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  00:10

And we're here to suggest that mathematizing is not about mimicking or rote memorizing, but it's about thinking; about creating and using mental relationships, that math class can be less like it has been for so many of us, and more like mathematicians learning and working together. We answer the question: if not algorithms, then what?

Kim Montague  00:33

So we've been asking for you to send us questions that you want to be answered. Last week, we had Pam tackle one question, and today we're gonna tackle another one. So this week's question is from Rachel Adler.

Pam Harris  00:46

Thank you, Rachel.

Kim Montague  00:46

 And Rachel says, "Thank you so much for your podcast and resources, I am most likely in the minority being that I'm becoming a teacher and not currently a teacher." Oh, we're so happy you're listening to the podcast.

Pam Harris  00:57

Yay!

Kim Montague  00:58

"I love math, and actually worked as a data analyst for the past 10 years. I love data and everything it can tell us. You can slice and dice it in so many ways to see something truly exciting and eye opening. I want to bring my data analysis tricks into the classroom as a way to assess the learning opportunities with my students. My question for you is, what sort of questions do you think can be answered through data analytics to help drive the lessons? I'm thinking more along the lines of formative assessment opportunities that I can tag and analyze, not just scores on a test." And then also, Rachel says, "Also, most importantly, do you have any advice for the first year teaching?"

Pam Harris  01:38

Okay, so we're going to tackle those one at a time. So Kim, remind me later because I'm going to go off on the first question. 

Kim Montague  01:43

Okay. 

Pam Harris  01:46

First of all, welcome to teaching, woo! 

Kim Montague  01:48

Yeah, excellent.

Pam Harris  01:50

And my most, I'm actually going to give you this a little bit of advice, survive your first year. 

Kim Montague  01:55

Right. 

Pam Harris  01:56

Like, don't quit after your first year, keep going. It gets better. 

Kim Montague  01:59

Yep. 

Pam Harris  02:00

No matter how good your first year is, it will get better. No matter how bad your first year is, it will get better. So hang in there, teaching is tough, and it asks a lot and it is worth every bit of it. Do try to get in a good place. That's helpful. So let's talk about this question that you asked. You said you're a data analyst, you'd like to work with data. That's phenomenal. I love to work with data. Jo Boaler has just come out with some really nice data talks. So a thing that I would point you to is to look at her data talks, I call them Problem Talks that deal with data. I like to have sort of the general term called Problem Talks. That means we're going to give students a problem, we're going to raise a problem raising an issue, a number, a graph, or a function, whatever. And then we're going to - a set of data - and we're going to ask students to solve that problem. And so I don't really call them data talks. I call them Problem Talks about data. But if you look for Jo Boaler, we'll put the link in the show notes. Jo Boaler's data talks have some really nice things that you can look at that could maybe help you a little bit, not really with your question, but at least about using data. So then your question was, what sort of questions do you think could be answered through data analytics to help drive the lesson, and specifically, not just scores on a test? I got to be honest with you, I've been thinking about that a little bit. And I will say, I'll tell you a little bit of experience that we had. Several years ago, when I began teaching, I was teaching in Michigan - a shout out to Michigan yay - I had a great time there, loved it. Taught some phenomenal people. When I was teaching there, one of the things that was just beginning to happen, were high stakes tests. So that dates me just a little bit when I was beginning teaching. And so our students were about to take - now this is one of the very first high stakes tests that came out. It wasn't tied to a class at all, or to subject. So it was kind of like, "Hey, we think ninth grade kids should be able to answer these questions." And some of us were a little bit... irritated is a good word maybe...frustrated that our students were going to be tested on things they should have learned before us. So some of that was data. And honestly, it was one of the first times that I'd ever heard of a box and whisker plot. I was like, what is that? A stem and leaf plot. Like, they were supposed to learn that in middle school? Okay. And so we were charged as high school teachers to review this data stuff that, specifically graphs to represent data, that the kids were supposed to have learned before us. So we kinda helped each other out a little bit. And my colleagues, at least some of them, decided that they were going to teach kind of like a whole, like class, a unit. Like they're going to take time out and teach the thing. And I said, "I wonder if I could just kind of wrap it into what I'm teaching." And the way that I decided to do that was every time we took something that was graded, so I gave a lot of short quizzes in my class. I would call those formative, though I did grade them, and then tests in my high school classes. And so every time, especially when I gave a test, so I didn't do all the quizzes, because I get a lot of them. But every time I gave a test, I would grade the test and then I would put up their test scores in a histogram. And I would say, "Alright, what can you tell us about -" now with no names attached. Of course not. 

Kim Montague  05:05

Yeah. 

Pam Harris  05:05

That would be shaming and that's not good. But without names, just the numbers. And they can sort of see you know like how many A's and B's? Well, it depended on how I set the bin width, right? Like if you think of a histogram, histograms are all about bins, and however many data points are in those bins is how tall the bin is in that histogram. And so how wide do you make the bins? I could have shown sort of A minus. I could have shown half grades, or if I made the bin at five points. And if I put them at 10 points, then I could have shown whole grades, how many students got an A or B. Or if I put them at, yes I did 100 point scale back then when I was teaching. And so if I put the bins even wider, in fact, I'll just let you guys think for a second, how wide would the bin had to have been in order for me to just show pass fail? Like that could have been a thing, right? And I always do this on technology. So I believe in the power of technology to look at things quickly. To be able to have the power of visualization. So I would have put their scores in a graphic calculator, and I would have shown that histogram and then changed the bins quickly. And so we could sort of ask and answer a lot of questions about the data. Then I would show a corresponding box and whisker plot. And then we sort of learned about, you know, we'd already kind of analyzed the data on the histogram. And then we would kind of learn about a box and whisker plot, by comparing. What do you see? Same data, but in two different representations. And so what comes out in a box and whisker that doesn't come out and histogram? Well outliers show up. What else can happen? The idea of the median shows up, and the quartiles are kind of there. You can kind of see range in both. Anyway, I'm sort of talking about the different representations. But you can, you can see different things in different, which is why we have different representations, right, because different measures of center and things can be shown better in different representations. So I would do that with their grades. And then depending on the day, and how much time we had, I might spend less time on analyzing the histogram and the box and whisker and I might spend more time in showing the box and whisker for their grades. And second period, like I showed first period, second period, third period, fourth period, sixth period, etc. And then I might be like, "Hey, y'all quit cheating. Quit telling your friends later in the day about the questions on the test. Look how their scores are getting better." To which I will tell you, my students always pushed back and said, "Oh, you're just getting better at teaching by seventh period." So we had a little bit, you know, we enjoyed each other and could kind of joke about that a little bit. So honestly, Rachel, that's one way I tried to use data to sort of analyze some things and use that to kind of drive the learning in my class. I think it also sort of drove a little bit where kids can kind of see, "Oh, I know what grade I got. Now I can kind of see what other kids are getting." I never wanted it to shame kids. I only wanted it to help them maybe see possibilities of "Oh, wow, other kids are doing better in here. Maybe I can get extra help. Or maybe I can ask more questions or take the homework seriously, or you know, like whatever to improve." I hoped it wasn't a shaming thing. The time we spent and the emphasis was on how the data was being represented, not where their scores fit in. So that's a thought. I know you said specifically more formative assessment opportunities. I'm curious, Rachel, shoot me another email. I'd love to hear more kind of about how you're thinking about using formative assessment opportunities to tag and analyze, then the scores on the test that I just told you about. Hopefully that gave you some idea. Oh, actually, one other thing I wanted to mention. I can think about another way that I collect data now that I didn't so much as a younger teacher. And that is more with a Landscape of Learning approach. So Cathy Fosnot, talks about her Landscape of Learning and where students sort of are in their development as mathematicians. So I've created Landscapes of Learning - Cathy Fosnot has created Landscapes a Learning for addition, subtraction, multiplication, division, fractions, decimals, percents, I think she's created some new ones for geometry that I haven't seen yet. But I've created ones for high school. So for linear functions, exponential functions, quadratic functions. We are working right now and getting that out to the world. So stay tuned. My team knows that whenever I say, "we're about to" that really means six months from now, so it's not quite ready. But high school teachers just know that that's coming. But if I think about a Landscape of Learning, it's much more about landmark models, big ideas and strategies. It's not about grades. We advocate taking that Landscape of Learning and kind of noting where students are, "Oh, this student is owning this model. This student is developing this model, this student is really using this strategy a lot. But I don't ever see this strategy, even though the numbers of the structure would sort of beg the strategy. I don't see them using that." Oh, I would note that on a landscape of learning. To me, that's a little bit more of kind of a single data point. So maybe now when I tell you that Rachel, you can think more, because you're the data analyst, you can think more about how you might, if I look at a single student, I have sort of these not own yet developing and using well kind of markers on this landscape of learning for these different kinds of junctures of models, big ideas and strategies. Maybe you can help me. How would you use those data points to drive learning? And I'd be curious to know. Now, your second question. Your second question was, do you have any advice for your first year teaching? Yes, but Kim, I'm gonna let start. You go ahead.

Kim Montague  10:38

Okay, so the first year. Wow, it's been a minute, but, you know, we refer to this in a different podcast episode. And I don't remember exactly which one it was. 

Pam Harris  10:51

We'll put it in the notes.

Kim Montague  10:52

So the sooner that you can get solid on your belief system, right, you and I both talked about, know your kids, know your content. That's kind of this huge, kind of our mantra. The sooner that you can get solid on your beliefs - what you believe about teaching and learning - the better off that you'll be, because then everything that you do, every decision you make will be through that lens. You won't be the person who sways back and forth all the time. 

Pam Harris  11:26

I'll try this. I'll try that. No this. No that! Shiny! Run!

Kim Montague  11:30

And maybe even more importantly, you'll be able to identify partners that have the same belief system, because I firmly believe that finding a teaching partner is so crucial. I was so blessed to have some really solid teaching partners over the years. And they make a huge difference.

Pam Harris  11:54

Yeah, I can definitely - in my first teaching experience, a gentleman who hired me, Scott Hendrickson, still may be the best teacher I've ever met. 

Kim Montague  12:02

Yeah. 

Pam Harris  12:03

Amazing, amazing guy. And I was so blessed to work with him the first two years, because it just set the stage. And then a little less in my next, well, the next place that I went, it was sort of me and eight men, and we talked a lot about football, and it was entertaining. But they weren't sort of mathematics teaching colleagues. We had very differing beliefs about how kids can learn and what teaching means and grades and equity and all sorts of things. And so wow, after having it and then not having it, I concur. Look for teaching colleagues that can be helpful. Now, in the age of social media, you can find those teaching colleagues on Twitter. I highly recommend MTBOS on Twitter, the MTBOS group, the IteachMath group, those are places where you can find teaching colleagues that can help. Kim, I think I may have cut you off. Sorry. 

Kim Montague  12:55

No, it's okay. 

Pam Harris  12:56

Are you good? 

Kim Montague  12:57

Yeah. 

Pam Harris  12:58

Okay, so then I would add a couple of maybe other things for you to think about in your first year. Ray Barton, I give credit to this. He was a T3 instructor. I went to a workshop that he gave right when I was beginning teaching. I will never forget him saying these words. He said, "Teachers get out of the four walls of your room, or over time, they will collapse in on you." And in that moment, he was teaching this workshop and I said, "I want to be you. I want to grow up and someday I want to give workshops to teachers." I remember thinking that as a first year teacher, that that's the thing that I wanted to do. Now, maybe that's not your goal. Maybe you don't want to grow up, I'm using that little facetiously, but maybe that's not your career goal to become a teacher educator. But maybe your career goal is just to be a great classroom teacher, and that's marvelous and I can totally support that. But don't stay within the four walls of your room or overtime, they will collapse in on you. So get out, go to teaching conferences, tons of stuff like that online now. But get out of yourself. Robert Kaplinsky uses the #ObserveMe movement. Invite people into your room. Invite their comment. Invite their reflection on your practice. The more that you can do that the faster and better you'll grow as a teacher. Another little thing that I would suggest: I used to hear teachers say, "Don't smile till October." So I don't agree with that. I definitely would smile. However, it is far easier to loosen up than it is to tighten down. So you're not there to be their friend. You are there to be their teacher. And I would highly recommend that you think through the way you want the first couple months of your year to go and then consider sort of loosening up. So it's not about being ugly. It's not about being mean. It's definitely not about shaming. But um, I would definitely be a little bit more of a stricter hard nose, that doesn't fly In here, this is what we do in here. So I'm setting the stage in here until about, I don't know the end of October. And then I could kind of relax a little bit and they would just sort of carry on. For example, when they walked in my room, they knew that from bell to bell, we were working. There was no downtime, there was no playing around, there was no late start. There was, if you've ever been to a workshop I do, I always say I believe in starting and ending on time. And I do. I believe in starting and ending on time. And during that time, we're working. And so I would ache every first month of school because I never sat down. I was up, I was circulating. We were doing stuff. I was asking kids questions. We were communicating. We were setting the stage for class that we work in here. We are thinking in here. And then come November, then I could kind of, I could like take a break. And kids would still walk in the room, "Okay. Alright. What are we doing today?" Not like frantic or anything but like, clear that we work in here. And so set that stage early, set it well, then it's always easier to lighten up than to tighten up. Tightening up just kind of doesn't work. It's really hard to do.

Kim Montague  16:10

I'm gonna add one more thing that relationships matter so much. And anything that you can do to form bonds with your kids, students is so important. If you can get them to trust you, then so much will be easier through the rest of the year.

Pam Harris  16:33

So much more will happen. Not even just easier, but happen, right? Happen at all. 

Kim Montague  16:36

Yeah. 

Pam Harris  16:37

Absolutely. So that's not about being their friend. 

Kim Montague  16:39

Right. 

Pam Harris  16:40

It's about a good teacher-student relationship. 

Kim Montague  16:42

See that you care. 

Pam Harris  16:44

That you care, yeah, that you honestly believe in them. That you will help them. That you're there for them. You believe in them. All of that is so, so important. Um, I'll just share a quick story. There was a moment in about halfway through a semester where I had two senior girls that were in my class. This was after several years at this particular High School. And we were chatting one day, and one of them goes, "What's with you?" And I was like, "What do you mean?" And they're like, "Dude, when we knew we were in your class," which, by the way, dude? What is this dude thing for women? I don't know. Whatever. Anyway, so like, "Dude, like, um, when we landed in your class, we were like, Oh, no, like, this is gonna be terrible. She's so stern." And they're like, "You're not like that at all." And I was kind of chuckling a little bit. And I was like, "What do you mean?" And they're like, "Your reputation around the school is that you work people hard, like that your class is difficult, but doable and fair, and that you are stern." And they're like, "You're not really stern. You're just a big softy. You just kind of come off that way at first." And I was like, "Sweet, that is a great reputation." Like I was loved. Now I taught high school. So maybe you're a little more touchy feely at the younger grades. But I was really clear at the high school level that we were working hard. And I loved the fact that then they said I was fair. And that my class was doable. 

Kim Montague  18:10

Yeah. So great.

Pam Harris  18:11

I'm gonna share a quick story that Kim doesn't know I'm going to share. I walked into my kids' school. So Kim was my kids teacher, right? Like not all the time. But she taught at the same school. And I walked into that elementary school - so Kim taught third, fourth and fifth grade - one day and there were these big doors at the beginning of the hallway. And I opened that big door. And Kim had a couple kids. And she was kind of letting them have it. Very sternly saying this is not acceptable in our class. We don't do that, we do this. Like she did all the good positive things about identifying clearly what wasn't acceptable and then identifying clearly what was acceptable and I believe in you guys. So this is the sort of stern and then followed very much with like, "I believe in you, and this is what we do here." And it was very positive. And then she sent them back in class. Now that whole time, high energy high, like, eyeball, she's like, looking in their faces. And they walked back in the room, these two kids, and she looked at me she's like, "Oh, hey, Pam, how's it going?" I will never forget, like this whole demeanor change. Like oh yah. What I learned from that: she was completely in control the whole time. Now don't get me wrong. She wasn't like ranting or screaming or anything. It was just this very like clear. Like stern, like serious, like, "Oh, I believe in you, like we are going to make this positive thing happen." And then it was all back to like normal. Like, "Yeah, Hey, what's going on?" You know, anyway, so have control of yourself. Especially the older you teach. I think teachers have to sort of figure out their own baggage. And you have to kind of figure out how you fit. I'll be a little vulnerable and upfront, I had to kind of figure out how I fit with the popular kids, with the jocks, with the like, whatever sort of section of kids there were, all of a sudden I had to realize, "Whoa, I'm treating them like the insecure kid I was in high school. I'm the teacher, I have to be the adult here." And it took me a minute, a hot minute, to figure out kind of my place as an adult. I think it's important for teachers to do that work. If you don't do that work, you're going to be like the student teacher I had, who I'll never name his name. Your name is safe with me. I will never say anything negative about you. But he literally stood up in front of my classes and said, "My name is Mr. So and so. But you can call me God, because I am the God of math." 

Kim Montague  20:33

Oh, geez. 

Pam Harris  20:34

And he could not hear that when they would ask a question, you know, a sincere question, he would say, "I taught that. I showed you that." He was so like insecure in himself. He hadn't dealt with his own stuff yet, that he then was not a very effective teacher. So I would highly recommend that again, get those good teacher colleagues that can help you monitor and reflect on your own teaching practice. There's some sort of non mathy first year advice. Hope you guys that come here for math advice in mind that we sort of took a little track on non mathy advice here for first year teachers.

Kim Montague  21:11

Excellent. Alright. So remember to join us on MathStratChat on Facebook, Twitter, or Instagram on Wednesday evenings where we explore problems with the world.

Pam Harris  21:20

If you find the podcast helpful, please rate it and give us a review. That way more people can find it wherever they get podcasts and we could spread the word more that Math is Figure-Out-Able.

Kim Montague  21:31

Keep bringing your suggestions and comments. We love hearing from you.

Pam Harris  21:35

So if you're interested to learn more math, and you want to help yourself and students develop as mathematicians, don't miss the Math is Figure-Out-Able Podcast because Math is Figure-Out-Able!