Dr. John Woodward is a nationally recognized mathematics author, writer, and speaker. He is the past dean of the school of education and professor emeritus at the University of Puget Sound in Tacoma, WA.
As a researcher, he focused on mathematics interventions for academically low-achieving students, particularly in elementary and middle grades. Dr. Woodward has published more than 80 articles and presented on mathematics education issues throughout the U.S., as well as in Canada, Asia, and Europe. He is the senior author ofTransMath, a math intervention program for middle school students. He also is the co-developer of NUMBERS, a math professional development program for K–8 teachers.
The public release of ChatGPT by OpenAI late last year has captivated, if not terrified, certain sectors of public education. A simple interactive screen allows users to create a range of “authentic looking” documents. ChatGPT essays are either free or fractional in cost.
Some have called ChatGPT the “calculator moment” for writing assignments. Is there a similar, potential effect in math? Should we be welcoming or fearful of this technology?
This podcast will explore programs like ChatGPT and what they mean for mathematics instruction. We’ll discuss other current technologies used in math education today, and reflect on potential, near-term improvements and how upgrades like the “intelligence assistant” now being developed by Microsoft using ChatGPT might be used in math classrooms.
Dr. Woodward will discuss:
How simple uses of technology today can add value to mathematics instruction and how it helps with assessment, instructional decision-making, and accountability
How assessment information can be synthesized across a classroom of students to help teachers make critical instructional decisions about grouping
How to use technology to assist teachers and save time
Key issues of concern for systems like ChatGPT, including that they do not rank or evaluate the quality of the information captured from the web, and ways to confront those issues
Ways to use ChatGPT to solve math problems, improve instruction and student engagement, and the program’s limitations and benefits
One of the great ironies that we've got going on now is that while secondary educators and college teachers are freaking out about the writing products that are coming out of GPT, in the world of work, that is going to unleash a whole new use and it's going to be used all over the place, right? That's the real world.
You just heard from math expert and author of TransMath® and NUMBERS professional development, Dr. John Woodward. Dr. Woodward is our guest today on EDVIEW360.
This is Pam Austin. Welcome back to the EDVIEW360 podcast series. We are so excited to have you with us today. I'm conducting today's podcast from my native New Orleans, LA. Today, we're excited to welcome Dr. John Woodward, a nationally recognized mathematics author, writer, and speaker. He is the past dean of the School of Education, professor emeritus at the University of Puget Sound in Tacoma, WA. In his research, Dr. Woodward focused on mathematics interventions for academically low-achieving students, particularly in elementary and middle grades. He has published more than 80 articles and presented on mathematics education issues throughout the U.S., as well as in Canada, Asia, and Europe. He is the senior author of TransMath, a math intervention program for middle school students. He is also the core developer of NUMBERS, a math professional development program for K–8 teachers currently being offered under the name of I Make It. Dr. Woodward is our guest today for EDVIEW360 as we discuss ChatGPT. Welcome, John.
Hi, it's nice to be with you.
You recently wrote a fascinating blog about ChatGPT and its implications for mathematics education. Before we dive into the specifics, let's talk big picture. Everyone's talking about ChatGPT and it's the source of a lot of concern for many in education. But just to start us off in layman's terms, what is ChatGPT?
Yeah, that's a great question and it's an even more complicated question if you want to put it in layman's terms. So, here's a little bit of something that's ironic. I actually asked ChatGPT that question, what are you? And I think the explanation it gave was fairly lucid and relatively simple. When you think about artificial intelligence, which sounds really, really daunting, you get below the surface and a lot of different systems are trained to do very specific things. AI has been used for quite a while to train object recognition. It's been used to train robots to do certain kinds of tasks, where ChatGPT is significantly different, and especially in the way that the public has received it over the last couple months, is It's what's called a large language model, and it's been trained on lots and lots of data.
Now, if you've used even Siri or Gmail and you've been typing and you see some words that appear in gray just before you're about to type them, that's word prediction. And, so, one of the aspects of ChatGPT is to take this ability to predict words and sentences, to construct sentences, to construct paragraphs and longer text in a coherent way, and then draw upon the vast amount of information that's on the Internet to construct answers to specific kind of questions. So, in a very layman like way, what's revolutionary or most unusual, at least in terms of how it's interfacing with education is it's able to produce lots of highly readable text that actually presents novel information. Now, sometimes, to be very candid about it, it produces what are called hallucinations, stuff that doesn't make any sense whatsoever. But for the most part, the training's gone on and where you have lots of data, you're able to present information that's relatively novel in its content, and surprisingly interesting because it's able to exploit the vast reaches of the Internet in terms of any kind of information that you're seeking.
So, novel, interesting information that could be intriguing, wouldn't you think Dr. Woodward?
Well, it's causing a huge headache, and the good news here for me is what's happening in the area of English language is a nightmare. All of a sudden, people who are expecting kids to write texts, interpretations of novels, you name it, they're all of a sudden starting to turn in all kinds of ChatGPT texts that have been created for them for free in a matter of minutes. And, this is, if you want to call it that, the calculator moment for English Language Arts. Fortunately, in the context of obviously this podcast, mathematics is our focus, and I think we can kind of at least present a more positive set of applications possibly that can be thought about in the context of ChatGPT.
All right, so the challenges in use can be something that may be a concern, but we are going to hone in on the fact that you know what, it's not going anywhere anytime soon, right? So, let's think about education. Let's shift the conversation to assessment and segue into how ChatGPT can be used. What are some of the ways that you believe it could help support assessment? How about instructional decision-making and accountability? Those are concerns for educators, right?
Absolutely. And as you know, my focus has been on academically low-achieving kids, kids who are in special education receiving math services. And, so, the very question you're asking goes back to a pillar that's been part of special education particularly for decades using assessment for all of the reasons you just articulated for accountability, for instructional decision-making, et cetera, et cetera, et cetera. And to answer this question, Pam, what it takes me to is the material that I've created for Voyager [Sopris Learning,] the TransMath program, and all of the assessment instruments that are in that particular kind of intervention program. And as I think about that, how could something like ChatGPT integrate and improve the various forms of assessments that are there? So, just as sort of an overview inside something like TransMath, you got everything from the assessments that are built in on a regular basis, the curriculum-based, if you will, assessments of quizzes and tests and even performance assessments, but broadening it out into a bigger circle you have placement tests at the beginning of the year, accountability tests at the end of the year.
And even for external accountability, you have things like Quantile measures that give you kind of a curriculum-independent understanding of how kids are progressing through a curriculum. But to come back to this in terms of a bigger picture, one of the things that's always the case when you're looking, just say for example, at the middle school level, it's the issue of how do you organize instruction in a coherent way for a relatively homogeneous group of kids? I mean, we started the TransMath project simply because when you look at a typical middle school, most of the kids are going to experience kind of a general education approach. Now, in so many cases, you have a high track class of kids in a middle school, whether it's stated explicitly or otherwise, you have a broadband of kids who are in quote, unquote the general math class, and then you have some kids who are either getting remedial or special education services.
In all cases, when you get into these second two tiers, the average math track class or the special ed class, you still have lots of variability to grapple with. And to make this issue even more complicated as we talk about it, once you place kids in a program, I don't care where you start, how you move across time becomes problematic. They may start at the same place, but the very nature of learning is there are different rates of learning. So, one of the things that got me thinking about in terms of ChatGPT is in the history of special ed, for example, there are all kinds of curriculum-based programs and curriculum-based measurement, progress monitoring, or, however you want to describe it. It gives you all kinds of information on individual students. But from a teacher's perspective, well, what do I do with this?
Right? I mean, I'm not going to do 25 different things with 25 different kids. That doesn't make any sense. Math today is about very much about relative homogeneous grouping, I believe, and what that affords in terms of the opportunity for interaction, dialogue, presentation to kids at roughly the same level of learning. So, if artificial intelligence or smart technology uses can integrate the various forms of assessment and capture how kids progress over time, one of the big benefits that could come from say something like ChatGPT is to say, "OK, here were these kids at this level of a program starting in say September, by November, where are they? What's the relative progress? And do we have an opportunity, let's just say by the end of the first trimester to regroup kids so that we again have more homogeneous grouping?" I think that's the real trick, is to give teachers the opportunity to, especially as you start to work more specifically with kids who are struggling, regroup them in ways so that their needs can be addressed in a much more intelligent fashion.
And while this might sound somewhat farfetched, this is the very essence of practice that goes on in some of the highest-performing countries in the world. This is a characteristic of Finnish education. And just to put a pin on this whole discussion about assessment, one of the things that people don't understand or realize I should say more than anything else about Finnish education is 50 percent of the kids by the time they achieve the eighth grade have had specialized instruction like this, this kind of dynamic regrouping. It's not special education as we know it in the United States, but it's a regrouping of kids in more homogeneous ways to meet their instructional needs. And I think that could be a very powerful way in which AI-like technology could be used in the background that's grounded in ongoing assessment.
And we started with assessment and you list all different types of assessments that teachers or educators are very familiar with, but you led with the idea, but it's beyond that, right? It's beyond. We have to look at the big picture. And one thing that really caught my attention, it's less about the reports of the reporting. So, quite often we're looking at those reportings and we should study the data, but the idea of it being more about fine-tuning for the next stage, which is how do we teach the kids? How do we regroup them and fine-tune for more appropriate instruction? Did I sum that up?
That's really important, and I can't help underscore it. You got it exactly right. This traditional problem with all this assessment, and I mean, I've been in the research world of special ed for too many decades that I can't even count. And, sure, you get this feedback that says child X is here, child Y is there, and teachers don't know what to do with all this diverse feedback in terms of where kids are, well, let's just look at what math should be for kids regardless of whether they have special needs or not. It should be interactive. It should be very much centered around give and take between teachers and classroom talk and a variety of things, all of which is grounded in groups of kids who have relatively homogeneous needs.
If you go to the one direction of 25 kids in 25 different places, you've either got worksheets or you've got drill and practice on the computers, which have very, I think, relatively limited success. I mean, it's not to say that they shouldn't be used, the technology-based instruction, computer programs and things like that, but they're not the answer. And if you go the other direction where the groups are too heterogeneous, as you find in a lot of middle schools, they move across time, you get stuck in the mud and teachers either move too quickly and kids are left further and further behind, or teachers sometimes regress to staying with the lowest achievers in class and not a lot of progress is made. All of that is functionally related to having highly heterogeneous groups of kids. So, if we can kind of think of regrouping kids using assessment in the background and helping intelligent decision-making, instructional decision-making, that could be a profound benefit for a lot of teachers. How do I organize kids and at different points of time?
All right, thank you, John. I appreciate that. Also, part of your legacy as a mathematics instructor is the way that you patiently help struggling students grasp those concepts to help them succeed. Let's think about curriculum development that helped lead the way in that direction. Where does ChatGPT fit for these kids who struggle? You kind of alluded to that in your previous question with fine-tuning, but can you elaborate on that please?
Sure. It's a great question. One of the things that caught my attention, I heard an interview with Sam Altman, who's one of the CEOs at OpenAI that developed ChatGPT, and he said within one of the first sentences on a podcast that 10 years down the road ChatGPT could be a math tutor. And I thought, well, what would that look like? What would tutorials...We have things like Khan Academy today where you pretest students or whomever they are, plug them into a scope and sequence and they do lots of drill and practice, and they move on to the next concept. And that doesn't take a lot of intelligent programming to do that. But when I think about the way kids across the board, and particularly kids who struggle, need help, one of the great virtues that's even available today on the Internet are an incredible array of resources that are available to explain concepts.
I mean, if I go back to the last edition we did with TransMath, one of the best things we built into the program were called Teacher Talk Tutorials that were brief presentations of concepts. They were animated, they were narrated, they only lasted two or three minutes, but it helped visually and auditorily convey the concept and it could be played anytime, anywhere. Well, amplify that out further. And for example, my youngest daughter who went through high school not too long ago, five years ago, with her friends, survived calculus by accessing all kinds of resources on YouTube to try to understand concepts. Well, OK, take that direction a step further. What if something like ChatGPT were able to not only harness the available information out there in a tutorial-like fashion around a particular topic, but if ratings existed, it could weed out the low-quality presentation of information from the high-quality of information.
Now, that's talking about something that could be done very, I think, relatively easy in the near term. It's just a matter of having some semblance of rating systems around or how frequently certain kinds of information's used and assimilating that for a teacher. I want to teach kids about equivalent fractions. I want to teach them about the concept of ratio, something like that. And up comes, here's some high-quality recommendations we might consider you passing along to your students as sources of information. Down the road, and I think this is where ChatGPT may go, certainly a decade out, is that you could conceivably construct interventions that are intelligently driven around topics. One of the things that's not talked that much about in terms of ChatGPT is it's associated program called Dolly, which deals with visual information. So, I could imagine if you put in the parameters, and this is again getting to be a little bit speculative, but down the road, you could actually design kind of a curriculum-development intervention for kids to help explain certain concepts.
And that could streamline things considerably in terms of curricular interventions, because the big story is it's one thing to learn about it in a classroom. Math as we know, is difficult. It's complicated. You got to come back to it another time. And to be able to access that understanding of the information at a second point in time, one that doesn't require the teacher to create all this stuff, that could be a huge gain for kids and individuals are trying to work with kids in different contexts to continually improve their understanding of a particular topic.
All right, so it provides an avenue for having access to something more. You use the term harness, high-quality supports for learning concepts. Absolutely love that idea. You actually moved forward with my next question here when we spoke to actually being a support for math instruction, now, this was specific to, "Hey, it can be a math tutor. Here is how we can harness all this information for students who need that extra support." When we're thinking about support, just for that initial direct math instruction, do you have any ideas on how ChatGPT can help support teachers?
Well, I've actually tried using ChatGPT to do exactly what you've talked about. I was actually surprised, and I'll get to the example here in just a moment, but I was actually surprised at how well the earlier version, one of the earlier versions just last December, that version of it handled my request. And here is the request. The request was, "OK, I'm a teacher. I have heard I need to use certain manipulatives to teach a concept, and let's just be specific here. I've heard that, yeah, I could use pattern blocks, those very things that appear in kindergarten, first grade. I can use that as the basis for teaching basic concepts of fractions." So, I put in ChatGPT, "How would you use pattern blocks in the context of fractions?" And it gave me, not detailed, but surprisingly lucid information about how those tools could be used.
Because the thing that kind of blows my mind, there are tons of teachers out there today, my daughter tells me this because this shows my age, but there are tons of teachers of the day who were trying to learn how to teach math through TikTok. I mean, go figure, right? That's kind of going around your elbow to get to your thumb, looking for TikTok influencers in math to understand how to teach. Well, now you can go much more directly to the issue just by asking something like ChatGPT to do it for you. How would you go about that…But now as more and more information gets aggregated on the Internet, something like ChatGPT has more to draw on to be able to help in terms of this kind of presentation of curriculum. So, there's a benefit, obviously, for teachers as learners, how to represent this kind of topic, that would be one way to come at it.
And I'll tell you just to show you how quickly things are changing, I'll give you just a vivid example of this. In December, I asked ChatGPT to simply calculate the volume of a cylinder. Now, this is something that is taught at the eighth-grade level in terms of standards. For whatever reason, and I ask it in six different ways. It was pretty simple. I gave it the height. I gave it the diameter of the cylinder. It kept giving me the wrong answer. He was always off by a hundred. In fact, I went to a calculator four times to make sure that I was right and it was wrong. In the most recent version of ChatGPT that was released about a month ago, ChatGPT-4, I asked it the same question.
Not only did it give me the correct answer, but it gave me a step-by-step explanation of how it achieved the answer. And I say all of this only to suggest how quickly things are changing. It kind of blew my mind that not only does it give me the right answer, but it's the formula step by step. Here's how I used it to achieve the answer I just gave you.
It is mind-blowing how quickly that changed for you. Just looking at that simple example here, you're looking at content that's already on the Internet, and I'm thinking high quality is what we're looking for, weeding through what's going to work best. So, that is a tool within itself to allow teachers to allow educators to have, hey, some resources at their fingertips. Is there anything more you'd like to add to share with us about the benefits for using ChatGPT in the area of mathematics? Right? Before we end our time together, John?
Sure. I'm going to close on something that I think is fairly novel, and I did some exploration on this before we got together on this podcast. And here's the starting point for this thinking. One of the wonderful things that I had the opportunity to engage in my professional career about 10 years ago, the Institute of Education Sciences had me chair a panel on problem solving, and I won't go into all the details around that, but it got me deeper and deeper into the issue of problem solving. Well, look at the state national standards. Probably the most common phrase used throughout all of these standards is use or do real world problem solving. Now, you say that to teachers and they say, "Oh, gosh, that takes too much time. I don't know where to start, how to go about doing it," all that stuff.
Well, think about, I'm just going to give you a novel circumstance for how something like ChatGPT could be used to orchestrate much more streamlined problem solving, and in doing so, give kids a vision of what is going to look like in the world of work at the same time. OK, so it's a real interesting twofer. How do you use this search capacity, which is already now built into Microsoft's Bing to orchestrate instruction to make connections to the real world from topics this kid's been exploring? So, here we go, let's go back to the volume of cylinders. It's an eighth-grade topic. I'm a teacher. I've been teaching about geometry, and we're doing cylinders and all that stuff, and let's just imagine this context and let's see if the listeners can wrap their mind around it. You've all driven on roads where going along on a road, you'll drive over a concrete pipe.
It's some kind of drainage system. You've got water on one side, maybe it's a stream that's moving under the road, but you can all imagine that over the road you drive and underneath is some sort of circular concrete pipe. Well, let's suppose that we put kids in the position of we are going to create a proposal for a contract to do the roadwork to install one of these concrete pipes. Now, that's the word problem. And in the context of the word problem, to make it real, we can give an estimate for how much it's going to cost to dig the ditch, fill it back in again. But the most important thing to make it real world is I'm not going to give you the cost of the pipe. Now, the goal here again, is to create a proposal. "Hey, we're going to provide these services. How much is it going to cost?"
And one of the key things that we're going to center in this problem is how much is it going to cost to remove the dirt, the dirt where the pipe was, which involves the volume of the cylinder. So, I can imagine an interactive session in a classroom, maybe two at most, where the teacher sets up the problem. You can even pull up a visualization of this kind of road and the pipe underneath that I'm talking about to set the stage for this, we know how much it's going to cost to dig it, put the pipe in, fill in the dirt, again, put the roadway on top. We don't know the cost of the pipe. We don't know how much it's going to cost to remove the dirt, and what we do is use ChatGPT to find out costs for pipe.
We calculate the volume of the dirt that's in the cylinder, otherwise known as the concrete pipe, and then we figure out, well, OK, how much is it going to cost for dump trucks, which are other geometric objects? They're basically prisms to haul off the dirt. Now, that kind of interactive thinking is not far afield of what really goes on in the world of work. We've embedded ChatGPT as a vehicle for moving this information forward and acquiring further information, and we're actually solving a real-world problem in its application. So, that's just a thumbnail of the ways in which we can address a critical thing for kids, which is to see, well, where in the world am I ever going to use this kind of thing, right?
And ChatGPT allows them to gain access to the information to help them to solve that problem.
And it's just going to be a tool that's there. In fact, just to come full circle to our discussion about writing, one of the great ironies that we've got going on now is that while secondary educators and college teachers are freaking out about the writing products that are coming out of GPT, in the world of work, that is going to unleash a whole new use and it's going to be used all over the place, right? That's the real world, right? Again, I'm happy to say I'm not a writing educator having to sort of deal with this issue, but I think that there's this whole way in which search and using information, and in this particular example I gave you, creating a word problem that doesn't have all the numbers in it, is much more akin to the way real-world problems actually evidence themselves for adults.
Thank you so much, Dr. Woodward, for sharing with us the positive aspects of using ChatGPT for mathematics. Thank you for joining us. It's been a pleasure speaking with you. Please tell our listeners how they can learn more about you, your math PD, NUMBERS, being offered as I Make It.
Sure. Yeah. And I think the best vehicle is to come back through Voyager [Sopris Learning,] contact the folks at Voyager, Voyager sales or whatever. They tend to communicate to me directly interests for things like, for example, the professional development services we author, and I'm more than happy to answer questions in that regard about particular issues that I've raised in this podcast and discuss them further.
All right. Thank you once again, Dr. Woodward. This is Pam Austin, bringing the best thought leaders in education directly to you.
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