In the Math-U-See world, the manipulatives ARE critical to successful instruction—but parents often miss how to capitalize on them. Join us for a conversation about how to get the best out of your Math-U-See experience.
Gretchen Roe: 00:00:04.917
Welcome to the Demme Learning Show. Our mission here is to help families stay in the learning journey wherever it takes them. This bonus episode was previously recorded as a webinar and was not created with the audio listener in mind. We hope you will find value in today’s episode.
Gretchen Roe: 00:00:23.281
Welcome, everyone. My name is Gretchen Roe. And it’s my pleasure to welcome you today for this discussion of math manipulatives and how they aid your student’s learning. I would like to welcome my colleagues. And I’m going to start with Lisa, ladies first, if you would introduce yourself and then Michael, and then we’ll get into the meat of our matter today.
Lisa Chimento: 00:00:47.212
Thank you, Gretchen. Yes. I’m Lisa Chimento. I’ve been with Demme Learning, formally as a full-time employee, since 2017. Before then, I worked for many years at the convention booths during homeschool conventions and got to meet many families. It’s an awesome pleasure and a privilege to speak with you and to support you in any way we can. I homeschooled my own children for 25 years. I have four. They are grown and flown. And I miss them dearly. But my heart really is to support homeschooling families. So we learn so much from each other. I have learned a ton since I stopped homeschooling. And so it’s really a joy to be able to continue learning and to continue sharing with you.
Michael Sas: 00:01:35.291
Yes. My name is Michael Sas. I’ve worked alongside homeschool families since 2005. I’ve been with Demme Learning for the last seven years. I do have two kids of my own. They’re eight and six. And much like Lisa, I just love speaking to families each and every day and hearing about your journey, hearing about your kids, and being able to help find a plan, especially when it comes to looking at math or spelling curriculums. Yeah, we’re excited about today. This has been a big topic. I hear from families about how do we use manipulatives effectively. So excited to be here, excited about this hour, and yeah.
Gretchen Roe: 00:02:11.175
Awesome. Well, we are, again, delighted to welcome you. Again, my name is Gretchen Roe. My husband and I homeschooled six children. Five of them are grown and flown, as Lisa says. They are college graduates living on their own. And the caboose in our train is a junior in high school this year. So I am looking at the conclusion of our journey, and it’s bittersweet. I have to tell you, I have enjoyed the years that I spent with my children tremendously. I would not have changed it for anything, but there were some days that I thought would go on forever, and I know all of you who are joining us today feel that way as well. So we have lots of things we want to talk about today. And I think where we shall begin is to begin talking about the things we most commonly hear about why parents feel like they don’t need to use manipulatives. And I’m really going to facilitate this discussion between Lisa and Michael. And Lisa, I wonder if you could maybe start with parents who haven’t used them before and aren’t sure how to really get the best out of them. I wonder if you could [broach?] that.
Lisa Chimento: 00:03:28.395
Absolutely. I speak with parents a lot. And I’ve often heard people say, “We’re going to order this curriculum. How do I know what to do with those blocks? I don’t know how to use manipulatives.” Well, fortunately, the Math-U-See curriculum also includes video instruction. And that video really serves kind of a dual purpose. It teaches the concept, but it also serves as a wonderful modeling tool for you, the parent, so that you don’t have that question. You’re not left in the dark. You can see Steve Demmei demonstrating himself with the manipulatives, not only to teach the concept, but then he works through several sample problems with the children. And so you get an opportunity to see him use the manipulatives in many different ways. That build writes say method that we have and that we espouse and encourage parents to use, is so effective. And those manipulatives are an enormous piece of that method. So don’t be worried if you’ve never used them before. If you think you don’t need them, if you’re not sure what to do with them, you will be given that instruction and a beautiful modeling opportunity with the videos.
Gretchen Roe: 00:04:41.603
And Michael, I wonder if you could capitalize on what Lisa have said about talking about the manipulatives and how they represent something.
Michael Sas: 00:04:49.640
Absolutely. Researchers show that manipulatives are best used when they represent something and are used over a long period of time. And so the manipulatives that we use are primarily going to be the same manipulatives all the way through Algebra 1 with a few exceptions. They are all different colors. They represent different numbers. And so you’re going to see it’s not just– if you have those green unit blocks, three of them will make her one three block. You’re going to also see that the colors that we use are the same colors throughout the program. You’re going to see the green is our uni blocks, our blue is our 10 block, our red is our 100 block. As we progress, you’re going to see into the decimals and percents. The red block is going to become our 100th block and our blue is going to become our 10th block. You’re going to see that also we come throughout our curriculum or you’re going to see our pink three block is the same as our third level in Math-U-See as our Gamma book. So the color theme is the same all the way through and it makes a difference as you’re progressing through math that the kids remember the colors and the numbers.
Gretchen Roe: 00:05:54.365
Absolutely. So I wonder now if I could ask Lisa to talk about the thing that we often hear, which is the resistant, particularly of an older student to using the manipulatives. Just getting all– pulling all the skeletons out of the closet real quick and then we’ll get to everybody’s questions.
Lisa Chimento: 00:06:18.194
Yeah. And there’s kind of two camps of kids. Some of them just gravitate towards those blocks. They want to start building them like their Legos. They don’t snap Legos. They’re not intended to because they’re not toys. They’re tools. And we want to make sure that students young and old know that their tools. So for the little ones in your household, careful that you don’t let them migrate into the toy box, but by the same token for the older children, to let them know these are not baby tools. These are not counting blocks. These are manipulatives that represent not only numerals, but objects, and when we are working with them, we are helping children to concretely and visually see the numbers and the processes, the operations. At the very lowest level, we’re talking bout place value and there’s a wonderful chart in the integer block kit called with decimal street on one side and the block clock on the other. But it goes all the way up through Algebra 1 where we are concretely showing a very abstract concept like factoring polynomials. And that’s not baby stuff. That’s not children’s play. This is an important tool to help children be able to do more than just solve an equation on paper or learn a tip or a trick or a ruler or a formula. We want them to understand the underlying concepts of math, and that’s where these manipulatives really shine.
Gretchen Roe: 00:07:53.326
Michael, I wonder if you could wade into that area about talking about that consistency over time. Lisa has illustrated they transitioned to one another. But what happens in a student’s mind to be able to have that consistency of use when a student applies the manipulatives through the different levels of Math-U-See?
Michael Sas: 00:08:19.637
Yeah. The way Math-U-See is structured is that every concept builds upon itself. We see math as much like a language that as you’re progressing, you need that foundation to be successful. And so the students are going to start to see why problems are solved the way that they are. I know it’s very eye-opening for me when I started to walk through how a foundational place value is and understanding mathematics. And those blocks really help us understand place value better. It helps us be able to have a deeper understanding of what we’re being taught. And so our goal with the manipulatives is not that we’re just building it, but we’re building it to learn and master the concept. And so our goal is that we’re building it with the blocks. We’re writing the full problem out, and we’re saying back what we are doing. By doing those three things together, it helps build that deeper understanding. And one of the concerns I would hear from parents as well, I don’t want them to have to use the box all the time. And that’s not our goal with Math-U-See either. Our goal is that they’re able to learn the concept with the manipulatives, and once it’s mastered means that they taught you how to do the concept, we move away from the blocks. And so when we get to the review pages and the test page, we no longer are using the blocks anymore because we’ve mastered it. So I would say it’s used as a tool but not a crutch. So they’re there to understand it, and then we move away from it once we understand the concept.
Gretchen Roe: 00:09:44.445
Lisa, can you talk a little bit more about the teach-back and the purpose of the teach-back that seems to be the unsung gold of a Math-U-See experience?
Lisa Chimento: 00:09:55.049
Yeah. Especially for families who have just started to use Math-U-See, they’re not familiar with the process. They may not be aware of the value of a student teaching back a concept to you. And it does have tremendous value. It serves multiple purposes. For one, it helps you to know whether or not your student is understanding that concept. Because math is so sequential and because Math-U-See follows the natural sequence of math. Every concept builds on the previous ones. So in order to be successful today, your student really needs to have mastered all of the prerequisite material that came before today. So when they are learning a new lesson, and you’ve watched the video lesson together, you’ve worked through the sample problems with Mr. Demme, and then you read the written lesson in the instruction manual, you might want to tackle that first page and let the student work on that. If the student is ready, you can ask them, “Can you teach that back to me? Can you show me what you understood today?” And for very young children, they might not have the verbal skills to do that, but they can certainly demonstrate with the manipulatives, but they should be able to do back for you what they have been singing done with understanding. And if they can verbalize it, you really want to look for words like this is this way because we really are getting to the why behind math. Not just the how-to but why this works this way. And if they can verbalize that, that’s an awesome thing. The other value and benefit of the teach-back is for the student him or herself. There is something that happens when a student has to formulate a way to explain something back to someone else, whether it’s verbal or through the demonstration with the manipulatives. They need to really think through that thing. And in doing so, they are integrating the information in a deeper way into their own brains and understanding it even better. And then to be able to spit that out to you is a skill that is developed. It’s not going to be great at the beginning, perhaps, unless you have a natural showman in your family, which we kind of all do. But there may be children who are hesitant or reluctant or shy. You can model for them what you’re looking for and demonstrate for them, pick a problem, maybe from one of the lesson practice pages, A, B, or C. And pick a problem and say, “Okay, let me see if I can build this one. And now I’m going to write it, and now I’m going to [sing?] it and this is why,” and then ask them to try one. And in doing so, they have an opportunity to understand it better, think it through, and then be able to verbalize to you. And if they’re able to do that, you know they’re getting it. And that’s what we’re looking for, that demonstration of understanding. Then you have the opportunity to let them continue practicing towards mastery and consistent proficiency.
Gretchen Roe: 00:13:04.599
One of the things I think that parents fail to take away from the teach-back is it seems like a simple premise. But if your student can learn the process of teaching back in the guise of mathematics, then they can extrapolate that teach-back process to a variety of other disciplines and skills. And that will serve your student well, particularly when they get into high school, they get into more complex sciences and those kinds of things where they really have to not just study the materials, but they have to be able to synthesize those materials and do that successfully. I’ll give you a small example. My son, Owen, is in a PreCalculus honors class this year. And I can read the words in the book, but I have no idea what they say. And I had actually said on more than one occasion, I hope to never have to use or understand PreCalculus or Calculus in my life. And he was preparing last week for a large test, and he said, “Can I sit down with you and explain what I’m doing with these computations?” We spent 45 minutes together and in that 45 minutes, I probably gleaned about 15% of what he explained to me. He has struggled in this class this year. He’s worked really, really hard, but his grades haven’t really reflected that he’s done as well synthesizing it as one would hope. And so he went in and took the test the next day. Bear in mind, as a parent, I couldn’t really help him. I could listen. I could ask some questions for clarification. But as far as being able to really understand the process, I did not understand the process to be able to say, “Yes, you’ve got that spot on.” But he’s a Math-U-See kid, and he’s learned that verbalizing the process makes a difference for him. And he walked away from that midterm exam with an 80. And an 80% is the highest he’s gotten this year and what he said to me was, you know what? He said, “I think the process of walking my way through verbally with you asking me questions is what made the difference.” And so I tell you that story as a parent so that you can recognize that it’s not just something else we’re asking you to do. There is a huge developmental leap that occurs when your child has to take that extra step to be able to explain it to you. And that makes a difference. Michael, I wonder if you could talk a little bit about parents who say, “My kid doesn’t need manipulatives. They can get the work done without them. They do all their math mentally.” And I wonder if you could address that just a little bit.
Michael Sas: 00:15:59.568
Sure. And I typically hear this from parents when they have a boy in the house for whatever reason. I was one of them too that– I thought it was my intelligence that I could be able to just picture it in my brain and be able to just write down the answer to show how smart I am. I think that has a lot to do with it because we– self-image is a big thing for boys. And even though you can do it, we as parents need to know that they understand those steps that go with it because there’s going to be a point when they no longer can do it. And that’s [going to hit?] as they get toward algebra. And so if it’s hard for– if they go their whole lives going up to– not showing their work and they get to algebra one and it’s like, “Oh. Now I have to,” that could be a very difficult process. And so a lot of times if you can even find a compromise where it’s, “You show me your work on these two. And the other two, you don’t have to do it. Just show to me that you understand what you’re doing.” That’s what we’re looking for. Because if they start to make these mental mistakes, you don’t know where the mistake is coming from. And so being able to help them show their work helps you verify that they understand the process. And so that’s why we don’t ask for the review pages and test pages [to be using?] the blocks. Because once we’ve mastered it, we can be able to at that point– be able to move on and make sure we’re maintaining mastery through the review pages. Now, if we’re struggling on the review pages, I always ask you to go back to do work on it. But yes, use the compromise. I use that a lot with my kids. It’s, “Okay. Let’s do this today. If you do this, then you don’t have to do it for these.” That goes a long way, I find. The other thing you’re going to find out too is our math lessons aren’t entirely long. If you’re doing more than a half hour, you’re doing too much math. And so you’re going to find it’s going to only take you 15 minutes to half an hour every day doing a lesson. And so being able to show your work and demonstrate that since it’s not a long period of time is important just for your peace of mind and also to make sure that they’re progressing properly through each level.
Gretchen Roe: 00:18:11.745
Lisa, we had several parents who said that they have children who have come into the program at different levels, and they’re finding that there are struggles with their student. And they’re trying to figure out how to figure out what the struggles are. I wonder if you could talk a little bit about that in general context, but also how the manipulatives would help the parent understand where the struggles might be.
Lisa Chimento: 00:18:36.079
Yeah. And it’s true. Math-U-See– because of the difference in our sequence from a school-based program or a grade-based program, it is sometimes hard to know. We are a placement team. Michael and Sue and Gretchen and I speak very often with families who are coming into Math-U-See for the first time, and the parents really aren’t certain. They can look at the grades that their kids got in school or if they’ve been homeschooling with maybe a different math program, but they’re really not sure exactly which skills have been mastered and which haven’t. And we can help you with that so please do reach out to us. We have diagnostic tools to help you see which skills have been mastered, and we would want to start the students from that point. Because it’s not about how old they are or what grade they’re in, if you’re teaching above their knowledge and they don’t have the prerequisite skills to support that, they won’t be able to be successful in those higher-level skills. It would be like saying, “Oh. I’m ready to build the fifth floor on a building that hasn’t finished laying the foundation yet.” It’s not advisable. And math is like building a structure, so we want to make sure that it’s supported all along the way at every level. The manipulatives are a big piece of that because, for many kids, they can solve– and I’m speaking from first person here, they can solve problems on a page with no trouble. I was that student. I loved puzzles, and I approached math like a puzzle. And I had a great memory. So the facts and the formulas were there. And if you told me what to do in an equation where it says a plus for a minus or a division or multiplication, it’s telling you what to do. But I bombed the word problems because those weren’t telling me what to do. Those were expecting that I would understand what to do. And that’s that understanding of the underlying concepts that the manipulatives are so powerful in teaching because you can see. So we really encourage parents, you can learn the facts and formulas, you can learn the tips and tricks, but if you forget them and you don’t know the underlying concepts, you won’t be able to take that knowledge of the math and apply it into real-life situations. And here’s where we go parents, your child may or may not be going forward in a future that requires higher level maths, but they’re going to need to use math everywhere in their lives. Whether they are a truck driver or a farmer or an electrician or a plumber or an engineer, they will meet math. If they’re a housewife and a mom, they will need math. So we want to make sure that they can use this math in their lives. And that’s where the manipulatives are so powerful.
Gretchen Roe: 00:21:27.061
Michael, will you talk a little bit about the differences in children and how learning preferences are reflected in your boys, and how you’ve had to adapt in order to make it work for two really different learning styles?
Michael Sas: 00:21:44.889
Sure. Yeah. I do have two very different boys. I have an 8-year-old and a 6-year-old. My 8-year-old is by the book. He will follow the instructions. He likes putting LEGO together. He likes cooking where he can follow the directions and do it exactly right. My 6-year-old has ADHD. He doesn’t like to sit. He does like to do things the way it’s asked him to do. He finds his own way of doing it and finds that to be the better way. And so the way that we do math is also very different in that part. I can expect my oldest to be able to do the build it, write, say it, and be able to explain it to me and it goes kind of just the way that you read it out of the instructor’s manual. For my 6-year-old, we do have to do compromises. We recognize doing 15 minutes or more of math at one sitting may not work out. So what I typically will do is put out five duplos and I will take one duplo away every two to three minutes to let him know that his time is coming to an end. Because 15 minutes doesn’t mean anything to him so taking one away and going, “Okay, we have four blocks left. When these are gone, you are done.” With the teach back too, I let him dress up as a teacher. And I sit down as a student and he gets out of marker board and he’s able to show me what he’s learned. And he likes dress-up day. He likes to pretend. And so we pretend a lot with him. So it looks very different for the two of them, but the end result is the same. And so we want to know that they understand the concept before moving forward. And so recognize it can look different for your two kids and the way that they explain it sounds different. Language is different for both of them. And so as long as we know they’re getting it, that’s what we’re looking for.
Gretchen Roe: 00:23:42.921
Thank you, Michael. I appreciate that. I want to say to the parents who are joining us live if you have questions, if Lisa or Michael or I have said something that has created a question in your mind, please feel free to put that information in the Q&A. We are happy to make sure that we are answering your questions as we go along here. And I think that probably the singular, most important takeaway here for Math-U-See is for me to be able to say to you, suspend your disbelief. From my perspective, I was a struggling math student. I struggled all the way through high school. I chose my college major based on what I thought was going to be the least amount of math to get a college degree. And I had no intention of ever homeschooling my children and found myself homeschooling for 21 years. It took me six years to find my way to Math-U-See, and one of the things that I discounted at the very beginning was looking at the amount of work in a Math-U-See lesson and what was required in a lesson. And my automatic go-to response was, that’s not enough math. Because I had the erroneous assumption that if you struggled with math, it was a better experience if you did more of it. And that’s not necessarily the case. Lisa, I’m going to let you talk a little bit about that connectedness between length of time of study and what happens in your brain.
Lisa Chimento: 00:25:19.274
Yeah. And if any of you have been on any of our previous round tables, you’ve heard us nag about this quite often. We’re all still learning. And this was something that I certainly did not know when I was homeschooling. But it is something that I have learned. Studies have shown it and we are proving it to be true every day with the products and the way that we recommend them, and that is shorter periods are more effective than long periods for understanding of new material and for long-term retention. If you take it in small bites over more sittings, it is going to stick with that kid longer than if you have them gobbling up a lot of material in a single sitting. And here’s the deal. This is another thing that we have repeated. For peak performance and best focus from that student, you can add two to three minutes to your child’s age, and that’s about the time that you want to shoot for for how much time you’re going to spend in this material. And it’s not to say that you can’t touch it again in the same day. You want to leave a long break of at least two hours or so. Do other things, go elsewhere, get them off the desk and getting their focus onto longer vision things instead of close work. Give them opportunities for their brain to rest from what they’ve seen and heard, and then come back and tackle a little more of it again later in the day if you feel it’s necessary. But sometimes it’s even better to wait until they’ve gone to bed that night. Give their brain that downtime to digest and integrate this information before you have them look at it again, and then come back fresh the next day. There is so much more benefit to that. And the idea of rigor that I hear all the time out there does not necessarily mean it’s going to benefit that child if you are pushing them to a place of mental fatigue and physical fatigue. They’re not going to retain it. And they might feel like– you might even hear them say today, “Oh, yes, I understand this,” and they can even show it to you. And then we have parents coming back and they’re baffled because the next day it’s like the child never saw it. “I don’t understand it. They explained it to me yesterday, but they don’t know it today.” Well, maybe you spent too much time on it yesterday. And sometimes when you go beyond that 15 or 20 minutes or for an older student maybe a half an hour, once you’ve gone beyond that time and you’ve pushed them to continue working, not only aren’t they going to retain it, but you may actually be undoing the good work you did in that first 15 or 20 minutes. So avoid the temptation to say, “We’re making good progress. Let’s stick with it.” No, if you’re making good progress, stop. Stop. Let their brain rest from it. And then come back to it again another time.
Gretchen Roe: 00:28:13.946
Lisa, I’m going to come back to you in a minute and ask you to recount what Steve talked about last week of what do you do with a child who sits down the next day and doesn’t remember. And Michael, I wonder if you could talk a little bit about how the digital manipulatives, either in the form of the app or the digital manipulative page, are a wonderful supplement to the manipulatives themselves.
Michael Sas: 00:28:39.207
Yeah, absolutely. We not only have the tangible manipulatives, but now on your digital toolbox, you will have a digital pack, which is going to include the DVDs all online, as we need to include the tangible teachers’ guide to include the digital manipulatives and some extra resources including more worksheets for the concept they’re learning. It’s going to include drill pages, other types of resources for your student. The digital manipulative specifically, looks exactly like the block Gretchen just held up. The only difference is that they’re on the computer. So they can actually flip around to show subtraction. They can be up for addition. We have them in the fraction overlays. We have them for the algebra decimal inserts. They’re all available to you. So it’s nice, I think, to be able to supplement that in, not making that your core way of using them because I always think actually touching the blocks themselves is the best way. But doing something different. If you’re traveling, now do you want to take the whole box around if you’re going to grandma’s for the day, or you just want something different to do than your normal routine, those are great things to use. Just to make it a little bit more fun, you can actually use a– you can actually write right onto those manipulatives as well. You can write out your problem using your mouse cursor, doing things like that too, to help just give a different feel for your day-to-day work with the Math-U-See Program, so.
Gretchen Roe: 00:30:09.784
I think that the digital manipulatives are a tremendous tool, and I want to make sure that parents understand that the reason that we have these manipulatives that we use is because they allow us to bring as many senses to the table as possible. They give us the kinesthetics of actually moving the manipulatives around. They give us the ability to speak to what we’re doing. They give us the visual component. We can hear ourselves say, “Okay, I know that 2 plus 4 is the same value as 6.” All of that is part of the learning continuum, but being able to do that in a digital environment is an additional way to augment and supplement that. And they also are, as Michael described, a terrific way to be able to take Math-U-See on the road without a lot of plastic. So that’s helpful too. Lisa, I’m going to come back to [crosstalk]–
Michael Sas: 00:31:07.808
I will say to just– [inaudible] just jump off [with?] Gretchen.
Gretchen Roe: 00:31:11.110
Michael Sas: 00:31:11.581
Or even if you’re not a Math-U-See customer, if you log into our store and create an account, you automatically have access to a digital toolbox. If you go to the website Digital.DemmeLearning.com, you will get access to the first three lessons for every level. And you’ll have access to the digital manipulatives. And so that is something a lot of customers don’t know about, or those that are just looking to see if they want to use it, that’s a good test tool to do that. So that is available to you. Just make an account on our store, and then go to Digital.DemmeLearning.com and you have access to all of those resources.
Gretchen Roe: 00:31:44.717
Thank you for saying that, Michael. And this just came up in a social media discussion last night, and I referred a parent to go look at the scope and sequence to one of the Greek levels. She was pretty sure her child had mastered all of the content contained in that level. Our table of contents is our scope and sequence since we teach math a singular concept at a time. So being able to look at that scope and sequence, she could look very quickly and say, “Yes, my child is capable and can accomplish all of the tasks in this particular level.” So if you’re looking at math, you see and you’re kind of on the fence going, “I’m not sure what level.” That is yet another tool for you to be able to use to evaluate the experience. Lisa, I want to come back around to Steve’s explanation last week.
Lisa Chimento: 00:32:35.146
Yeah, this was really neat. Gretchen interviewed Steve Demme last week, and he had so many wonderful things to share, but this was one that I had never heard before. He mentioned that one of his sons, when he was teaching him math, they would do the first day, they would watch the video lesson, they would work with the manipulatives, they would read the written lesson, and they would do some of the work on that A page. And then when he would come back the next day, that child was very– there was a lot of anxiety in coming back and being expected to be able to teach back. And so what he decided to do after some hit-and-miss with this was he took over what his child was expected to do. And he said, “Okay, so I’m going to take some of these problems from the A or B page and I’m going to build them and write them and say them.” And it sort of let his kid off the hook for the moment but it also took that anxiety level way down. And that’s one thing that we want to mention here, just to throw this in. Anxiety happens sometimes, particularly when we’re taking on a new challenge. Every new lesson for a child is like a new struggle. You have to cross that line from, “I don’t understand this at all.” till the lightbulb goes on and then suddenly, it makes sense. And that’s a struggle in between. And that can sometimes produce anxiety for a student. And when anxiety enters the situation, learning stops. So you want to do whatever you can to bring the anxiety down. And if you taking up that second day and saying, “Instead of putting you in the hot seat of having to show this to me, I’m going to do a review for you. And I will do a couple of problems and then let’s see if you can try one after me.” It might help ease that child into it because now they’ve not only had the opportunity to review material they saw the day before, but they’re getting a second modeling opportunity. Somebody showing them exactly what’s expected here and how it all works. And that may be the key for you if you’re having trouble with your children, either using the manipulatives or demonstrating and doing the teach-back for you.
Gretchen Roe: 00:34:56.217
Great. Thank you. I appreciate that. And we have a wonderful question in the chat and I’m going to use this as an example because we hear this frequently. “How can I help my daughter with fact fluency? Currently, she’s on Beta, and she’s pretty good at facts, but sometimes she blanks out on something so easy as four plus one.” And I’m going to let both of you answer that. Michael, I’m going to ask you to start. I know you have different ways of addressing this, so.
Michael Sas: 00:35:26.931
Yeah, I think one of the things we’ve learned through time is when I hear a parent tell me, “My student’s struggling,” I can almost guarantee you they don’t have their facts mastered. Most of the time, if we could pass first grade and we don’t have our addition-subtraction facts memorized, typically they never become memorized unless we stop to work on them. What happens though, is after first grade, we develop a habit, and that could be counting on our fingers. It could be using a number line. It could be using an abacus, tally marks, you name it. We find a way to get to that answer. And so what what happens as we progress through math is, if I had a bigger problem like you’re in Beta, we’re doing multiple-digit addition, subtraction. But 18 plus 14, what will happen is 8 plus 4 – 9, 10, 11, 12. Now we have to look back at the problem and remember where we left off. We have to remember to carry 10. And now we go 10 plus 10 plus 10 – 32. You may get the right answer, but now I have increased the likelihood of miscounting, of losing my spot, of forgetting steps. And also, my brain is working overtime, because I’m thinking about all of these things. And so our philosophy on facts is that we’re going to do the same thing of building it, writing it, and saying it through the Alpha level. We believe that flashcards and drills are great tools to use when they’re memorized but not necessarily to memorize. Because if I would put a flashcard in front of a student and go, “What’s 8 plus 4?” They go, “12.” “Great. Next one, 7 plus 5.” “I don’t remember that one.” “Come on, bud. You got this yesterday. What’s going on?” This is where Lisa has talked about with anxiety, is students will shut down at that point. They will get nervous, because they want to please parents so badly that they’ll shut down. And so the other thing that happens is we focus so much on speed with drills and flashcards. So we need to go fast. Well, if we’re struggling with something, telling you to go faster just creates more and more anxiety in me, right? And so what we’re going to ask to do is take a step back and get used to the blocks. Come up with a way to remember each one of them. For instance, if we had 3 plus 4 – in my family, the three pink block is the three, pink, little pigs – combining that with the four yellow pineapple block, equal the seven white vanilla ice cream block. What that’s doing is allowing them to start to picture those blocks in their mind, much like rolling a dice. If you roll a dice, you get a seven – or a seven. I’m sorry – a five, you don’t have to count the dots to know it’s a five. You know the pattern, and you can picture the pattern in your head. We’re trying to do the same thing where we’re building it with the blocks to picture it. Write the full fact down. Because one of the great things about writing the full fact down is I can start to picture that fact. Because when I do a flash card, even if I’m great at pitching the flashcard, the flashcard doesn’t give me an answer. I have a blank answer at that point. So we’re writing the full fact down. And we’re saying it, because when you say what you’re writing, it forces you to pay attention. But it says you remember 40% more than you just simply looking at it. And so we’re doing those things together to help build that fluency. And we stay on those facts until they’re memorized. And we don’t move forward. And then we keep reviewing them to make sure that they’re getting better and better at them. So if we are struggling, and we’re in Beta, I recommend taking a step back, because like I said, they never become memorized unless we stop to work on them. And if we’re trying to do two things at once– I’m always wanting to go back to the habit that I’m used to, and that’s counting on my fingers. So we want to work on those alone, and then go back to where we left off.
Gretchen Roe: 00:38:59.933
Lisa Chimento: 00:39:01.005
Oh, golly. I don’t know that I have anything to add. Michael, you covered that beautifully. Yeah, I think that it is important for parents to take notice because you might assume that your student has that fact memorized. One of the other things that Michael didn’t mention that students often do is count in their head. So they might not be visibly counting on their fingers or looking like they’re counting, but they might be counting in their head. And so it’s might be worthwhile for a parent if they are starting to see the kids freezing on some of these facts in higher level books to stop for a minute and just review some facts, take some facts out. You can use flashcards for this as an inventory tool and just say a couple of facts to them in random order – don’t do them in numerical order – and just give them a fact and then watch. Do not rely on workbook pages to tell you whether or not your students know their facts because they can be counting and and then writing in the answer. What you need to do is look at them and observe and say, “Give them the fact,” and then watch. Are their eyes going up to the ceiling? Is their head bobbing? And then you know they’re counting for their fact. And they really don’t have it memorized. So it’s worth taking that time to find out. Now, if you have the Alpha materials at home, you’re working in Beta, and you came through Alpha, you can go back and just review those lessons on the facts and do what Steve does in the thing, in the video lessons. Build the fact out, make sure that they can put down on the table the two add-ins in the fact, and then show which one is the sum. And then like Michael said, write out the entire fact. And you know what? You can give them a choice. How do you like to see that fact as a horizontal number sentence or set up in a vertical orientation and the answer at the bottom? Whichever way they prefer. And you’re giving them an option so that’s always a nice thing. Helps reduce anxiety, gives them a choice. And then have them say it out loud. The more they can write out the whole fact and say it aloud, the best. And even when you quiz them on the fact, I heard one parent say to me, “My child always needs to repeat the fact after me. I don’t want him to do that.” That’s actually a good thing. His brain is making the connection between the numbers that are being added and the answer. That’s a good thing. Let him say the whole fact aloud and then the answer. So you might want to try a couple of those things, Natasha, and make sure that those facts are learned. If they are, if you do quiz them and that child does have all of the facts memorized, then you have to see if maybe the concept that they’re learning in Beta hasn’t yet been learned and in trying to get through the problem and put that concept in operation to play, their brain just isn’t able to do the both things at once. So maybe go back and review the concept, watch the video lesson again, work with the sample problems and the manipulatives, and build it, write it, say it, until it becomes more understood, better, smoother operation for them. And then suddenly those facts will pop back in for them.
Gretchen Roe: 00:42:19.884
I think it’s the last thing I want to–
Michael Sas: 00:42:20.478
Last comment on that.
Gretchen Roe: 00:42:22.252
Go ahead, Michael.
Michael Sas: 00:42:23.212
Oh, I’m sorry. I was going to say, I believe that math fact mastery is maybe the most boring part of math and the most necessary. And so make it fun. Do things like we have. Everything that is kind of that way for us, we make into a party. So we have math fact parties. That throughout the week, if we can get a certain number memorized, we don’t have to do math that day. We can go play Legos together. We can go to the park together in this place. That there’s some kind of reward there to tie it to it. Again, I’ll memorize. Maybe we have a pizza party. There are things like that that are there because it’s hard. One of the things I also do is I celebrate the different facts that they get memorized. “Hey, we didn’t have this one memorized yesterday. Today, it sounds like you do. That’s great. I’m proud of you.” Celebrate those little victories with them because it’s a lot of work. And it doesn’t come easily for a lot of kids. And so celebrate those small things. Make it fun. But keep the processes the same. Keep it consistent. It has to be consistent and you have to do it daily. I mean, repetition is important. So it’s such an important piece. And I don’t want to– it sounds like a lot of times we just, “Memorization, it can’t be the reason they’re struggling.” Well, 9 times out of 10, it is. So make sure we get those memorized and continue forward. So that’s a great question. Something we’re all very passionate about is fact mastery and why it’s important as we progress through math. So great question.
Gretchen Roe: 00:43:53.454
I think it’s also important to recognize that we can use our kids to discern why they’re struggling. And sometimes it’s the context. So in Natasha’s example, she said, “To have a child who suddenly blanks out on something is easy as 1 plus 4.” 1 plus 4 is easy for us as an adult, but now you’ve put me in a three-digit by three-digit addition problem and 1 plus 4 is only one of the things in there. Now, all of a sudden there’s a bunch of stuff stacked up here. It’s not just 1 plus 4. And I find it to be tremendously valuable to say to a student, “What happens with your brain when you don’t remember that? Where does your brain go?” And one of the most valuable examples I have had of that is having this conversation with a mom who said she in turn had the conversation with her daughter, and her daughter said, “Mom, I don’t know. My brain just feels like it’s full of fog.” And that was the clue that what we thought was an easily well-known and honed fact was not. And so having that conversation makes all the difference in the world. And sometimes when we homeschool, we actually put our kids at a disadvantage because we’re the mom or the dad sitting across the table. They want even more to please us. And so they will act as though they know some things that they don’t really know just because they want us to be happy. So being able to give them permission to say, “I don’t know that. My brain is full of fog.” What a powerful visual example to understand what was happening to that student in that moment. And I think if we can give our kids those kind of exchanges, it makes life much easier. Two more things I wanted to bring up. This was said in passing by both Michael and Lisa and I want to illustrate this for you. When you go through math you see in the Alpha level, you will see us build manipulative problems horizontally. What we have learned in the development of aim for addition and subtraction is that this is not necessarily the easiest way for a student to see it, particularly if a student has a learning struggle like dyslexia. This requires the student to go across their corpus callosum to recall the fact and what you may find is if you ask the student to turn those blocks 90 degrees, now all of a sudden 4 plus 2 equals 6 is easier for them to visualize because this does not require crossing that corpus callosum. So if you have a student who’s struggling with factory call, try something as simple as flipping the blocks 90 degrees and see if that doesn’t make a difference for you. I want to address a question here that several parents raised, and I’m going to let both Lisa and Michael address this question. And that has to do with, why can’t we just use a calculator for math facts. All of us have these little devices here that do so many wonderful things for us. Why can’t we just default to the calculator for that computational math? Have at it, guys.
Lisa Chimento: 00:47:31.986
Okay. Oh, gosh. We have a lot to say about this, I think. First of all, I don’t know if this is true for everybody else, but I noticed that for myself if I have been working on math stuff and I’m using the calculator a lot, my fluency with math facts goes down. Michael mentioned this earlier, math is very much like a foreign language. If you’re not using it on a regular basis, it’s really easy to lose it. And we want to keep that fluency strong and if you are allowing your student or even yourself to continually use a calculator, their brain is not getting the constant exposure and daily practice of using what it needs to recall that material. And I think it puts them at a tremendous disadvantage. The other part of it is something else that Michael mentioned. When they are having to work on a multi-step problem, there are a lot of things to put into place. Consider a long-division problem. If you’ve got a three-digit by three-digit division problem, every digit you’re dividing is four or five steps. You have to divide. And then you have to multiply. And then you have to subtract. And then you have to bring down the next number. And then you have to go back to the beginning and start with the next digit. For each one of those steps, if they have to take their focus off of what they’re doing and plug that number into their calculator, get the answer, and then bring their focus back to what they were doing. It’s so easy to lose your place. You make unnecessary errors, but it’s constant interruption. And the last thing a child needs, particularly one who already has some focusing issues, is more interruption in the process. It also burns up a tremendous amount of brain battery that doesn’t need to be burned up. Your child only has a certain amount of mental energy to bring to their task. If they are unnecessarily expending it on this in and out of the problem, then they’re going to become mentally fatigued much more quickly. A long division problem is long enough. You don’t need to make it even more tiring for them. And then if they have to face more problems on the page, that’s when you start to see additional errors happening that didn’t need to happen. And then they become exasperated. I just say, “Don’t do it to them.” Now, when they get into the higher level concepts, Pre-Algebra, algebra one and on and they’re having to do things that have a great number of steps with a lot of multiplication and division in there, sure, let them use the calculator for those cumbersome things. If they’re figuring out – oh, I’m blanking now – the area of a solid figure and they have to do all of this outside area, that’s a lot of multiplication with that. Let them use a calculator for it. But for the daily work, let their brains stay exercised, otherwise, they atrophy.
Michael Sas: 00:50:40.797
Yeah, I don’t have a lot to add to that, Lisa. But I will say I haven’t heard many parents say, “I’m allowing my kids to use a calculator.” And we’re hearing, “Well, see my school has allowed my kids to calculate.” And so I will say kudos to those parents for recognizing that because I always say easier isn’t always better. It may seem easier at the time, but I was thinking about this the other day about how much math I have to do in my head on a day-to-day basis. It’s not just figuring out these type of problems, but it’s like, okay, I have to wake up at this time and how many minutes do I have before I have to be ready for this? Or if I buy four of these cans at the grocery store, how much is that going to be? I do all this mental math all the time. And so being able to help them understand how they get to that answer. The calculator doesn’t walk you through the steps. That just gives you the final total. And so helping students to be able to understand the full concept and be able to understand why they do each of these steps, the calculator doesn’t help you do that. And so there is a time and a place for a calculator, absolutely. But during these lower level, allow your student to be able to work it through. And sometimes we don’t put enough stock into the struggle of learning, I think. And it’s okay to struggle through something. It’s okay that things are hard. But it’s also important as a parent to encourage your students through those difficulties that it’s okay things aren’t coming easy because that’s why we’re learning. That’s what we’re doing this today. It’s okay if it takes a few days or a few weeks to learn this concept. Let’s go through together and celebrate these victories that we have as we’re learning this process. And I think calculators steal that from us. Steal the victories. [It feels as?] these moments that we can have with our kids and how we see the light click on. And so easier isn’t always better. I think that’s what I come away with when I hear of kids using calculators.
Gretchen Roe: 00:52:35.663
I want Lisa and Michael to think about what your closing words will be because we’re coming to the bottom of the hour. I do want to follow up and say that I’ve had the privilege the last eight years to work often with families who have children who learn differently, either diagnosed with dyslexia, dyscalculia, those kinds of things. And I have to tell you, often I have encountered students who have received that diagnosis, and it’s not the end of the experience. Frequently, I find that that diagnosis comes, and then if they’ve been in a public school environment this school starts shortcutting the process and making things easier, but not creating a greater degree of knowledge for the student. So here it gives me the opportunity to promote our placement specialists and suggest to you as a parent to have a conversation. If you have a student who has been in a school environment, and the only thing they’ve ever been taught is to use a calculator, maybe it’s time to have a greater conversation. I have to tell you, I’ve found a great deal of success over the years with doing some placement analysis as Lisa mentioned earlier. And analyzing, where did the wheels come off your student’s wagon? If your student has aspirations of mathematics beyond high school, we need to give them that foundational skill set that Lisa talked about. We need to [report?] that concrete, take out the cracks, and give them the ability to move forward. Because frankly, as the SAT and the ACT are now imagined, there are calculator free portions of the exam. And even if your student has accommodations, they won’t be able to get through the exam under the time constraints. We want to level the playing field for kids, and part of doing that is to use the diagnostics or placement specialists have available to them and help you have a better mathematical experience. So if you’re joining us live or you’re watching the video and you think something doesn’t add up here – and no pun intended – I really recommend that you reach out to us. And now in these closing minutes, Lisa, if you have any closing words about manipulatives or the greater skill of math for our families, I would appreciate it. And Michael, I’ll let you have the closing words.
Lisa Chimento: 00:55:00.245
Thanks, Gretchen. Yeah, we’ve been talking a lot about the integer blocks, but I want to bring up one thing, and that’s the fraction overlays. This is my baby here. They are my favorite tool ever because they are the thing that helped me understand fractions when I was teaching my kids. Like I said, I had a great memory and I could solve the problems on paper. But if you had to ask me, why it is that when you multiply two fractions you get an answer that’s smaller than the two numbers you started with, or of less value, I could not have explained it to you. And I often see moms on Facebook and other places saying, “Oh, we never used the fraction overlays. My kids were able to do it without.” I would challenge you. Ask your child, why is it that when they multiply two fractions they get a number that’s smaller? And yes, they can do it on paper. But do they understand the underlying concepts? Can they solve word problems easily with the fraction word? If not pull out those fraction overlays, show them, ask them to show you, and be able to teach back the concept. They are such powerful tools. My favorite moment at a convention was having an engineer dad come to the table and go, “I don’t know if my kids need these.” And I go, “Just let me give you a minute.” And I showed him how the fraction overlays work. And that man stood there with his mouth hanging open. He was impressed. And when an engineer is impressed with a mathematical tool then you know that it might be worth taking a second look at. So that’s just my little plug for the fraction overlays. And they are consistent with the blocks, and you’ll see how. But they are well worth the time. Thank you so much for this opportunity to speak to you. If you have questions please contact us. We love to support homeschooling families and answer your questions. And I look forward to speaking to you.
Gretchen Roe: 00:56:58.576
Michael, I’m going to interrupt just for a moment here. Lisa is one of our Algebra 1 subject matter experts. She provides support to families with Algebra 1 all the time. And I will tell you from personal experience, often the root cause of a child’s weakness in Algebra 1 is that they don’t understand how to add, subtract, multiply, and divide fractions. The downside is when you get to the Epsilon level, often you have a student who is hitting their teenage years and they– I’m going to adapt a line from a movie, “Fraction overlays, I don’t need no stinking fraction overlays.” And the truth is they do. And you need to, as a parent, pony up and understand how those things are used so that you can give your child the greatest advantage possible.
Michael Sas: 00:57:50.640
Gretchen spoke just briefly about placement. One of the things that we typically will do– the three of us and including Sue Walker who isn’t with us right now will do is speak to families about where do we start. And one of the biggest fears I hear from families is, “I don’t want my students to start over.” And neither do we. But what we do want to do is identify that first gap that they have and address only that gap. Because most of the time other gaps naturally fill in, and most of the time it only is going to take you a few months to get them caught back up. What we’ve done as a team have come together a lot of cases, and identified ways to speed line this process, and to give you the tools necessary to be successful in helping your kids get caught up. We are not having to buy all five levels over again to get them through. This is an expensive journey. That’s what a lot of families worry about is how expensive it is. A lot of times it’s not. A lot of times we can do things for free or a very minimal cost to get them caught back up to where they left off. But not going forward causes a lot of problems. I remember talking to a family probably a year ago now. They had a daughter who was doing Algebra 1. And the mom said, “She cries at the table every single day. It’s so hard for her.” We found out multiplication packs were the first thing that she didn’t have memorized. We worked on that for a few months. We did some things with fractions, and with decimals and percents, and Pre-Algebra. And we gave her a pre-test for Algebra 1. She got a 100% on it. Her mom said she did cartwheels down the hallway. She was so excited. So those are the sort of things that we get excited about helping with is to– yeah, you can push forward, but you’re going to have trouble going forward because they’re going to have tears every single day. But I guarantee this family that took the nine months to work on it, they’re going to get farther down the road than they ever would’ve if they wouldn’t have taken these nine months. And so we’re passionate about this. We’re excited to work with you. We want you to have success. And so please give us a call if you have any questions. We’ll work on a plan together to help your student get caught up or move forward if that’s the case. So thank you again for joining us.
Gretchen Roe: 01:00:02.837
This is Gretchen Roe for the Demme Learning Show. Thanks for joining us. You can access the show notes and watch a recording at DemmeLearning.com/Show or go on our YouTube channel. Be sure to rate, review, follow, or subscribe wherever you may be hearing this, especially if you really enjoyed it.
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Here is the link to the Grey Carson interview mentioned in the live session. This is a Math-U-See student, who obtained her Ph.D. in Applied Mathematics at the age of 19.
We had an in-depth discussion about using the fraction overlays.
Further, sometimes difficulty with word problems is solely due to not understanding the underlying concepts, and that’s the first reason to use manipulatives. They give such a strong understanding of those concepts. Second, there are word problem tips in the Instruction Manual, as well as some additional word problems available there after four of the lessons. Check the index in the back of the Instruction Manual for those word problems and tips.Upcoming Episodes
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