Shaping Mathematics To Be Creative, Entertaining And Rewarding
Matthew Peterson, Co-founder, Chief Executive Officer, and Senior Scientist at MIND Research Institute, spoke about his involvement in the Institute and the overall state of mathematic learning in our nation. Peterson points to a number of alarming statistics that indicate how high school students are graduating with drastically inefficient math skills. The lack of mathematic problem solving is not only a hindrance to professional development, but it threatens our nation's growth as a whole. Peterson shares a variety of new teaching methods that not only engage students at younger ages but offer interesting creative play to the field of mathematics.
Rod Berger: Well, Matthew, it's so nice to catch up with you. It's been a few years since we last spoke. The MIND Research Institute has continued to grow and expand, and there are lots of different things that you're doing. But before we get to those events and the different ways you're looking at expressing math; your experience of that for not only kids but adults, let's just talk about where we are with math education in the last couple of years. As we look back to our original conversation, have we made progress? Where do we stand? I feel like this is a constant conversation between both academics and practitioners in the classroom and I would be curious as to your take.
Matthew Peterson: You've put a dagger into my heart here. (laugh) I am not happy with the overall progress. It's slow going. MIND has made a lot of progress. We are now over a million students, 1.1 million students. We're still at that, you know, (0.42 effect size) our organization is shooting for our 0.8 effect size which is the minimum effect size needed that could get 90% plus students proficient in math across the entire nation. When we get to that point, it will be an important point in history. It will say, "Hey, it's possible to have an education system where virtually all students coming out of it have a deep understanding of math. They can apply math to solving challenging problems, and the lack of mathematical ability is no longer an inhibitor when facing STEM careers and things like that."
RB: It's incredible when you put the statistics and the numbers behind that discussion. I don't think the general public would think about that. Take me inside that chasm between where we are now and the 0.8. What other variables need to change or contributions from people outside of what you're doing that can help make an impact of that size?
MP: So what all needs to happen for us to get there.
MP: Yes. Well, you talked about the statistics. Let me first touch on that because maybe not everyone realizes that in the United States, only 30% of students are proficient in algebra, even after the end of high school. So out of our education system, only 30% are proficient, and proficiency is not a very high bar. It is a statistic that people should be aware of, and it's going to hurt us as a nation because more and more jobs are requiring mathematics. There's work for us in the development aspect. There are patriotic elements because China and India are pumping out more PhDs and engineers than we are. If we talk about our global competitiveness as a nation, education is the number one thing that we need to address.
So, what is it going to take to get there? I think it's going to take some innovation. We need a lot more learning to happen than what is currently happening plus a depth of understanding. There is also just the ability to perform mathematically on things that are routine. We have non-routine problem-solving that people call "creative reasoning" and that's great, and we need to, as a nation,continue to push that, but it's also a fact that just routine mathematics; time, procedures, etc., we can't even get those to happen at scale. It's a multifaceted problem. What is it going to take to get there?
There is a lot of innovation, and our non-profit research organization (MIND Research Institute) has been investing a lot of resources into these particular issues. I think we have at least three big areas of development that could, and I'm hoping will lead to something produces dramatically more math achievement than what is happening currently.
RB: And what are those three areas?
MP: The three areas are not easy to understand. But one is experiential knowledge of mathematics. Acquiring excellence in math is tied to other areas of achievement. It's no pain, no gain. You have to go beyond your comfort zone to get to that level of mastery on some of the mathematics.
Even just getting your multiplication tables down to automaticity, a lot of students don't get there. Even though they can get there, if you ask them, "what's seven times eight?" they reply, "Oh, it's 56." You want them to say 56 as fast as the color grass is green. You say, green. You don't have to think about it. You want those things down.
Most of our students do not have it that way, a straightforward kind of thing. Mere rote memorization. Even rote memorization, getting it to the point where it's automatic and fast, hat takes a lot of work, lots, and lots of practice just to achieve. It's not even getting to solving algebraic equations and other non-routine mathematical problem solving. That is the real end zone, but you have to have the foundation.
I said there were three things and you asked what those three things are, and I started talking about this. (laugh) But it's a big word salad. It's very difficult to build this level of mathematics where you can own it. If you see the world mathematically; you can apply math to modeling the world and solving challenging problems. There's a lot of work to get there.
There is a baseline, which is not painful, and to do it is very rewarding and very easy. It is experiential knowledge where you experience mathematical ideas. It's very fun to have experiences about numbers and operations and other mathematical concept become your good friends that you know. So, one is building up student's intuition and experience about numbers; number sense, operations, and mathematical concepts. There's a lot of work to be done there, and it's very rewarding and very fun for kids. We need math to be more engaging and more fun.
On top of that is when you started getting into the no pain, no gain territory is being able to perform problem-solving and other mathematical skills at a high level where you have a mastery over it, you have ownership over it. I see kids outside, over and over, trying to do some skateboarding maneuver, which is a lot of work, they get scraped up knees, they go over and over and over until they master and it looks awesome. They need to be applying that same thing to math. So there are some breakthroughs there.
One of the things in math that's missing is that instant informative feedback as you're performing the mathematics; being able to see the instant ramifications and the results of the mathematics that you're doing. Too often teachers say, "Oh, solve this problem, and you go." And you do something, submit it, and then later you get the result of right or wrong. It is not the same feedback that you get when you're trying to do some skateboarding maneuver. You get it right then; it's instant.
The other thing about skateboarding is that you can be creative in skateboarding. You can perform new moves that other people maybe have never done before and show off. You can do that in mathematics too. There are things that you can learn in mathematics that if you showed it to someone, they would say, "Whoa, I didn't know that you can make that. How did you do that?" "That's impressive." We're using a game-based system, like playing video games, but where you perform at the level where you're getting feedback, you're willing to put an effort because it feels good to get better at like skateboarding or any other type of thing that kids put effort into, music or other places. You can be creative. Mathematics can be a creative medium. You can create awesome artwork with mathematics. You can do amazing stunts. You can do all kinds of things, but we don't give students the ability to show off and to exert their mathematical powers in interesting ways.
So, does that give you a sense of different areas? Spanning the three areas?
RB: It makes sense.
MP: We've already been on a pretty long rant. That was a lot of talking for one question. (laugh)
RB: (laugh) No, no, no, it colors it in. It helps to share that math can be creative. You can be innovative at the individual level. I believe that's something that's a change in the narrative. I think it is quite refreshing.
I'm glad you brought up game-based learning, and the timing is very interesting to me that we're speaking today. I received a text message from a superintendent in a State that I will not mention; is at an event today with a group of superintendents. I want to get your feedback on something he shared.
The superintendent sent me a text message and said, "This is very concerning to me." They were talking about math as superintendents, and they were talking about game-based learning as a vehicle to learn math. It sounds like the tenor in the room was, "We've got to be careful. Stay away from games because they're going to be focused on the games and they're not going to learn math."
RB: I have my opinion, but I want to know what is your opinion?
MP: I agree with the superintendent. You have to watch out because so often when organizations take a game-based approach to learning mathematics, they'll say, "Oh, we're going to have students solve a math problem. But, to make it cool, we're going to let them do a little bit of video game stuff and then give them the problem." And then they have to solve the problem before moving on and doing more video games.
RB: The math problem is not often embedded in the actual game experience?
MP: So often it's not, and then the math becomes an obstacle. "Wait, I was just playing this game. Now I have to do this stupid math problem." Then they start to like math even less as a result, and it's not effective because they're spending most of their time on the game part and the math part is annoying.
RB: So then, if we're looking at the skateboarding analogy, it's sort of like saying to a kid, "Okay, in between your skateboard routine, we need you to do 20 pushups and then go back to it."
MP: Exactly. There are many pitfalls and many examples out there of really wrong approaches to game-based learning. Now, there are also good approaches. The good ones are great, and we should encourage them because they're intrinsically motivating. You get informative feedback that's right there; feedback about your solution to that mathematical problem and why it worked or why it didn't work. It's powerful, and when you put in the game-based system, it can adapt to you, and it can also make you want to try harder, over and over again to put in the effort necessary to get to that level of mastery.
RB: Matthew, let's talk a little bit about a couple of events that are coming up for you and your organization. Tell us a little bit of that because I think it's fascinating the way you're looking at the way in which we experience life in society and tying things together so we can also learn.
MP: You're talking about the couple of events that we have coming up?
MP: Yes, so we have a big math fair. We do math fairs across the country. The math fair coming up on November 5th is in Costa Mesa, California. If people want to know what our math fair looks like, you can go to mindresearch.org/mathfair. There's a video on there from our last one in Chicago. It's exhilarating. Thousands of people showed up. Bright students. It's amazing that they would come to a math fair on the weekend. They come away very happy that they attended and often parents will say, "Oh, we're going to show up just to give them some exposure to math." And they end up staying all day long. They thought they were just going to be there for half an hour because that's how fun it is.
We have interactive mathematical theaters. The audience participates in the mathematical mystery that is being solved in that theater event. There are also hands-on math games, fun mathematical problem solving that is a collaborative. A lot of learning happens. There's also a game-a-thon component where kids can work with game developers on building games to teach math. It's a great event.
The thing that we're doing differently, this year is we are using food sciences in the culinary arts to give a new lens, a new window, if you will, into mathematics that people don't normally get to appreciate. Time, taste, flavor, and aroma are placed on a graph. If you have a graph of a recipe, let's say with different proportions and one ingredient on the x-axis and one ingredient on the y-axis, the typical recipe will expect a particular proportion which will be a line that goes to the origin at a different slope, one particular slope through that space.
If you have points in that graph and then taste different recipes, can you tell the difference? What was the different ratio? Can you see that based on the flavor or other aspects? Can you point on the graph which recipe you think that was? Getting them to connect taste and food-related sensations to graphical and mathematical concepts.
We also have hands-on exhibits, where kids get messy with dough, doing some fun mathematics. The night before the Math Fair, we have our annual non-profit fundraiser and this year, it's called, "Taste of Math" and we are inviting local and national celebrity chefs. They're fantastic. We have some big names coming that are creating unique culinary creations with fascinating mathematical elements to them.
A couple of examples: We have Eugenia Cheng. She is a mathematician out of Cambridge. She was on The Colbert Show and recently in The New York Times. She's a dynamic speaker, and she wrote a book called, "How To Bake Pi," the number pi. (laugh)
It's a real cool book. She'll be there. We have the "Master Chef" for Campbell Soup coming and talking about how ratios break down at "super" large scales. If you made a gallon of soup, you might put one bay leaf in the recipe, but if you are making a million gallons of soup, you won't put in a million bay leaves. The ratios break down at large scales and how that works in the mathematics. That's fascinating.
There are so many different takes we have represented. We also have one guy that's into spices, salsa and capsaicin and the amount of capsaicin in recipes. Plus, Scoville heat units that measure the intensity of the heat of spices and the mathematics involved. A wide variety of really fascinating mathematics tied to extremely delicious food.
RB: Well, I've got to say as we close Matthew is that in corporate America, we talk about open door policies with leadership and those that are potentially working at companies. When I think of you and our time chatting today and previously, is that you have an open door policy. What I like about it is, you're welcoming in people, students, kids, and adults, into a math ecosystem that is approachable, engaging, new and progressive.
I want to applaud you for that because when I reflect on my experiences in school in math, it was not that at all. It was much more of a closed-door policy, and you just did the best that you could.
I wish you well and the "Taste of Math" and the Math Fair, sound like amazing events. If I can make it out there at that time, I would love to be a part of that and taste some interesting food while learning along the way.
We want to thank Dr. Matthew Peterson of the MIND Research Institute.
Matthew Peterson, Ph.D., is Co-founder, Chief Executive Officer, and Senior Scientist at the MIND Research Institute. Matthew oversees the Engineering Sales, Marketing, Development and Education Services activities for the organization. The creator of ST Math, Matthew leads a team in developing math learning environments that initially convey sophisticated concepts visually, rather than verbally, enabling students to gain a deep conceptual understanding of mathematics regardless of language proficiency.
Matthew, who as a child struggled with traditional language-based instruction due to dyslexia, created MIND’s ST Math® software program to enable students to learn math through his unique non-language-based visual approach. The revolutionary program has proven to raise students’ math scores on standardized tests and currently reaches over a million students.
Matthew has spoken at numerous national and international math and education conferences, before the National Mathematics Advisory Panel, and recently was featured at TEDx Orange Coast. After completing his undergraduate degrees in biology, electrical engineering and Chinese language and literature from UC Irvine, he went on to obtain his Ph.D. in visual neuroscience from UC Berkeley.