More Math for More People
CPM Educational Program is a non-profit publisher of math textbooks for grades 6-12. As part of its mission, CPM provides a multitude of professional learning opportunities for math educators. The More Math for More People podcast is part of that outreach and mission. Published biweekly, the hosts, Joel Miller and Misty Nikula, discuss the CPM curriculum, trends in math education and share strategies to shift instructional practices to create a more inclusive and student-centered classroom. They also highlight upcoming CPM professional learning opportunities and have conversations with math educators about how they do what they do. We hope that you find the podcast informative, engaging and fun. Intro music credit: JuliusH from pixabay.com.
More Math for More People
Episode 3.15: Where Joel and Misty discuss pickles and reprise a conversation with Dr. Leslie Dietiker
It's National Pickle Day. Come celebrate with your pickle spear and listen to the More Math for More People podcast!
This week we have a reprise of a very interesting conversation we had with Dr Leslie Dietiker of Boston University. Dr Dietiker is one of the key authors of the CPM courses and she talks with us about the mathematical storylines that are a key part of each CPM course.
We also have another update from our Join Them on Their Journey teachers.
Enjoy!
Send Joel and Misty a message!
The More Math for More People Podcast is produced by CPM Educational Program.
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Well, here we are. It is the 14th of November 2023, and this is episode 15 of season 3 of the More Math for More People podcast. Cheers.
Speaker 2:Hello, there, I'm. Joel.
Speaker 1:And I'm Misty.
Speaker 2:And you're listening to the More Math for More People podcast, an outreach of CPM educational program.
Speaker 1:We have a lot of conversations about math and math education on this podcast. We're passionate about continually improving the way math is taught and we hope that you learn something in every episode that helps you become better at what you do.
Speaker 2:And we hope that you have some fun and laugh as well. That always makes things a little more interesting.
Speaker 1:Yep, we're pretty passionate about having fun Joel.
Speaker 2:So please have a listen and we think it'll be well worth it. Boom.
Speaker 1:We're starting off the podcast this week with an announcement. If you're listening to this on the day that it released. Tomorrow, november 15th, is the final day for the early bird pricing for the 2024 CPM teacher conference. So if you get registered by tomorrow, you can save $75 on the main conference and you can save $75 on the pre-conference. On November 16th. The prices go up, so get yourself registered. You want to save money, so get yourself registered by tomorrow, november 15th. End of announcements. All right, joel. So here we are. Yep, it is the 14th of November.
Speaker 2:It is.
Speaker 1:And, as usual, we're going to have a national day of segment. So, what is the national day today?
Speaker 2:Today is National Pickle Day.
Speaker 1:National Pickle Day.
Speaker 2:Not to be confused with Pickle Ball Day. That was a different episode. Oh, that was a different thing.
Speaker 1:Yeah, yeah, yeah, you have to go back to episode three.
Speaker 2:That's right.
Speaker 1:But yes, no, not pickle ball.
Speaker 2:This is National Pickle Day, national.
Speaker 1:Pickle Day. That's right. It's confusing that we have so many things to start with pickle. Well it just makes me think of, like, getting into pickle. That's a baseball thing. It's not that either. Maybe it is, I don't know actually.
Speaker 2:Getting into pickle is a baseball thing.
Speaker 1:Yeah, when you get into pickle you never heard that.
Speaker 2:I've heard that, but I didn't know it was a baseball thing.
Speaker 1:Well, it's like a baseball thing when the runner gets caught between the bases.
Speaker 2:That just sounds like trouble.
Speaker 1:Well it is, but it's called to get them into pickle right. And then they have to throw the ball back and forth and you know there's ways.
Speaker 1:They do it so that they don't interfere or obstruct, and when you're impiring, that's what you have to really start watching for is interference and obstruction. But we used to play it when I was a kid too. We used to try to play that, but it was hard, because the people just throw the ball back and forth, back and forth, back and forth, and then you're not trying to get from one base to another. I don't know. We tried to mimic it as a game. It seemed like it was going to be more fun than it was it was, it didn't live off to your expectations.
Speaker 1:It didn't really live because only there's only two people throwing the ball back and forth. There's not like the whole. You have to trade off players and lots of other nuances to it.
Speaker 2:So it sounds like it might be worth another try and you could do it on today.
Speaker 1:I could do it today.
Speaker 2:I'd have to find some people baseball.
Speaker 1:Mitts and gloves and a baseball Two things to be a base. Yeah, but I could do it. It's true, I could do that.
Speaker 2:How open would your neighbors be if you came out the front door with your glove and you said all right, everybody who's in for a pickle, and then who wants to play pickle? Right here in the street? Maybe, okay, I don't know.
Speaker 1:Anyway, I don't think that's what the day is about. No, oh, okay, is it about things that are cured and pickled? Yeah, I know.
Speaker 2:That's vinegar or otherwise fermented. Fermented foods.
Speaker 1:Fermented foods yeah.
Speaker 2:I think it's interesting that the word pickle comes from pickling. But I think it's interesting. But the earliest that archeologists have found evidence of pickling was back with Cleopatra and Julius Caesar. In that time I'm not sure what that year was.
Speaker 1:In the something BC Egyptian times.
Speaker 2:Very, very old times of the earth.
Speaker 1:That's very specific, yeah, and I think fermenting things naturally and this is more than just things To preserve them.
Speaker 2:It's literally a cucumber on this day, but it is to preserve those cucumbers. It's not pickling, it's the pickle itself is the celebration of the day.
Speaker 1:Oh, okay, but the archeological thing was that about cucumber pickles or pickle.
Speaker 2:Oh, I see. Yes, that's the first. It is about the cucumbers, the first evidence of pickled cucumbers.
Speaker 1:I see, I wonder if they were savory or sweet. Probably they were savory. They might have had pickle vendors and they might have, and they could have Put them on a stick.
Speaker 2:Yeah, do you like a dill or a sweet? What's your favorite?
Speaker 1:If I am going to have a pickle. Well, so I grew up eating dill pickles, like kosher dill pickles. My dad liked a particular kind of pickles, particular kind of pickles that we always had, and that's the way I associate the taste of a pickle, because that's the pickles we always grew up with. And then when I go places and they have like pickle spears or something like that and they're like dillier or saltier, swooshier, I don't know.
Speaker 1:They're just different to me. I'm not as fond of them, gotcha, but I like pickles on my hamburger If there's other things with it, if it's just a cheeseburger and then they put the, just the mustard in pickles, just some pickles, not enough.
Speaker 2:You gotta have tomato or something.
Speaker 1:Tomato something else to go with it yeah.
Speaker 2:Do you like pickle in your tuna fish?
Speaker 1:Yes.
Speaker 2:I do too.
Speaker 1:I do like pickle in tuna fish, for sure, and I will still have pickle in my tuna fish now.
Speaker 2:There's a place I like they sell these sandwiches and I always get a pickle dill, pickle quartered with my sandwich every time I see, yeah, yeah.
Speaker 1:I used to make fermented things, and I wear not so much pickles.
Speaker 2:Okay.
Speaker 1:Other fermented things, like naturally not with vinegar, because that's the thing A lot of pickles nowadays are they're not actually fermented, they're just vinegar, cured Vinegar.
Speaker 2:Yeah yeah, it's a quicker process maybe, or something I used to be part of a pickle of the month club, wow, and every month they'd send a box, two jars every month, and they would be from local stores of different areas and they would be man sweet or spicy or something. They could have those in there, but they were all the like a pickle spear.
Speaker 1:So it wasn't like kimchi or other kinds of thing, like not like mixed, like pickle.
Speaker 2:They were pickles, but different flavors, and so there would be maybe some of that stuff in the juice itself to give flavor to the pickle. Yeah, that was fun for a while. It's a lot of pickles to eat.
Speaker 1:Yeah, like two jars a month.
Speaker 2:Yeah.
Speaker 2:It's more than my normal habit. I'll tell you this too. Recently and you were there, we were in Tempe, arizona, and during that time I stayed with my mom and we were actually talking about that. When you get a cramps, athletes now are drinking pickle juice and they even yeah, they sell like a shot of pickle juice for athletes. Now, when you get a cramp, and oddly enough, I was swimming in the pool and I got a cramp, immediately we ran into the kitchen, got me a shot of pickle juice. I think either it really worked or I just had enough time between that that running into the house, I didn't run somebody else ran into that.
Speaker 1:I understand, because you had a cramp.
Speaker 2:I had a cramp. It seemed to work right.
Speaker 1:So it either really worked or it was just correlation.
Speaker 2:Correct, yeah, one of the two I see I see, well, that's interesting.
Speaker 1:I would think it's just the salt, but you could just eat salt Pickle juice.
Speaker 2:Pickle juice, it's the way to go.
Speaker 1:All right well it's National Pickle Day so you could join a Pickle of the Month Club, or you could just eat whatever your favorite pickle is.
Speaker 2:Drink juice, eat the pickle, Drink juice even if you don't have a cramp, maybe.
Speaker 1:Yep Preventative, I don't know. But it is National Pickle Day, so go and enjoy.
Speaker 2:Enjoy it.
Speaker 1:So this week we have something a little different for you. We're going to do a reprise of a conversation that we had on season one of the podcast, and we're bringing this up in particular right now because when teachers embark with CPM, the three pillars can be challenging Collaborative learning, problem-based learning and mixed-space practice are embedded into the program and teachers can work really hard to bring these into their classrooms in full and complete ways. Personally, I think that mixed-space practice can be the one that is the most challenging of those three, because it's the one that, in some ways, makes CPM the most different from other programs that strive for collaborative learning and include problem-based learning activities in their curricula. Mixed-space practice is the one that is hardest to get. It's the hardest to understand and sometimes the hardest to implement, and a big part of the mixed-space practice pillar is the storylines of the CPM courses. So we're going to go back to a conversation that we had with Dr Leslie Dietiker back in October of 2021 and was on podcast 13 of season one, where we had a conversation with Dr Leslie Dietiker around the mathematical storylines. So here you go, enjoy. So we're here today with Dr Leslie Dietiker.
Speaker 1:Dr Leslie Dietiker is an associate professor of mathematics education at the Wheelock College of Education and Human Development at Boston University. She teaches courses in mathematics and pedagogy to future high school mathematics teachers, as well as research and theories in mathematics curriculum to masters and doctoral students. She is an elected board member of the International Society of the Design and Development of Education and is on the advisory board of the CPM educational program. Dr Dietiker also designs and leads professional development for schools and districts in the Boston region. Dr Dietiker taught high school mathematics and computer science at a public high school in San Francisco, california, for 17 years. She has received a national board certification and is also a lead author of seven CPM textbooks. So welcome, leslie.
Speaker 1:And thank you for being here with us today on the podcast. How are you today?
Speaker 5:Thank you so much for having me. I'm doing well.
Speaker 2:Great.
Speaker 1:So you were involved with the writing and editing of CPM courses for some time and have been instrumental in the development of pretty much all the current courses. One of my first memories of you was when we were working on the Making Connections writing project in Davis in 2008. And this was the very first time that I had ever heard of a mathematical storyline and this is a pretty important feature of CPM courses turns out. So I would love to hear what you could tell us about mathematical storylines. What are they and why are they important?
Speaker 5:So interesting. Thank you for those memories I got to say. It brings me back and what's really on my mind right now that you say that is how much it maybe has changed. But back then the mathematical storyline was really conceptualization that I think supported my thinking in how content can unfold in a textbook or in my classroom. And what I remember vividly back in those days where we were really talking about tasks and lessons and chapters and books, is that we could talk about those things. So those things we had words for, we had words for definitions and if we wanted to have some kind of exposition where we defined something, we had toolkits or we had math boxes or things like that. We have words for tangible items of curriculum materials.
Speaker 5:But there was limitations in terms of language for thinking about how mathematics evolves and changes across a lesson and when I would think about how certain choices might set up or not set up or ruin a development of a lesson, some kind of mathematical progression. I didn't have any language for it and I think it was I can't remember which textbook I was working on where I finally maybe hit upon the idea of story, but as far as I know, it just evolved over time in my thinking. So yeah, but back then I think it was just kind of language, and then I would talk about it with various writers and I think that I felt like at least it was helpful. Then later I went and dug into it a little bit more, learning about what narratives are and learning about stories and thinking about them more deeply and realizing how really, as authors, we had already started to embark on a path of really recognizing the power of thinking this way, because there are a lot of affordances that it helps to shed light on.
Speaker 1:Sure. So if you had to describe or define what a mathematical storyline is, how would you, succinctly, if you can, say what is it? Where would I see it? How would I know what it is?
Speaker 5:Yeah, well, I think actually what's really important is to first think about what a story is. So, for example, thinking about a story I like to use Wizard of Oz, for example, because a lot of people have familiarity with that story and I think about how the story opens. I'm thinking about the movie and the story opens and we get introduced to Dorothy and we learn. All we learn about her is that she lives on a farm, she's a young female, she's unsatisfied with where she is and she has these characters around her family members and animals and things. And that's all we know at that point. And so we have to recognize that as a story. We get introduced to things and what the story is going, the substance of the story, the characters, the things, the setting. And at that point of that story, I don't really know what's going to happen. I might imagine something about it, but I'm really just guessing at straws. Maybe it's about her life, maybe it's something she's going to get in an accident, I don't know what it is. And then suddenly the story advances.
Speaker 5:It introduces this tornado and it throws her into this new land, and suddenly there's all of these strange things happening to her in this new land, and that right there now tells me that the change there has, tells me something is now developing about. We're now going to see her in this conflict, where she is now afraid where she is. How is she going to get home? And so the story has done something to us as an audience. It has set up a chance for us to wonder OK, we know where she lives. She's now far away from that. We don't know anything about where she is. And so now it sets up an opportunity to ask questions and wonder now how she's going to get home.
Speaker 5:What is this Oz? Who's the wizard? And the rest of the story, then, is really about answering those questions and having twists and turns about how the wizard maybe is not actually a wizard. Maybe we find out he's a fraud, for example, but we think he is a wizard, but now we now know he's not. And so stories work on us by drawing us in and getting us invested in a set of questions, and those questions then are what we then watch the rest of the story or read the rest of the story to try to figure out. It is a truth, it's like it's a pursuit of truth. So a book or a story kind of sets us into some kind of world of which we're not. We, then, are seeking knowledge, or we're seeking truth for it and from it. And so if we can take that idea of a story and now think about mathematics, we can see that in mathematics we also experience things similarly, where we think about how we might.
Speaker 5:In a lesson we might start very much like the Wizard of Oz, where we're introducing a triangle or a polygon, or maybe it's a function or something like that, and at that point nothing's happened, nothing's advanced. All we have is a character, we have a setting. Maybe the parabola is on a graph, maybe there is some details about it, we know about it, symmetry and so on. So we have some information about it, but nothing's happened, and so there's no way to guess where the story is headed. But after we might suddenly, in this task with this parabola, we might be given a challenge where we're going to be trying to transform the parabola so it accomplishes something like, for example, find the parabola where the basketball will go into the hoop, or something like that, of which now there's something to look forward to. Can we transform it Suddenly? We might start asking questions that then get us invested in trying to figure out some kind of truth in the story. So you asked me for a succinct. That was a great description. I also know you Leslie, so.
Speaker 1:I knew that was not a really reasonable request. Right, right, right, oh good, good.
Speaker 5:So yeah, yeah, yeah. So I guess the succinct answer is to seeing how mathematics unfolds kind of that connects a beginning to an ending, so that somebody who's experiencing can send a through line and predict where it's going.
Speaker 2:I was just going to say when you were writing that, did you think one book at a time, Because I feel like I see those stories sometimes through many courses. So it was that a thought when you were writing for the books.
Speaker 5:Yeah, I do see stories between and across all of the books and I was lucky that when we were writing the connections books at least for the algebra and geometry connections for example we were doing them sequentially so we could have that take and same thing with the making connections it was a little harder.
Speaker 5:We were simultaneously creating the two courses at the same time and while we did have an overarching sense of how a story could go, there were so many details in the crafting of those lessons that altered the stories as we were writing them that it was really hard to think that way and I think it shows in the way in which the courses there might be places where we didn't get to take advantage of some aspect of the story because whoever was crafting, let's say making connections to, didn't yet know how making connections one would end and only that. But then we had revisions. That happened Pretty large revisions that happened after first year, so that significantly probably was altered. The later courses then that got to take content and reshape new courses. Maybe they had an eye toward that, but I don't know.
Speaker 1:Yeah, when we took the making connections courses and then pulled them apart and re-sequenced them for common core standards, there was some nice things because we could avoid some of those overlaps that had been in the books because they were trying to meet lots of different standards and at the same time, we tried to really really keep that storyline, Unless we had a really good reason to move the order of the things around or were forced to because of where the standards fell and we had to pull things apart. We tried to really maintain a lot of the storyline that was there and improve it if we could, Because we're like, oh, this would be a great place to add some connections between the pieces that are happening in this course.
Speaker 2:Right, right, when I started teaching with CPM, I was using that making connections book and right then they switched to the core connections and then I switched to the integrated. So it's interesting to hear this background because how it's all pieced together and the thought process behind that. So that's really cool.
Speaker 1:Yeah, I like how. There's two things I thought about when you were talking. One is I like the idea that the storyline it's kind of an analogy or metaphor, but it's not at the same time because the characters in a story, as I'm learning, like the example that you gave about Dorothy I'm learning about the characters as they're doing things in the story, right as things are happening to them and as they're responding. I'm learning about, oh, what the Cowardly Lion is like and what his personality is and how he behaves in his attributes basically. And so in a mathematical storyline we learn those similar kinds of things about characters that are now mathematical ideas about what a parable it does and how it behaves and what if we do this and what happens to it, or different shapes and things. And I like that, that similar kind of idea between those two things For sure.
Speaker 5:Oh yeah, right. So you can have a story that's action-oriented, for example in a movie. You can also think about, like what are the mathematical actions? Do we ever have lessons that are really solely squarely action-oriented? Absolutely Right. But you can also have like a deep character development, a lesson on fractals, for example, or something where it was really around the investigation of this mathematical object. Sure.
Speaker 2:I remember I used to read a series when I was younger called Choose your Own Adventure Books. There's some of that in there too. Let's see where it goes.
Speaker 1:Well, because as each person interacts they're going to get a different thing from whatever the development is, whatever is happening. My other thought was some of the things as we think of the course as a storyline. In the progression then the teachers become cooperative storytellers with students. The teacher is sort of aware of where the story is going, but there are other elements to the story and pieces and perspectives that students might have as they're seeing where the story is going. So the teacher becomes that sort of storyteller, but not in a telling like this is what happens way, but in a sort of like hey, this is the journey, and kind of join the students in that story. It's really cool.
Speaker 5:Yeah, yeah, what you're touching on I think is super important because that is a risk with using this metaphor is that people might think of the old school. I'm now going to tell you the story and I do think of it more like Gorilla Theater, where the audience participates and it's a co-construction. But, yeah, the teacher may plan the story right, or the textbook may have a planned story, but what happens in the classroom, of course, is very different, and that's actually what my research is right now. Very cool.
Speaker 1:So we've talked a little bit about what they are, what they're important, how they've impacted the design of the curriculum. They're deeply embedded in it. For sure. What you think would be an important thing for teachers using CPM to know about mathematical storylines? In addition to this you're not the teller perhaps part of it what else do you think teachers would need to know?
Speaker 5:Yeah, I think one of the things that I think I like asking teachers to do is to think about the stories they like and think about the variety of stories that maybe they hold appreciation for and what purposes those different stories serve for them, and then to think about the stories that their mathematics lessons offer and try to see that same variety or same opportunities. So if usually when I ask teachers what kinds of stories they like, I give variations because obviously different people like different kinds of stories, but often they tell me it's going to be something that sucks them in, that they can get invested in, that they can't put down, that they want to keep reading, and I ask them to think about what would a mathematics lesson have to look like to make you similarly feel that way, and why shouldn't we at least try to make that happen? I think that there are stories that don't grab us, and I'm certainly not one to think there's like a quick fix. Right, we can't make every lesson. It would actually be worse if we made every lesson a fabulous story, because then it would get so predictable in that way that it wouldn't work anymore, right?
Speaker 5:So if you think about it, stories work best when they offer us something that's rich to think about, but yet they're not predictable, they're not leading us through the nose, and then have teachers then apply that reasoning to thinking through what kinds of opportunities they're offering, what kinds of stories they're offering in class. So one of the exercises I like to do, especially with CBM teachers, is to look at the stories that we've designed within a textbook and start to recognize them for what they are, because it's quite possible that with this new metaphorical way of looking at a textbook, that they might see some new affordances. When I say that, I mean they might see some opportunities they didn't originally recognize. If I think back on my long teaching career, and.
Speaker 5:I think about the various ways that I interacted with textbook materials. I can remember times when, actually, I would turn to a textbook and say, okay, no, I need a task.
Speaker 5:I need something to introduce this idea. Or maybe I'm opening up a textbook and say, okay, what can I assign for homework? Or maybe I'm saying, okay, what materials do I need to go get ready? So there are various questions we ask of our curriculum materials when we interact with them. They're resource, they're a tool, and so what's a potential story is one of the questions we can ask. We can say, okay, let me see what are the possibilities here for how I might make mathematics like aw, how could I give my students a sense of awe? Or can I create a spin? Or is there any opportunity for surprise or possibly other kinds of aesthetic experiences that, when we think about stories that move us, we might recognize. Those are powerful moments for us.
Speaker 5:And then they might notice that we've actually not every single lesson right, but that we've created opportunities for surprise and for suspense and for wondering, for curiosity.
Speaker 1:One of the things that I remember when we were writing that we would often do is we would what if? Well, what if we changed the order of these two ideas? Like, I think we, many of us, we grew up with some sort of like oh you teach this, then this, then this, then this, right, this sort of progression of whatever traditional learning it was, and we did a little bit of well, what if? What if we did this lesson or this idea first? How might that change the way kids engage with this next concept? And there were sometimes and I think that's one of the in my opinion, one of the most amazing things about the geometry book is the doing of symmetry before congruence and that just that whole idea of like oh, we're going to investigate this and then this other idea comes out of it, and sometimes it's. That is one of a big challenges when teachers, when they're first implementing, because they're like well, that's not the order it's supposed to be.
Speaker 3:Right.
Speaker 1:Because they're used to some other story and then but kids don't know that story and kids can engage in these ideas in a different way and with the tools that they have at that moment. And I love how we really thought about those ideas, because everywhere else I was like oh this would be great, because then they could think about this and this and this.
Speaker 2:It reminds me of learning tangent before sine and cosine. Yeah, like it's just a different way of thinking about it and so much in math too has that idea anyway. Like numbers are we're discovered because what if this thing would happen? We're saying it can't, but what if it could? And then we learn so much more, yeah, I got to say you're bringing me back.
Speaker 5:I want to credit one of our CPM writers from long ago, carlos Cabana, who I worked with on many of the early textbooks algebra connections, for sure.
Speaker 5:But even before that I remember working with him on calculus and having deep discussions around how we were going to sequence content and it was just such a pivotal moment, I think, like while I was completely on board with totally changing the kinds of experiences students had with mathematics and really trying to think about what would a calculus textbook look like if it was completely problem-based.
Speaker 5:That's where my head was, and I remember distinctly discussions around how we were going to start and everything that I was coming up with was from my preexisting beliefs of sequence, of what content of calculus. You have to, of course, start with limits, and then you do continuity, and then you yada, yada. And he, at one point in the middle of the discussion, he's like I think I just realized that you're assuming we're going to start this sequence and I'm not assuming that why not start with integration? And I'm like it was like a bomb detonated. I did not see that coming and I wasn't, quite honestly, I wasn't accepting it. For a little while. I had to really think through it and talk about it and then suddenly I realized, yeah, why don't we?
Speaker 3:And that's actually why the calculus book.
Speaker 5:yeah, exactly, it takes time.
Speaker 3:Yes, exactly.
Speaker 5:And so I had my own little time. And he was right. That's the fascinating part let's get them involved in area under a curve. Why not start there? And then we could develop limits through that. Yes, why not do that? And suddenly it was like everything then changed after that for me. It was like I suddenly realized I need to let go of whatever content assumptions that I have.
Speaker 2:Awesome.
Speaker 1:Well, thank you so much for joining us.
Speaker 2:Thank you.
Speaker 1:We really appreciate this time with you. Anything else you you're like oh, I wanted to make sure I said this thing.
Speaker 5:Yeah, I think that one of the things that we need to do as teachers is we need to listen to ourselves and when we notice that we have opportunities and we recognize, oh gosh, I don't want that student to share that idea yet because that's going to what sometimes I think the phrase is is give away. The punchline, I guess, is the way I think sometimes teachers think of it. It's a recognition that we see opportunities for moments of surprise or for deep wonder and that those are the things we can lean into. I think that that kind of is what all of us probably can tangibly recognize that has happened to us and in many ways, those are the voices inside us that give us an opportunity to recognize how is this happening? How are we seeing? How come I can recognize this moment here and maybe start to turn that into more deliberate choices that we make when we start planning our lessons or deliberate things that we do within class.
Speaker 3:Oh, thank you so much, leslie Well thank you for what you guys do.
Speaker 5:I've enjoyed listening to you, excellent. It's so strange to be talking to you now, actually, because I'm it's kind of like I'm listening to a podcast and then I, you guys, are talking to me, so that's very strange.
Speaker 1:It's an interactive podcast at this moment. That's right, all right.
Speaker 2:Thank you, great Thank you. It's that time again when we hear from our participants and the join them on their journey. We're happy to have another update from our teachers and let's take a listen and what they're up to.
Speaker 4:Hi, miss Dianne Joel. I just finished my first quarter with CPM and things are looking up. I've been using more STTS that's study team and teaching strategies with my students and they seem to be responding well. I just recently tried the jigsaw and Paris check and loved the conversations and the mathematical ownership that I saw students taking. I really saw students have authority with the math that we were learning and they really it was cool to see each student take some part in explaining and owning the mathematical skills that we were developing. If students got stuck, that also became apparent and I could see really what they were getting stuck with and I really got a window into their thinking and it was just really awesome to see that. I've also been letting groups work more on their own and been sitting down with the struggling groups and working on problems with them and I feel like that's been going really well. I've seen students helping each other, really awesome collaboration and conversations happening. I just love the structures that CPM provides and I think students are responding well to it.
Speaker 4:I'm still resisting going over all the problems. It's like a struggle I've been having. When it seems like most students are not understanding a particular problem, I'm like, all right, hey, class, let's everybody write this down. I think I could save on time if I let back on that and let students struggle together. I'm working on developing a poster, as is recommended, where we go to the board and think about what to do when we're stuck. I think that could help if I had a place in the room where to refer to when teams are stuck. That just brings up one of my biggest struggles is with time in my regular integrated one ninth grade math class. Time is our enemy. We seem to always run out of time and when students are learning and collaborating it's just a beautiful thing and when that happens I have a really hard time cutting it short. Just the other day a girl got stuck with something and this other student was being really patient explaining and teaching that student what they were doing when they were doing transformations on the plane. When I see beautiful teaching moments and learning happening, I'm going to let it happen and we'll get there. That's one of my struggles. I know I got to keep working on finding those critical problems and focusing on those, but when awesome things are happening in class, it's something to celebrate. I just love how many resources CPM has.
Speaker 4:I've been looking into more STTS and brain breaks. I highly recommend checking out the team support and the team resources tab. The brain breaks I hadn't really thought of or known about some of those ideas and it just sounds really cool. I'm excited to try it. I also like the ice breakers. I want to do more of those. I've printed off some interview questions to get teams more familiar and acquainted with each other, more comfortable working together. My advice would be to just keep trying things out. That's how I've been learning and how I think I've come across some of these things that are working out well with my students. Also, to let students find their way and to recognize that I'm here to support them as needed. But it's a lot better when students teach and when students say things than when I do. That's something I'm learning as we're going and as students are becoming more confident and confident as well. Thanks for listening and can't wait to report next time. Take care.
Speaker 3:It's Maggie, and this is where I am on my journey. My students have just taken the chapter two test from Inspiring Connections, course three, and we call them, instead of a chapter test, we call them a check for understanding. And what I'm loving about the chapter two test from CPM is that it's really comprised from content in chapter one and chapter two, and so what I've done is I've broken it down so that the students are actually getting three different grades on, like the three different major topics in chapter one and chapter two. So it was covering, like scatter plots and association, the transformations and then learning your functions, but more specifically, looking at proportional relationships and being able to compare different proportional relationships using the unit rate. And so I have just returned the assessments to the students and they were so happy and it was like a time for them to celebrate because this was the second time that they had been assessed on it, and not that the first time didn't go well. But I know that whenever you're doing something, the second time around you're always more confident, and so I know that the students will do well when they feel confident, and so, given that this was really essentially a reassessment, they felt really confident and I even saw that where, on the assessment, at the top of each page, it's basically a circle with essentially two eyes and the students have to fill in what the expression is, and it was really interesting.
Speaker 3:I had never done it, to be honest, I kind of was like this is kind of silly, but it gave me a little insight into what the students were thinking, and so even those little things of what are the students feeling leads to great conversation afterwards. Now, you would never use that in terms of grading it, but when you're handing them back, you could have the conversation of oh, I see that you were a little nervous, but you did very well. How can we make you feel more confident or what are ways that you can do to double check your answer? Math is always amazing because, especially with CPM, you can represent things in different ways. So if it's a graven, you're not feeling 100% confident. Could you change it into a table so you feel more confident in it? So it's leading to more conversation. But then also the opposite had to happen, where I saw that they based off this smiley face or this feeling that they felt pretty confident, and in going through, what I noticed is that maybe they had rushed through it. And so it leads to that conversation of how can you make sure that you double check or make sure that it's not you're checking it for those simple mistakes? Did you add the unit rate? Were you able to double check? And so it was nice to kind of build that rapport with the students when we return the assessments, because you can lead to different conversations.
Speaker 3:The last thing, just to wrap this up in terms of the assessments so the students do the assessments, we hand them back and they got three different grades of the three different learning goals and I have them add a glow, so something that they were really proud of, and then a grow. And I try to make sure that it's not necessarily content specific for the grow, because at this point they had already reassessed it twice, although we may reassess again, but it could be. The glow could be I double checked my answers or the glow could be is that I took my time and I didn't rush. And then a grow. It could be is that I didn't use the ruler, even though I had a ruler on my page, or we're getting into expressions and combining like terms, so knowing that they're removing them, that direction.
Speaker 3:I did have a student that shared. I want to make sure I use colors because I know that that's helpful for me. So we're trying to build their repertoire of skills that can be applied to any assessment and the nice thing is that I have a record of it so it's not living in their notebook, but also the parents have it. So we're going into parent teacher conferences and it's nice because I can also reference I'll look at this as a focus area or this was a feedback so really utilizing the tools that we already have and having them the students put in their own language what they're working on and what their feedback is overall. So I'm excited for our next assessment and seeing how they can build on their grows and continue their glows.
Speaker 1:That's it for now. So that's all we have time for on this episode of the More Math for More People podcast.
Speaker 2:For more information on Stay Connected, find CPM on Twitter and Facebook. You can find our handles in the podcast description.
Speaker 1:The music for the podcast was created by Julius H and can be found on Pixivaycom. Thanks, julius. Join us in two weeks for the next episode of More Math for More People. What day will that be, joel?
Speaker 2:It's going to be November 28, red Planet Day. So in the first season I guess we talked about Pluto being a planet, or not being a planet for that matter. But today's day we're celebrating Mars. And way back, and they say in about 400 BC, babylonians began keeping records of celestial events and they called Mars Negro or the King of Conflicts, probably because of its color and how that's associated with blood when they would go to war, and so that that conflict was known way back then that it must be the Red Planet's vote. That's kind of the history of Red Planet Day, but we'll dive in more. We'll see you out in November.