Why Standard Teaching Fails Our Students - Part 2

T1I Worksop: Candy Problem segment 2
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Speaker 4: [00:00:00] Hey everybody, it's Cheri Dotterer, your classroom coach.

Speaker 4: We are here at Tier 1 Interventions. I am with my co host, Jonily, and we're going to be talking today about the candy problem.

Speaker 3: Today's reference task Is the candy problem.

Speaker 3: I do not have a PowerPoint on purpose because I want us to see how organic. I'm gonna do everything we just did with today's candy problem. I wanna show you just how simple it is. Hold on a second. Yes, go ahead.

Speaker 4: You're gonna need to repeat because we need to actually introduce the podcast so that I have that on tape.

Speaker 4: So

Speaker 3: let hour and a half ask for a minute. Oh no, it's not an hour and a half just. Just let me pause. I went 50 minutes

Speaker 4: astray.

Speaker 3: It's

Speaker 4: okay. It's okay. We're going to pause, and we'll create an introduction to the podcast, and then we'll get into the instruction. [00:01:00] Hey everybody, it's Cheri Dotterer, your classroom coach.

Speaker 4: We are here at Tier 1 Interventions. I am with my co host, Jonily, and we're going to be talking today about the candy problem. Go for it, Jonily. How does one

Speaker 3: problem in math teach dozens of standards from preschool through high school, increase number sense, at the same time increasing fact fluency, and providing sensory based, experiential, contextual, conceptual learning?

Speaker 3: We can do it all in less time with more impact using what we call reference tasks. The candy problem is one of 12 reference tasks that we use at Minds on Math. The 12 reference tasks are exactly the same for every single grade level and every single ability level. The reason they're exactly the same is they are so [00:02:00] flexible and versatile that I can reach my highest level student, my highest ability student, and my most struggling student with the same exact lesson.

Speaker 3: And I can teach 8th grade content and 2nd grade content. with the exact same lesson. When we master this art of instructional facilitation using reference tasks, we can teach more in less time. And to give you an example, in 30 minutes a day, for 30 days, I can teach all of my standards for one grade level.

Speaker 3: And Get all of my kids very close to mastery in that time. The reason we're not getting those results now is because we are using many wrong, yes, there are wrong, instructional moves and facilitation techniques. So today we're going to focus on the candy problem. [00:03:00] I do not have a PowerPoint on purpose today.

Speaker 3: Because I just want to show how much can be used with the candy problem and when we make it linear, we extract the complexity and we extract the experience. that students are going to have from it. So I'm going to write candy problem and I'm going to share with you the situation for the candy problem.

Speaker 3: And then we are going to talk about four deficits that we complain about in schools that we know our students have. And we are going to reverse those deficits with the candy problem. So here's the situation. Two boys share 90 candies. That's it. [00:04:00] That's all I'm going to tell you right now. When I facilitate this with my first graders and with my Algebra 1 students, I do it in the exact same way.

Speaker 3: Today's problem is the candy problem. We have two boys and 90 candies. Then I say my favorite three words. Tell me about this situation. The first thing many of my students say is, Oh they each get 45. Awesome. If they share the candies equally, they will each get 45. Now, if my first and second graders know that each kid gets 45, that's actually pretty amazing.

Speaker 3: But then I say, Here's another twist. The two boys are not going to share these candies equally. The two boys are going to share these candies unequally [00:05:00] such that boy one gets two pieces for every three pieces boy two gets. And I'll say to students, look, there's lots of reasons why one boy is going to get more candies.

Speaker 3: Maybe they did more work. Maybe they got more stickers. Maybe they got more they filled up more cards. And so In the prize box, one kid gets two and one kid gets three. Kids understand fairness and fair isn't always equal. There's a amazing educational book by Rick Warmly, W O R Mally, Rick Warmly, fair isn't always equal.

Speaker 3: And he's alluding to instruction in which when different students get different instruction, it's fair, but it may not be equal and exactly the same. So we have, I have this conversation with students that there's [00:06:00] lots of reasons. There's reasons I get paid a different amount than the other cashier at the department store.

Speaker 3: Okay, so there's lots of reasons for unequal sharing. We're not going to go down that rabbit hole. I'm just telling you the facts, and oftentimes we want to make too many inferences in mathematics, which means we're bringing in lots of other variables. When I say don't extract the complexity, I'm not talking about the, I'm not talking about the depth of the mathematics.

Speaker 3: What I'm talking about is we do want to get rid of the complexity of all of the other variables. We want to keep the situations and the facts as simple as possible, so that we can make the mathematics as deep as possible. I'll show you that through this example. So I'll use my favorite three words again.

Speaker 3: Now tell me about this situation. [00:07:00] Then I might have kids turn and talk. I might have them act it out. I might have them work on something individually. I'm going to give them two or three minutes to just process. Often times when we ask kids to tell us about, or what do you see, what do you notice, we don't give them time to process.

Speaker 3: So when we give them the time to process, then I can bring us all back together and say, tell me about what you talked about. You're going to get lots of different reactions from students. Then I'm going to ask my next favorite prompt, What math questions can you create?

Speaker 3: One of the typical math questions is, How many candies will each boy get? But that's only one question that we can create to answer for the candy problem. What I'm going to do now is, in my classroom, I'm going to have [00:08:00] students take about four minutes to create math questions and It's very difficult for students to not only create math questions, but create math questions and not have the urge to solve.

Speaker 3: See, when we focus on thinking, reasoning, and sense making in the right ways, kids organically have the urge to solve. When we focus on solving and answer getting, kids do not have the urge to solve. And let me say this again. In our classrooms, we should focus much less on answer getting and solving. And when we do that, we will actually get more answer getting and solving.

Speaker 3: So I'm going to give kids some time to create some questions. It's going to be awful. I'm going to give them some examples. I might say, how many candies will student one get in the first round? And then [00:09:00] kids will try to answer that, and I'll be like, no, I'm not asking you to answer it. I'm giving you an example of a question that you can write down.

Speaker 3: And then I will say to students no. Everybody write this question down. See, we're just creating questions now. We're not solving them. But see, this creates the urge for kids to solve, and I'm not letting them solve. And this creates a really good productive struggle. So if I say, okay, everybody write down this question.

Speaker 3: Write down this question in your notebook. Okay. How many candies, and I'm not going to spend the time to write it, How many candies does boy one get after round one? And they might be like, what does that mean, round one? If we're passing out candies to two boys, and this boy gets two for every three, another question I might ask is, Because this is always important.

Speaker 3: What [00:10:00] is our skip counting number? The number one way to improve number sense. is to practice counting. The number one way to improve number sense is to practice counting. The candy problem is a perfect way to do that. There is a progression of counting, and I'm going to map that out today. But the reason we're writing these questions That may never usually typically be asked with the candy problem is because I want kids to be able to develop good question creating because again asking questions is a very innate inborn intuitive strategy thinking

Speaker 3: when kids enter school we negate that ability you see we're doing [00:11:00] all these wrong things. If you've ever met a toddler, two or three year old, we can learn how to ask questions from two and three year olds because they are innately curious. School negates the urge for curiosity. School negates our ability to formulate good questions.

Speaker 3: What we need to do is re extract the student's innate, inborn, intuitive skill of question creating. When they get back to being good at that skill, the better math students Are the ones that can create better questions. So if we want to improve achievement of our most struggling math students, one of the number one things that we can do is have them [00:12:00] create the questions by them creating the questions.

Speaker 3: They increase their understanding of the mathematics. They don't even have to solve those questions, they just need to create them. Solving and answer getting does not increase math understanding and achievement. Solving and answer getting does not increase math understanding and achievement. Thinking, reasoning, sense making.

Speaker 3: And question creating increases math understanding, math learning and math achievement. What math questions can you create? After four or five minutes of kids creating questions, me modeling that explicitly and having them copy down these questions and not allowing them to answer them, then I say, okay, go ahead and put everything away.

Speaker 3: We're not going to do any more with the candy problem today. We're not going to do any more with, go ahead and put this [00:13:00] away. Open up your terrible textbook to page 264 because this is what I've been told to do. And this is what the people in charge making decisions think is the best thing to do. So now we're going to open our book to page 264.

Speaker 3: And you're going to go on to your lesson of the day that has nothing to do with Candy Problem. And actually it does, we just as adults don't have a good understanding of math enough to be able to connect it to what the book actually has. We are just we're just doing so much damage. If you've been through the educational system, K 12, math classes, if any of you have done that yourself personally you can get compensation by calling

Speaker 3: 614.

Speaker 3: So there really should be a lot of lawsuits about the damages that we've done. To kids brains [00:14:00] mathematically. I'm getting real snarky today, but I can't help it. Okay, now back up because the purpose of this reference task. The candy problem is to teach a variety of standards. I'm going to share my screen and I'm going to show you.

Speaker 3: The standards list. For some of the reference tasks, we have a pretty robust standards list. The candy problem has probably the most standards attached to it for any reference task. The candy problem is all about division. And division is my favorite operation. Division should be the first operation that we teach.

Speaker 3: Not addition, not subtraction, not multiplication. Division should be the first operation we teach when kids end their preschool. And we [00:15:00] don't call it division, because how dare we? It's not in the standards that some, arbitrary person decided, we can't put that word in preschool. So instead of using the word division, we call it sharing.

Speaker 3: If you've ever met a preschooler, and you've tried to not share something, they will be able to give you a full lecture on what sharing is. And sharing equally. They've actually just defined division. Okay? Forget addition, subtraction, multiplication. The only operation we should be teaching is division.

Speaker 3: And then we can teach addition, subtraction, multiplication through division. Because division is just sharing equally. Division is not just dividing. Hear me. There are two mathematical understandings that we want kids to have, procedural and [00:16:00] conceptual. Both are essential. Procedural understanding is dividing and long division.

Speaker 3: I am not saying those are not important, but they are the most shallow form of division in mathematics learning. So procedural algorithmic relates to the act of dividing. Division is very conceptual. To improve number sense, we explore division, not dividing. It's the difference between Sarah's analogy, the person who cooks with a recipe, and the actual chef who doesn't need the recipe, but could also use the recipe.

Speaker 3: See, the chef can do both. The person cooking with the recipe that has to have the recipe is much more shallow and [00:17:00] less talented. We want our kids to be more mathematically talented, so we want them to have both. Division is also skip counting. Division is groups, division is ratio and rate, division is fraction, and here's our two boys 90 candies problem.

Speaker 3: If you look at kindergarten, I have listed all of the standards for kindergarten that we can teach through the candy problem, which is about division, sharing and counting. So if we are counting to 100 by ones,

Speaker 3: then I'm going to have kids act out the candy problem and to make it a little simpler for Kindergarten, I could say that[00:18:00]

Speaker 3: the first boy gets one for every two the second boy gets. Now, I wouldn't do this with my kindergartners. But some kindergarten teachers that are afraid to be complex with their students. Want it in this very simple form. So I wouldn't do this, but I'm going to tell you how you can do it so that you're more comfortable from where you are and this radical instructional method that makes people upset.

Speaker 3: So I could say the first boy gets one piece and the second boy gets two pieces every time. And I could pair students up such that they can count by ones and they can count by twos. See, I can make these numbers anything I want. Now you have to be careful because as a teacher, you have to have enough math knowledge, which oftentimes we don't.

Speaker 3: My [00:19:00] secondary math teachers sometimes have less math knowledge than my primary grades teachers because our secondary teachers can do the math, but don't often understand the math. So I can do a 1 to 2. Sharing unequally with 90 candies, but I probably wouldn't want to do a 1 to 3 and I'm not going to tell you why you see.

Speaker 3: Not only are the situations that we use, that we call reference tasks, extremely important, but the way that we deliver them is extremely important. You can do it wrong. There is a lot of user error. But one of the most important things we overlook are the selection of the numbers that we choose when we're creating these [00:20:00] problems.

Speaker 3: So if I want to teach

Speaker 3: all of these kindergarten standards, Represent addition, counting with objects, decomposing numbers, more, less, putting objects in categories. These are two categories. This is the category when I put One block, two blocks, three blocks, four blocks, and this is the category when I put two blocks, four blocks, six blocks, eight blocks.

Speaker 3: By the time we get to first grade, one of the number one, I'm going to say, high leverage concepts that is actually written in the standards for the first time in grade one. And you can see it right here. I just [00:21:00] copied and pasted this. Is this word iterating? Iterating is mathematical practice number eight.

Speaker 3: See, we forget about the eight mathematical practices. We have our content standards to teach, but we also have eight mathematical practices. The eight mathematical practices are exactly the same from kindergarten through high school. They're not any different.

Speaker 3: The mathematical practices are ways of engaging in mathematics. These are actually more important than the content standards themselves. I can get more achievement with the content standards by focusing on the mathematical practices. Mathematical practice number eight is engaging in repeated reasoning.

Speaker 3: Repeated reasoning is exactly this word, iterating. It means I'm going to repeat the same action over and over again. We know from research [00:22:00] that repetition is one of the most important things that we can do in our lives. to create something habitual. The problem with math worksheets is that's not iterating, it's not repetition, and it's not repeated reasoning because every problem is different.

Speaker 3: So we think we're doing repetition when we do a typical math worksheet with 10 problems, but we're doing the opposite of repetition. We're actually doing a switch tasking. Because every problem is different. Iterating and repetition means I use the same problem, the candy problem, and I have kids act out and use manipulatives to show counting by one, counting by two.

Speaker 3: Now kids have all the tools they need to do candy problem over and over and over again. And this is where cognitive science and neuroscience comes in with the word that we use interleaving, which [00:23:00] is out of context random mathematics. Like the candy problem, I give it to kids, interaction one, create the math questions, I go away from it, we opened up our textbook to page 264, we did our regular lesson of the day, I bring back the candy problem, but not until about three weeks later.

Speaker 3: This is interleaving at its best because I'm bringing in an out of context situation from what we're currently studying. I'm also using another cognitive science approach called space practice because I've left space between the first time kids engaged with the candy problem and the second time kids engaged with the candy problem.

Speaker 3: Because the first time we just created a bunch of questions. Now I'm going to give kids manipulators and tools that they can act out the candy problem. And I can change the numbers. to differentiate what I want kids to skip count by. So when we look at the grade one standards and we want kids to iterate and do repeated [00:24:00] reasoning, not just in grade one from, but from grade one now through high school, that's the example of iterating.

Speaker 3: Two months later, when I bring the candy problem back, I might say, you know what, we're going to go back to, we want those two boys to share 90 candies. Such that the boy one gets two and boy two gets three, but you know what now instead of 90 candies We're going to do 120 candies. So we're going to do the same repeated reasoning, but now we have more candies.

Speaker 3: So I actually, in my first grade standards, when I'm skip counting, adding within 100, I'm teaching all of those first grade standards. Second grade, Same thing. These are the standards. Third grade. If you are a third grade teacher, you can teach the majority of your content. Now, look at third grade for a moment.[00:25:00]

Speaker 3: There are five pages of standards. That we can teach through the candy problem for grade 3. This is powerful. This is powerful because imagine if we started giving exposures of the candy problem in kindergarten, 1st and 2nd grade. And now in grade 3, we can start candy problem. having kids already experienced it 10 or 12 times in previous years.

Speaker 9: So when I

Speaker 3: introduce candy problem at the beginning of grade three, I'm going to say, tell me about the candy problem. Tell me about this situation. They're going to tell me everything they've done in the previous years about the candy problem. I'm going to listen to that. And then as a third grade teacher, I'm going to then design the rest of my lessons based on where they left off with the candy problem.

Speaker 3: And it doesn't matter if we have move ins

Speaker 8: or kids that are. [00:26:00]

Speaker 3: We don't, it doesn't matter if we have move ins or kids that are habitually absent because every time we interact with the candy problem, we start there from the very beginning. I'm a brand new school year. I'm a 6th grade teacher. I'm going to put candy problem up and I'm going to say, some of you have seen the candy problem before.

Speaker 3: You don't have to have seen it, but some of you have seen it before. And some of you have done lots of different variations. But does anybody remember the original candy problem? There's always an original candy problem. And if they don't, we celebrate forgetting. You guys, forgetting is necessary. When you forget, it allows an opportunity to re remember.

Speaker 3: When we re remember, it deepens the neural pathways in the brain, strengthens and grows our brain, so that our brain becomes stronger, and we can think better, [00:27:00] reason better, and decision make better. If they don't remember, then I just tell them. You'll be surprised at what they do remember. Now, for those of you that have never seen this before, I'm gonna introduce the candy problem to you right now.

Speaker 3: We have two boys. Everybody okay so far? And I'll say that to my kids. Everybody okay? Got two people. The original candy problem is 90 candies. Now that can change and be different. And for those of you that have never seen this before, these boys are sharing the candies unequally. Such that one boy gets two and the other boy gets three.

Speaker 3: See how quick that is to just introduce it to kids that have never seen it before? And then when I say, tell me about this situation, tell me what you've done in the past, and kids are sharing, the kids that have never seen it before are picking up on that pretty [00:28:00] quickly. And they're going to get a chance to engage in it soon.

Speaker 3: And that's the beauty of a reference task. A kid that has never seen it is experiencing Interaction 1. At the same time, a kid that's experienced it before is experiencing Interaction 17. Doesn't matter.

Speaker 3: It's going to be beneficial no matter what the students get from it. Just like you as adults. Some of you listening to this today have never seen Candy Problem. So you don't even begin to know the depths of what this can do for our high school students. Some of you that have seen the candy problem, you've used it with your kids for years.

Speaker 3: You've up leveled it for years. You've seen all the variations. Your kids have created variations. You use the candy problem at a very deep level. So even for adults, the more interactions we have with the candy problem over [00:29:00] time, the more depth that we get with this problem, and the more standards we can teach.

Speaker 3: We're helping each other out when we expose the candy problem every year, and people are like how many times, for how long? If you want an answer to that, I'm going to tell you the minimum guideline. Show the candy problem and have kids experience it for 12 minutes in August or September. And then in November, have them experience it for another 20 minutes.

Speaker 3: And then in January, do another 20 minutes. And then in April, do another 20 minutes. Look at how many interactions that is, and it's not even taking your whole class period. And you might say, Jonalee, we can spend 40 minutes once a month on Candy Problem because it teaches so many standards. Great, but if you haven't had as many exposures or interactions with Candy Problem, you're not going to be able to facilitate that in your classroom for that much time with your kids.[00:30:00]

Speaker 3: So start with the minimum. We're all at different levels, and we need to differentiate our implementation as adults so that we can continue to grow over time as well. But if we're all focusing on the same small chunks, candy problem, and I want to point out for a moment my friends Jesse and Kay, because that's another reference task.

Speaker 3: And here's the power of reference tasks. For those of you here that don't know Jesse and Kay, You'll get to know Jesse and Kay because the more interactions you have with me, the more you'll learn about Jesse and Kay. What was the original Jesse and Kay problem? Because again, there's a lot of variations.

Speaker 3: The original was Jesse starts with 50 and gets 5 a day. Kay starts with no money and gets 7 a day.

Speaker 3: The reason I bring that up is,[00:31:00]

Speaker 3: these are so simple, it seems that they wouldn't be very powerful. But I have my third graders solving multi step variables on both sides equations just by having the Jesse and Kay Foundation. So just believe me when I say that a focus on a few of these chunks, and focusing on our instructional delivery, and then using all of these cognitive science methods by bringing them back and taking them to another level, and using blocks.

Speaker 3: Grid paper, all of those sensory materials to act this out in lots of different variations are going to get the depth of understanding of not only the mathematics, but improving number sense at the same time, because the foundational concept [00:32:00] that kids are missing that are holding them back from high level achievement in mathematics.

Speaker 3: is the simple act of counting. What I'm going to share with you now are is a progression of counting and four areas of deficits that students have that we are frustrated with in schools. There's two things we're going to do now. We're going to look at counting progression. And I'm facilitating some of this with kids.

Speaker 3: I'm going to talk to my kids about we need to be counting all the time and there's certain ways that we need to be counting. We're going to practice that and then we're going to iterate that again and again. The second thing that I'm going to teach you all as adults is through this lens of deficits.

Speaker 3: That our kids have, that we want [00:33:00] them to overcome. And again, none of these can be explicitly taught. Now, one of the things that we try to explicitly teach, which is just so ironic to me, is growth mindset. There's two different mindsets. Carol Dweck did a lot of research on this. More successful people have a growth mindset.

Speaker 3: Less successful people have a fixed mindset. This is a great concept, and this is absolutely what our kids need in schools. But the way that we deliver it is with deliberate, explicit instruction. I have literally seen teachers do a guided notes page. On growth mindset, that is so ironic and so backwards because you're teaching growth mindset through a fixed mindset instructional process.

Speaker 3: [00:34:00] Growth mindset cannot be explicitly taught. It must be experienced to be improved. Same as number sense.

Speaker 3: I'm pausing because this is really essential. There are four deficits that our kids have that also cannot be explicitly taught. It needs to just be a part of the culture that they experience day in and day out. Number one, focus and engagement. My kids don't have focus. They're not engaged. They're not on task.

Speaker 3: I can't get their attention. Dah. That's a me problem, not a student problem. Number two, individualization.

Speaker 3: I've actually talked about this a lot today [00:35:00] when I've given different examples of how to give students access to these different mathematics problems. The way that I individualize is to focus on one problem,

Speaker 3: What kids engage in is different. I might have some kids acting this out with blocks and tiles. Other kids might just be using paper with tally marks. Other kids might not even need a paper with tally marks. The adaptations Or, see here's where we get a little bit off in schools with special education, we want to modify everything.

Speaker 3: Modify is changing. I don't want to change the problem. I don't want to give kids a different easier problem. Remember when I said the one to two? We can do that, but I wouldn't. I would keep the [00:36:00] problem complex, but I would just adapt it so that it's accessible to everyone. I would accommodate for those kids, not modify.

Speaker 3: Our number one go to in special education with mathematics oftentimes is to modify. Oh, kids can't get it, so we need to modify, we need to change it. Know what we need to modify and change. is your instruction. That's what needs modified. So in order to get individualization, we keep the same problem, but give different accommodations for students, sponges, blocks, etc.

Speaker 3: So that all kids can have access to this problem. I want all kids to have access to Jesse and Kay.[00:37:00]

Speaker 3: Number three, individualization already leads to this, and that is accessibility. Got ahead of myself because I already talked about that before I wrote it. I'll just repeat it. What we think accessibility means is through modifications. Giving them a different task, a different lesson, a different problem.

Speaker 3: Oh, gosh, my kids can't do skip counting. Or my kids can't do division. So let's give them addition problems. No, this is also an addition problem. I can treat this as an addition problem or a division problem. By the way, if I want to know how many boys, how many candies each boy gets, I'm not going to be finding two thirds of 90.

Speaker 3: Some of my top students, my highest achieving students, [00:38:00] based on data and scores, will find two thirds of 90 to solve this. And that is not accurate. So just a little FYI there. And then finally, how do we increase Memory and retention of content.

Speaker 3: Now think about this for a moment. In schools, these are the things that we are most frustrated with. The lack of focus and engagement. The frustration that every kid needs individual, what we think, individual lessons. They don't need individual lessons. They need individualized. And how do I individualize?

Speaker 3: I gain their perspective by using Tell Me About. We can create accessibility so that all kids can do the same problems, but we're going to give blocks, scissors, centimeter grid paper, pennies. [00:39:00] To allow that accessibility for everyone. And then finally, Gosh, these kids just don't remember. I taught it, and they don't remember.

Speaker 3: I taught it, and they don't remember. The problem is you taught it. You didn't engage them in an experience. And that is the biggest proof I want you to take away from this morning. Which is Oftentimes, when we explicitly, deliberately, and intentionally, step by step teach it, that's when the least amount of memory and retention occur.

Speaker 3: When I say it, the kids hear it. When they say it, they learn it. Now, I'm doing the exact opposite of that model today because I'm talking to you as adults, and you're not saying any of this. The way that I'm teaching you today It is very different than the way that I teach kids. [00:40:00] When you have access to Tier 1 Interventions course.

Speaker 3: One of the modules is Candy Problem, which is what we're recording today. If you're watching this recording, this is the module for Candy Problem. In your resources, there is a folder of audio files of me doing Candy Problem in multiple grade levels. So there are 25, 35 minute audios of me actually doing the lesson with actual kids.

Speaker 3: The facilitation with students is very different than the facilitation that I'm doing right now with you. Let me pause for a moment. That was a lot. Thoughts, comments, questions.

Speaker 4: Hey, everybody. This has been Tier 1 Interventions. We'll see you next week. So check us out. Bye, everybody.