Pam Harris  00:01

Hey fellow mathematicians. Welcome to the podcast where math is Figure-Out-Able. I'm Pam.

Kim Montague  00:08

And I'm Kim.

Pam Harris  00:09

And we make the case that mathematizing is not about mimicking steps or rote memorizing facts. But it's about thinking and reasoning about creating and using mental relationships. We take the strong stance that not only are algorithms not particularly helpful in teaching, but that mimicking algorithms actually keep students from being the mathematicians they can be. We answer the question, if not algorithms and step by step procedures then what?

Kim Montague  00:37

So sometimes inspiration for the podcast comes from others asking really good questions. So @MrJames_MH, I think that's 'James Myklebust, Myklebust-Hampshire?' You can tell us if we butchered that. Sorry about that. Anyway, he asked on Twitter, "What makes a rich task rich?" And we thought that that was such a great question. Right? 

Pam Harris  01:00

Great question. Way to go? 

Kim Montague  01:02

And it's a thing that people mentioned in Math Ed a lot right now. Right? Rich tasks, and what are rich tasks? And what should they include? How do I find them? So we thought that would be a great conversation starter.

Pam Harris  01:13

Yeah. And so sometimes people will, like you said, call it a 'rich task', an 'open task', an 'open middle task'. Sometimes people refer to them as 'three act tasks'. Thanks, Dan Meyer for that. Sometimes people will refer to them as 'investigations', sometimes as an 'inquiry learning activity'. So there's sort of lots of different kinds of names or terms out there that sort of describe this, I don't know, this amorphous thing and I think often they all get lumped together and, "Oh, yeah, discovery learning that that thing." So we thought today when we got James' question, James. Can I call you James, Mr. James, Mr. James MH from Norway? When he asked that question, which by the way he's been great to interact with on Twitter. Twitter's such a weird world, right? Like we feel like we know each other and we don't even know how to say each other's names. But he asked a great question, what makes a rich task rich? So we thought, well, we read through the, helped me, what's that called on Twitter? 

Kim Montague  02:18

Comments.

Pam Harris  02:18

What? The comments yeah, It's called a thing. It's like a stream.

Kim Montague  02:22

A feed. 

Pam Harris  02:23

A feed? No. Whatever, the list of responses that came from his tweet, and Sean Walker, so @SeanPYPParis, on Twitter said, "The need to think, perhaps think creatively or critically or through metacognition. But learners should need to think." So awesome. We totally agree, Sean, that a rich task is richer when students need to think and I love the creative, critically and metacognition, thinking about thinking, thinking about your own thinking and how your brain is thinking. I think those are all wonderful parts about a rich task. Also, what would be some other things that would be noteworthy? Well from a favorite person to interact with on Twitter, Tad Watanabe, and I may have just totally butchered his name as well. Has been lots of fun to interact with him on Twitter. He pushes back often on things that we say on the podcast. We appreciate his really thoughtful responses. He's written several blogs in response to the podcast. Thanks a lot, Tad. We appreciate it. I'm honored that you would think about what we're talking about and respond. He posted a phenomenal list that we really, really like. He said, "My mentor, Grayson, H. Wheatley wrote in 1991," which, may I just in a little aside, that's the year I started teaching 1991. That's when I started teaching- "that had a rich educational activities should." So a rich educational activity should have and he put a colon and then he listed a bunch of things. And we think it's a pretty cool list. We thought we'd focus on a few of them today. So we liked, well, I think we liked them all. Right, Kim?

Kim Montague  04:09

Yeah, absolutely. I remember seeing on the feed-

Pam Harris  04:13

Feed, no. I still don't, tread. It's the thread, Kim. It's a thread, that thread, the Twitter thread. There we go. I feel better now.

Kim Montague  04:21

I'm so not a Twitter person. 

Pam Harris  04:25

That thread Tad put in this list from his mentor, Grayson Wheatley, about what makes a rich task rich. And we'd like to talk about a few of them. So, Kim, start us off. What was one that struck you?

Kim Montague  04:39

Okay, so one of the 10 that he posted that I thought really resonated with me was that it was about inviting students to make decisions. And I really, when I read that, I really liked that because I feel like when you invite students to make decisions, an invitation sounds lovely, right? And I think that when kids don't feel like they can make decisions, that's when they sit back and wait for the teacher to tell them what to do. 

Pam Harris  05:06

Absolutely.

Kim Montague  05:06

They just like, wait it out and they, but an invitation means: You can think, and you can decide, and you're a part of this. So I love that one in particular.

Pam Harris  05:16

And it's not just: Hey, decide which rule to use here. Which thing that I've had you memorize belongs with this problem. It's not that kind of invitation.

Kim Montague  05:25

Or which of these two problems do you want to solve? Right? Like, sometimes we give them options. It's not that it's, it's more about deciding how they want to tackle something.

Pam Harris  05:36

Yeah. Like, what relationships are pinging for you right now? And how does that, how do you want to follow that? What are you going to do with it? Nice, nice. I like that one as well. 

Kim Montague  05:44

What about you?

Pam Harris  05:45

Okay, I'll tell you one that struck me. He said, "Be replete with patterns." Oh, I love that one. And part of the reason so 'be replete', like be full of, have tons of patterns. Now, I really like that, because I've seen some things that people call rich tasks, or they say that they're, you know, like really engaging activities or something. But they're really just like, dressed up. They're just 'frou frou'. They're just, what they're not, is something that is replete with patterns, where there's so many things happening, that you get influenced by those and you get sort of caught up in the patterns, and you're intrigued and interested by what's happening. And early in my teaching career, when I would land on a task that was replete with patterns. That's the kind of task that I would be like, "Ooh, that! Like, yes!" And it would be really, especially as a curriculum designer, so I consider myself a curriculum writer. I'm very intrigued by those tasks that just have enough patterns going on that I can dive into it. And I can be, you know, really getting at what's happening and starting to solve a problem. And then see more patterns and see other directions that I could go and add new things that shed light on what's happening. And then after, even after we've answered, that we can go from there, like there's just so many patterns happening, that it's rich, and that you can take different paths and that you can connect them back together and really use those patterns to help make sense and realize what you're doing. I think that to me, that's a sign of a really nicely designed multiple access rich task. 

Kim Montague  07:35

That's cool. Yeah. 

Pam Harris  07:36

Alright, your turn.

Kim Montague  07:39

So another one that I really, that struck me. I'm not exactly sure why it did. So I'm thinking about it. But one of them that he listed said to "promote discussion and communication". And I think sometimes we have fake conversations where it's like, the conversation isn't.

Pam Harris  08:03

I can tell you the one I heard just the other day. 

Kim Montague  08:05

What? 

Pam Harris  08:06

Okay, so tell us all about how you do this thing in your family and your tradition and then talk about, and it was, that's fine. I don't have a problem with that happening in class. I think we should connect with our students personally. And, "So see, like, hey, the number five is in this problem? Okay, let's solve this problem." Like it was this, again, I'm all for getting to know students and connecting with their culture and their background. But not in this weird, fake, you know like, "Oh you said a number like, oh, there's five people in your family. Well, hey, let's do some numbers in this problem." Like not trying to make this weird, strange connection. It's not just conversation for conversation's sake. If you want to get to know kids, great. But don't try to make this, like warped sort of like, kids see through that. I mean, unless you're totally goofy about it, then that's another thing. 

Kim Montague  08:58

Yeah. 

Pam Harris  08:58

It's okay to be goofy.

Kim Montague  08:59

Well, and I might also wonder about, personally, the idea that something would promote discussion and communication, because math is really interesting to talk about. And I have fabulous conversations with my personal kids. And the idea that there could be something that we're talking about a problem or a situation that is promoting that discussion, that gives us a richness to talk about, I think is really interesting. So, you know, I could ask them a bunch of questions that is like a yes or no question. But to have something meaty enough that you want to continue to explore it further in conversation.

Pam Harris  09:33

Something that's 'replete with patterns'. 

Kim Montague  09:35

Yeah, maybe. Could be.

Pam Harris  09:38

I think it is, if there's a lot of patterns that can promote discussion and communication. Yeah, absolutely. I was in a teacher workshop not too long ago where a teacher said, "Don't make me work in a group. I hate that. I've never liked group work." And I thought you've just never been given a problem that was worth communicating about. That was worth, that you were interested enough to like see how someone else was thinking about it. You've been in situations where the answer was all that mattered, and you were able to solve it. And then you were done. Because I say that, because then in that workshop, we had plenty of conversations with this particular teacher, as we did things that were interesting enough to encourage and promote that discussion and communication. Cool. 

Kim Montague  10:20

Alright. What else struck you.

Pam Harris  10:21

Yeah, I want to mention one that I'm really glad was on the list, because I believe this, but I don't know that it would have made my list unless he'd suggested it. So it is now on my list, because I totally agree. And it is that that task should "lead somewhere". Now, I may take some flack for this one. And I don't know maybe Tad and his mentor Grayson Weatley will too. The idea, are there cool problems out there that are worth playing with just to play with? Sure. Are there cool problems out there that are interesting, and that are fun, and that are intriguing, that don't lead anywhere in our typical K 12 curriculum? Absolutely. Do I want them to go away? No. Do I want to have them front and center in my math classroom? Maybe we wish we had time for more of that. But I'm going to suggest that there's enough out there that does lead somewhere that we can use those. We have a limited amount of time. And we really want to help our students develop. I'm a realist. I think we have standards. I think it behooves us to meet those standards. So let's do rich tasks that aren't just rich for rich sake, but they are also leading somewhere. That they are going to help us get more sophisticated in our mathematical thinking. And I think that can be an important thing. If not, I think we run the risk of disenfranchising some kids. I don't know the right word, of taking a group of kids and sort of like, we might get them excited about something. But if we don't help them be successful now, so that they can continue to be successful, that we're doing them a little bit of a disservice. That doesn't mean y'all, that doesn't mean that I'm not going to bring beauty and creativity and art and like as much of. But I think we can do that. I could bring all of that in and still lead to important mathematical ideas that are going to be important for students to own to be successful in today's world. Did I say that well enough? I'm going to take some flack for that, huh? 

Kim Montague  12:40

It's okay. 

Pam Harris  12:42

So lead somewhere. I agree with you, Tad. I agree with Grayson. They should lead somewhere. So one other one, they were all good, right? We liked all of them. But another one I really liked, and I was happy to hear was "be extendable". And I think that what's interesting to me is that I would want a rich task to be extendable in a couple of ways for the class itself. And I think that speaks to your: it's leading somewhere. But I also like the idea that we could have a rich task that's extendable for individual students. Something that could maybe be generalized, or maybe that's something that I can come around and I could say like, "What about this? Have you considered this? Oh, I see that you-"  What would work all the time?

Kim Montague  13:27

Yeah. And those conversations come with more students than not, I would think in my classes. But it's something that is not just, it's one single problem. It's one thing that you're supposed to accomplish for the day. But it kind of matches up with your 'leading somewhere', and maybe we just read those a little differently, but I love the idea that you can have a rich task that you can extend when students are ready for that extension.

Pam Harris  13:56

Absolutely. Yeah, I think those are different because 'lead somewhere' doesn't - I'm not sure I'm going to do any more justice than we already have. But 'lead somewhere' means that there's a big mathematical important place that we're heading because of it. And 'be extendable' to me means that it's more differentiate-able. That there's different sort of extensions that kids can go off on and find good mathematics in, but also extend to where it's leading. Like it doesn't- 

Kim Montague  14:29

Yeah.

Pam Harris  14:29

Yeah.

Kim Montague  14:30

And hopefully in a couple of ways, right? Hopefully not just like, "Oh, you're done with problem 1. Now you do 1 B or 2.

Pam Harris  14:36

No not that. Like bigger, cooler, like, yeah, like side tangents almost that illuminate and add to the beauty of what's going on. Absolutely. Okay, so for just time sake, I'm going to add my last favorite one that was a part of that list was 'have an element of surprise'. Bam! Could not agree more. That is one of my biggest goals. When I write a problem string, I am always trying to stick just a little bit of a (click sound), a little bit of a (pop sound), a little bit of 'hmm uh', like yes. Like this moment where kids go, 'ooh', like I just like that sort of pop that you can have when there's a little bit of an element of surprise. I think Dan Meyer has a talk about that. There's just a really nice emotional satisfaction that can happen when there's this little bit of an element of surprise. I think that's brilliant. And if I could, I'm going to add to of all the lists and everything that I would add the word 'intrigue.' I like to get kids really intrigued in what's happening. And if the problem itself is intriguing, I think that's really helpful. I'm going to add also, that I think it's nice if it's a low on words, high on images. So we don't have a lot of words to wade through, but we can sort of get the feel and the gist of what's happening with images. And then also I like it when there are strategies that are visibly model-able. Like I would like to be able to model visibly, the thinking and the reasoning and the way that students are using relationships. I think that makes for even a better rich task. Kim, do you want to add anything? At the end?

Kim Montague  16:21

Oh, gosh, always right? I feel like we have lots to say about rich tasks, but I'm looking at the time. And so you know, I know I have more things that I would want to say. And I bet you do too. So-

Pam Harris  16:32

Yeah, I'm thinking of lots of examples that we could talk about that would help exemplify what we just talked about. So should we do another episode? 

Kim Montague  16:37

Yes. Let's do that. Alright,

Pam Harris  16:38

Let's totally do another episode. So stay tuned. Next episode, we will continue our conversation about what makes a rich task rich. Thanks again for asking such a wonderful question, Mr. James. Myklebust-Hampshire, from Norway. We appreciate that question on Twitter. Alright, y'all, if you want to learn more mathematics and refine your math teaching so that you and students are mathematizing more and more, then join the Math is Figure-Out-Able movement and help us spread the word that math is Figure-Out-Able.