WEBVTT NOTE This file was generated by Descript 00:00:00.242 --> 00:00:04.432 Welcome to Better Teaching, Only Stuff That Works, a podcast for 00:00:04.432 --> 00:00:07.892 teachers, instructional coaches, administrators, and anyone else who 00:00:07.892 --> 00:00:09.482 supports teachers in the classroom. 00:00:10.322 --> 00:00:12.952 I'm Gene Tavernetti, the host for this podcast. 00:00:13.267 --> 00:00:16.707 And my goal for this episode, like all episodes, is you laugh at least 00:00:16.707 --> 00:00:20.387 once, and that you leave with an actionable idea for better teaching. 00:00:21.097 --> 00:00:24.817 A quick reminder, we will be sharing only stuff that works. 00:00:24.837 --> 00:00:27.987 No cliches, no buzzwords. 00:00:28.292 --> 00:00:34.159 So my guest today is Bill Davidson, and this summer Bill Davidson is entering 00:00:34.159 --> 00:00:36.549 his 24th year working in education. 00:00:37.189 --> 00:00:42.709 He's taught in Philadelphia, Los Angeles, Southern Sudan, and Monterey, California. 00:00:42.709 --> 00:00:42.759 Yeah. 00:00:43.239 --> 00:00:46.506 For the past 12 years, he's worked independently as as an elementary 00:00:46.506 --> 00:00:50.326 math trainer specializing in the Singapore and math curricula. 00:00:50.846 --> 00:00:55.046 Now, you may recognize Bill's voice, because he's also the 00:00:55.336 --> 00:00:59.806 host of the podcast Centering the Pendulum, a podcast about education, 00:01:00.016 --> 00:01:02.717 educators, and teaching practices. 00:01:03.167 --> 00:01:09.557 In fact, I was attracted to Bill's podcast and how I became familiar with 00:01:09.557 --> 00:01:12.387 Bill because of the title of the podcast. 00:01:12.732 --> 00:01:16.762 As I just said, there are no cliches, and one of the cliches that I hate most in 00:01:16.762 --> 00:01:18.972 education is the swinging of the pendulum. 00:01:20.222 --> 00:01:23.692 when I heard the centering of the pendulum, I said, this is, for me. 00:01:24.112 --> 00:01:28.566 And, Bill, before we get started, let's center one thing on the pendulum. 00:01:29.166 --> 00:01:32.806 Let's, agree that we are not going to talk about the fact that kids 00:01:32.816 --> 00:01:35.336 should learn their math facts. 00:01:35.868 --> 00:01:36.918 I'll try not to say it 00:01:37.730 --> 00:01:42.960 how controversial is that, we need to even talk about that? 00:01:43.280 --> 00:01:47.240 So Bill, I'm excited to talk to you, and one of the reasons that I wanted to 00:01:47.240 --> 00:01:51.946 talk to you is that I met you, again, the first time I became aware of you 00:01:51.946 --> 00:01:56.782 was through your podcast, but then we had a chance to talk, a little bit 00:01:56.832 --> 00:02:01.678 and to share some emails about, Word problems, story problems, application 00:02:01.748 --> 00:02:07.687 of math, and then, you have a new book coming out, Infusing Dynamism into 00:02:07.687 --> 00:02:13.057 Daily Problem Solving, Five Alternative Methods to Practice Tape Diagramming. 00:02:14.267 --> 00:02:18.277 I thought, man, this is a great chance and a great time to, to catch up with you. 00:02:18.831 --> 00:02:19.761 why this book, 00:02:21.270 --> 00:02:22.410 there's a couple reasons. 00:02:22.710 --> 00:02:27.413 first of all, I, think you mentioned that I specialize in Singapore math, but also 00:02:27.413 --> 00:02:31.184 Eureka Math, which I think has a lot of. 00:02:31.712 --> 00:02:33.542 Connections to Singapore math. 00:02:33.912 --> 00:02:38.056 The majority of the early writers, at least of the Eureka math 00:02:38.056 --> 00:02:42.086 program, Engage New York were first Singapore math writers. 00:02:42.096 --> 00:02:49.197 So I, I find that the programs are very similar and they both specialize in 00:02:49.197 --> 00:02:55.017 what Singapore math calls bar diagrams, what Eureka math calls tape diagrams. 00:02:56.071 --> 00:03:00.671 I find the same problems arose with both Curricula and all the schools 00:03:00.671 --> 00:03:01.941 and teachers I've worked with. 00:03:02.561 --> 00:03:03.411 Why this project? 00:03:03.421 --> 00:03:05.441 First, I like projects. 00:03:05.761 --> 00:03:08.463 As a teacher, I always had a project going. 00:03:08.463 --> 00:03:12.703 I ran science fairs, I founded a school newspaper, I did video yearbooks. 00:03:12.713 --> 00:03:17.563 I like working towards something professionally outside of the actual job. 00:03:18.413 --> 00:03:20.433 I find it, that does a couple things. 00:03:21.238 --> 00:03:27.010 One, it gives me, something to wake up and do and get excited about. 00:03:27.700 --> 00:03:34.050 Two, it helps me articulate philosophies and ideas and just grow professionally. 00:03:34.050 --> 00:03:36.960 It's good self professional development and I think I become 00:03:36.960 --> 00:03:38.460 a better trainer when I do that. 00:03:39.250 --> 00:03:42.120 Now, why the book and why this specific book? 00:03:42.478 --> 00:03:45.558 Originally, and I know I said I wouldn't talk about basic skills, 00:03:45.558 --> 00:03:49.728 basic facts, but I was the fluency writer for Engage New York Eureka 00:03:49.728 --> 00:03:51.628 Math, the 3rd through 5th grade. 00:03:52.086 --> 00:03:56.466 was the 3rd through 5th grade fluency writer for Engage New York Eureka Math. 00:03:57.356 --> 00:04:01.496 Part of me thought I was getting typecasted as I, I only work with fluency. 00:04:01.846 --> 00:04:04.306 I wanted to do something for problem solving because I think I have some 00:04:04.306 --> 00:04:06.026 things to offer problem solving. 00:04:07.156 --> 00:04:08.966 Bar modeling, tape diagramming as well. 00:04:09.247 --> 00:04:12.132 But why might it be useful for teachers? 00:04:13.442 --> 00:04:18.052 between 2014 and the start of the pandemic, I was supporting a lot 00:04:18.052 --> 00:04:22.332 of schools in the implementation of Engage New York Eureka Math. 00:04:22.752 --> 00:04:26.472 One of the main challenges that teachers were encountering was 00:04:26.472 --> 00:04:30.472 fitting each of the lesson components into a one hour math block. 00:04:31.232 --> 00:04:35.352 The lesson components were, begin with fluency, an application problem, 00:04:35.352 --> 00:04:40.902 so a problem of the day, And then a concept development with a debrief. 00:04:40.932 --> 00:04:46.534 Those were the four components and most teachers just weren't finding the 00:04:46.564 --> 00:04:48.934 time to do the application problem. 00:04:49.604 --> 00:04:52.104 And as a result, they were skipping over it. 00:04:52.374 --> 00:04:56.484 I thought this was a mistake, but I understood why it was taking place. 00:04:56.484 --> 00:04:58.204 They were under time constraints. 00:04:58.294 --> 00:05:06.336 So I, thought rather than skipping it entirely, can you find a way to honor 00:05:06.743 --> 00:05:12.643 the purpose of an application problem, of a daily word problem, even if you don't 00:05:13.223 --> 00:05:18.413 have the students engage in a redraw right process for 10 to 12 minutes. 00:05:18.793 --> 00:05:23.533 And therefore I started to develop a few different methods so that the 00:05:23.533 --> 00:05:28.233 students could still work with problem solving, so that they could still 00:05:28.233 --> 00:05:35.576 work with tape diagrams without doing every stage and procedure, in what 00:05:35.576 --> 00:05:40.891 you do to solve a word problem, And, therefore you wouldn't be neglecting 00:05:40.901 --> 00:05:44.861 the kind of higher order thinking, problem solving thinking that you're 00:05:44.861 --> 00:05:50.256 doing, and I've I made five alternative methods in this book, so five different 00:05:50.256 --> 00:05:53.886 ways to do problem solving without just doing a standard word problem. 00:05:54.381 --> 00:06:00.326 So one of the, one of the things, Bill, that, when we spoke that I was so excited, 00:06:00.326 --> 00:06:04.737 the hair on my arms was coming up I hate to tell you this, but you weren't my 00:06:04.747 --> 00:06:09.817 first choice to sending this material, and so I was looking for somebody that 00:06:09.817 --> 00:06:14.357 would actually respond because the people, the math teachers I were sending 00:06:14.357 --> 00:06:20.317 to hadn't thought about teaching word problems in the way that you talked about. 00:06:20.567 --> 00:06:27.221 for example, if you could expand on what you mentioned, one of the methods that 00:06:27.221 --> 00:06:30.871 you just referenced was redraw right. 00:06:31.256 --> 00:06:31.636 Yes. 00:06:32.021 --> 00:06:33.711 Could you, expand on that a little bit, 00:06:33.916 --> 00:06:38.898 Yeah, so that's the recommended, I guess procedure that Eureka 00:06:38.898 --> 00:06:41.478 Math, provides for, teachers. 00:06:41.758 --> 00:06:46.499 Read a word problem, draw a diagram or a math picture of what you read, 00:06:46.768 --> 00:06:53.048 write a number sentence or equation to solve, write a number sentence to solve. 00:06:53.763 --> 00:06:55.083 And that's how you solve the problem. 00:06:55.493 --> 00:06:59.063 Now, and that just provides the students a loose structure on how 00:06:59.063 --> 00:07:01.523 to go about doing a word problem. 00:07:02.553 --> 00:07:04.318 it's a loose structure, but it works. 00:07:04.607 --> 00:07:05.247 Every time. 00:07:05.882 --> 00:07:06.872 I think so. 00:07:06.926 --> 00:07:11.343 I saw, there was a book with a let, like the 11 steps to solving any word problem. 00:07:11.683 --> 00:07:13.313 I think that's too much. 00:07:13.383 --> 00:07:15.493 I, and I think the kids are looking at a wall the whole time. 00:07:15.883 --> 00:07:17.923 Honestly, and I know a lot of people disagree with me. 00:07:17.923 --> 00:07:20.083 I'm not big on underlining keywords. 00:07:20.523 --> 00:07:25.713 I'm, I beginning represent what you read, and then students may do that in addition. 00:07:25.713 --> 00:07:28.653 I, I, think it can be over formulaic. 00:07:28.653 --> 00:07:32.673 I like that structure because it provides a lot of room for 00:07:32.678 --> 00:07:35.347 idiosyncrasies within a structure. 00:07:35.471 --> 00:07:39.464 what I've found, and, again, I don't want to give you a blister patting you on 00:07:39.464 --> 00:07:46.718 the back of all the things that we agree upon, but the idea of keywords, underlying 00:07:46.718 --> 00:07:49.179 keywords, cross out what's important. 00:07:49.652 --> 00:07:49.982 Okay. 00:07:50.002 --> 00:07:50.912 What's the key word? 00:07:50.912 --> 00:07:50.942 Okay. 00:07:51.492 --> 00:07:52.442 What's important? 00:07:52.502 --> 00:07:53.602 You don't know that. 00:07:53.622 --> 00:07:58.002 To me, what you just talked about, the read and draw, the draw is what allows 00:07:58.002 --> 00:07:59.922 the students to understand the problem. 00:07:59.972 --> 00:08:02.352 And now, what's important? 00:08:02.392 --> 00:08:03.722 Now, what are the key words? 00:08:03.871 --> 00:08:08.065 but the idea that, oh, every time you see all together, it's that's 00:08:08.085 --> 00:08:09.615 not a, that's not a math strategy. 00:08:11.324 --> 00:08:11.984 I agree. 00:08:12.174 --> 00:08:15.822 And I think it was Leonardo da Vinci said, to draw is to think. 00:08:15.832 --> 00:08:18.582 So we read, how do we represent what we read? 00:08:19.442 --> 00:08:25.367 And, we need students to get in that practice of I read, I represent. 00:08:25.797 --> 00:08:30.083 Now, another, piece of this in my evolution, this comes from way back, 00:08:30.131 --> 00:08:35.041 as a sixth grade teacher, I found, especially at that age, you'd have, 00:08:35.561 --> 00:08:37.111 students would read the problem. 00:08:37.451 --> 00:08:39.491 Some would answer it very quickly. 00:08:39.521 --> 00:08:41.451 they had a mental model of everything that was going on. 00:08:41.461 --> 00:08:45.051 They'd have an answer within the first 20 or 30 seconds. 00:08:45.591 --> 00:08:49.441 And other students would, I see a word problem, I put the pencil down. 00:08:49.861 --> 00:08:51.391 I quit before I start. 00:08:52.261 --> 00:08:54.311 we'll get into complexes maybe later. 00:08:54.901 --> 00:08:59.491 And I thought at best I engaged maybe 40 to 50 percent of the class 00:08:59.671 --> 00:09:01.481 in kind of reasoning about this. 00:09:01.481 --> 00:09:03.661 But I thought it just lacked dynamism. 00:09:03.671 --> 00:09:05.611 It wasn't interesting to be a part of. 00:09:05.621 --> 00:09:06.651 I didn't like it. 00:09:06.671 --> 00:09:10.481 It was an uncomfortable drawing to the math flow. 00:09:10.625 --> 00:09:16.653 and so I wanted to find ways to keep everyone engaged. 00:09:17.218 --> 00:09:21.328 Ten years ago, I created a five book collection, what I call problem solving 00:09:21.328 --> 00:09:25.952 ladders, where you give students couple sentences without a question. 00:09:26.482 --> 00:09:32.902 They draw what they draw a representation, and then they answer a series of 00:09:33.442 --> 00:09:37.392 problems that escalate in difficulty, thus the ladder metaphor, right? 00:09:37.602 --> 00:09:42.012 And so my goal is every child will confidently answer a question 00:09:42.012 --> 00:09:46.537 correctly, Every child will feel challenged and have to think. 00:09:47.487 --> 00:09:50.257 And then there'll be a couple other questions in the middle. 00:09:50.747 --> 00:09:55.687 And that way you have a below grade level, above grade level, and 00:09:55.687 --> 00:09:59.107 grade level all housed within the same eight to 10 minute activity. 00:09:59.300 --> 00:10:02.210 If I can, I'll get into another thing I bumped into. 00:10:02.800 --> 00:10:07.970 Another thing I bumped into is often Especially with newer teachers, 00:10:08.159 --> 00:10:14.464 you would get 4th, 5th graders to really begin resisting drawing. 00:10:14.747 --> 00:10:18.177 Some would see it as a sign of weakness, okay, I don't need to 00:10:18.177 --> 00:10:19.517 draw, I'm too smart for that. 00:10:20.207 --> 00:10:27.704 Some students would, feel, especially early on in implementation of 00:10:27.704 --> 00:10:29.958 Eureka Math, Singapore math. 00:10:30.351 --> 00:10:34.873 They wouldn't be that proficient with the models and comfortable drawing, 00:10:34.873 --> 00:10:37.383 so they would just say, I won't do it. 00:10:37.713 --> 00:10:39.253 Now, what do teachers do? 00:10:39.533 --> 00:10:41.493 you can keep begging them to draw. 00:10:41.893 --> 00:10:46.233 You can keep, you can create this friction, or you can maybe take a 00:10:46.233 --> 00:10:51.246 more passively aggressive approach to getting them to recognize the 00:10:51.246 --> 00:10:55.796 relationships that bar diagrams do, the visualization of word problems. 00:10:56.286 --> 00:11:00.454 And, therefore I came up with a couple methods like two diagrams. 00:11:00.963 --> 00:11:05.290 one is a correct depiction of the word problem, the other is incorrect. 00:11:05.855 --> 00:11:07.405 Which one is correct? 00:11:07.885 --> 00:11:12.701 Now, as soon as they've got an A and a B problem, the assignment is to 00:11:13.101 --> 00:11:14.771 determine which diagram is correct. 00:11:14.771 --> 00:11:18.341 So you have to analyze to participate in class, right? 00:11:18.721 --> 00:11:22.140 Whereas if I just give you a word problem, don't have to diagram to 00:11:22.140 --> 00:11:23.610 participate, to try to solve it, right? 00:11:23.724 --> 00:11:28.854 Another method I use in this book is, here's a diagram, Could you create 00:11:28.854 --> 00:11:31.794 a word problem to match the diagram? 00:11:32.054 --> 00:11:37.524 That's harder, but it's also to participate in the activity, you need 00:11:37.524 --> 00:11:40.624 to critically analyze a math picture. 00:11:40.716 --> 00:11:47.509 And I think those things may Make the math experience for students, the math problem 00:11:47.509 --> 00:11:51.999 solving experience for students, much more dynamic than here's another three 00:11:51.999 --> 00:11:54.449 sentences, read it, draw it, write it. 00:11:54.479 --> 00:11:56.569 It gets very mundane if we do that. 00:11:56.569 --> 00:11:56.899 Mm 00:11:57.129 --> 00:12:02.769 as you talk about that, and as I was, looking at your book, 00:12:03.734 --> 00:12:07.724 I think two things happen that are very powerful for teachers. 00:12:07.744 --> 00:12:13.695 The first thing is that, what don't the kids know how to do, and what don't the 00:12:13.695 --> 00:12:17.705 kids want to do, because nobody wants to do what they don't know how to do. 00:12:17.725 --> 00:12:19.865 They only want to do what they know how to do. 00:12:20.974 --> 00:12:25.404 You just articulated the fact that students have an issue, it's, they 00:12:25.404 --> 00:12:30.514 haven't practiced, they have a, a phobia, or it's too easy, whatever the 00:12:30.514 --> 00:12:34.676 reason, they don't do the, diagram. 00:12:34.746 --> 00:12:40.247 The visual representation, but the way that you've presented it and the 00:12:40.247 --> 00:12:44.987 way that you've just described it, where, okay, here's a, representation 00:12:45.007 --> 00:12:46.667 and here's one that's wrong. 00:12:47.127 --> 00:12:51.877 Now they can get repetitions of just that part. 00:12:52.227 --> 00:12:56.922 And the way that you've presented it with problem after problem, If that's this part 00:12:56.932 --> 00:13:01.422 that's stopping the students from being successful, this is what I tell teachers. 00:13:01.452 --> 00:13:06.332 If you know the part that's being, that's stopping them, practice that. 00:13:06.582 --> 00:13:08.112 Forget the rest of it for now. 00:13:08.332 --> 00:13:13.948 You could just take this problem, practice it, and then the other thing before I lose 00:13:13.948 --> 00:13:19.822 my train of thought, which is interesting to me about, teachers not asking kids to 00:13:19.822 --> 00:13:24.392 do the diagrams because they think that they are uncomfortable or, whatever. 00:13:24.831 --> 00:13:30.021 I don't know a lot about engineering, but I know my brother's an engineer 00:13:30.101 --> 00:13:31.831 and they sketch out everything. 00:13:32.491 --> 00:13:37.791 So I, don't know how you could be in a STEM school or a STEAM school and that. 00:13:38.361 --> 00:13:40.241 And that we don't demand. 00:13:40.417 --> 00:13:43.967 part of the way we do things in this school is, we're going to draw 00:13:43.997 --> 00:13:46.087 some sort of visual representation. 00:13:47.282 --> 00:13:50.863 And it also creates common diagram for discussion. 00:13:51.308 --> 00:13:53.818 teachers, do the students need to become expert diagrammers? 00:13:53.818 --> 00:13:57.373 I think it's ideal that they do, but Sarah Cottingham, one of my guests 00:13:57.373 --> 00:13:59.943 at my podcast, she would have the right word, and I'm just, I don't 00:13:59.943 --> 00:14:01.253 have the word with me right now. 00:14:01.473 --> 00:14:05.213 She would say, you, students need to take in information the same way so 00:14:05.213 --> 00:14:06.923 that you have a shared understanding. 00:14:07.473 --> 00:14:11.583 But you can hold a group of students together in a discussion about 00:14:11.583 --> 00:14:16.373 a word problem, if you have a common model to work from, right? 00:14:17.193 --> 00:14:21.613 I, I don't, I'm, I regret this, that I'm working on a podcast right now, I 00:14:22.283 --> 00:14:27.488 recently introduced, in, interviewed Scott Baldridge, a research mathematician 00:14:27.488 --> 00:14:33.926 at LSU, and he said that, they're creating a problem out of a math 00:14:33.926 --> 00:14:37.106 graphic is something mathematicians do. 00:14:37.156 --> 00:14:41.181 Now I don't have the details, but that is another method, 00:14:41.330 --> 00:14:42.670 that I'm using in this book. 00:14:42.670 --> 00:14:46.890 And so he said it has a lot of mathematical relevance longitudinally 00:14:46.890 --> 00:14:51.673 as students go to greater, to work with higher levels of math. 00:14:52.950 --> 00:14:56.966 I think one of the things that I found, and I don't know if you found this, but 00:14:57.016 --> 00:15:01.532 I've worked, for the past 20 years in schools throughout, California, a few 00:15:01.532 --> 00:15:05.198 out of state, and I can go to a school and work with the math department. 00:15:05.258 --> 00:15:10.780 I go to any middle school in California, regardless of economic status, overall 00:15:11.214 --> 00:15:15.364 scores, state scores, and say, oh, what do your kids have trouble with? 00:15:15.625 --> 00:15:19.095 fractions, integers, and they can't do story problems. 00:15:19.415 --> 00:15:24.519 and so that tells me, if it's happening everywhere, that tells me it's not the 00:15:24.519 --> 00:15:30.461 kids, that there's an issue with your methodology of teaching word problems. 00:15:30.691 --> 00:15:35.331 I, remember, As working with a high school staff and there was a time 00:15:35.331 --> 00:15:38.951 during the training that had a chance to talk one on one with this very 00:15:38.951 --> 00:15:41.561 experienced teacher and he was very nice. 00:15:41.561 --> 00:15:45.101 I don't know how you are, working with some very experienced teachers 00:15:45.101 --> 00:15:48.618 there, they've been to a million trainings and they're very nice to you. 00:15:49.188 --> 00:15:51.208 and then they'll tell you, here's what I really think. 00:15:51.798 --> 00:15:56.808 And so we're chatting and he says, what my kids can't do the simplest. 00:15:57.469 --> 00:15:58.369 word problems. 00:15:59.129 --> 00:16:01.259 And I said, so how do you, teach him? 00:16:01.699 --> 00:16:03.169 He goes, let me show you a problem. 00:16:03.447 --> 00:16:06.815 And he showed me a problem and he says, that's pretty simple. 00:16:06.835 --> 00:16:10.242 That should be easy for an algebra student, but they can't get it. 00:16:10.772 --> 00:16:13.022 So I asked him, so how do you teach it? 00:16:13.334 --> 00:16:15.174 He goes, then I give them this problem. 00:16:15.704 --> 00:16:19.784 and the point is there was no strategy for teaching. 00:16:20.134 --> 00:16:23.295 And I think that starts in elementary. 00:16:23.565 --> 00:16:27.781 I think, we talk about, there are people talking about, should we have 00:16:27.791 --> 00:16:30.121 math specialists teaching elementary? 00:16:30.744 --> 00:16:36.914 I don't know about the level of math that people teach. 00:16:37.404 --> 00:16:41.854 I, think, minimally, if you're teaching, you should have at least an understanding 00:16:41.854 --> 00:16:43.194 of what's going on in algebra. 00:16:43.204 --> 00:16:47.464 If you're teaching second grade to be able to know that, but you should 00:16:47.484 --> 00:16:50.811 also be able to teach word problems. 00:16:50.983 --> 00:16:55.193 not, here's a strategy to work for this concept we're working on, and then, oh, 00:16:55.193 --> 00:16:59.235 and here's another one next time, and then here's, no, and again, that's what I 00:16:59.245 --> 00:17:03.545 thought was so powerful about your book, that you have problems starting from 00:17:04.050 --> 00:17:07.150 you have it advanced through the grade levels and then even within the grade 00:17:07.150 --> 00:17:13.391 levels and the content areas, and also, from less difficult to more difficult. 00:17:13.701 --> 00:17:18.703 And so for me, another big benefit of this book for teachers would be 00:17:19.143 --> 00:17:21.103 the teachers can see the repetition. 00:17:21.613 --> 00:17:24.758 The teachers, it's a meta learning for them. 00:17:24.788 --> 00:17:28.058 And I think the light bulbs would just absolutely go on and say, 00:17:28.148 --> 00:17:29.918 wow, now I know how to teach this. 00:17:30.717 --> 00:17:31.617 so let me start here. 00:17:31.796 --> 00:17:36.716 I don't think many students will become proficient at solving word problems unless 00:17:36.716 --> 00:17:44.701 their teachers are regularly presenting them with robust, rich word problems. 00:17:45.411 --> 00:17:51.224 Now, assuming that's in place, I still see several reasons why what you've 00:17:51.224 --> 00:17:55.354 described might occur with students still not getting, becoming good at them. 00:17:56.328 --> 00:18:01.508 I, think solving word problems can be very tiring for students. 00:18:01.508 --> 00:18:04.538 They require a lot of thinking, a lot of persevering. 00:18:04.795 --> 00:18:09.205 But there's also not an algorithm or formula to master when it 00:18:09.225 --> 00:18:11.125 comes to solving word problems. 00:18:11.475 --> 00:18:15.695 I can teach students 3 digit plus 3 digit addition, and through a procedure 00:18:15.988 --> 00:18:19.321 they can get, a lot of repetition with it, and they can master it. 00:18:19.621 --> 00:18:23.211 Same with long division, same with adding fractions with unlike denominators. 00:18:23.391 --> 00:18:26.151 You do this, now you do this, you have an answer. 00:18:26.663 --> 00:18:29.753 But that isn't the same with word problems. 00:18:29.753 --> 00:18:32.635 I find that, every one of them is a little bit different. 00:18:32.635 --> 00:18:34.165 There's not a set formula. 00:18:34.185 --> 00:18:36.705 There may be a set approach to solving word problems. 00:18:36.705 --> 00:18:37.425 Read, draw, write. 00:18:37.807 --> 00:18:43.425 So if I get the problem in a practice set wrong and I get corrective feedback, 00:18:43.515 --> 00:18:46.745 I can't necessarily use that corrective feedback to solve the next problem. 00:18:46.885 --> 00:18:47.425 Does that make 00:18:47.775 --> 00:18:48.335 Yes, it does. 00:18:48.365 --> 00:18:48.655 Yes. 00:18:48.675 --> 00:18:49.025 Yes. 00:18:50.081 --> 00:18:54.816 now, pedagogically, I think too often I see teachers, they present a word 00:18:54.816 --> 00:18:57.756 problem, and then they start talking to students through the word problem. 00:18:58.006 --> 00:19:01.106 I'm going to draw this, now I'm going to draw this, I'm going to put the question 00:19:01.106 --> 00:19:09.410 mark here, I see that it's 354 fewer, so now I know to subtract, and now I solve 00:19:09.410 --> 00:19:15.035 this and I add that, and they talk them through a two, Step word problem, and I 00:19:15.045 --> 00:19:20.415 think the kids by and large are hearing blah blah blah blah blah blah blah So I 00:19:20.415 --> 00:19:26.200 think you know if solving word problems requires critical thinking, right? 00:19:26.490 --> 00:19:31.350 They need to present the approach to solving them through critical thinking. 00:19:31.700 --> 00:19:36.809 I believe in asking the students questions, to guide the modeling of 00:19:36.809 --> 00:19:41.509 it, and not telling the students, this is how I solve the word problem. 00:19:42.026 --> 00:19:45.799 I think teachers, and I know I've been very guilty of this, Anytime I present a 00:19:45.799 --> 00:19:51.812 word problem, I first ask the students, depict, draw, diagram, what you've read. 00:19:52.302 --> 00:19:57.002 And even if that's 30 to 45 seconds, I need students to write something 00:19:57.002 --> 00:20:01.917 down so that they're beginning to work on it actively rather than passively. 00:20:02.267 --> 00:20:05.237 Too often I see teachers We read a problem and then the teacher is the 00:20:05.237 --> 00:20:07.097 first one to talk and the students watch. 00:20:07.337 --> 00:20:09.876 I think that's, flawed, flawed teaching. 00:20:10.252 --> 00:20:15.075 And then I think at some point the teacher, they do need to model, they, the 00:20:15.075 --> 00:20:17.165 students need to see an expert diagram. 00:20:17.385 --> 00:20:19.045 They need to see an expert model it. 00:20:19.328 --> 00:20:23.767 but they need to begin the process of drawing themselves, and, on 00:20:23.777 --> 00:20:28.637 audio, we, I can't demonstrate what I'm describing, but, even in some, 00:20:28.797 --> 00:20:33.421 let's take a simple problem, a farmer collects a thousand chicken eggs. 00:20:34.211 --> 00:20:37.101 He collects 300 fewer duck eggs than chicken eggs. 00:20:37.672 --> 00:20:43.372 which bar or which tape would be longer, the chicken eggs or the duck eggs? 00:20:43.407 --> 00:20:46.957 I'm asking a thinking reasoning question for the students 00:20:46.957 --> 00:20:48.577 to craft a diagram, right? 00:20:48.867 --> 00:20:50.950 Instead of, doing it for them. 00:20:51.433 --> 00:20:57.677 Lastly, I think the place where a lot of schools bump into problems or challenges 00:20:57.697 --> 00:21:01.647 with students not doing word problems well is, and I don't have data to back 00:21:01.647 --> 00:21:07.713 it up, but there's usually an inverse relationship between the age level of 00:21:07.713 --> 00:21:12.947 students and their comfort with word problems, meaning that A higher percentage 00:21:12.947 --> 00:21:17.947 of students shut down when they see word problems as they advance in the grades. 00:21:18.747 --> 00:21:22.672 And the reason for this, I think, is usually in kindergarten, first 00:21:22.672 --> 00:21:24.802 grade, they try some problem solving. 00:21:25.512 --> 00:21:27.052 They're very willing to try it. 00:21:27.492 --> 00:21:32.841 But as the grades pass on, the students start to associate word problems with 00:21:32.841 --> 00:21:34.901 a time that they can't be successful. 00:21:35.751 --> 00:21:38.341 And it increases as the grade levels go up. 00:21:38.871 --> 00:21:43.416 And, by the time they hit fourth or fifth grade, they see a paragraph, 00:21:43.636 --> 00:21:44.766 and they put their pencil down. 00:21:44.916 --> 00:21:46.106 I've been here before. 00:21:46.516 --> 00:21:47.866 I know I can't do it. 00:21:48.040 --> 00:21:52.291 And to me, that's a complex and a very real complex, but I'm not a 00:21:52.291 --> 00:21:56.631 researcher, but I believe if a complex can be formed, it can also be reversed. 00:21:57.276 --> 00:22:01.096 But the longer the complex holds, and as adults, we have them in our lives, right? 00:22:01.596 --> 00:22:01.986 yes, 00:22:02.766 --> 00:22:06.916 You can reverse it, but it takes a lot of work to reverse it. 00:22:07.280 --> 00:22:13.290 My belief is elementary school teachers need to start reversing them as quickly 00:22:13.290 --> 00:22:20.340 as possible, and hopefully prolong them taking hold in the first place. 00:22:20.410 --> 00:22:22.010 And I think that begins in kindergarten. 00:22:22.609 --> 00:22:25.865 I absolutely agree with, a lot of what you said. 00:22:26.375 --> 00:22:31.684 And, I'm going to layer on something when you talked about when you, 00:22:32.194 --> 00:22:33.634 the teacher presents a problem. 00:22:34.119 --> 00:22:39.852 Before the teacher does it, there should be some, should be the student attempting 00:22:40.262 --> 00:22:42.812 to draw the diagram to do whatever. 00:22:43.112 --> 00:22:47.532 And before that, what the teacher has done is just what you said. 00:22:47.662 --> 00:22:51.222 When I see this problem, this is the first thing I think about. 00:22:51.282 --> 00:22:53.518 Is this, bar greater or anything? 00:22:54.036 --> 00:22:55.326 which, bar is going to be longer? 00:22:55.496 --> 00:23:00.201 So as the students now start to take over it, That language 00:23:00.211 --> 00:23:02.315 should echo in the student's head. 00:23:02.505 --> 00:23:04.085 So it needs a lot of repetition. 00:23:04.275 --> 00:23:09.815 The other thing I want to talk about one of my, buzzwords that 00:23:09.815 --> 00:23:14.352 I don't like at all, and how it relates to this, and this is grit. 00:23:14.922 --> 00:23:16.452 you got to persevere. 00:23:16.652 --> 00:23:21.186 I think that's one of the, one of our, math practices, perseverance. 00:23:21.726 --> 00:23:22.466 here's the thing. 00:23:22.767 --> 00:23:27.497 I can ask a student to persevere if they have a strategy. 00:23:27.877 --> 00:23:32.475 Okay, all right, you give a problem, you're walking around, 00:23:32.515 --> 00:23:33.845 kid hasn't done anything. 00:23:34.315 --> 00:23:38.115 When I tell teachers the first question to the student is, so 00:23:38.115 --> 00:23:39.285 what's the first thing you do? 00:23:39.835 --> 00:23:41.415 Oh, I should draw a tape diagram. 00:23:41.665 --> 00:23:42.515 I'll be back. 00:23:43.315 --> 00:23:46.445 And then you come back and then you say, how did you know to do it? 00:23:46.485 --> 00:23:48.545 How did you know that was the longer one? 00:23:48.745 --> 00:23:50.985 And again, you should hear the words echo. 00:23:52.278 --> 00:23:54.408 telling a student, Oh, come on, try harder. 00:23:54.738 --> 00:23:55.438 Keep, thinking. 00:23:55.508 --> 00:23:58.108 No, we have to give them a strategy. 00:23:58.273 --> 00:24:02.963 If they've tried the strategy, that's all I can, that's all I can do, because I do 00:24:02.963 --> 00:24:08.823 agree, just because they work through this structured approach doesn't mean they're 00:24:08.843 --> 00:24:13.319 going to have everything, be able to draw on everything to solve the problem. 00:24:13.559 --> 00:24:14.299 But you know what? 00:24:14.344 --> 00:24:15.434 you've done your best. 00:24:15.714 --> 00:24:19.795 It's to me, it's like writing, you learn the principles of writing when 00:24:19.795 --> 00:24:24.025 you're young, you don't become a great creative writer till much later. 00:24:24.145 --> 00:24:27.585 And I think the same thing in math, but you have some, 00:24:27.585 --> 00:24:29.695 structural skills to fall back on. 00:24:30.049 --> 00:24:34.559 Yes, I think I have high expectations, so I give my students hard 00:24:34.559 --> 00:24:35.789 problems, and I don't help them. 00:24:36.479 --> 00:24:38.559 I think that's false expectation. 00:24:38.857 --> 00:24:43.847 and so I think one thing everyone needs to understand in learning anything 00:24:43.917 --> 00:24:48.793 in school or outside of school, You have to feel some level of success or 00:24:48.793 --> 00:24:50.743 you're probably unwilling to persevere. 00:24:51.173 --> 00:24:53.393 I know that I was in danger of flunking out of college. 00:24:53.393 --> 00:24:58.268 I, I was higher than a fourth grade reading level in 10th grade, but I scored 00:24:58.278 --> 00:25:00.148 that because of the time constraints. 00:25:00.688 --> 00:25:04.478 And I, I, got to the point, I didn't think I could read a book. 00:25:05.003 --> 00:25:09.463 And so I went to the school, Landmark College in Putney, Vermont, where 00:25:09.493 --> 00:25:12.600 they was specialized in helping students with learning disabilities. 00:25:12.600 --> 00:25:18.750 And a teacher helped me realize I could read an adult book and get through it. 00:25:18.850 --> 00:25:22.110 but I, but my complex had overcome me. 00:25:22.900 --> 00:25:25.150 And so I was able to do more than I thought. 00:25:25.570 --> 00:25:29.920 And I don't know how conscious of it I was, but problem solving letters, which 00:25:29.920 --> 00:25:32.280 was the original alternative strategy. 00:25:32.550 --> 00:25:34.970 which is a part of this book. 00:25:35.893 --> 00:25:38.003 is the first step to solve a word problem. 00:25:38.173 --> 00:25:42.563 I always think, students say, I don't, I can't solve a word problem. 00:25:42.573 --> 00:25:46.973 You might not be able to solve what is being asked, or that might be a big 00:25:46.973 --> 00:25:49.763 challenge, but more than you think you do. 00:25:50.013 --> 00:25:55.963 And if you can piece together what you know, you're building a ladder towards 00:25:56.303 --> 00:25:58.183 being able to solve complex things. 00:25:58.838 --> 00:26:03.539 I want to make sure that I mentioned, I guess I likened it to solving a 00:26:03.539 --> 00:26:07.709 word, a standard word problem as an athletic contest or a performance. 00:26:08.309 --> 00:26:14.019 You do that once or twice a week, but you have to practice the little pieces, right? 00:26:14.259 --> 00:26:16.279 And the, isolated skills in between. 00:26:16.279 --> 00:26:21.529 So I always recommend to teachers do a standard word problem once 00:26:21.539 --> 00:26:25.279 or twice a week and spend the other days tinkering with it. 00:26:25.669 --> 00:26:32.259 with the pieces, isolating skills that students need to be able to 00:26:32.259 --> 00:26:33.769 solve word problems independently. 00:26:33.969 --> 00:26:40.499 But we almost need a coach's or a, director's mentality when looking at this. 00:26:41.554 --> 00:26:42.984 and permission not to do it. 00:26:42.984 --> 00:26:47.174 I don't know about Eureka Math or New York Math, but most of the texts 00:26:47.184 --> 00:26:51.324 that I see the teachers are using, there's a, skill that's introduced, 00:26:51.324 --> 00:26:54.334 they do a little practice, and then here's your application problem. 00:26:54.334 --> 00:26:55.104 Same day. 00:26:55.794 --> 00:26:56.334 Yeah. 00:26:56.664 --> 00:26:59.854 and, so how do they do those application problems? 00:27:00.882 --> 00:27:05.307 they'll give them a trick that works for, again, instead of the structure. 00:27:05.673 --> 00:27:07.550 I liked, Who cares if I liked it? 00:27:07.580 --> 00:27:10.800 But I think it was real important what you said about, maybe you can't 00:27:10.800 --> 00:27:12.290 solve it, but what do you know? 00:27:12.540 --> 00:27:18.470 Again, getting back to, a STEAM or a STEM program with science, what 00:27:18.470 --> 00:27:19.840 are we teaching kids in science? 00:27:19.850 --> 00:27:20.850 Scientific method. 00:27:20.924 --> 00:27:21.793 what's one of the steps? 00:27:21.803 --> 00:27:23.703 What do we know already? 00:27:23.954 --> 00:27:28.586 and I think that's the same thing because again, cue that a 00:27:28.586 --> 00:27:32.436 teacher could ask a student who's struggling, what do you know already? 00:27:32.801 --> 00:27:33.521 I'll be back, 00:27:33.850 --> 00:27:34.590 Yeah. 00:27:34.640 --> 00:27:40.475 And if we forget test scores, standards, grades, everything, ultimately what do 00:27:40.475 --> 00:27:45.495 we really want is a child to realize their potential on a regular basis. 00:27:45.835 --> 00:27:49.465 And so if we give the students opportunities to succeed on a regular 00:27:49.465 --> 00:27:53.309 basis, I don't know whether you get to grade level or not, but I'll sleep 00:27:53.309 --> 00:27:56.719 well at night as a teacher knowing I gave you a chance to succeed. 00:27:57.219 --> 00:28:01.009 And there are problems that are greater than an individual teacher. 00:28:01.029 --> 00:28:05.369 But for me, I always thought, I'm teaching sixth grade. 00:28:05.369 --> 00:28:07.789 I've got a second grade, a child on a second grade level. 00:28:08.113 --> 00:28:11.413 It's unrealistic for me to say they're going to enter seventh grade 00:28:11.833 --> 00:28:13.383 prepared for seventh grade math. 00:28:14.233 --> 00:28:15.423 What can I do? 00:28:15.619 --> 00:28:19.239 Make sure they're on a third grade level by next year or, beyond. 00:28:20.049 --> 00:28:24.789 it may seem very simple, but I think we can often lose that as teachers because 00:28:24.789 --> 00:28:26.709 we're overwhelmed by other pressures. 00:28:27.040 --> 00:28:31.450 and, and often not having technique or, the content knowledge 00:28:31.455 --> 00:28:33.250 to know how to, get there. 00:28:33.872 --> 00:28:39.450 a lot of times teachers will ask me questions during trainings or, what about 00:28:39.472 --> 00:28:41.802 these kids that are, below grade level? 00:28:42.174 --> 00:28:46.674 And I'll say, you know what, if you do what we're talking about, they'll 00:28:46.674 --> 00:28:48.898 do better, but nothing's magic. 00:28:48.910 --> 00:28:52.470 if somebody is expecting you to do that, it's, not, but what can 00:28:52.470 --> 00:28:54.074 you do to help them get better? 00:28:54.408 --> 00:28:59.924 Okay, so you have this, this structure that again, I'll be, I have to be honest 00:28:59.924 --> 00:29:04.384 with you, the first time we spoke and you were talking about, this, I didn't get it. 00:29:05.034 --> 00:29:05.424 Okay. 00:29:05.764 --> 00:29:07.444 I needed the repetitions. 00:29:07.454 --> 00:29:11.446 Once I saw it in the book and I saw the problems, and I saw the 00:29:11.446 --> 00:29:13.916 explanations why one graph worked. 00:29:14.306 --> 00:29:15.666 And the other one was it? 00:29:15.796 --> 00:29:18.126 You go, okay, and guess what? 00:29:18.321 --> 00:29:21.911 And then they're similar, and then I see a pattern. 00:29:22.161 --> 00:29:25.961 And I think that's one of the things as in your book, they're patterning, 00:29:25.961 --> 00:29:32.851 there are patterns that emerge beyond the patterns that we usually hear 00:29:32.851 --> 00:29:37.481 teachers talk about with respect to, oh, look at, I add three and look at 00:29:37.481 --> 00:29:41.741 what the digits add up to, or whatever it is, looking for patterns that way, 00:29:42.211 --> 00:29:47.101 versus What you're doing is developing patterns in this problem solving. 00:29:47.101 --> 00:29:48.871 Am I off base or is that something 00:29:49.001 --> 00:29:50.276 No, it is correct. 00:29:50.305 --> 00:29:53.185 and I think, maybe if it's possible. 00:29:53.870 --> 00:29:58.937 You could share a link or a PDF in the podcast notes, it'd be good 00:29:58.937 --> 00:30:03.097 if teachers could preview visually what we're doing, or listeners could 00:30:03.097 --> 00:30:07.051 preview what we're doing visually, as I talk, if it's possible. 00:30:07.157 --> 00:30:14.358 but basically, so the book consists of 152 problems from 2nd grade. 00:30:14.738 --> 00:30:17.258 through maybe late second grade through early sixth. 00:30:17.588 --> 00:30:22.158 Okay, originally I wanted to do it K to six but logistically I didn't. 00:30:22.468 --> 00:30:24.008 It just wasn't going to work out. 00:30:24.341 --> 00:30:30.001 Basically that's 152 problems but there's six different ways that 00:30:30.011 --> 00:30:32.016 you can use each of those problems. 00:30:32.016 --> 00:30:36.436 So it's actually, in a way, you could say there's 912 problems in the book. 00:30:36.605 --> 00:30:39.095 so yeah, there is a logical progression. 00:30:39.105 --> 00:30:43.665 I used a popular math curriculum as a structure for me to write 00:30:43.665 --> 00:30:48.510 problems, to work the students through second through fifth grade. 00:30:48.744 --> 00:30:54.859 And we're touching on every major topic, arises in tape diagrams and 00:30:54.859 --> 00:30:59.496 bar models, and basically the problems gradually become more sophisticated 00:30:59.496 --> 00:31:00.826 as we work our way through the grades. 00:31:01.166 --> 00:31:04.076 Initially, they're standard single bar diagrams. 00:31:04.676 --> 00:31:12.394 Or comparison diagrams, and then gradually we get into fraction, of a set, fractions 00:31:12.394 --> 00:31:17.314 times fractions, divided by fractions, and then pre algebra problems as well. 00:31:17.374 --> 00:31:20.454 I'm not sure if that got to what you were talking about or not, 00:31:20.821 --> 00:31:21.461 Yes, it did. 00:31:21.461 --> 00:31:27.301 Because wherever I am as a teacher, I think it helps to see that progression 00:31:27.361 --> 00:31:30.908 and that modeling I think again, the way the book is presented, and we'll 00:31:30.908 --> 00:31:35.661 get something we'll talk about, But what to put in the notes, but again, it 00:31:35.661 --> 00:31:41.758 is a good for teachers who don't feel confident about doing the instruction. 00:31:42.088 --> 00:31:43.928 And I've done. 00:31:43.968 --> 00:31:44.848 That's what I found. 00:31:45.338 --> 00:31:49.042 you know that phobia that you talked about, I think 00:31:49.052 --> 00:31:50.747 you catch that from teachers. 00:31:50.997 --> 00:31:54.389 Sometimes, and so it's important that they're competent. 00:31:55.189 --> 00:32:00.049 I've worked, with teachers before, new teachers and we do, a one day training 00:32:00.049 --> 00:32:02.138 and there's, she goes, Oh, thank you. 00:32:02.258 --> 00:32:04.718 I did not know how I was going to teach math. 00:32:04.738 --> 00:32:09.478 I had no idea how I was going to teach math now is my way, the only way, the 00:32:09.488 --> 00:32:11.718 best way, but it's a way that works. 00:32:11.898 --> 00:32:15.358 And so now the teacher no longer has that. 00:32:15.778 --> 00:32:19.021 That beer, and it becomes a meta for them. 00:32:19.696 --> 00:32:25.672 I'm excited about this because, again, I was obsessed with, with word problems. 00:32:26.272 --> 00:32:28.362 In fact, I was on a campaign. 00:32:28.402 --> 00:32:34.202 I think you know that to change them from word problems to story problems, because 00:32:34.242 --> 00:32:38.392 so that the kids could help understand that, there's something going on here. 00:32:38.682 --> 00:32:39.412 There's a flow. 00:32:39.572 --> 00:32:42.147 We have some, some things going on. 00:32:42.537 --> 00:32:45.817 And in fact, I had done a lot of reading. 00:32:45.817 --> 00:32:49.025 I had done a lot of research how people teaching then I 00:32:49.035 --> 00:32:50.275 had a chance to talk to you. 00:32:50.275 --> 00:32:51.835 I said, no, I'm not writing anything. 00:32:51.835 --> 00:32:55.259 I think Bill has got a lot of this covered in the same way. 00:32:55.822 --> 00:32:59.709 I think those folks who, struggle teaching word problems. 00:33:00.744 --> 00:33:04.504 I think this is going to be a great episode for them, because 00:33:04.524 --> 00:33:05.644 that's what it was about. 00:33:06.025 --> 00:33:11.505 It, this was about story problems, not talking about them or research. 00:33:11.545 --> 00:33:13.535 No, this is how you can do it. 00:33:13.535 --> 00:33:14.414 Yeah. 00:33:14.545 --> 00:33:18.045 I guess it may seem out of place, and I don't know whether it'll be edited 00:33:18.045 --> 00:33:23.836 out or it could be patched earlier, but I should have began with this, I, for 00:33:23.876 --> 00:33:31.126 probably close to 15 years, I've, often delivered workshops on bar modeling 00:33:31.126 --> 00:33:37.176 or tape diagramming, and I found it very normal for teachers to do this. 00:33:37.696 --> 00:33:41.946 to leave getting excited about teaching bar diagrams. 00:33:42.956 --> 00:33:47.450 But then they would get in front of students and it would 00:33:47.470 --> 00:33:48.990 be scruffy in their delivery. 00:33:49.010 --> 00:33:51.100 The students would not share the same joy. 00:33:51.460 --> 00:33:56.370 And I it took maybe a while, a couple years of reflecting on it. 00:33:56.370 --> 00:34:00.070 But the teachers already had the prerequisite skills to solve everything. 00:34:00.070 --> 00:34:03.440 So this seemed new and interesting and dynamic, but 00:34:03.440 --> 00:34:04.870 students are like, they're eight. 00:34:05.000 --> 00:34:05.850 They, I don't care. 00:34:05.850 --> 00:34:09.735 This is just, This is now my normal, right? 00:34:09.995 --> 00:34:15.405 And so they weren't finding that their students found the same joy 00:34:16.275 --> 00:34:19.325 in, in, in these representations. 00:34:19.905 --> 00:34:24.440 And in order for students to get what we want out of them, 00:34:24.440 --> 00:34:28.520 we need to change the way they experience, problem solving sessions. 00:34:28.975 --> 00:34:29.985 Bill, thank you. 00:34:29.985 --> 00:34:30.305 I think 00:34:30.545 --> 00:34:30.825 Yeah, 00:34:31.455 --> 00:34:36.338 like I said, teachers are going to get a lot out of this and, we'll put in the show 00:34:36.338 --> 00:34:40.779 notes, how to, access your book and we'll put a little bit of a sample in there. 00:34:40.809 --> 00:34:42.466 We'll talk about should be. 00:34:42.756 --> 00:34:48.345 And, thank you so much for, being on Better Teaching, Only Stuff That Works. 00:34:48.905 --> 00:34:49.505 My pleasure. 00:34:49.585 --> 00:34:50.895 I really appreciate the opportunity.