Why Standard Teaching Fails Our Students - Part 1

T1I Worksop: Candy Problem segment 1
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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.

Kirk: I want to have conversations with you. About content and pedagogy and conversations about how we can stop hurting kids.

Kirk: Between kindergarten and third grade, half the kids decide they don't like math.

Kirk: Everybody. And that's

Speaker 3: on us.

Kirk: That's

Speaker 3: on

Jonily: us. It's complete, and I don't it's bigger. It's a big problem. You understand. I'm just preaching to the choir. It's the content. It's the standards. The contents are driven by the standards. The standards are chosen by politicians. And none of it is based on neuroscience.

Speaker 3: And to add to that, the biggest problem are the textbook resources.

Kirk: [00:01:00] Yes, and that's, of course, the biggest that is

Speaker 3: the

Kirk: profit center of education.

Speaker 3: Yes, it is. And and the Yes, Sarah. Yes. Also, and the I would say teachers are prepared

Kirk: in the wrong way. Now. Yeah,

Speaker 3: there you go. There you go.

Kirk: Colleges in.

Kirk: 11 years. 11 years ago, I spoke at a middle school math teacher, college prep thing. Anyway, they, they're being they're not given the tools they need to be successful in classrooms. And again, it's not teachers. It's on how they're being prepared. They're being prepared to teach math the way it was taught in the last century.

Speaker 3: And I was just gonna say that doesn't start when they get into their pre service methods courses. It starts in kindergarten.

Kirk: Yes, it starts with the way they were taught. But then their way that they're being taught to be teachers is the same way that they were taught. And it all needs [00:02:00] to change.

Speaker 3: It

Speaker 6: sure does.

Speaker 6: It sure does. I've been struggling with the intervention specialists I work with and just jumping to algorithm and all that. And I was just trying to have another conversation and impress upon and she says there's no wrong way to teach math. Oh. Thank you. My soul just, ugh. I, it's,

Jonily: yeah.

Jonily: You know what? Let's do this for just a moment right now. Let's, I'm going to type that question in the chat. I like this. Very impromptu, organic. Very important deliverable message. Here's the question I want us to just converse about. This is not planned. I'm just doing it based on what Kirk and Natalie and Sarah have just interacted with.

Jonily: Here is the question, and I'm not going to ask it in a good way, I'm just going to put it out there, and I'm going to type it in the chat. Is [00:03:00] there a wrong way to teach math?

Kirk: Yes. Lots of them. Lots and lots of them. The wrong way, the only right way to teach math is the way that the student understands. And that's not going to be the same for everybody.

Kirk: Is there one right way to teach math? No. There are lots and lots of right ways to teach math. And there are lots and lots of ways to teach math wrong. If the student isn't learning, you're doing it wrong.

Speaker 3: Oh my gosh, say that again! Louder for the people in the back!

Kirk: If the student isn't learning, you're doing it wrong.

Speaker 3: That's the key. And Sarah, that's who

Kirk: I work with.

Speaker 3: I like your comment. If you limit [00:04:00] accessibility, what are the right ways in tier 1 interventions? That's what we're teaching. We're teaching the right ways. So let's. Not even talk about those for a moment. But let's give more examples now and more profound statements of what are the wrong ways, the ways that students don't learn wrong.

Speaker 3: If your students are failing the assessments.

Kirk: Yes, Amy,

Speaker 3: we're doing it wrong. Kids need to be able to talk and explore with manipulatives and math.

Speaker 6: Correct to Teresa's point. What about the special needs student? They've been like, if you jump straight to an algorithm with those kids, that's the worst way to start because they're not even getting any conceptual understanding.

Speaker 6: They might get an answer, but

Speaker 8: you're saying to how many exposures do they need versus the child who can do it with 3 and 4 and they need what? 60? You know what I'm saying? You've got that exposure issue.

Speaker 6: That's what I'm up against. They're [00:05:00] not getting it. So let's just give them a trick.

Speaker 6: They're not getting it with a trick either. They're they might be getting an answer. If all you want's an answer. Great. But they still don't get it. They still don't have an understanding. I'd rather put more time in with those exposures and conceptualize it and they'll, make more progress that way.

Kirk: Okay, this isn't profound, but the wrong way to teach math is to not use manipulatives. To not use at least visual representations, but concrete is better.

Speaker 5: I just talked with our 3rd grade intervention specialist yesterday at school because she said okay, so we're working on subtraction and. To be able to subtract a larger number if.

Speaker 5: Three digit minus a two digit, whatever, right now. They, the third grade teachers would like [00:06:00] them to be able to draw the hops on an open number line. So if you're writing 89 to 176 or whatever it might be, the goal is that they would take the 89 and hop to the nearest 10, so they have that one.

Speaker 5: Then they're going to be like, oh, I can count from 90 to 170. So that would be this really big hop plus 80 or whatever. And then I would have to have all those other little, or I could hop then from the 70 to the 6 and know, okay, that's only 6 more. And then add those all together to find out.

Speaker 5: That, that's the answer, that's the difference between them. So I get that, because Jonalee, we work with right subtraction is distance. But Sophie was like, my kids don't understand that hop. They don't have the number sense to understand and grasp that. [00:07:00] Number the gravity of what those numbers mean in between.

Speaker 5: So for first grade last year or the year before I had little 120 grids. We shrunk them so that they were the same size as the base 10 blocks. And so I was like, I will give you some of these, but then we were going to shrink grid paper and cut it into strips so that they can have a long strip, but they could put okay, I need one centimeter cube to get from 89 to 90.

Speaker 5: Lay out my tens, lay out my ones. So then they could. Visually see how much it is and then what and then they could transfer it to it like a blank line, but still be able to use the base 10 blocks to be able to count it.

Speaker 3: So let's let's unpack this piece. [00:08:00] Because there's a lot here and I did something on purpose that I want to talk about.

Speaker 3: Okay, so what I was doing was I was, I want you to, as adults, I want you to analyze. The facilitation of the instructor, me, based on my adult student, Amy, so I was documenting some different things and I did something on purpose here so that we could then talk about it. But I'm not going to say what that is right now, because I want to make a very huge statement.

Speaker 3: We think this is visual. This is not visual. Pops, jumps, dips, number line are the most abstract. [00:09:00] That's the highest level of abstract. So when we are using number line,

Speaker 3: Even if I have kids physically moving on a human number line, it is still abstract. And we think that it's concrete, conceptual, visual, contextual. But this does not help our struggling student at all. Let me say this. It's one piece of it. But if we stop here and don't dig deep, just like to Natalie's point.

Speaker 3: We can do this strategy and have kids mimic it, and then copy it down and try their own. And we will probably get short term results. And we think that we're doing the right thing. But the problem is, two weeks later, three months later, three [00:10:00] years later, there has not been any type of ingrained innate learning.

Speaker 3: So Amy said a few things that I want to settle on here, and I happen to have centimeter block paper, okay, and scissors. In order to, because really, if this is all we do, it's the wrong way. It's wrong. Because not all kids have access, not all kids are going to learn, and we are limiting the amount of exposures that kids can have to all of their senses.

Speaker 3: When I look at this, I will actually Let me back up for a minute because I think there's a whole art to this also. We believe many times that if we take the time to just do this one problem and it takes 20 30 [00:11:00] minutes to just engage in it, we think that's a waste of time.

Kirk: I have to stop you right there.

Kirk: Go ahead.

Speaker 3: Yes.

Kirk: The sessions when I spend 20 30 minutes on one problem are the best sessions that my students have. They learn the most. They get the most out of that.

Speaker 3: Tell us more about that. And let's talk about also the connections with how the brain learns and what that digging of depth does.

Speaker 3: Or just tell us a little more, Kirk.

Kirk: I don't know about, I don't know if I'm going deeper. I'm, my students all hate math. They, they all have 504s or IEPs. A lot of them have reading tutors, speech therapists occupational therapists, physical therapists. That, those are my kids, and what I, it takes 20 minutes to go over vocabulary.

Kirk: I literally [00:12:00] the other night I met with a young lady who's in 7th grade the first time, and we were talking about angles. And she knew, now, granted it's a new unit, but I also, Work with another student from her team and the math teacher doesn't teach the math teacher hands out worksheets at the beginning of class and collects them at the end of class.

Kirk: That's their math class. So I don't blame her for not knowing vocabulary, but we vertical angle adjacent angle. Supplementary complimentary. We I taught her the vocabulary and then she could do the problems herself. So we had to take the time, and do multiple examples of vocabulary of what these things mean, draw them with different angles so that she could put them, it wasn't just one picture that she had memorized, she knew what those things meant and could apply them in different contexts.

Kirk: Yeah, we took 30 minutes to do one problem, but [00:13:00] we talked about a lot more than that.

Speaker 3: And that is the pure essence of depth, because if we focus in on one problem, but many words, many ideas, many aspects of the problem,

Kirk: any visuals and as much kinesthetic as possible, which is hard to do with angles and doing online and whatnot, but we do is what we can anyway.

Kirk: Yeah, you talk about math more than kids need to talk about math more than they do math. Yeah. Boom! But that's my statement. I'm hiding again.

Speaker 3: There we go. Someone typed that in. Kids need to talk about math more than they do math. Just like this here. I might say to students, as a teacher, I put all of these symbols, these are just symbols, these are just other symbols.

Speaker 3: I have not [00:14:00] created a contextual, conceptual, visual, sensory experience with, this is just a different algorithm, it's just different symbols. So what I might do now is, I might say to students, using my favorite three words, Tell me about what I wrote up here. And how does, remember we get depth through asking questions that begin with how does, how do.

Speaker 3: How does what I wrote here relate to what Amy was talking about? Now instead of just standing there and staring uncomfortably, I might say 40 seconds, turn and talk, go. In that 40 seconds I, as a teacher, am assessing what the kids are saying, and I'm also planning how I'm going to respond to their thoughts, instead of trying to do it on the spot whole class.

Speaker 3: [00:15:00] So a student might say, that's not 90 jumps, where'd she get 90 jumps from? Because remember she said the six, so see kids are going to, to Kirk's point, kids are going to start talking about this just by giving time, that's it, just give time. Now, the reverse of that is many of the teachers that I work with and coach say, that's what we don't have is time.

Speaker 3: No. We have so much time with these kids. We have more time than we need with these kids, but what we're doing is with our poor instructional delivery, we are wasting a lot of time. So if we actually choose correct instructional delivery, it will take less than half the time of doing traditional, typical Incorrect, ineffective instructional teaching, and that's the counterintuitive [00:16:00] part.

Speaker 3: Lots to talk about here. And then, I've got my squares and my paper here. I'm going to give kids some tools. I'm going to give them centimeter grid paper. I'm going to give them some scissors. And we're going to be like, okay, here's the one block that Amy was talking about. So I'm going to cut one and this is actually centimeter paper because when Amy says you centimeter blocks grid paper still is not visual.

Speaker 3: So this can be very abstract. This can be very abstract. Because it's two dimensional. And so when we get this piece of the centimeter block, and we have a centimeter. This is not a centimeter cube because it doesn't fit, but centimeter cubes will fit. I don't have one right in front of me. Then we can be like, okay, Amy was talking about one.

Speaker 3: [00:17:00] Here's the one, everybody cut out a one. And we're going to make everybody do this and cut out a one. That gets us to 90. So if I'm going to put a 90 here, I have to put a 176 over here. So let's just document the one. Because what we have to also teach and model is for kids to replicate this thinking. So if kids can't replicate on their own this thinking, then we haven't taught them, they they haven't learned.

Speaker 3: So I've got this one, I've got the one block, and I could tape that up there, magnet it, whatnot. Then I have Now I can now create this kind of double number line where I've gone one part and I made it to 90. Okay, sometimes we call these tape diagrams. This is not a tape diagram because it's not two dimensional yet.

Speaker 3: I'm going [00:18:00] to get there. So that 90 and then if I go 100, 110, 120 130. See, a lot of kids will have to write this down instead of trying to keep it in their head because they don't have that short term headspace, but they will grow their short term headspace and working memory. as they start doing this repetitive reasoning.

Speaker 3: So then we skip count all the way to 170 and then we've got a bunch of 10s. Right now I don't even care how many of those are. It doesn't matter to me. And kids could actually find out because instead of a one strip now, I'm going to have each of them cut out a bunch of 10 strips. and figure out how many of those.

Speaker 3: We'll tape them or glue them or magnet them. And then we finally get to 170 and then we have six more and we're going to cut out six more of [00:19:00] these. We're going to have centimeter cubes. Now these 10 sticks with our centimeter cubes, base 10 blocks, there is an attached 10 stick. So now we can relate this.

Speaker 3: to a centimeter cube, a 10 cut out to the 10 stick for base 10 blocks. If I have 100, if I end up having 10 10 sticks, then I can use a flat to then represent that. So we can start to look at ones, tens, hundreds. Now what I'm going to do right here, and This is not norm. This is nobody would even think of doing this next.

Speaker 3: But this creates

Speaker 3: Instead of mile wide, inch deep, it creates very three foot deep depth. [00:20:00] And here's what I'm going to do now. This is a penny, because I have one centimeter block. So I'm actually going to get coins and represent this as this, a centimeter block, and a penny. My ten sticks I'm going to get dimes, I'm going to have my ten cutouts, I'm going to have my ten sticks with base ten blocks, and I'm going to have a dime for each one of those.

Speaker 3: The reason I'm going to do that is we know that the three most abstract concepts that students struggle with are time, money, and measurement. Anytime I'm doing number line, that is measurement. A ruler is still abstract. A tape measure is still abstract. It's not until I bring in the two dimensional [00:21:00] centimeter grid paper and the centimeter blocks to make it more concrete and then relating it to the money symbols so that kids have a representation of all.

Speaker 3: One of the things that I always say about number line to make number line more concrete and visual And the intervention for number line. So if I'm an intervention specialist, hear me now, if kids have an assignment where they have to do things on a number line, one of the best interventions. is to make that number line two dimensional.

Speaker 3: So now they can see space two dimensional instead of line, linear, one dimensional. And so then I can have this one part. All those tens and the six. Now, I don't mean to worry about [00:22:00] this being scaled. I don't mean to worry about this being scaled. Kids might be, and they might be like, Oh, that needs to go over.

Speaker 3: Okay, yeah, we can fix that. We can, as we understand the problem more, we can start to scale and have a better proportion of our bar model. But all we have to do on a number line, and I'll show us over here, if I make, A number line with fraction and let's say we're doing zero to one and we're doing fifths today.

Speaker 3: The best way to help students and intervene is to draw the bar model. and lengthen those tick marks because this now gives kids access to number line that they never had before. And then if I want to get real fancy I'm going to do my hundreds [00:23:00] charts like Amy said and I'm actually going to cut those out or a blank chart so I can show fraction

Speaker 3: and I can use my paper strips for paper folding.

Speaker 3: When you're listening to this, you might think, okay, I'm bored. I'm disengaged. John Lee, you're taking way too long for one point here, but then you're missing the point. This is what instruction should be like. And as a facilitator of this type of instruction, you're going to get anxious. You're going to get impatient.

Speaker 3: You're going to get frantic because you're going to feel like nothing is happening. Because we don't understand the way that the brain has to consume information. So now let me just take this a step further. We've got this, we've got our base 10, we've got our pieces, we've got all of that. [00:24:00] Now kids can physically hold on to, with centimeter blocks, the value of this distance.

Speaker 3: Remember the subtraction sign is our number line, it's distance. from 89 to 176. Now what makes this progression of instruction impactful and powerful is because I saw Krista put in the comments about integers subtracting negative numbers. So you all know that this instructional practice is transferable.

Speaker 3: Some of our strategies expire and don't work in later grades with different types of numbers. So the strategy is only good for whole number, multi digit number. Those strategies do not give us, love it. Those strategies do not give us the [00:25:00] progressions that we need to continue to make sense, think and reason and solve.

Speaker 3: So if I do another problem one day, and I can even do this with my third graders, actually, I do this with my, I do this with my third graders. I, my third graders do these problems because they can solve subtraction of integers because they know this strategy. They know. That this symbol is my number line, and I start at negative three, I start at negative three, and I have to land on negative seven, I have to go to negative seven, and I can look at my hops and jumps here, oh gosh, zeros here, I might need that as a placeholder there, and I can look at subtraction, remember subtraction is the distance from the second number to the first, so from negative three, To negative seven subtraction.

Speaker 3: [00:26:00] So it doesn't matter what numbers you use. You can do fractions, decimals. You can do anything you want to because this strategy is so transferable. So once we're here, again, I could make this much more visual and I could say, okay, negative three, negative four, negative five, negative six, and look at what this does.

Speaker 3: to this abstract number line. Now I actually have Because those jumps are abstract because kids don't know what they're counting. Sometimes they think they're counting the peak, but they're really, they need to be counting the space. This is why kids struggle with measuring with a ruler, because they don't know what they're counting.

Speaker 3: And so we need lots of practice counting the space. So I've got one distance, two, [00:27:00] three, four. And one of my target questions with kids is, How much time is it from one o'clock to three o'clock p. m.? Kids that struggle with counting spaces will tell you it's three hours. One o'clock to three o'clock p. m.,

Speaker 3: they'll say one o'clock, two o'clock, three o'clock. Those are the kids, If we ask that question to any kid, we know which kids need this intervention. Now, these interventions, we'll take this from dyslexia philosophy. Necessary for some, beneficial for all. Necessary for some, beneficial for all. So the point is, I have four spaces here.

Speaker 3: But then, in seventh grade, we're always like is it four, is it negative four, if we start at negative three, and we go to seven, we moved in the left direction, so it's going to be negative. Distance is never negative. Direction [00:28:00] is. So I had a 7th grade teacher about a month ago, and she was so excited about her human number line they did with sidewalk chalk in the parking lot, and she said, oh, to do negatives, I have kids walk backwards.

Speaker 3: No, absolutely not. Absolutely. You're building a misconception. Walking backwards is still a positive distance. The direction we go, I could go in the negative direction, in the left direction, walking forward. It doesn't matter which way I'm facing, what matters is the direction we're going. And the biggest issue is, we as adults don't know this.

Speaker 3: We don't understand it. If we put this video on Facebook, we will get blasted today. Why would you ever make kids do this? We didn't invent math. Math is a phenomenon that already exists. [00:29:00] What we did was we put our own strategies and symbols to it. And this is different than reading, by the way.

Speaker 3: Reading, the skill of reading, is not innate, inborn, intuitive. I can prove that because I can give a book written in English to someone from Germany that speaks no English. And I could say, here's a book, I want you to figure out how to read this and then tell me what it's about. Reading must be explicitly taught.

Speaker 3: Mathematics has two understandings, the rules, algorithms, and procedures that we as humans, they're man made, that we made up, that do need to be explicitly taught. But those don't do anything for our thinking, [00:30:00] reasoning, and sense making, and they don't do anything for our conceptual understanding, and they don't do anything to improve number sense.

Speaker 3: If we're going to compare reading to math, I say compare reading to number sense. Number sense is an inborn, innate, intuitive understanding of number. Think of predator prey. I use this example all the time. Animals have an intuitive, inborn understanding of number. Some better than others. That's why some animals get killed.

Speaker 3: Let's just put it out there. Johns 2011 showing that six months old, six month olds Already have an intuitive sense of number, some better than others. We need to tap into this in schools and then improve it. Number sense cannot be explicitly taught. Number sense [00:31:00] can only be experienced to be learned.

Speaker 3: These two instructional progressions that I just shared with you is the way students can experience number sense. Subtraction is distance is improving number sense, counting spaces instead of lines, and with that strategy and that way of thinking, it's not algorithmic, it's a phenomenon that is transferable no matter what types of numbers you use.

Speaker 3: Now, let me stop talking

Speaker 3: and read some of your comments, but you guys talk to me. Can I go? Please.

Speaker 4: So you are talking about that intuitive, innate nature of number sense versus the unintuitive nature of numbers and algorithms and [00:32:00] procedures. Cognitively, you are talking about cognitive alignment. Versus cognitive dissonance. What is going on in the brain that is creating this disconnect?

Speaker 4: It's logical. It is not being able to activate. I'm going to go high level. It's not being able to activate your neurotransmitters in the right manner so that you can effectively learn. Which is something I've been talking about all week. And. One of the reasons that I was talking about integrity all week is because without intuitive nature and true alignment with understanding, we're not going to get those neurotransmitters to work so that learning happens.

Speaker 4: There's a big block in the middle, and we have to overcome that, and what [00:33:00] John Lee is teaching is helping students overcome that.

Speaker 10: Other thoughts?

Speaker 3: It is so let me go ahead. I didn't wait long enough. I thought I had really good wait time there. Krista. Go ahead, girl,

Speaker 11: middle of a curriculum adoption of course, a study in our district. And it's scary to me looking at some of the curriculum that our district is looking at, because they were already there are already out there talking about the science of math.

Speaker 11: But it looks a very much like a reading model where it's the gradual release. I do we do you do sort of thing. [00:34:00] And it's scary to me because it's getting a lot of traction and there's a lot of people that are attracted to it. And so I'm really worried about what kind of curriculum. Our district is going to end up with at the end.

Speaker 11: And 1 of the ones that we were previewing later. Earlier last week was they did have the number line and they were talking about how it was concrete and visual because they were walking it. But they gave you explicit directions on the direction the kid needed. Face, and they talked about walking backwards to show that you're doing negative and positive.

Speaker 11: Oh, my gosh. Yeah. So that really connected to me and it's. We, I think we just have to be careful because there are people out there that are, they say all the right buzzwords, but it's all in the wrong context. And it's really scary right now.

Speaker 3: It's very scary right now. And 1 of the things that you guys put in the chat here is presenting multiple [00:35:00] models and options is going to be confusing.

Speaker 3: What we've done wrong in the past. That we continue to do wrong is we extract the complexity from mathematics so that students are successful, but they're successful on such a stripped version of mathematics. That we get those short term gains, but we don't get any depth or long term learning, and we aren't creating mathematicians.

Speaker 3: We're creating rule followers, direction followers, and compliance. That is nothing of what math should be. Mathematics should be the complete opposite. If you're a scientist or a mathematician, And you're actually doing this in real life. You are not sitting and following recipes step by step.

Speaker 3: You are following, you [00:36:00] are solving, or you're, I'm not even going to say solving. You are experiencing non routine problems. Just for the pure experience of it, because some of those problems don't even have answers, but it's the process of going through that experience of thinking, reasoning, sensemaking, and figuring out that grows the brain and that gives us the experiences we need to be true mathematicians or in my terminology Maffineers.

Speaker 3: So if you want to create compliance, direction followers, rule followers, and mimickers, then you will do the gradual release, whatever, all the hubbub. Sarah.

Speaker 12: You saying what you just said about no, you said something with cooking or whatever, and it's really funny. That's a really great analogy for me because I love to cook and I love [00:37:00] to bake and everybody's always Oh you're so good at baking.

Speaker 12: You're such a good cook. And I'll be like, No, I said, I pull up recipes. I follow the recipes like line by line. You put me in a kitchen and you're like, here's some ingredients. Make something. It's not happening. I so admire people who like go on these cooking shows and they just Create amazing things, but that's not me.

Speaker 12: I'm the like step and so I love that analogy because we need math thinkers who you're like here. This is the problem. How are we going to solve it? And they're like, okay, let me dig into it and figure it out without someone like Giving them the step by step, yeah.

Speaker 3: And both are important. Both are absolutely essential.

Speaker 3: However, the non routine conceptual [00:38:00] is going to enhance the routine procedural. And we keep fighting against that. So we want the algorithmic procedural routine, the step by step, the gradual release to improve. The way that improves is to create stronger thinkers, reasoners, problem solvers, and mathineers.

Speaker 3: Great point, Sarah. Other thoughts?

Speaker 4: We keep talking about forgetting is necessary,

Speaker 4: and if we are going to just barrel through, we're not giving people chance. To forget

Speaker 4: so if you have a teacher who is all about getting the solving the problem, they're not giving the student chance to experience the problem.[00:39:00]

Speaker 10: We need to be careful to when that step by step is brought in. I just, saw one of my former students this past week and she had made so much growth when I worked with her a couple of years ago just really make it. And it was with adding and subtracting and just for giggles, I gave her a couple of problems and she totally.

Speaker 10: Has no idea what she's doing anymore because somebody sat her down and showed her the traditional algorithm. And now she has no idea how to make sense of adding and subtracting because somebody just brought it into her and said, here, just do it this way. And now it's just it's all that work.

Speaker 10: And that building of understanding has just been thrown out the window.

Speaker 3: We [00:40:00] continue to negate. Number sense thinking, reasoning and sense making. We continue to negate that. We continue to actually force students into reverse learning like they're unlearning and we negate this through poor instructional delivery.

Speaker 3: That focuses on step by step algorithmic. Two things, Kirk. One, you're, no fight. Vertical number lines are much more conceptual. Because temperature is much more conceptual for kids. then length. So no that's not an argument at all. And random question, how much time between exposures for interleaving?

Speaker 3: There's no [00:41:00] science or rule to it. I say at least two days, sometimes two months, sometimes two weeks, sometimes three weeks. Just whenever we get to it.

Speaker 3: The opposite of interleaving though, remember interleaving is defining your chunks. I have about 30 or 40 chunks that I teach on. That's it. Defining what your essential chunks are, and then doing those in cycles. So I might do 8 of my chunks, and then cycle those 8 back in, and cycle those 8 back in. One of my chunks might be 176 minus 89.

Speaker 3: That might be one of my new chunks. A three digit minus a two digit set up in this way. Number selection is important. Nothing happens by accident. The whole point of everything we've just done up to now is [00:42:00] look at how one problem, one problem taught so much content and created so many discussions

Speaker 3: in lots of different areas. The point of tier one interventions and creating a strong core general regular classroom where the first line of defense is students first instructional experience they get that needs to be the best instructional experience because then we can avoid the need for tier two and tier three interventions because the majority of kids should get exactly what they need in their classroom.

Speaker 3: If we have a logistics problem and we have a staff shortage problem because we don't have time or people necessary to [00:43:00] do all the Tier 2 and Tier 3 interventions that we need, the only remedy we need is to fix Tier 1 and Tier 1 interventions has 12 reference tasks. that teach all of our standards from preschool through high school.

Speaker 3: But the flavor, just like Sarah was using the cooking analogy, I can cook using a recipe, Amy can cook using the same recipe, Sherry can cook using the same recipe, Teresa can cook using the same recipe, and all of our food is going to taste different.

Speaker 3: But there's an art to cooking. Let's suppose we don't have a recipe, and you're just thrown a bunch of ingredients and say, Try to make something delightful. You've gotta have a deep knowledge of spices, ingredients, combinations. You need [00:44:00] to have a much deeper understanding to cook without a recipe, and you even get better at cooking with recipes with that deep knowledge.

Speaker 3: Just like I was saying about number sense. The more we give experiences that improve student number sense, the better they're going to be at solving those step by step procedures and algorithms. But the point is, one problem, one example can teach a variety of things.

Speaker 6: My all the kids like to say, Oh, we're cooking or they cooked. That means you did good. So of course, so we made up we're cooking with Ms. West this week and I have a whole, like I make songs all the time and so now it's the whole thing. We're cooking with Ms. West. They're cooking.

Speaker 6: Yeah. Glad to know all my little songs are. [00:45:00] And you are Gordon Ramsay. Yeah, but I, one of my kids, I was like, Oh, you're cooking today. And she looked at me with total serious Miss West, where'd you learn to talk like that? I'm like, because of you. Come on now. You got what do you mean where I learn to talk like that here every day?

Speaker 11: I think this week has been you are burnt now because too much

Speaker 8: too much. So JC's in the kitchen, not in the house anymore. Jay Z in the kitchen

Speaker 3: with a sweaty back and foot and my broken tooth.

Speaker 8: She's flipping pancakes in the kitchen.

Speaker 3: Y'all know what I'm talking about..

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