Episode 64: Top Ten Ways to Get Students Problem Solving with Dr. Nicki Newton and Ann Elise Record

The top ten list created in this episode and links to resources are in my blogpost.

Transcript

Melissa Milner 0:09

Welcome to The Teacher As... podcast. I'm your host Melissa Milner, a teacher who is painfully curious and very easily inspired. In this third season, I explore my interests as the main focus of the episodes. If you have listened to seasons one and two, first of all, thank you. Second of all, this season will be a little different. It will still be centered around interesting topics and their connections to education. I'll continue to have interview episodes, maybe a top 10 episode here and there since they are very popular, but also some episodes will be just me sharing about a topic. Similar to my Podcasting with Students episodes from season two. New episodes come out every other week. If you enjoy the podcast, please share it with anyone you think would benefit from listening. It really helps the podcast grow. Thank you for supporting The Teacher As... I hope you enjoy season three.

Ann Elise Record 1:06

I am Ann Elise Record and I'm an independent math consultant. I live here in Concord, New Hampshire.

Dr. Nicki Newton 1:12

I'm Nicki Newton, and I'm an independent math consultant. And I live in Connecticut.

Melissa Milner 1:18

And I'm Melissa Milner, very excited. Host of Teacher As... very excited to have Dr. Nikki and Ann Elise Record back here. This is our third one, right?

Ann Elise Record 1:31

Yeah.

Melissa Milner 1:31

It is the third top 10. So this is exciting. So let's get the audience caught up on how this works. Because they might not have listened to a top 10 episode before. So Dr. Nicki and Ann Elise have their own picks of the top 10 ways for students to practice problem solving. And they're working together to create a collaborative top 10 list. So what happens is there is a player A and A player B. So Player A will have pick 10,8,7,6,4, and 3, that means they have two more picks. And they have one veto, which I'll explain in a moment. Player B has fewer picks number 9,5,2, and 1, but they have the top two picks, and they have two vetoes. So let's talk about what a veto is. Basically, there's two reasons why someone might veto a pic. So for instance, if Dr. Nicki shares a choice, and Ann Elise loves the idea and wants it higher on the list, she can veto that choice. She or Dr. Nicki can play it again higher up on the list. Then Dr. Nicki, now for her turn has to come up with another pick to replace the one that was vetoed. The other reason for veto would be Dr. Nicki shares a pic. And Ann Elise says that shouldn't even be on the list. So that's another reason why a veto might happen. If your pick is vetoed, you then need to supply another pick to replace the one that got vetoed. So the hope is that you guys have come with a lot of options and you're ready like if something gets vetoed, etc. So are there any questions before we flip the coin to see who gets pick a or pick B?

Ann Elise Record 3:27

No, I think we're good.

Melissa Milner 3:29

Good. All right, Ann Elise, do you want to decide on heads or tails? I'd like heads, please. All right, Ann Elise heads, here we go. It is heads. So Ann Elise, do you want more picks and just the one veto but your picks are mostly higher up on the list? Or do you want less picks, but two vetoes? And your two pick... two of your picks are number one and number two on the list.

Ann Elise Record 3:59

Oh my goodness, it's so hard to decide. I thought the coin toss was going to decide for me?

Melissa Milner 4:04

No, it decides whether you... who gets to choose if they want a or b?

Ann Elise Record 4:11

Oh my goodness, I will be Player A. I will do the more picks.

Melissa Milner 4:15

Okay.

Ann Elise Record 4:16

I think before we get started with the how we want students to explore problem solving, like what what the whole environment's going to be as you're doing problem solving. It's important to talk about the different problem types, the Cognitively Guided Instruction, the research of Thomas Carpenter and his colleagues of researching how children problem solve, and they're able to identify various problem types and even create a hierarchy that some are more difficult than others. And with addition and subtraction, it actually includes 15 different problem types, which is kind of mind blowing, because in a lot of the consulting work that I do, I'll ask people to write me a problem that could be solved by either addition or subtraction. And I typically get two problem types and not the other 13 get mentioned. So like well, it's when we think of it off the top of our heads. And so if we're making up our own story problems as I had in my classroom, I thought I was creating great problem solvers. Because I had a keyword poster that could help them take a word to find out what operation. And turns out the the problems I was writing were the easiest version of the problems, and I use the keywords where the children would be successful. I was not aware at the time, in my years in my fifth grade classroom, that there are different problem types. And of course, I was not setting them up for success at all. I was hindering them, and kind of sending the message that here's a trick to help you get this right answer and not be valuing the process of problem solving and reasoning and thinking. And so just want to put that at the outset that the suggestions that we have this exploration of problem types, we want to make sure we're exposing them to all the different types of problems. So 15, that involve adding subtracting nine that involve multiplication and division. And those are single step problems, of course, then again, multi step that combine these single steps. So it's a really, it's a, it's a lot, but I know that my brain has benefited so much by learning about them. And by modeling them with the structure, the underlying structure, the story problem, I think is really can be providing access for so many more of our students than we have in the past.

Melissa Milner 6:17

Definitely. And I can go ahead and put all that info in the episode on the episode webpage. All right. So I think we're ready to start with pick 10. Get ready. Because Dr. Nicki, you might want to veto, I we'll see. Pick 10 Ann Elise.

Ann Elise Record 6:38

Okay, I would like to start off with a routine called Bet Lines. So it was an article in the NCTM magazine a while ago. But what happens is you are revealing the story problem sentence by sentence. But after each sentence, the students are going to predict what information will come next, and eventually predict what the next question is going to be. So it really slows down the problem solving versus reading the whole story. And then let's get to action to solve it. It slows it down and makes them bet on what is coming next. So I enjoy doing that with students.

Melissa Milner 7:13

That's amazing. We've done that before. It's they get so frustrated, but it actually really helps them think things through and predict. All right, Dr. Nicki, what are your thoughts on that one?

Dr. Nicki Newton 7:26

I'm gonna let that one stay.

Ann Elise Record 7:29

All right.

Melissa Milner 7:31

All right. So pick nine, we're ready for Dr. Nicki?

Dr. Nicki Newton 7:34

I would say no, I just think this belongs on the list. Whether it's nine or higher. I like Picture That where you show the students a picture, and you ask them to tell you what is the story that goes with that picture. And I like it, because practice to say about reasoning, says that kids should be able to contextualize, they should be able to tell problems, not only just solve problems, right? So we oftentimes decontextualize but we want kids to contextualize. I don't think we do that enough in schools, whether you just show them the picture, or along with that genre, you could just show them an equation or show them a model or show them an expression that the idea of getting kids to make up the problem.

Ann Elise Record 8:42

Yeah, I love that idea of having the students write their own story problems, I think that really helped it to be culturally relevant. You know, we want to get to know our students and what can make to help them be able to see the math all around them in their lives and make sense of that. And so providing them the opportunity to write story problems. I think that added layer of us knowing the different problem types, we can see what problem types they're making up to see where we want to have our instructional responses, whether it's small group or whole group, that knowledge is just so important. And I think it allows us students that ownership of creating those stories of problems and and making it relevant to them.

Melissa Milner 9:21

Okay, Ann Elise, are you fine with it being here on the list? Would you want it higher up? All right, we are smooth sailing. All right, we are already on pick eight. All right, Ann Elise.

Ann Elise Record 9:34

Okay, my goodness. Um, so I also like I mean, Nicki had mentioned the decontextualized and contextualizing right, so we have a story problem, and whoever we're engaging in that story problem, we can eventually come to concretely picturing the structure and pictorially but then abstractly having the equations. And I think is really important that when we're working with the equations that we have options and and talk about whether these options will work and whether they won't work for the situation given to us. Because often students will, will they kind of see work problem solving as like this drudgery thing, this like necessary evil of math, and they want to like pluck the numbers out, Graham Fletcher calls them pluckers. So they pluck out the numbers and try to find a word that can tell them what operations are not attending to the story at all right? And then getting this answer and hopefully the answer is right, and they can move on. But I like to have different equations written, that have the same numbers as the problem. But I also incorporate those equations like putting the answer or the symbol for the unknown, on the left hand side of the equal sign, right, the foundational idea of equality, because these are the kinds of things that, you know, when the students are taking these necessarily, I wouldn't say the necessary it's just a reality of our life. I don't believe that they have to be in place. But the standardized assessments and high stakes testing, right, a whole other conversation to have. But the writers of those questions, know the typical misconceptions of kids, and they want to see do students really have conceptual understanding of mathematics? They aren't trying to trick the kids, they're trying to see like, if you have reasoning, you could answer this question really quickly. If you're gonna go down a road of an algorithm and clunk out answers, what are the most common mistakes in that procedure? And then those are the other possible answers, right? Like they know ahead of time, what they're doing when they're when they're writing these problems. And so I've seen questions like that, where it has a story problem, and but then it says, Stevie thought to solve this problem by using eight plus five equals the unknown. What other equation could he have used to solve it? And so it's like it's not getting the answer. It's the here's some other equations he could have used. And within that can be the commutative property of addition so changing the order of the addends putting the answer on the left hand side, but also there isn't a commutative property and subtraction. So they might see an equation of two minus eight equals that. But that's not what the story situation is. Not that you can't do that. I want students to understand not have those rules that expire. Could you could take a larger from a smaller just end up below zero. And in the north country of New Hampshire, where I lived for a very long time are cut off temperature for recess was zero. So our kiddos knew about negative numbers. But But yeah, so I think that that as part of the problem solving, tossing out different equations, say, "Which of these and I'm not telling you how many there are, which could work for the situation, and which won't work for this situation." Similarly, like a 40 divided by a 32. I'm sorry, not 44 divided by 32, right like that. There's no community to property and division. So we want our students to get familiar with the look of those equations and what those equations mean, the symbols and abstract numbers. So that's my suggestion for #8.

Melissa Milner 12:47

Do you have a jazzy name for it? Situational equations or something.

Ann Elise Record 12:50

Sure. I like it.

Melissa Milner 12:52

Okay. Dr. Nikki, thoughts on this one?

Dr. Nicki Newton 13:00

I like that. I'll keep that.

Ann Elise Record 13:04

It would be so awkard if she said,, "Oh no. Veto." After all that I talked about.

Melissa Milner 13:09

No, that I think that throughout high school, I mean, it should be elementary, all high school that kind of a here the which ones work for this situation. Yeah. Very cool. Any other thoughts? Dr. Nikki before?

Dr. Nicki Newton 13:28

No, I think that's a good one. My I think it also speaks to the idea. Um, Phil Darrow talks a lot about not just focusing on answer getting, right. And to think about when we're problem solving. Is that what we're doing? Are we just answer getting? Or are we really trying to get kids to think about the problem? So I think if you give them multiple equations, as Elise said, then that makes them to slow down to think about, "Does this match? Could this work?"

Melissa Milner 14:09

Absolutely. All right, this is this is amazing. I can't wait to have this list on the episode page. It's just people are going to be looking at this for years to come. So Ann Elise, you have seven and six. So here's number seven.

Ann Elise Record 14:27

Oh my goodness. Oh, my. Okay. Okay. So part of this I can speak from experience myself that when I grew up learning math, it was very formulaic, procedural, follow these steps, and I could do it. So I thought I was a math person. I had no negative emotions attached to math. I just, you know, it was fine with me. But even when I began teaching, I didn't think about math visually at all. We had a consultant come to my school named Tom Sherston, and he was the first one that showed me visual ways of teaching math like pattern blocks for fractions. I had never had that in my training program, I had no idea and that was not in my textbook that I was teaching from. So the thought you could use pattern blocks for fractions and things like it was mind blowing to me. And that began my mind of this visualization of mathematics. And over the course of time, I met so many other mentors, like like Dr. Nicki as well, that showed me all these other ways of representing math. So I've learned and grown, my brain has changed to think differently about math than they ever did before. I think one of the most major things for me, has been using bar models, or we call them tape diagrams, or strip diagrams, in the structure of the story situations. I know that I have gone to several of Greg Tang conferences and workshops and you know, that's very heavy with the tape diagrams. And you know, the Singapore Math, and it has transformed my competence of like solving middle school level problems where I can get the right answers. But to explain why I went to the algebra representation, I wasn't visual. Now my brain thinks visually, because I'm visualizing those situations with fractions and ratios, proportions, that means crazy powerful. So I really think it's really important that our students model the structure of the story problems. And my favorite online program for doing that is Thinking Blocks/ It's on Math Playground. It's called Thinking Blocks they have, you can choose the story structure that you want. So when you go into that site, it's a free site. You just search Google Thinking Blocks. But it's within the Math Playground site. You can choose, you know, younger, adding, subtracting, but then regular adding, subtracting, multiplying, dividing, even up to like middle school, math of ratios, proportions, fractions, those kind of things. But you choose what structure that you want. And when you go in there, it'll have a story problem in there for you, but you need to drag the bar models over, you need to drag over the labels, and then you have to check it. So you can't you can't compute any answer. Because doesn't allow you to do that yet. You got to drag it over the bars, drag over the labels, then you click on the check mark to double check it. It'll either give you feedback and say no, you got to fix this, or Yep, you're good to go. Then you drag over the the numbers and the question mark for the unknown. Check it and then and only then do you compute the answer and insert the answer to see whether you're right. So you really are zeroing in on the structure of the story problem in this visual way. And it's really slowing down that problem solving. But I just I love it so much. I know the power it's had in my own understanding of the story problems. I now visually see the structure. When I read a story problem. I'm not I'm no longer having to say particularly like story problems that have you a comparison. But it says like, how many more does this person have than the other but then you're given the information that you're actually looking for the smaller number, not the larger but yet the word more suggests the larger one like your brain is like fried. But now I'm like, Oh, I see the structure and becomes easy because I'm familiar with it now. Right? So so I really I highly recommend the the Thinking Blocks that students when they have independent practice and using technology, their technology time can be this fabulous practice of seeing the structure of story problems, and slowing down their problem solving. So that would be what I would suggest for number seven.

Melissa Milner 18:16

That's amazing. And I just want to say Zearn z-e-a-r-n is also really good with slowing it down with those tape diagram models. Yeah.

Dr. Nicki Newton 18:30

Is Zearn Free?

Melissa Milner 18:31

Zearn is free... Yeah, it's it's fantastic. There's some good stuff in there. And it teaches and it fix it tells it'll reteach if they're stuck. But this Math Playground, I definitely have to get in there. I want to start using that this year with my kids. So Dr. Nicki, what do you think about Math Playground Thinking Blocks.

Dr. Nicki Newton 18:53

I'll go along with that. I want to add some things to that. Math Playground I really like for what Ann Elise just said they have several parts. So Ann Elise was just talking about the video section, where you go and watch a video and they show you how to set it up. They have some other parts. One of the parts is independent practice, where the kids have to set it up on their own, they get all this feedback. And if they can't be can't read it, you can push a button and it will speak to them. The other part that I really like about Math Playground is they have it where you can do it yourself. So there's I always tell people, there's two pools, and you can go in and pull up whatever problems you want. But a lot of teachers aren't good at bar diagrams. If so, you know, none of us are that's not the way we were raised. So if you don't know what the answer is, you can push "show us the model." So I tell people go in there and just push "show us the model" until you finally figure it out. And then it'll generate a new problem. So you don't have to tell your kids, I don't know what it is, you just say, let's all take a look at what they did. And then you just got to play it off and do it. So I like that feature. And they also have a feature where you can make up your own problems and solve, but I tell people don't swim in the pool without the lifeguard. Because if you can't swim, so if you know how to bar diagram, and you're really good at it, you go there and make up your own problems. But if you're like, not so sure... you need to swim in the pool with the lifeguard, because lifeguard has to push that little button. And it'll tell you, this was the diagram. So I love I love thinking blocks. And I think people should use all the aspects of it. But that makes that reminds me also of like Greg Tang, he doesn't use Thinking Blocks. But he uses the part/ part/ whole mat or some of the virtual manipulatives sites, right. I like of course, Braining Camp, I like Polypad. I also like Cool Math because they have fun little monsters. So that idea of modeling virtually, I think is really important.

Melissa Milner 21:21

I'm sorry to interrupt. You said Braining Camp and then what was the second one poly

Dr. Nicki Newton 21:27

Polypad. It's from Mathigon, and it's just that they have some cool tools.

Melissa Milner 21:34

Okay, thank you for that. Excellent. Oh, I'm just I get so inspired every time we do this. Like I'm gonna go right now.

Ann Elise Record 21:43

So I just want to also mention that. So yeah, feel I was talking about not the videos, but the kids solving the problems on their own. But so I'm glad you mentioned the videos, because oh, there's so much to explore on that site that you can watch a video to show the kids what it is. But I also wanted to mention the Greg Tang Generator is a really helpful tool as you're dipping your toes into this world. So they aren't super rigorous problems. But they're the single step problem types. But the thing is that you can choose on his site, what the operations you want the added or subtract or the multiply, multiply, divide those two sets of problems. But you can choose the problem type and then what the unknown is. So you can really drill down to make it be a structure that you want, and then it generates it for you so you don't have to make up the story situation. And then when you press on hint, it will show you a bar diagram that matches that structure. And I love these cuisenaire rods, because cuisenaire rods when you keep the numbers within 10. I do always suggest that you use numbers less than what's the current grade level expectation of the kids because you're focusing on the structure and not the calculation of the answer. So if you leave the numbers within 10 for the structure than a Cuisinart can be rods can be the concrete representation of a part/ part/ total, that is proportionally correct. It's not just a line in the middle for the to addends, right,

Melissa Milner 23:01

that that is such an amazing tip. Yeah, yeah, keep those numbers low. Let them focus on Yeah.

Ann Elise Record 23:07

Exactly. But also, when you're if you're having like an independent work time station in your classroom, and you have like a problem solving workstation, you may want to differentiate a little bit from the problems that kids are solving, but we want them in that place of productive struggle, we don't want frustration. So you can choose on his site, what problem type and where the unknown will be. And the number range for adding subtracting, you've got like zero to 10, zero to 20, zero to 100, and zero to 1000. You're another choice of application division problems. Those are basic facts. But it'll print out 10 for you. So then boom, there you go print those out, put them into a baggie, and then when the students go to that workstation, when they're working independently without your scaffolded support they're having the structure and the CGI research does show that progression of difficulty of them, so have an easier ones for them and that independent practice. So it's a way of quickly for teachers who did not have time to make up their own stories or to find these to print out 10. But you have that intention ahead of time of what exact structures do I want. And you can do random, which would have all the random, but I like that power to just like boom, I've got 10 I cut them apart put them in an envelope and then when the kids go to that station. They know which envelope they're going to.

Melissa Milner 24:20

That's fantastic. I just...you mentioned CGI. So cognitive guided instruction. Do you want to give like a really quick blurb about what that is? If people don't know.

Ann Elise Record 24:28

Sure. So that's Thomas Carpenter and his colleagues were they they they wanted to research how children problem solve. And so they gave them story problems and did not tell them how to do it. They said go ahead and solve it, do it in any way that you want to. And they were able to determine four different basic problem types for the that involve adding and subtracting. So you have an add to story problem where there's a change, there's action happening where there's an increasing of objects over time. And you also have a change where it can be decreased in the objects were typically subtraction we think of that with things being broken and eaten and given away. And then we have part/ part/total where there's no action at all. They're just different categories, like two kinds of birds in a tree. There are five birds in a tree. And some are Bluebirds. Some are Robins, well, there, there's no action, the no birds flying in the tree or flying away from the tree. They're all there. They're just different types. And then finally, the comparison story problem, where we have like maybe five blue birds and three Robins, how many more blue birds than Robins. But the thing is, in those four basic problem types, the unknown could be at any of the three spots. And there are three versions of the comparison that are easier, and three versions that are harder. And that's where you get to the 15 types. For multiplication and division, you have the equal groups one they are all very familiar with, then there are arrays, we've got rows of equal size rows and columns, with the area model being the measurement version of that super powerful model for multiplication and division. And then the multiplicative comparison, you got a larger group, a smaller group, that larger group is an iteration of the smaller group, it's a number of times bigger, you take that smaller group and you repeat it over and over. So those are the problem types. But again, the unknowns could be at any of the spots. And that's where subtraction can come in, and the division in these different problems structures. So a whole lot to explore. There it is mind melting work, you think it would be really easy. And it completely is not. In fact, in my consulting work, the hardest problem types to work with are the adding and subtracting it is what sends people like over the edge, because it's mind melting is like what is this happening?

Melissa Milner 26:31

That was a really good explanation and very succinct, because it's, you know, an entire book, but so I think we're moving on because there's no veto for the Thinking Blocks. So Ann Elise, you have picked six.

Ann Elise Record 26:47

Alrighty, so for pick six, I'm gonna go with a routine called Infogap, the information gap. So the way this routine works is, you would have ahead of time created to, you know, let's say index cards. So you take a story situation, you take out the data, and put the data, the specific like number information on one of the cards. And the other card, you have the rest of the story problems. So essentially, it's like a numberless word problem for one of the children. But the other child has all the data that you need. So the kids have to communicate to each other, they have to ask the person that has the story card has to ask the person that has the data, information to get the data that they need. So it's a it's a whole routine. That I just think it's amazing because it just it's making the conversation happen over and over of the story problem. And then once they have gotten all the information that they need, then they go off together and solve the problem together, but just called Information Gap.

Melissa Milner 27:50

I love that. Dr. Nicki, what do you think of Infogap, or Information Gap?

Dr. Nicki Newton 27:56

I love that. But I'm going to veto it. I really want three reads in there. Three reads is where they read the problem three times. The first time they read it, they read it for to figure out what the problem is about.

Melissa Milner 28:14

Wait, I'm going to ask I'm going to stop you Sorry. So why are you vetoing Infogap first of all.

Dr. Nicki Newton 28:20

Just because there's not that many spaces left and although I love Infogap, I think that three reads deserves a place instead of it.

Melissa Milner 28:32

But you don't get to choose that. You could choose that for number five, but if you if you veto Ann Elise gets to pick again

Dr. Nicki Newton 28:40

Oh, okay, well I veto it.

Melissa Milner 28:43

Okay. All right, Ann Elise.

Ann Elise Record 28:46

Well, the three reads was my number one choice. That's, I want that at the very top of the list.

Dr. Nicki Newton 28:53

It's not gonna be at the top so put it here.

Ann Elise Record 28:55

Oh snap. Oh snap.

Melissa Milner 29:00

Or put whatever you...Ann Elise, you put whatever you want. This is your pick.

Ann Elise Record 29:06

Well, good gracious. Now I'm stuck.

Dr. Nicki Newton 29:09

If you want it on the list? You better..this is your opportunity.

Ann Elise Record 29:12

I guess I kind of put it here. Oh, man. You're you always surprise me. You Oh. All right. So so my favorite routine, Melissa. (Dog barking)

Melissa Milner 29:21

I just want to say the dog agrees.

Ann Elise Record 29:23

Yes. He's defending his mother. That's right. So, so my favorite routine for problem solving. I'm sharing here at number six, because I'm forced to do it's called Three Reads. And I've actually seen it in some curricula, but it's not in the way that I like to do it. So I want to make sure that I'm clear about how I like to do it. It's not my personal belief it's San Francisco Unified District. So Dwayne Habecker. There are a lot of videos on YouTube of him doing this in classrooms. He's done a lot of work on this and that he has a Twitter where he puts out a tape diagram challenges and put a story problem now everyone to share their tape diagram model. So I love that work. So the three reads would be that you have a story problem. It can be anything from the textbook that you have, right? But take off the last question and have everything else up there. Now the teacher reads the story problem first to everyone. And then the kids talk to each other about what is the story about just in general? What is the story having to do with. Then the teacher and the kids together choral read the second read. And we then talk about the quantities like what quantities do you see either implied, like implicit or explicit, that are mentioned in the story, that we can then record those on the boards were kind of extracting out the information, the data of the problem. And then what I love is the kids...then they read it again, a third time, and then the kids make up the questions that could be used to solve. That's the piece that when I was in the district recently, they mentioned how they have three reads in their curriculum. But when I asked him about it, they didn't. The part three was not the kid generating the questions. And I think it's such a crucial piece of that exploration and problem solving. It's for the kids to knowing this data, what are the things we could solve and then having a choice? When the kids are actually solving it is, you know, you have variety of questions, you can leave them all up on the board, get them into random groupings, and have them choose what question that they want to solve. So the kids have a little ownership of that. Or you could choose instead to pick one of those questions and have everyone solve that same question is probably going to be the one that was on the problem in the first place. And they go off in groups. And they saw that and navigate to a gallery walk of how everyone solved the same problem, but different ways, different ways of getting to that, that answer. So I think it allows a lot of ownership with the kids a lot of choice, and so important that they generate questions that could be asked. So that's my favorite way of experiencing problem solving and it's at number six.

Dr. Nicki Newton 31:58

Well, but it's on the list.

Melissa Milner 31:59

Oh, man. You. It's on the list. But I mean, you have choice four and three, but you probably have things you want.

Ann Elise Record 32:10

Well, she's got two vetoes, Melissa.

Melissa Milner 32:13

That's true. All right. Yeah, get it on there. Okay, great. So I'm going to assume that Dr. Nicki is not going to veto that.

Melissa Milner 32:23

No, I'm not gonna veto that.

Melissa Milner 32:27

Alright, so believe it or not, we're at number five, Dr. Nicki.

Dr. Nicki Newton 32:32

I would say Three Act Tasks. Because, you know, they're engaging. They make kids think they make kids use information. They make kids estimate. I just think that they're, you know, they can be really good. they have the potential to be really good. So I would put Three Act Tasks. There's lots of places online now that have them. And I just think that they're good. I think they belong on our list.

Melissa Milner 33:08

Fantastic. I've used them. They're, they're amazing. And there are a lot actually, you're right, there are a lot of resources for them. Ann Elise, what are your thoughts about number five, Three Act Tasks?

Ann Elise Record 33:22

Yeah, I mean, those are phenomenal. I know they, I think they should be higher than five. So I'm curious what other ones she has on our list that she would say are higher than that, because that that's separate than what I was thinking about of engaging with problem solving. So now it's opened up a whole other world of information for me. So the only reason I would veto it would be to have it be higher on the list, because it's so...

Dr. Nicki Newton 33:45

It's not going to be higher.

Ann Elise Record 33:48

Oh, but no, it could be higher. So you definitely you can tell it works. I can veto it and then you have to pick another one in its place.

Dr. Nicki Newton 33:57

Right, but you can pick it higher than I can veto yours.

Ann Elise Record 34:01

Oh snap. You're always thinking ten steps ahead. That's how my cuisenaire rods didn't end up at the top of the list and your beaded number line got up there.

Dr. Nicki Newton 34:12

Let it go.

Ann Elise Record 34:13

Oh, all right. I'm gonna leave it there. But I do love it and I would put it higher on the list.

Melissa Milner 34:19

All right, this is hysterical. All right. All right. So we we have one veto used by Dr. Nicki. We are at number four, Ann Elise.

Ann Elise Record 34:30

Okay, so four I would put numberless word problems. They are the well, the creator of it was in a district with Brian Bushart and he then created the whole blog post and materials and it's amazing so numberless word problems would be having a story problem, but you literally take out the numbers because that's the whole issue with the problem solving is kids want to just pluck the numbers out right? So they're not attending to the story situation. So there's a wonderful blog post that you wrote, wrote with lots of links on it. And he also has some slide decks already to go. To start off with that, all you need to do is just bring it up on the screen and you click the right arrow. He has different prompts for you down below we can prompt the students with but it's just slowly revealing the numbers over time and then having the question be open again, like, what question Could we be asked once we have this data and then having the students predict or make up what story question it is in that problem. So I also really love he's got some extra ones that are available for different grade levels. It's particularly one that I just thought was amazing. It's the tallest person in the world met the shortest person in the world is a man and a woman. And so the visual image of that they they were in Egypt in front of the pyramid. And so you see a picture of this gentleman who's immense, and this little woman. And so he has that for different grade levels, because he's talking about either the inches that they are or the centimeters that they are. So the numbers can be appropriate to the grade level. But I just think that's so amazing. And so it, you know, just immediately engaging and thought provoking so, so lots of resources at the fingertips for teachers to already have some of them already made for them.

Melissa Milner 36:09

Fantastic. Dr. Nicki, what do you think about numberless word problems at four?

Dr. Nicki Newton 36:16

I totally agree. I love it. And actually, the slide deck that Ann Elise was referring to. He's got it organized by problem types. So it's even better.

Melissa Milner 36:28

That's fantastic. I again, very inspired. All right, we're barreling right now. Believe it or not, we're at number three, Ann Elise.

Ann Elise Record 36:39

So I need to eat my words, in terms of what my favorite way is for students to problem solve, because I can't believe this didn't even make my list but it's revolutionizing classrooms. I think it deserves to be at number one, maybe Nicki will agree, I don't know. But the the book by Peter Liljedahl Building Thinking Classrooms is unbelievably changing the classroom experiences. And I've been doing this in my seminars with teachers, as well as being in classrooms with kids, and it is mind blowingly powerful. So this is my last choice. This is number three, so I'm putting it here. But it is the his his research he researched he was he asked for volunteers of people that were like the best of their craft of teaching kindergarten to 12th grade. And then he went and watch them teach. And it came away from that experience trying to find out like, what's the science behind teaching what's the best, most impactful way for kids to learn. And he found that 95% of the children in those classrooms of these revered teachers, were not doing any thinking. They were mimicking. So they were they were mimicking a procedure the teacher was teaching them and with a variety of success, and 95% of the kids and so he researched then micro research every tiny little move you can do to see what is the most impactful he is grad students, they interviewed kids, they did I mean just incredible amount of research. And he has 14 recommendations for us. And I've really only delved in the first four or five, but it is life changing. So the first one is to have visibly randomized grouping, where you, the kids can see it's visibly random grouping, it's not that I thought ahead of time as a teacher, I got these kids going together and these kids going together, they can that they can tell it is random. Because too often when we are grouping our kids together, we're sending a message that we don't believe the kids can do it. And that then they end up feeling that they're invisible in the class and that they're what they have to say doesn't matter. And if they're not one of the faster answers and being revered for all, you're a high flyer, you're this great kid or they begin feeling less of themselves and their identity is affected as well. And so that visible randomized grouping means everyone has a voice everyone has something to contribute to our community of learning together. So that's the first thing. Secondly is we're having the kids stand up at nonpermanent vertical surfaces. So they research having the posters be on tables or up on the walls, and the most impactful was on the wall. So kids are standing up in groups of three, they have one marker, because the person doing the writing with the marker does not write their own thinking. So you have to communicate with each other and you can't have one person taking over the group problem solving up here. Now I can do it and I'm going to solve it. So just those few moves is dramatically different for the classroom of and you're giving them a rich task. So what I've done in my seminars is I will take a three act task, so I love to do the donuts one. There's one of the Krispy Kreme Doughnuts had the largest box of doughnuts there are 32 rows of 25 donuts in each row. And then there are three layers. And so I show that picture of that image and then there everyone's in their groups of three determining how many donuts that is. So you can do the three act task. But when the kids are doing the problem solving part of it, they can be standing up at these posters so the knowledge is visible around the room so you can see what other groups are doing is not a matter of us stealing from each other. It's all of us as learners working together, and and celebrating that we all bring different things to the table and that and having that climate that we're going to all celebrate the achievements of everyone, even if it on ourselves that we're gonna celebrate someone else learn something today. So it's just it's a powerful revolutionising thing for classrooms. And I think that that problem solving experience is so much enhanced when you do it in that kind of a structure. And I hadn't thought of that to make the top ten in terms of problem solving, but it is hands down smazing.

Melissa Milner 40:30

So I think what you're saying before I throw it to Dr. Nicki, is that the structure itself, of the standing up at the posters and randomly grouping is what you're saying is number three.

Ann Elise Record 40:44

Yeah.

Melissa Milner 40:45

Okay.

Ann Elise Record 40:45

And, and you use rich tasks. So the three act tasks, that Dr. Nicki mentioned, not necessarily three act tasks, but any kind of rich tasks that allows multiple pathways to get to the answer, or even multiple answers. Another one that I love that I've been doing in some fifth grade classrooms with kids is, and you tell the story of the kids out loud, that they found it was better than putting on a worksheet. So you tell them the story of an art class was doing a painting project. And there were six cups leftover that had various amounts of paint fractional amounts in the paint cups, and a little girl had not been a part of it, she walks in, and the teacher says, you're welcome to use any two of those cups. As long as your cup doesn't overflow with paint, you're welcome to choose any of those two. So her criteria is you got to pick two fractional amounts that will not go over the whole. And the fractions are like five tenths and five twelfths. Those are same numerator, there was 1/3 and 1/5. And then it was like three sixths and three fourths. And that's that all those choices, there's not one answer. So the kids can be picking and choosing illustrate these two cups, but they had to make their thinking visible to others, they had to use pictorial or abstract ways to show what their thinking was. But that kind of a task is so rich, it's not getting an answer of adding this fraction and this fraction, it's like all these different pathways, and all these different solutions. And I found in classrooms that some students want to go right to like the algorithm of adding fractions. There's one group I had in the classroom that had shared the 5 tenths and five twelvths. And they converted them to 60ths. And then they had gotten five 60ths and simplified it all the way down to 11/12 to prove that that cup would not have overflowed. And I thought that was great. Like, yes, absolutely, you're right. And that was pretty much it didn't have much else on their poster. The next group that we went to, to share with the class this, this young man was like, we were kind of thinking that we didn't have to know exactly how much of the cup was full as long as didn't overfill. So we're thinking that by five tenths is a half, and five twelves is a little less than a half. So that wouldn't have overflowed.

Melissa Milner 42:52

I love when they use benchmarks. That's great.

Ann Elise Record 42:54

Yeah. And they were thinking and reasoning, right? That's the thinking. And so often we go down to those procedural ways of solving they're not really thinking and reasoning, right? So, so that that group had tons of combinations of two cups because they weren't doing the calculation. They were in common denominators. They were thinking and reasoning that 1/3 and 1/5 couldn't overflow the cup.

Melissa Milner 43:18

And then at the end, do they walk around and see each others?

Ann Elise Record 43:22

Yes, exactly.

Melissa Milner 43:23

I love that.

Ann Elise Record 43:23

And as the teacher is a facilitator of the learning, so as you're walking around, you're not giving the answers to them. Whether they're right or wrong. You can put two groups together and say I want group one to look at group twos poster and what do you see if they're thinking how they made their thinking visible for us to tell what their thinking was? Then the kids can find commonalities and differences between their two different ways that they went about to get their answer. So it's a really rich... it incorporates so many of the math practices that we want to have happen in classrooms. So yeah, really, really powerful.

Ann Elise Record 43:53

Amazing. Dr. Nicki, does this stay at number three?

Dr. Nicki Newton 43:57

It does. I've always loved that work of thinking classrooms even before he published the book. I used to read his his articles and stuff, and I just find it to be profound.

Ann Elise Record 44:13

Well, I can't wait to hear your top two.

Melissa Milner 44:16

All right, this is amazing. Okay, so not vetoed. So we're down to Dr. Nicki at number two.

Dr. Nicki Newton 44:25

I'm gonna pick worked examples. I love worked examples. So there's a variety of types. There's at least four types of the main worked examples. I'm just gonna talk about two of them right now. One of them is, you know, their work examples are problems where you either give the kids the wrong answer or the right answer and you say, Michael, solve the problem this way. And it's wrong So, what did he do wrong? So you might say, three plus blank equals six. And maybe Michael said the answer was nine. The kids have to argue why that's incorrect. Or you might say, Melissa did the problem this way, and it was correct. And she said three plus three equals six. And she's correct. So explain why she's correct. A twist on that is where you say, So and so thought this way, and so and so thought that way, and it was correct and why. So I love those problems, because they require that kids reason. There's a tremendous amount of Well, I don't know, if there's a tremendous amount, there's a really good research on how doing worked problems with kids, actually really helps them to get stuff that they're doing wrong. Because they get to see, like the same errors that they're making up on the board. So kids are like, I don't know, they said, Jerry did it wrong. But I did the same thing Jerry did so. So they, they get to see all that's wrong. And of course, the name. You don't they're not the kids in the class. So I love the power of that. And that it's evidence based. We know from the evidence that that kind of process helps to, to help kids problem solve. And there, there's some really good articles written about how to do it, because one of the important things is you do a worked example. You talk through it, and then you immediately give the kids another worked example, and have them solve it. So I'm just fascinated by that research. And I don't think we do it enough. In schools.

Melissa Milner 47:14

Great before I shoot it over to Ann Elise, I just want to say that we just started using illustrative Math. And those worked examples are throughout the work that we're doing this year. It's very exciting to see and I didn't know they were called worked examples. But a lot of the this kid did this, this kid did this. Are they both right? Are they wrong? Who's right? Who's wrong? Yeah, there's a lot of that like each, like I'd say, a few a week that come up. So they're really great. But I like the idea of then giving them another one right afterwards. That's great. All right. So, Ann Elise, worked examples at number two, what do you think?

Ann Elise Record 47:54

I love it. Okay, awesome.

Melissa Milner 47:56

Awesome. All right. So believe it or not? We are at number one.

Dr. Nicki Newton 48:02

Well, number one, I picked open questions. I love the work of Marian Smalls. I think she's a brilliant educator. And I'm highly influenced by her. And so the idea of an open question is, I wanted to read something that I had tweeted. This was by Ritchhart. But it says, asking authentic questions, that is questions to which they're not predetermined answers, is extremely powerful creating a classroom culture that feels intellectually engaging. Such questions allows students to see teachers as learners, while fostering a community of inquiry. So I love that idea that when you actually are problem solving, there's there's no predetermined answer. So in like the example that Ann Elise gave with the paint, it's a brilliant problem, because there's no predetermined answer. There's no one right way to think about it. So I just saw something the other day that I loved, is I'm gonna give you two examples of open questions. One was we were looking out the window and we saw 10 legs. What did we see? And you ask that like it's great. first grade, second grade classroom, you get the wildest answers. What did you I thought two humans a cow and chicken? Or I saw five chickens, or I saw a cricket and a cow. I mean, it's just so fun. You look out the window and you see ten legs. What could you have seen? It's an open question. And also the questions like, you know, elapsed time you say, "Susie left her house and she was gone for 20 minutes. When could she have left? And when could she have come back?" So it's open and, and kids stretch into it. So some kids are gonna say she left her three, three came back at 3:20. That's the safe way. But other kids are going to try the in between numbers, you know, so they'll stretch themselves. So I love open questions. I love the possibilities of open questions. And I love you know, Marian Smalls work?

Melissa Milner 50:46

Well, I'm really glad you shared this because we've been so into this new math program, that that book has been sitting on my shelf, our principal bought it for us last year. And it's just been sitting there. And now I'm gonna pull it out. And I thank you for reminding me of the awesome resource. Ann Elise, what do you think about the open questions at number one, you do have a veto?

Ann Elise Record 51:12

No, no, no, I think that's wonderful. I love that. I love that. I love the openness are clearly open questions. I love the openness of the kids to kind of enter that in a place of their own entry level, right? That where they are going to like that love that elapsed time problem where the the kids can make up like what the time is going to be and enter that task wherever their readiness level is, right? I just That's an awesome, awesome idea.

Melissa Milner 51:39

Well, I have to say this has been the smoothest, most inspiring. I... this is fantastic. And I am going to put on the episode page, an honorable mention was it information gap or info gap.

Ann Elise Record 51:52

Yes. I had heard of it as info gap.

Melissa Milner 51:56

Okay. Yeah, that's definitely honorable mention.

Dr. Nicki Newton 52:00

I'll agree with that. I did want to mention a few more resources.

Melissa Milner 52:05

Yes. And I also we can go through and do any discards of things you didn't get to.

Dr. Nicki Newton 52:10

Okay. I wanted to mention, South Dakota Counts. If people Google that South Dakota had a federal grant, and on they did tons of CGI problems by grade level. Now, they did all the problems for every grade level. So you have to go through and you're not going to do all the problems in kindergarten, you only have to do four of them and et cetera, but but they have all the problems for all the grade levels. And they have also a different, you just Google South Dakota Counts. But they also have if you go, South Dakota Counts Multiplication, they have a really good multiplication with the grade, the grades, like if you're in third grade, do second, if you're in fourth grade, do third, etc. But those are some really good resources. Two other resources. I've written two books on problem solving, called Problem Solving in Action, grades K-2 and 3-5 that has all the problem types and all the discussion about that. I also wrote a series, it's still up on Amazon by grade level for all the problem types at each grade level. And I did that many years ago. But so those are some other resources I wanted to mention.

Melissa Milner 53:32

I'm very glad you did. Did you have any pics Nicki that you didn't get to do?

Dr. Nicki Newton 53:39

No I think I got all my picks.

Melissa Milner 53:41

All right, Ann Elise. How about you? Were there any picks that you didn't get to draft?

Ann Elise Record 53:45

Nope, those were all the picks that I had. But I do have two resources that I do want to share as well.

Melissa Milner 53:50

Terrific. Terrific.

Ann Elise Record 53:51

One is Teresa Wills is amazing. She's got an incredible set of resources, of doing of working in mathematics virtually. And she does what are called Mathurdays where every Saturday she hasn't done it recently, but she's I'm sure she'll get back to it. She's just wonderfully generous with her time and do that. But they're all recorded on her webpage. So it's teresawills.com, you can go to her, her Mathurdays recordings. And that's where I got that fraction task from. So I didn't make that up. It was something I want to say my memory is it was Virginia Department of Ed that had it. So she had used that task on one of her Saturday sessions. And teachers are joining in and then it gets recorded. So you can see how you can be modeling, solving things in a virtual world like using Google Slides. And that's where I got that task from. So I want to make sure I give credit to that. But also to let everyone know that when I'm looking for a rich task that I want to be able to do I go to her site and see what she's done. On those Saturday sessions because I can listen to that task being implemented and people solving it and the different ways they thought about it. So it's a really helpful place that I like to go and it's so generous of her to have that for us. And secondly, I want to mention that Braining Camp is a virtual manipulative site, their manipulatives exactly match the colors of the manipulators, you can buy on the company Hand to Mind, they partnered with them to kind of make their apps look identical. And they're a phenomenal virtual manipulatives site is it is called Braining Camp is really relatively cheap for schools to get it where you get access to 16 different manipulatives. But it also within there have tasks that you can already made for you, rich tasks you can give the kids and assign them. And you can even do a live session where you're watching them work live. So I highly recommend you check out the Braining Camp site. One of my favorite things is that they created webinars, they have webinars that I've been honored enough to work over the pandemic, I began working for them because my consulting work was going down, I couldn't be in schools, and they had a higher demand. And they really wanted people to learn about the mathematics and not just how to use a tool. So I began training districts that purchased their program. And then I began doing webinars. And they gradually gradually opened it up to more wonderful math educators as well. So Dr. Nicki and I have done several of them together, these are all hour long webinars that are completely free for anyone. You don't need to belong to Braining Camp to watch these. So you go to brainngcamp.com and look on the tab for webinars, you will see a whole slew of them, but lots and lots of different people. But I have been lucky enough to do several of them. And in particular, there are two that she and I did together on the problem solving types. So one for the adding, subtracting one from multiplying and dividing. And you can be introduced to what all the problem types are, as well as how we can model the structure using various concrete tools. In the virtual world, of course, we can do it concretely Cuisenaire Rods, the Rekenreks, things like that. So I want to make sure that everyone knows that that is a wealth of hours and hours of wonderful math PD that people can have.

Melissa Milner 56:53

Unbelievable. All right, so I'll say it again, all of these resources will be linked on the episode page. And also we'll have the transcript of this exciting draft. And I just want to say thank you so much again, third time, we're gonna do this hopefully a zillion times more. But thank you so much, and I can't believe people, there have been so many downloads. The first one we did was that 2020 No 2021 In February, unfortunately, right before my husband passed. That's how I remember this.

Ann Elise Record 57:36

I'm so sorry.

Melissa Milner 57:37

That was our first one. It has over 700 downloads and and climbing. And then the second one you guys did has like 300 something downloads and you keep advertising it.

Ann Elise Record 57:50

I do.

Melissa Milner 57:52

People keep coming and listening.

Ann Elise Record 57:54

Because it's so much fun. We have such a good time together. We laugh.

Melissa Milner 57:58

So they're really they're really popular episodes. So I think we will hopefully be keeping this train rollin. So thank you again Dr. Nicki and Ann Elise for taking time out to do another draft.

Ann Elise Record 58:10

My pleasure, loved it.

Dr. Nicki Newton 58:12

Thank you for inviting us.

Dr. Nicki Newton 58:15

For my blog transcripts of this episode, and links to any resources mentioned, visit my website at wwwtheteacheras.com. You can reach me on Twitter and Instagram @melissabmilner and I hope you check out The Teacher As... Facebook page for episode updates. Thanks for listening. And that's a wrap.