Ep 4: Top Ten Influencers

Pam Harris  00:02

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

Kim Montague  00:08

And I'm Kim. We answer the question, if not algorithms, then what? 

Pam Harris  00:13

In today's episode, we thought we'd share some of the biggest influencers on us, those who have really impacted our work. 

Kim Montague  00:21

Yeah. And there are a bunch of people who have influenced us both in teaching and pedagogy. But today, we're just gonna stick with those who have really impacted our mathematics and teaching mathematics. So, um, Pam, you've probably impacted me the most on my math. So let's talk a little bit about those who have influenced you, but start with your early influencers.

Pam Harris  00:44

Okay, cool. So how do I even start because there's so many and to be really clear, we're only going to be able to mention a few today. So if I leave you out, please know that it's just because we had to choose a few. We're going to shout out 10 influencers today. And right now we'll start with the early influencers. So first, I'd like to shout out to Janie Schielack at A&M who gave me an early reading list. I had met her and I asked her one day, "Hey, is there a better way to teach elementary math?" And she gave me a reading list to start with. And one of my first memories is I picked up some replacement units by Marilyn Burns. And as a secondary high school teacher, I'd never heard of Marilyn Burns. It's funny now because now I know right, Marilyn Burns like every, if you teach elementary math, of course, you've heard of Marilyn Burns. She's a venerable force in the teaching of math. And what really impacted me by reading her work was that it gave me this inkling that math and math teaching just might be different than I had originally thought. And it kind of set the stage for me to really want to dive into other possibilities. One thing that I was really impressed and to continue to be impressed with her work is that her math is correct. Her mathematics are solid. And so it was really good for me to be able to dive in and get this sort of flavor. And this feel for how math and math ed could be different. Janie also gave me a couple of the books, Investigations in Data, Number, and Space. That's one of the NSF curriculums that had come out, Investigations in Data, Number, and Space, and I read some of the number books. And it really was fascinating to me, again, it had a different picture of what math could be like. And what I was really clear, I didn't learn math that way. But I could recognize that I could have, that I could have done more thinking and reasoning about math, if I'd had some of the tasks that were in Investigations in Data Number and Space. And I was so interested in sort of some of the games that they were playing in there and some of the rich tasks that they had, that I began to work with my kids' teachers and do some model lessons in their classrooms. I used those. Kim, the very first time that you and I met in that one workshop, we played Close to 100. Close to 100 was a game from investigations.

Kim Montague  03:06

Yeah, I remember when you started doing work in our schools, and that one of the pieces that you brought to us was Investigations. And it's funny that I'm thinking about it back now, because do you remember that my principal at the time kind of wanted to know, "Hey, is this legit? Is it like, is this gonna fly in our school?"

Pam Harris  03:27

Yeah, you came and told me that she came to you guys. And she's like, "Who's this Pam? She's this mom in the district. Why are we changing everything according to what she's talking about? Maybe, we need to go to the real training." 

Kim Montague  03:40

Mhmm, and so we did! We did. A couple of us went to the official real Investigation training. And I remember so clearly, even all these years later, feeling like we knew what was going on. And I remember calling you on the car ride home and putting you on speaker and saying, "Oh my gosh, we have got this stuff down." And not even just having a clear picture about what was happening in Investigations, but really understanding a lot more deeply what was happening then gosh, even the leaders could express. So like you'd gone to this like correct training.  Yeah, 

Pam Harris  04:25

To make sure that what I was doing with you guys wasn't just some crazy craziness and, and you guys realized that because of some of the other work that we had done some of the things that I had brought into the training that we were doing Investigations in Data, Number, and Space really well. We like, we were seeing kind of, we weren't making some of the common mistakes that were being made around the country. It was sort of interesting and I remember when you and I were talking about that I think your principals even in the car, right? She went with you guys. 

Kim Montague  04:54

Yep. 

Pam Harris  04:54

Yep. And the more that we talked, we realized that one of the huge influences that had been on us and on the work that we've been doing with Investigations, the reason that we were implementing it so well, was because of some other work that we'd read. We had been reading Cathy Fosnot, and Martin Dolk's Young Mathematicians at Work series. And that series was really the lens through which we then did everything else. And I don't think it was until that point, when you and I both realized, oh, there's something like we knew Fosnot and Dolt's work was really good. Right? But we hadn't quite realized how much it was influencing everything else we were doing. And the more work that I've done over time, that has continued to be true that I recognize that now I look at math and math education through this very important lens that Fosnot and Dolt gave us in their Young Mathematicians at Work series. They do this brilliant thing in the beginning of each of their four books. So there's a series of four professional books. They have Constructing Number Sense Addition and Subtraction, Constructing Multiplication and Division, Constructing Fractions, Decimals and Percents and Constructing Algebra. They do this amazing, brilliant thing in the beginning of each of the books. In the first chapter, they describe a math class and it's a teacher launching a rich task. And it's a cool, rich task. They are brilliant curriculum writers, and they show the interaction between the teachers and the students. And it's, a fascinating study of what math could really be like, what math teaching could actually be like. And then part of the brilliance is that in the second chapter, they wreck it. So it's like they tell about a teacher in the first chapter that launches this rich task and how well it goes and the interaction between the kids and the questioning and the conferring. And then in the second chapter, they have a fine teacher trying to do something almost like what you saw in the first chapter. But then this well meaning teacher does just these little things that make it nosedive. That make the task not truly problematic. That's a phrase from Fosnot "a truly problematic situation". Instead of making it truly problematic, it turns it into more of a word problem. And again, so well meaning teacher, trying to get reasoning out of students, trying to do rich tasks but because of some just little things that sort of go awry, kind of wreck it, kind of make it not go well. And so it's this sort of example in chapter one, and then this non example in chapter two, and that's just part of what you can get out of their work that can really help you kind of ferret out. Oh, like I could take something like Investigations Data, Number, and Space, take a good rich task and I could inadvertently kind of wreck it, kind of make it not go as well. Or I could do some of the questioning and conferring and teacher moves that are happening in chapter one and make it be this rich experience for teachers and students. Little things that fine teachers can either sort of implement and make the things go really well or  not implement and kind of undermine what could be really good learning. It's really fascinating stuff. 

Kim Montague  08:07

I'm so glad that you brought it up. She's amazing, right? You remember the first time that I ever went to New York City? 

Pam Harris  08:15

Uh-hum.

Kim Montague  08:16

Yeah, we were about to take the district wide training.

Pam Harris  08:23

And up to that point, I'd been doing kind of the vertical training. So like, if a K-2 teacher would come to training. For half the day, they would come to me and I would kind of do this vertical, big, big picture. And then the second half of the day, they would go to a grade level specific training with grade level leaders. And at that point, you were one of our, I think, third or fourth grade grade level expert teachers, right. 

Kim Montague  08:44

Yep. 

Pam Harris  08:45

But if we were going to take it district wide, we needed to have, there were too many teachers for me to be able to do that big training all in one room. And so we needed more vertical trainers, and we were trying, we created you to be one of those vertical trainers.

Kim Montague  09:00

Yeah. And so that in true district fashion, right, they sent me to New York, to meet Fosnot and to do work with her. And do you remember that I called you. Apparently, I call you after training, but, 

Pam Harris  09:13

Yep.

Kim Montague  09:14

I called and I remember standing on the street of New York with a piece of pizza and calling you and kind of screaming through the wind and saying, "It's not Fos-not it's Fos-no." Because for all of that time, we had been saying her name incorrectly. So you remember that?

Pam Harris  09:30

Because,I totally, her name is spelled F-O-S-N-O-T and I'd never met her. I had just read her and so I called her Fos-not. And  I was looking forward to you sharing all this great math learning, all this pedagogy and everything. And of all the things you could tell me was I'm eating New York pizza on the street of New York and we're pronouncing your name wrong. Sure enough, and so -- Yep.

Kim Montague  09:52

Yeah, to this day. When I see something super traditional. I like to call it a Fos-not.

Pam Harris  09:57

Yeah, sure. You'll call me and you'll go," Hey, Pam! I've got a Fos-not for you." We'll sort of chuckle about that a little bit. So yeah, everybody you might have seen her name is pronounced Fos-no, Cathy Fosnot. She's fabulous. Yep.

Kim Montague  10:10

Okay, so those are some great k-5 leaders. What or who would you say has the greatest impact on your higher math?

Pam Harris  10:21

Yeah, you bet. So we're still talking about some of those early influences. So I'd really like to give a shout out to my cooperating teacher, Pam Giles. She was one of the very first teachers to teach with graphing calculators. I'm gonna date myself a little bit. Graphing calculators had just come out when I was a student teacher. And in a huge way, that was the first time ever that I got a glimpse of what mathematics really is, that I could type in a function into that graphing calculator, and I could mess with the parameters. And all of a sudden I could see those, the parent function shift around and I could play with the math. I could test things out and I could sort of teach myself things. I could actually see that the stuff that the book was telling me was true actually happened like it was there. And through Texas Instruments and their T Cubed, Teachers Teaching with Technology program, I really learned to leverage the power of technology and the power of visualization, that there was a connection between visual mathematics and the symbolic mathematics and that that connection was important. Sometimes, even today, teachers will say, "Oh, yeah, it's all about multiple representations." To which I'll push back on a little bit. And I'll say, "It's not really just about the multiple representations. It's about the connections between the multiple representations." And so I really give a lot of credit to Texas Instruments and T Cubed and a lot of learning. I met some phenomenal, fantastic educators that really, not only were helping me understand the math better, but their passion for teaching kids really caught hold. And I was able to sort of work with them remotely, not just the people in my school, but I started to have colleagues in the bigger world. And be able to share strategies with them. At that same time one of those T Cubers was Jerry Murdoch. And he, Jerry Murdoch and the Ellen and Eric Kamischke, had written a series called Discovering Algebra, Discovering Algebra and Discovering Advanced Algebra. And Kim, I can't tell you when I met Jerry and I started reading their books. That was the point, they were again, one of those NSF funded projects. I got a hold of their very first version of their book and it was paperback and it was two huge paperback. Like just the algebra one book with these two huge paperback books. I read every page. They had written notes to the teacher about the math, I was learning. I mean, I'd been teaching high school math already, about I don't know like six years by that point. I was learning so much about the mathematics as I read their teacher books. Sometimes I'm actually still sad a little bit. They then had a publisher that got a hold of it. The publishers are fine, but they did what publishers do and they cut out a lot of that stuff. They kind of made it more refined. And in the process, they got rid of what I thought was some really, really excellent notes to teachers. So my hats off to the Discovery Math folks, who gave me a good start to, to really talk about what it meant to have kids think and reason in higher math.

Kim Montague  13:18

And it's kind of come full circle a little bit with your work with Discovering Algebra.

Pam Harris  13:21

Oh, yeah, so now I joined the authorship team. Jerry Murdoch, passed away a few years ago. I got to meet his wonderful wife, wonderful, wonderful people. And so I sort of took his place on the authorship team for Discovering Advanced Algebra and I really feel lucky to again now be working with Kamischkes to continue to write. So yeah, really. Feeling really blessed there.

Kim Montague  13:42

Yeah, that's really cool. You've had some really influential people in your past. So we're still learning and growing right? Along with those names -

Pam Harris  13:50

Yah, never die. never die! 

Kim Montague  13:52

Along with those names, who is currently on your influential lists? Like who should we want to know about?

Pam Harris  13:59

Yeah, so let's talk about my top five current influencers. So unfortunately, we're going to skip like we kind of talked about my top five, beginning and now we're going to kind of go into the current. So we'll skip a bunch, but currently you might find it interesting that Cathy Fosnot is still on that list. She is a brilliant curriculum writer. Just last year I went to visit her in the booth, "Hey Cathy, how's it going?" And I overheard her talking to a teacher who asked her about CRA, that modeling idea of concrete representational abstract. And I kind of hadn't ever heard Cathy respond to that. I had a feeling, I've read enough of her stuff, and feeling I knew kind of what she would say, but not quite in this way. She smiled. She got that Cathy Fosnot smile on her face. And she kind of shook her head a little bit. And she said to that teacher, "Oh, that's really old research." And then proceeded to talk about their sort of perspective on models and modeling and modeling in mathematics. And I really appreciate that perspective. Because from a secondary person, Cathy will say she's an elementary math researcher. From a secondary perspective, she's spot on. All too often I will meet really good elementary people that have kind of a limited view of how it would go up in higher mathematics. But the way that Fosnot and Dolt talk and write about modeling mathematics works for secondary, for higher math as well. And so it's really important. And so stay tuned, listeners, because we have planned some podcast episodes where we're going to talk more about models and modeling in mathematics. And how it's not really about concrete, representational, abstract, but there's a whole different way of looking at models in mathematics. Um, you might have noticed that lately on social media, we've put out some graphics. We've asked teachers, "Are you looking at two models, if you had to choose is it two models? Two strategies? One of each? How are you seeing?" And we'll sort of give a picture of two models or sometimes two strategies or sometimes one of each. And it's fascinating to see the confusion that's out there, that people are really a little bit unclear on the difference between models and strategies. And then they're also unclear on the difference between a model of a situation and a model of student thinking and that those are different. And that sort of impacts kind of how we look at things like Singapore Math and some other things that are out there. So, again, stay tuned. We'll try to do justice to those big ideas in some upcoming episodes.

Kim Montague  16:24

Yeah, I'm looking forward to it's really important stuff. So who else Pam? Who's making your brain think right now?

Pam Harris  16:30

Yeah, so talking about the power of technology: Desmos. If you teach secondary math at all, you're familiar with Desmos, the online free graphing calculator. It's not just a free online graphing calculator. They have come up with some teacher tasks and teacher activities. Hit their teacher activity center. Check out some of their most popular, you'll see some most popular things like the marble slides and some other things. They're cool. They're good. They're excellent. I recommend them. But also note that you could do some really nice things with card sorts. Teachers, if you're about to do some remote instruction coming up this fall, we're feeling for you on that. We're gonna have some Facebook Lives coming up that will talk all about how you can do some real math teaching remotely. But also check out Desmos. Even if you're a K-5 teacher, I think there's some things that you could do with card sorts in Desmos. You make your own so easy. I swear, it's easier to make a card sort, in Desmos than it is to make a, by the way, I'm saying words card sort. Kim and I have made plenty of card sorts by hand, right? Where you copy him off and you cut them out and you laminate them and the whole... It's so easy to create a card sort on Desmos. So check those out. Also, they have a thing called polygraphs. That's one of their types of teacher tasks. Superduper way of teaching properties and vocabulary, one of the harder things to teach. We'd like to teach vocabulary just in time, where you sort of put students in a situation where they need to use the vocabulary and bam polygraphs do that. It really puts students in this position where they need to talk to each other about what they're seeing on their screens. And in order to do that, then you supply the vocabulary that they can use. So, some fantastic ways of really getting kids to learn. If you're teaching remotely, again, this coming school year, I would highly recommend, especially middle school, high school, though there are some pretty fantastic elementary tasks as well. But middle school and high school, I would definitely look at using Desmos to do some of those remote teaching and not only remote also in classroom but both. They could be really handy. If I was in a middle school high school classroom this fall, I would be using Desmos remotely like I said and in class. So really good. And then let's move on to another influencer. Kim, you know, I was really hesitant to get into social media. I'm not. It was a whole conversation, I'm like, "Kim teach me how to Facebook." I mean, I'm not a big fan of Facebook. I think there's some really kind of weird things. There's the comparison trap that my friends were getting into on Facebook and I think there's some things that we have to be careful with. However, I also really appreciate the MTBOS atmosphere. Now I'm saying I'm sort of pronouncing this thing and no one knows how to pronounce. M-T-B-O-S stands for the Math Twitter Blogosphere. And some people pronounce it M-T-B-O-S some people pronounce it MTBOS. It literally is a group of fantastic mathematics educators who got together and said we can harness the Math Twitter Blogosphere. We can share with each other and learn from each other and I'm so glad I dove into that world. Y'all if you're not familiar with MTBOS, sometimes it might look a little bit like it's kind of a secret club and you don't know how to get in. I kind of looked like that way to me too at first and at conferences. I just started kind of hanging out with people that said they were involved and sure enough, that's what you do. You just like dive in and and know that when you dive in, we will welcome you with open arms. I know that a lot of people use the hashtag MTBOS and the hashtag I teach math. I think both of those are fine hashtags to sort of follow on social media to really get involved in kind of this group of people that are really out there to help each other. It's the, one thing I really like about it is people are in there, just to let you know, share things that they create, share ideas that they have, and really blog about the way they're teaching. I'll mention a specific person that's in the blogosphere out there right now that I'm learning from right now has really influenced my, my really recent work is Peter Liljedahl, and his work with the Thinking Classroom. I think his books about to come out. So I recommend that you check that out. He has suggested that we can get kids up at vertically, non permanent surfaces. So think of a whiteboard or chalkboard something that I can erase really easily. And by getting people up at those vertical, non permanent surfaces that kind of get people thinking and really put them in an atmosphere of problem solving and kind of a different way, a different energy than when they're sitting at flat tables. So I'm not totally doing that justice right now. But that might be a place where you look up if you want to get some inspiration, Peter Liljedahl. You can find him and his work The Thinking Classroom. And then all of the chats and slow chats on Twitter inspired me to create Math Strat Chat.

Kim Montague  21:23

Yeah, we love Math Strat Chat, right. And you heard us talk about it if you've listened before. You can join us on Math Strat Chat every Wednesday on Facebook, Twitter and Instagram. It's just where Pam throws out a problem and ask people to share their strategy and comment on each other's strategies.

Pam Harris  21:40

Yeah, totally. It's like, it's like one big number talk. Just kind of, though I would call it a problem talk. So I'm really talking about numbers. We're talking about problems. But it's just this huge problem talk, where I throw out a question. People from all around the world throw out their answers. And I'm really loving that lately, a lot of people are helping me comment on other strategies. That's probably my favorite way for people to participate, is to read the question, solve the question the problem, whatever it is, submit your strategy. And I even like it when people say, "Hey, I've just solved it. This is what I'm thinking about before I look at anyone else's." And then they go and comment on other strategies. So that's like my fav, you can totally just lurk, you can just come and just see what other people are doing. But it's also really great for you to submit your strategy, even if it's one that someone else has put in there, because it kind of gives all of us an idea of what are some common ways that people are thinking about a problem. And who knows, you might have the first of its kind and then we'll sort of celebrate you as woohoo! That's the first time we've seen that strategy tonight. So love to have you join us on Math Strat Chat.

Kim Montague  22:41

Excellent. Who else Pam? Who you got anybody else you want to share about?

22:46

Alright, just real quick, Jo Boaler. I think if you're in Math Ed these days, you've heard about Jo Boaler. Her brain research really helped me think about time and speed and that fast does not equal good at math. And that visual models are as important as Cathy Fosnot suggests. Their work on making thinking visible works really well in tandem. Jo Boaler has given me some words to talk about how my brain works differently when I'm either pulling from rote memory sort of retrieving from memory versus when I'm thinking, reasoning and mathematizing. And then the last group that I'll just mention, I'm so grateful for the university students and the teachers that I work with every day in workshops. I learned from them, I now listen to those that I'm working with differently than before. I'm really working hard to understand their thinking and their reasoning. It's my place to practice and refine my own teaching and submit ideas that I'm grappling with.

Kim Montague  23:49

Yeah. Thanks for sharing those with us. We would love to invite you to think about who's been influential in your math teaching. Who's helped you become the teacher you are today, and you can share that with us on social media and hashtag Math is Figure-Out-Able

Pam Harris  24:03

Cool, so did you know that if you like a podcast and give it a review then more people can see it. it'll show up more. The podcast sites will suggest it to more people. So true stuff if you don't mind, if you actually like the podcast then click that Like and give us a review. If you're interested to learn more you can check us out on our website mathisFigureOutAble.com. So if you're interested to learn more math and you want to help students think like mathematicians then the Math is Figure-Out-Able Podcast is for you. Because math is Figure-Out-Able!