Episode 114 of the 10-Minute Teacher Podcast
From the Cool Cat Teacher Blog by Vicki Davis
Follow @coolcatteacher on Twitter
Po-Shen Loh @poshenloh, National Math Coach and Carnegie Mellon Professor gives us a refreshing take on teaching math. From giving kids problems with the right level of difficulty to solving problems with students, learn how to take any math student to the next level. You’ll also learn about the open source resource, Expii invented by Po-Shen Loh and how you can use it.
Below is a transcript modified for your reading pleasure. For information on the guests and items mentioned in this show, scroll down to the bottom of this post.
Inspiring Math Excellence in the Classroom with Po-Shen Loh
[Recording starts 0:00:00]
VICKI: Today, I’m so excited about our conversation with Po-Shen Loh @poshenloh. He’s a professor at Carnegie Mellon and also coach of the USA International Math Olympiad team , and founder of Expii. And I do want to give a shout out to my friend Junior Bernadin at Ron Clark Academy, because he emailed me and said, “Vicki, Po is awesome.”
Po-Shen Loh founded Expii, but we’ll learn more about what that is later in the show. The site is for high school and middle school students. If you’re working in Math or gifted, it is a site to check out.
See Junior Bernadin’s previous show on the 10-Minute Teacher: How the African Step Dance Ignited Kids at Ron Clark Academy
How do we help students get excited about math?
VICKI: So, Po, people ask you all the time about math and helping students do better in math, and people get excited about math. What’s your answer to that?
PO: Yes. I actually do get this question quite a lot because I work as a math coach. The answer I give is maybe a little bit disappointing for people who are looking for a recipe of, just do this problem or just do these problems or just read this book.
Actually, I just give the answer, work on things that are hard for you but not impossible. What do I mean by this? So I take inspiration actually from athletic coaching, where what you do to get better is to try to do things that challenge you. What I’m saying is that things for which your chance of success when you’re doing them might be somewhere in the range 25% to 75%; actually we might call that a zone of proximal development.
Don’t believe this number? Listen to Jane McGonigal talking about this in her TED Talk, Gaming for a Better World
How do we get students in their “zone of proximal development” or appropriate level for math problem difficulty?
PO: Now, with regard to math practice problems or studying math in general, I actually use the same philosophy. So, for example, sometimes students who are struggling might be on the below end, in the sense that they have an even less than 25% chance of succeeding at these questions.
Then, of course, what we understand is we have to give them more basic questions that they have a better chance on. But on the very high end, the same problem is also true, where we hear about some of our students being bored in class or just trying to get those high 90%.
Actually, if you ever talk to a sports coach and said that you were going to the gym to lift weights and you were lifting weights that you were basically sure you could lift, coach would say, try lifting more. And so that same idea is how I approach the math learning.
TIP: This story Po shares about math problem difficulty relating to athletic training is one that many students and teachers can relate to and understand. Use it when you introduce challenging problems to students.
What is Expii and how can K12 Teachers use it?
PO: And that’s actually why with Expii the philosophy was, to build a system where we could collect all of the practice problems that people came up with around the world, creative comments open license them, and then serve them to people using this mechanic where we would sense what a person can do and pitch them that question, which is that 50% success probability question.
VICKI: I love this. So it’s adaptive and free. And it just adapts to what a student knows to give them questions that are challenging but not too easy.
PO: Yeah. And the key idea I had here was that, we have millions of people all over the world doing practice problems. And if we use the Creative Commons license system, we can basically pull all of this global knowledge from our wonderful teachers and our students and collect – we don’t have to collect other people’s questions; we can write our own questions. But once we write them, they’re permanently free.
So, by using the Creative Commons Licensing system for these math problems, you can pretty much use these problems as you wish (except to sell them.) This means that you can write your own textbooks, share them, or use them as you would any other OER or open education resource. This makes Expii valuable for math teachers and students because of your flexibility in using them.
What makes Expii unique?
PO: And then the idea is that if the software can use the fact that the world is doing these problems to figure out which problems are easy, medium, hard and so on, and then use that statistics in the software to actually feed you a question that is statistically at your level, then you actually have this dream of reaching these questions which are at your level, starting from how ever basic to actually how ever impossibly difficult. But for you, at that point, it won’t be impossible; it would just be 50-50.
So, this means that the algorithms help students solve problems within their zone of proximal development. They’ve done the calculations for you. This helps give students problems at their appropriate challenge level. This is a free site to share with math teachers although it may take some getting used to, particularly for students who have not been challenged in math.
How can creative problem solving happen in math class?
VICKI: Po, you also talk about creative problem-solving. Now, there are a lot of people who just think, you know, math worksheets; math is math; nothing creative in math. But you disagree. How?
PO: Right. So I think that a lot of people think that math is about memorizing formulas and concepts and sines, cosines and logarithms. And this is indeed what we see in worksheets. But, actually, those are the triumphs of mathematicians who did creative thinking. What I mean is that the formulas that we learn are the results of creative thinking of the people who found the formulas. And I think that the biggest value of math as a subject is that it lets people get that creative discovery of analytical ideas.
So, for example, I just told you about sines, cosines, logarithms; these are things that previous mathematicians did. But when you work on creative problems, which can be challenge problems, then you get a little taste of that feeling that the mathematicians of old had when they did that.
So, for example, when I think about creative math problems, some of the challenge problems in your books or on your exams might be this kind; but, also, I come from the background of math competitions, in the sense that I work with – well, the Mathematical Association of America is the organization that manages the United States’ participation in this International Math Olympiad.
Learn More: The International Math Olympiad
What is the Mathematical Association of America and what K12 resources can I access?
PO: And the Mathematical Association of America is a historic and distinguished organization with over a century of work in promoting and advancing mathematics. And along that time, some of the things that they created are some really high-quality problems created by professional mathematicians, where the questions themselves are not things that you’d immediately recognize as, oh, I see this, I just use that formula; but rather they’re questions for which when you look at the question, you say, I have absolutely no idea how to approach this, and then you spend the next 15 minutes, 30 minutes being that professional mathematician yourself, coming up with a new way to solve the problem. And that art of creative discovery is actually what gives this taste of creative problem-solving in mathematics.
I mentioned this; I mentioned Mathematical Association of America so that I can maybe point out a few resources that maybe people can use. These are accessible, findable online. They run competitions called the American Math Competitions. And the old questions on these contests, called the AMC 12 or the AMC 10 or the AMC 8, or even there’s a wonderful middle school math competition called Math Counts; if you find these old problems, these are a treasure trough of questions that you can think about where you wouldn’t expect a student to immediately know how to do it.
The old questions from previous math competitions. These are used to help put bright students on the path to participate in the International Math Olympiad.
- AMC12 Math Problems (grade 12 and below)
- AMC10 Math Problems (grade 10 and below)
- AMC8 Math Problems (grade 8 and below)
- Math Counts, middle school competition, shares a problem of the week you can have your students solve
What are the benefits and challenges of using challenging math problems?
PO: And the fun part is the student wouldn’t have the pressure of feeling like they’re supposed to know how to do it. And instead, the student would have this feeling of discovering a park; or when you go into an unknown place, this, at first, scary feeling of, oh, no, I don’t know what to do, followed by the pleasure of, well, let’s try and let’s learn while we try. So these are ways that one can find such questions.
VICKI: Do you think some teachers might be scared of introducing these problems into their classroom that they might not know how to help the kids?
PO: That’s a really interesting question. One thing I should say is that it is actually – I’ll agree; it’s a scary moment to be in a classroom, in front of the classroom, without knowing how to solve the problem.
This is, by the way, how I feel when I teach one of my classes at Carnegie Mellon, which is the math problem-solving class. And I basically am the moderator at the front of the room while people are putting forward ideas on how to solve a problem. And when they go on their new ideas, sometimes I don’t actually know where those ideas will lead. I’ll agree that this is a scary feeling.
But I also feel like sometimes it humanizes me as the teacher, where what I mean is that the students start to see that we’re all just working together to try to solve these things. So there is definitely a moment of scariness, maybe several moments of scariness. If you have the time to build up this rapport with the students, where you all feel like you’re in it together; my sense I get from teaching this class at Carnegie Mellon is that in the end, everyone really seems to enjoy the activity much more because it feels very unscripted, and it feels like the whole room, including the person at the front of the room, is working together to solve this problem.
Is it OK for a Math teacher to say “I don’t know?”
PO: And also, by the way, if I don’t know how to do something, I will say, I don’t know. And then sometimes we’ll just try to figure it out ourselves. If I can’t figure it out during the time, what I’ll say is, well, let me try to figure it out and I’ll tell you next time.
VICKI: Do you realize, Po, that you have just given all of our K-12 teachers listening permission to say I don’t know; because, Po, you’re a professor at Carnegie Mellon, and you’re admitting you don’t know to your class, and everybody would just expect that you knew how to work all the problems out there, right?
PO: Oh. Well, you’re right.
PO: And I will say, the permission to say “I don’t know” is something that I think we all deserve.
Because I think that one message that I like to communicate to my students is, first of all, I don’t know everything; but second of all, if I ever encountered something I don’t know, I am extremely curious to figure out what is true. And that’s actually what they see. Basically, what my students see is that, whenever we get to a point where I don’t know something, suddenly I get really interested in trying to figure out how to do it. And we’ll pull up Google; you know, anyone can help. And I’ve learned so much from teaching my class, where students have taught me things that I didn’t know before. But I think that this mentality that the students will get is that, actually, nobody just knows something; we all discover it from a point when we didn’t know it before.
VICKI: Well, we’ve heard so many great things. And, teachers, check the show notes, because I’ll put links to all of these resources as well as to Expii, which has a fantastic website. I’ve never heard of it before. And I think it’s just a treasure chest for math teachers everywhere. But I think even besides these resources, one of the greatest things that you have gotten today, math teachers, is an encouragement to solve problems with your students, to say “I don’t know,” and to be in it with them. And it really makes for a remarkable experience in math.
PO: I’ll actually say, this is what makes it fun for me to play as a teacher as well. I used the word “play” because I always feel like the unknowns are the most exciting things to attack. Thank you.
[End of Audio 0:09:28]
[Transcription created by tranzify.com. Some additional editing has been done to add grammatical, spelling, and punctuation errors. Every attempt has been made to correct spelling. For permissions, please email firstname.lastname@example.org]
Bio as Submitted
Po-Shen Loh is a math enthusiast and evangelist. He is the national coach of the USA International Mathematical Olympiad team, a math professor at Carnegie Mellon University, and the founder of expii.com, an education technology startup providing a free personalized learning platform on every smartphone.
As an academic, Po-Shen has numerous distinctions, from an International Mathematical Olympiad silver medal to the National Science Foundation’s CAREER award.
His research considers a variety of questions that lie at the intersection of combinatorics (the study of discrete systems), probability theory, and computer science.
As an educator, he led Carnegie Mellon University’s Putnam team to its first-ever #1 rank among all North American universities. His approach to coaching the national Math Olympiad team received significant press coverage after the USA’s historic back-to-back #1-rank victories in 2015 and 2016. Through Expii, Po-Shen extends his activity to the global mainstream, combining algorithms and crowdsourcing to deliver a free artificial intelligence powered tutor for the world of math and science.
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