do the same thing in an American classroom. The students will raise their hand and go, sorry, we haven’t learned this yet. Why are you asking us to do something we haven’t been taught? So, you, you can see how you can’t just take an instructional strategy that works in one country and bring it into the other, because you’re not bringing everything else in.

[00:21:05] Jim: You’re not bringing in the parents and the students. And the teacher training and the curriculum materials. And so unless you import an entire cultural system, which I think is impossible, it’s very difficult to learn from those things. On the other hand, our analysis says you need like three kinds of experiences in the classroom in order to learn math deeply.

[00:21:28] Jim: First of all, Students need to struggle with important mathematics, you know, in other words, it’s like anything else if I want to learn to play a musical instrument, I have to spend time practicing the musical instrument. I can’t just think about practicing musical instruments. So students need to actually engage working hard in mathematics, but they also need to connect.

[00:21:50] Jim: The work that they’re doing with important mathematical concepts. And so, they those need to be made explicit. And then that level of sort of challenge and always changing the context in which you’re applying mathematics needs to be continually changed and made more challenging over time, you know, what’s related to the concept in psychology we call deliberate practice.

[00:22:15] Jim: those principles are important, but what we need to do is figure out how we can implement those principles with American students in American classrooms in an American context. And I think that’s what we should be focused on, is that, rather than arguing about, what topics should be included in the curriculum, or what do we think of reform teaching.

[00:22:36] Albert: Yeah, those are some pretty keen observations again, just bringing back a lot of my own personal memories of students kind of just shutting down after presented them with a challenging question that they had to, wrestle with but, let’s keep digging into this topic here.

[00:22:51] Albert: And so I want to ask you a question about Algebra I, and then we’ll move on to geometry to maybe kind of think about how this could work and what this might look like in these [00:23:00] specific courses. back in 2008, the National Mathematics Advisory Panel. You know, so they reviewed, I think, is more than 16,000 research publications and then issued this report back in 2008 and believe some of the main findings and points that the report was making was about Algebra I being this gateway course to higher level math.

[00:23:21] Albert: So, is it after even the release of this? It doesn’t seem like we’ve made much progress in terms of Algebra I and figuring out how to teach that better. And what do you think could be done to improve the way we teach algebra?

[00:23:35] Jim: Well, I actually have a lot of ideas about this. I think part of the problem is how do we define algebra? I think many teachers define algebra the way students do, which is, oh, you got to learn the steps. So, for example, in our high school math… Textbooks. We still have one step problems and two step problems, right? And those are problems that could be solved by doing one step, like subtracting something on one side versus ones that require two steps.

[00:24:04] Jim: But if you talk to a mathematician, they have no idea what you’re talking about with a one-step problem and a two-step problem. It’s just that math teachers have tried to figure out a way to spoon-feed steps to students, and in my opinion, you know, teaching the steps of solving a problem is really the enemy to understanding because as soon as students tend to think their job is to remember the steps you taught them, then they shut down their thinking.

[00:24:30] Jim: They’re not thinking. I think algebra is critical to higher-level math because if it’s taught right, algebra is a language for representing the relationships among variables, and it’s really quite amazing. So. in elementary school, we teach students two plus three equals five, and they can write that as a number sentence.

[00:24:53] Jim: And then we say two plus x equals five. Well, if 2 plus x equals 5, x is only going to be one number, is 3, so why are we bothering to teach them to subtract 2 from both sides so they can isolate x? That seems like overkill, and I think the student’s kind of know that. But if we instead said 2 plus x equals y, then you’ve opened up a whole new world, which is, oh, y is a number.

[00:25:20] Jim: We don’t know what it is, but whatever it is, we know it’s 2 more. Then X and that’s just a very powerful yeah, algebra. So I think what we need to do is teach algebra more as a system for representing quantitative relationships and talking about them in a more abstract way. I don’t think that’s what happens in our modern-day classrooms.

[00:25:43] Albert: Yeah, yeah, well, I, you know, I definitely resonate with that. You know, back to your point earlier, you said we kill curiosity in the way we present math — nothing I think kills curiosity more than trying to have to regurgitate steps. And I mean, you know, just imagine these homework problems that students get all the time.

[00:25:57] Albert: It’s basically 30 exercises, rinse and repeat with different numbers, plugging in things. And you know, I could see how that could get boring, where you know, your present math a different way. I mean, I’ve always thought of algebra as thinking about the way numbers and other mathematical objects combine.

[00:26:19] Jim: You know, there’s an order and structure to that. And there’s some beauty there that I guess we don’t really quite emphasize. It’s beautiful and you don’t need to know that much in order to begin understanding that beauty. But you do need to drop the idea that your job is just to remember. The steps, right? Right. I mean, the most common question students ask in high school is, why do we need to learn this? Yeah. And quite honestly, you know, if I say two plus x equals five and teach them to subtract two from both sides, it’s like, when am I ever gonna use that? Another thing that in my recent work, we’ve been working on teaching statistics and data analysis to high school students.

[00:26:54] Jim: and I think that, data analysis is like the best answer [00:27:00] you could ever come up with as to why you should use algebra, but the algebra for data science is not so much about solving for X, it’s about functions and using the value of X to predict values of Y and what we’re finding is if you can get students, to engage in How do they summarize patterns of data and then showing them that you can, for example, summarize this pattern with a straight line?

[00:27:25] Jim: suddenly the equation for a straight line represented as a function, they think, yeah, that’s pretty cool. And then as soon as they see different patterns, they say, well, too bad there’s not a function that has a curve in it. We go, yeah, actually there is. Would you like to learn about it? That’s what we need to do with algebra is we need to figure out how to make it relevant and interesting to students. Which doesn’t necessarily mean it’s relevant to their everyday life or anything like that. It just has to be relevant. To something that’s interesting, like, how do I explain this pattern [00:28:00] in data?

[00:28:01] Albert: Yeah, well, we could go on and on about Algebra I, I think, let’s kind of shift it to geometry a little bit just to weigh in on that. The other main course that our high school students take and Euclidean geometry has been really a fundamental form of mathematics that’s really shaped education in the West and I’m sure in other places. Could you talk a little bit about geometry’s role in math education? How we might do that more effectively? Yeah, what are your thoughts on the teaching and learning of geometry?

[00:28:26] Jim: Well, I think just like algebra is our way of teaching students to represent quantitative relationships in an abstract way, geometry, I think, is most useful because it allows us to teach deductive reasoning, which is really an important part of getting to higher mathematics. So, the idea that you can say, well, if this is true, then what should follow? And when I, you know, I remember being in high school and, and I loved that I could reason from well, that’s half  of that, then that must be the same as this other angle, etc. Where it all fell apart for me, is that geometry was not about that.

[00:29:10] Jim: It was actually about dividing my piece of paper into two columns and writing. Yeah, right. And all that. Which, again, it’s very similar to the way we teach algebra. It’s turning it into a bunch of steps you have to memorize. And I could never, you know, figure out why it mattered, what was an axiom, and et cetera.

[00:29:30] Jim: And so, it’s connecting what we’re doing in geometry to students’ thinking, because people are naturally curious unless you tell them curiosity is irrelevant in this situation, which is basically what we’re doing in high school math. We’re saying, yeah, you’re curious about things, but this is math. You just need to follow the steps. So, I think geometry is really important. Very important opportunity to teach deductive reasoning. So, for example, one of the ideas that I love in geometry is the idea that you can draw an auxiliary line. That line didn’t exist before. But once I draw it, I can say, well, if that line has these characteristics, how do I know it has them? Because I drew it to have those characteristics. Now I can reason from there and answer other questions that I couldn’t have answered. Without it, and in statistics, you know, there’s a similar idea which I think is quite similar or analogous, which is the idea of a sampling distribution. There’s no such thing really as a sampling distribution. It’s a mathematical object that we make up. But once we do that, we can use it to answer questions about data.

[00:30:39] Albert: Yeah, that’s fascinating. That’s true. I’ve never made that connection between a sampling distribution and auxiliary line. That’s an excellent metaphor. So last question here just to give you the last word. You’re aware of the recent NAEP scores that highlights an ongoing education, educational crisis and, and learning loss from the pandemic. Yeah. What would you say, to school leaders and teachers to, address this issue of learning loss particular with respect to math education?

[00:31:05] Jim: Well, I think learning loss should be addressed by addressing learning. I mean, I think the reason learning is lost is that it was never very deep in the first place. And what we’ve seen in our study of community college students is if you just memorize a bunch of things. If you let time go by that, those memories just start to go away because they’re not connected to anything.

[00:31:27] Jim: So as long as we emphasize learning of math as a memorization task, memorizing steps and procedures, then that learning is going to go away. If we can really change the culture of teaching and learning. Forget about learning loss. If we can learn more deeply and teach with understanding, then learning will be more resistant to disruptions by covid or anything else that comes along in the future.

[00:31:50] Jim: So, I don’t think we should just try to address learning loss by doing more. Of what we already do. But I think learning loss is actually great evidence to show that what [00:32:00] we did wasn’t actually working. It wasn’t sticking with students. And the whole goal of education is to prepare students for a future time.

[00:32:08] Jim: Well, if that learning goes away just because they didn’t go to school for a year or two, we haven’t done a very good job teaching it.

[00:32:15] Albert: That’s an astute observation. Certainly, helps us to, recast the problem and perhaps think of it with a different paradigm. So anyway, thanks Dr. Stigler for your insights and for being with us today. And I definitely had a lot to chew on even for my own interest in mathematics and education.

[00:32:32] Jim: Thank you. I enjoyed it.

[00:33:01] Charlie: Alright, we’re back with this week’s Tweet of the Week. It is from Education Next and it says student mental health has declined. By April 2022, 70 percent of public schools reported an increase in the percentage of children seeking school mental health services compared to pre-pandemic levels. I wish I knew the answer to this, but all I can say about it is that I have certainly seen with my own kids and their friends the struggles, particularly after the pandemic that seemed to be.

[00:33:27] Charlie: Greater than before, and I sure hope that we can come up with some, you know, with some effective ways addressing it. So, thank you so much for joining us this week. on the Learning Curve Charlie Chieppo, your guest host. And I really want to thank Professor Albert Cheng for joining us.

[00:33:43] Charlie: It was great to have you, Professor Cheng. Hope you’ll come join us again.

[00:33:47] Albert: Sure. Yeah, it’s great to be with you and pilot the ship with you.

[00:33:49] Charlie: Thank you. There you go. All right. Well, thanks very much. Next week, we hope you’ll join us. We’re gonna have Nina Rees, who is the president and CEO of the National Charter School [00:34:00] Association.

[00:34:00] Charlie: So that should be certainly an interesting one as there’s not a lot in the education world these days that I think is more controversial in charter school debate. So that should be an interesting one, and we hope you join us next week.