What Does Mastery/Teach Back Look Like? [Show]

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Gretchen Roe: 00:00:05.062
Good afternoon, everyone. This is Gretchen Roe, and it is my great pleasure to welcome two of my wonderful colleagues here to have a conversation about the teach back and mathematics mastery. And you might be doing math and going, “Well, but wait, Gretchen, there’s only one of them here.” Welcome to Technology Tuesday, where my colleague Lisa’s computer has just decided to update her Zoom as we began this episode. So Lisa will be joining us shortly. And in the interim, I’m going to do a little bit of housekeeping, and then I’m going to let my colleague Abby introduce herself. My name is Gretchen Roe. I’m the community relations coordinator for Demme Learning, and it’s my very great pleasure to welcome all of you today to join us for this conversation about the teach back and mastery. We know that this is the third rail of academics as far as math is concerned from Math-U-See. And we want to make this clear for you. We want to encourage you, and we want you to know that this is something you can do. Each of us comes to the table with an entirely different point of view. My point of view is math is spelled with four letters for a reason. I’m not a mathematician. I didn’t even like math, but Math-U-See made it possible for me to educate six kids and five of them are now college graduates. And I’m grateful for the experience. I wouldn’t say I’m a confident mathematician, but I know how to do it now. And boy, I tell you what, that was such a game-changer for me. And now I’ll let my colleague Abby introduce herself. Abby, welcome.

Abby Franco: 00:01:46.118
Thank you so much, Gretchen. Hi, everyone. I’m Abby Franco. I am the training specialist here at Demme Learning. And so basically what I do is I train teachers in the schools, charter, public, private, how to implement Math-U-See in their classrooms. So that’s what I do each time I have a school customer to work with. Before I joined Demme Learning, I was a seventh and eighth-grade math teacher in the public schools of Georgia where I live. And before that, I was a high school math teacher. So I’ve been around the block a little bit with teaching kids math. So glad to be here and hopefully answer some of your questions you guys have about mastery related to Math-U-See.

Gretchen Roe: 00:02:29.887
Well, this is one of the reasons that I completely love the opportunity to work with Abby because we are about as polar opposite as you can get as far as our love of mathematics is concerned. But we’re both Georgia Bulldogs, so we’re excited to be able to share with you all today. Really, the first thing I would like to talk about is mastery. What is it? Define it for us. Help us understand.

Abby Franco: 00:02:56.216
Yeah. So mastery is basically allowing students to perform math at their level that they’re currently at. So what this might look like is it’s not tied to maybe their specific age or grade level that they’re in. It’s rather based on where they can perform mathematically. So if you look at any research done about mastery-based programs, you may see results in higher achievement across the board. And this can even reduce math anxiety. So if any of you are working with kids who have anxiety about performing in math or just have a really strong dislike towards math, which is pretty common, you may find that approaching this in a way which is mastery-based, the way it’s intended, you may find that they might show some more confidence. They might feel like they can find a way to show that they’ve mastered the concept with their instructor. And we’ll talk more, I believe, later about those varying ways of seeing how mastery can be shown with the curriculum.

Gretchen Roe: 00:03:58.039
And, Abby, as long as we’re talking about mastery, one of the questions that we got in the questions that were submitted to us is, “Help us understand the difference between spiral – what parents refer to as spiral, the educational field refers to as incremental – and a mastery-based program.” Give us an understanding there.

Abby Franco: 00:04:22.023
Yeah, so spiral, you kind of start with the basics, what foundation they’re going to need, and then you physically think of a spiral. You’re building on top of that with higher, higher-order thinking, more difficult problems until they reach the top of their math learning. So with mastery-based, the intention is that they master a concept before moving on. So let’s say you’re working on single-digit addition, you want to master that concept before moving on. I always like to give the example of long division. A lot of parents reach long division with their kids or teachers, and they think, “My kid can’t long divide.” But it may be that they lacked mastery in single-digit addition, single-digit subtraction, single-digit multiplication that are all components of long division. And so we really want to have that mastery of a concept before moving on to those more difficult, rather than, touching on it when we get back to long division. “Oh, we need to quickly reteach single-digit addition because they don’t remember it.” But with mastery, they would have mastered before moving on to that point.

Gretchen Roe: 00:05:30.550
So does it mean, then, that if I’m talking about a mastery-based program, I absolutely can’t move forward until I have 100% of something done? And I know the answer here, but I want to hear you say it, so.

Abby Franco: 00:05:45.277
No, it does not mean that. So mastery for your particular students, maybe you’re thinking in terms of the worksheets. Let’s say you are working on a lesson with a student and they have showed signs of mastery. Maybe they’ve showed you they can teach it back using that build-right same method. Maybe they’ve made a model of what you’re learning, whatever it may be. And then they don’t need– if you’ve looked through the student workbooks, there’s six to seven pages per lesson. They may not need to complete all seven for a lesson to show mastery. They don’t have to complete 100% of the work that’s offered to them in that book. And so you may find that they only need one of those lesson practice pages before they’re ready to move on to a systematic review page. And so you can kind of– that’s why we really encourage parents to be checking in on their students as they’re going, providing that scaffolding, providing any teachback that’s needed or reteaching that’s needed before assigning another page. But like I said, that may not be the case that they’ll need all the pages that are available to you in the books, so.

Gretchen Roe: 00:06:54.516
And you made a great suggestion when we were having our planning meeting last week. What do you do with those extra pages? I mean, I’m a good German. I bought the material. You will do all the pages because I spent the money. What’s a good way for a parent to utilize those pages they didn’t need?

Abby Franco: 00:07:13.095
Right. So I always encourage, don’t just throw them out or put them back on the shelf and forget about them. You can use them to review for later points in the year, maybe that you want to even save them for a following level. They’re great to use for review. They’re great to use to prepare for unit tests or those lesson tests. So if you don’t use them on the spot, especially those application and enrichment pages. If you don’t use them with a particular lesson, always take a look at them and see if there’s another point that you could use them. Whether it be for a review or to do some sort of other activity with it, there’s always a way you can still use those later down the road if you want to.

Gretchen Roe: 00:07:56.042
I think I spoke with a parent years ago who said that she kept the extra pages for when her kids uttered the B word in the summer, I’m bored. And she would say, “Well, let’s do some math.” And that was a way to keep their brains engaged when they weren’t actively doing mathematics. And I think that’s a wonderful idea as well.

Abby Franco: 00:08:16.086
Absolutely. Yeah, I love that.

Gretchen Roe: 00:08:17.719
Abby, can you talk to me a little bit about error analysis? You had mentioned this the other day, and I’ve never heard it quite explained the way you explained it. And I think this is awesome. So can we talk a little bit about it?

Abby Franco: 00:08:33.056
Absolutely. So error analysis is one of the ways that we can see mastery with our students. So error analysis is basically giving the students a problem that’s already worked out. So the work is there shown for them along with an answer. And they are basically checking that work, analyzing for errors to see if there were any errors made and then explaining what those errors were and how they can be corrected. So I loved doing this in my own classroom with my kids. I worked with middle school students, and I know this is one of the questions that was brought up is how do we deal with those middle grade students who do give us that pushback as far as wanting to show mastery or talking about what they’re learning, anything like that. I learned really fast that middle schoolers love to correct me. And so I would always project a problem on the board that was something we touched on earlier in the week, completely worked out by me with a few errors in there. And so they could come in, even if they were fighting me to get a pencil and paper out, that’s okay. Just look at it, read it, look over it. And if they can identify the errors and they can correct them, that is a sign of mastery. I always say that professionals make mistakes. Whether you’re a professional athlete, professional musician, whatever it may be, you’re going to make mistakes. It’s inevitable. And so by giving them the ability to correct those mistakes, that is what makes them a professional or a master at that concept.

Abby Franco: 00:10:10.392
And so I loved doing this, like I said, with middle school students, because one, it not only gave them the opportunity to work without necessarily having to get a pencil and paper out, but two, it’s also a great on-ramp for all levels of students. So if you have students who maybe have a hard time categorizing steps or remembering a lot of steps or kind of how to approach a problem, you’re giving them the majority of the work, but they’re identifying what’s wrong in that work. And then this can even get them in a habit to begin doing this to their own work. Okay, before I submit this, let me read through it. Let me grade my own work and see if I made any errors that I can catch before turning it in.

Gretchen Roe: 00:10:54.293
Wouldn’t that be your lips to God’s ears?

Abby Franco: 00:10:56.505
That’s right. I’m like listening–

Gretchen Roe: 00:10:56.585
[crosstalk] is praying for that particular thing. Come back to this again because I want you to explain in a little bit more detail what that means if you’re a parent sitting at a table trying to get your student to do that. But because Lisa’s computer has finally decided to play nice, I would like her to have the opportunity to introduce herself. Lisa, welcome.

Lisa Chimento: 00:11:20.976
My name is Lisa Chimento, and I’m a Customer Success Consultant and Placement Specialist here at Demme Learning. My husband and I homeschooled our four children for 25 years. We used Math-U-See and graduated all four kids. And I’ve been here with the company for almost seven years now, full time, and before then at the booth at conventions. And I’m so thankful that I’m here. [laughter]

Gretchen Roe: 00:11:49.754
We say flexibility is a sign of intelligence. Welcome to Mensa. We’re delighted to have you. And we’re going to talk a little bit more in-depth as far as the mastery component. But just to bring you up to speed, Lisa, and maybe to recap for the– we have a couple of parents that I noticed just joined. What we’re talking about is using error analysis as a way to get your reluctant student to figure out what you did wrong. And there is not a parent on the planet who doesn’t know of a child who’s happy to point out to you your own errors. So, Abby, can you explain how a parent would do that? Basically, what you’re saying is the parent works out the problem first. But what’s the critical element here?

Abby Franco: 00:12:39.099
So I would say for parents working out the problem, I would say choose a word problem is what I kind of geared more towards. If you’re concerned about maybe not having the level of understanding enough to do this, look at the books, watch the videos, check out the answer keys in the back of those instruction books. Those can help you if you’re not maybe yourself feeling super confident to work out the problem. But choose a word problem. Find the steps that are in the books, in the videos, wherever it may be, in the application enrichment pages, write out the steps that are required, maybe make a few– and what I would actually suggest is make sure you’re making errors with the concept, not necessarily always just computational problems, but understanding the concept. So then that way you’re really testing whether the student has mastery of the concept. And then you can also include some calculation errors too, but.

Gretchen Roe: 00:13:39.957
So I follow what you’re saying there, but for parents who might not understand what we’re talking about, when we’re talking multiple-digit multiplication, you’re saying start the second line without adding the zero or something like that.

Abby Franco: 00:13:53.366
Yes. Yeah, that’s a great, great way. Maybe so with multiple-digit multiplication, maybe you switch the over and the up dimensions and then you can see that the steps in the standard form maybe don’t match what they build. Taking that zero away, adding numbers in the wrong place values. That’s a big thing that students kind of mix up is making sure you’re combining the like kinds. And so it could be anything like that. Maybe you have an explanation portion and something’s wrong with the explanation in regards to the concept. So it could be little errors like that. Maybe the building, you make a little mistake if you have maybe you build it next to the problem you’ve done and they can arrange the blocks to where they’re supposed to be. It could be anything. Maybe if your students are only just ready just to touch a little bit, just make one error. Don’t make too many. Maybe just leaving out the zero like Gretchen. That’s a big one that students miss out on. Or just maybe they’re only ready to identify a calculation error, and that’s kind of where they’re ready to start. So like I said, it’s an on-ramp. So you can help students at all levels of understanding to enter into this problem based on what errors you make, what type of problem you’re using, and things like that.

Gretchen Roe: 00:15:14.687
Yeah, and I think when we had this conversation the other day, this was fascinating to me because this is a way to start your mathematical experience in a day that is a very low obligation on the part of the student. The pressure is not there. And, Lisa, I wanted you to talk about– you brought up Steve’s conversation about teaching Joseph. And I wanted to revisit that because I think this is really valuable. Steve taught me more in that one video about teaching Joseph than I think anything that he taught me in the lower levels. So I would love for you to recount that for our viewers today.

Lisa Chimento: 00:15:57.380
Yes, that was news to me too. When I watched that interview, I was really fascinated and I thought it was really brilliant. He mentioned Joseph would tend to freeze up a little bit. So if they had done the math one day and came back the next day, instead of asking Joseph right away, “Are you ready to teach this back to me,” he went and picked a problem off of the workbook. And he taught it to Joseph. He modeled for him what he was wanting to do first, and so he modeled that teach-back. He worked out the problem. He verbalized his steps as he went. He built it with the manipulatives. He wrote it out. And so he was using all of those different– all that different sensory engagement, and he was showing Joseph what he wanted.

Lisa Chimento: 00:16:44.371
And it kind of took that pressure off, instead of hitting him first thing in their lesson to be able to do that. And then I think he said, “Let’s work on this one next,” and maybe they kind of eased into that one. Maybe Steve did a couple of the steps and asked Joseph to fill in the missing steps. There’s lots of different ways around that. But if you’ve got a child who’s going to kind of freeze up and not know what to do right away, giving them that reminder, refreshing the whole process for them really does take that pressure off and make them less anxious about it. And I love the idea of making an error yourself. And you can do it purposefully to try to get your child to see if they can catch the error.

Lisa Chimento: 00:17:29.170
But the other thing is that if you as an adult make an error, you have the opportunity to now model for your student how to respond to that error in a very non-stressful, non upset way. Because we do have a lot of kids out there that are terrified of making errors. And for the adult to make an error and then go, “Oh, that didn’t work. Let me try this,” and just kind of make it no big deal. And then you’re modeling for your student even how to be able to handle when they make an error.

Gretchen Roe: 00:18:03.025
That in and of itself, I wish I could revisit my kids’ younger years because that perfectionist, the German in me, you must do it right the first time, that’s really hard. And it’s hard to surmount. And perfectionists aren’t born, they’re made. And we need to allow our kids to make those errors. Lisa, you said something so valuable when we got together last week and I’m going to quote you and then I’m going to ask you to explain it. And that was, “Mistake making needs to be normalized.”

Abby Franco: 00:18:38.666
Yeah.

Lisa Chimento: 00:18:39.454
Yeah, it absolutely does. And I think parents need to hear this and students need to hear this. I speak with a lot of parents and students throughout the week if they need a little help in one of their books, if they’re stuck on a problem. And I mentioned to the parent, “Listen, don’t grade the workbook pages, grade the tests,” but the workbook pages are there for learning. This is where learning is happening and making mistakes are part of learning. So we don’t want to discredit a student for making a natural error. Nobody is going to be a master at something because they saw it once on a video.

Abby Franco: 00:19:17.159
Right.

Lisa Chimento: 00:19:17.451
They’re going to need that practice. They’re going to need to put it into practice and work it through several times. And the mistakes actually, you have an opportunity as an adult to reframe those errors as golden opportunities for better learning, for deeper understanding, and better retention. And this is also, I’m going to bring this up because it has to be said, this is also where that universal fight that parents have with their children, particularly teenage boys, about showing your work can maybe resolve itself in a peaceful way. Because this is universal. Right? I mean, every parent I talk to. This is often a fight. And it is a hill worth dying on because it’s going to come back to bite them later if they don’t make a practice of it. But here’s an opportunity that if they have made an error, they can go back and review their work and see if they can find out in that multi-step problem where things went sideways. And if they can identify that error on their own and correct it, they will probably not make that mistake again because it will be ingrained in their brains. And so it’s worthwhile to say, “Listen, you need to show those steps because we have a lot of steps to these problems. We don’t know where the error happened. If you haven’t shown your work, you haven’t learned anything. You’re going to probably make that error again. Let’s not make this a process that has to keep repeating. Let’s learn from this mistake. Make sure you show every step and then you can find out where it happened.”

Gretchen Roe: 00:20:55.888
And Lisa, in the time that we have worked together, you taught me something very valuable. And that is I was that parent that if you made 80%, I was happy, let’s move on. But tell me why I shouldn’t have been happy with that.

Lisa Chimento: 00:21:11.290
Well, 80% isn’t a bad thing. It’s a good thing. But you need to take a look at what happened in that 20%. It might have been careless errors. It might have been a child working too fast and he made a computational error. No big deal. Maybe he missed a step. Maybe he dropped a negative sign. Little things like that can happen. It doesn’t mean that they don’t understand it, but you really do want to look at the errors and take a look at errors over time and see if you’re finding a pattern to those errors. Because if there is a pattern, then that’s an area where you need to pause forward motion temporarily for and go back and do some refresher on the instruction. Because if you continue and there is a gap, you are now building on a gap, and that’s going to create weakness going forward. So take some time now, invest a few of whatever time is needed now to go back in and fill in that gap. Give them strength, give them confidence, equip them for what’s coming afterwards.

Gretchen Roe: 00:22:16.215
If Lisa had been sitting at my school table 20 years ago, it would have been really helpful because this information would have changed a lot of my kids’ mathematical experiences. But she wasn’t there. And so we have a great question that has been asked. And you both are going to laugh when I read this question because this lady was listening in on us last week. So bear with me while I read the question. It says, “I have a 12-year-old who is still in the middle of gamma, lesson 23. How do I make sure she gets far enough to meet the math requirements by graduation?” And I know that when we homeschool, we’re doing that because we don’t want. Whatever situation it was that we saw in a public school that we thought we could provide an equivalent education. So I want to talk about two things. Abby, I want to talk about lesson 23, because I know we had this conversation last week. [laughter] And then, Lisa, I want you to talk about meeting the math requirements by graduation. So Abby?

Abby Franco: 00:23:28.481
Yeah. So with lesson 23, if you’re not familiar, that is about multiple digit multiplication and how to model it using the build right say method. And so what I come across a lot is teachers will say, “I’m stuck. My students don’t know what’s going on here. How do we get past it?” And my first question is always, “Did you make sure that the students saw how to build the single-digit multiplication problems and the two-digit by one-digit?” Basically the previous lessons before 23, because those will provide that foundation. Even if your student showed you that they have mastered their skills of single-digit multiplication or double digit by one digit, then it’s still going to be helpful and I would say crucial for them to see those built conceptually, concretely with the blocks, because that’s going to help provide the understanding they’re going to need as they enter into those multiple digit multiplication problems. And so what that might look like is zip don’t skip. So even if your student placed at that time or you kind of zip through those other ones, we don’t want to just skip them altogether because we think our student knows them. We still would like to zip through them quickly. Even if it’s a concept that you feel your student already knows or has gone through, still go through it, build it with the manipulatives, model it with them. Maybe you don’t go through all the practice pages and all the systematic review pages for that lesson, but you’re still touching on it. You’re still exposing that to them. The more they are exposed to it, the more likely the opportunity will come that it’ll be in their long-term memory. And so that’s what I would recommend. That way when they get to that lesson 23, if they feel stuck, they may just not have that proper foundation from the previous lessons. And then with lessons that come after that, maybe you can implement that zip, don’t skip methodology to make sure that they do get through the rest of the material before they graduate.

Gretchen Roe: 00:25:40.114
Right. Lisa. I mean, this is the most common scenario that we hear from parents. I have a 12-year-old who’s in the middle of Gamma and I’m looking down the road and I’m freaking out. What do I do? And I know that you have encouragement for this mom.

Lisa Chimento: 00:25:56.102
Yeah, and I think a lot of it is because the parents feel intimidated if they are not confident working with the manipulatives themselves. And I’m really thankful for the parents who have called in and said, “I don’t understand this. Can you walk me through it?” And when we do, and so I’ll refer to the video, but I’ll also have them open up that instruction manual. And very often they haven’t yet done that because in those lower levels, I think a lot of parents feel like I don’t really need the instruction manual. I just look at the solutions, but we can get this from the videos. But the instruction manuals are laid out in a very organized, systematic way. And they show you diagrams of how the blocks should be set up for setting up these problems. And so they will be helpful. So I have them open up the instruction manual and then I say, “Okay, now get out these blocks,” and I tell them the specific blocks and where to put them. And then I hear, “Oh,” and then it becomes clear and they make sense. So that’s the thing to remember. If you don’t feel confident, please give us a call because we will walk you through it. But don’t be afraid to attempt that with your child because you feel intimidated. Like I said, it’s okay for you to not know. You can say to your student, “Listen, we’re learning this together. This is okay. We’re not going anywhere until we both feel good about it.”

Lisa Chimento: 00:27:16.059
But the other thing that I want to mention with regard to that high school requirements and catching up or whatever terminology you want to use, I love what Abby just said about zip not skip because it does reinforce what they do know and it brings connection to them of what’s coming afterwards. And that connection is paramount really to future understanding. The thing to remember is that with every single lesson in every single level of Math-U-See, mastery is always the goal. It’s not stretching out a curriculum to last a school year or filling out a quota of workbook pages. And I know a lot of parents use the program like that, but that’s not how it’s designed And, particularly, if you have a child who’s had to step back to fill in gaps, keep this in mind. Let them show you mastery as you go. And when they do, move on. They don’t need to be sitting there doing the every single page if they’ve got it. Move on.

Gretchen Roe: 00:28:18.767
Well, the other thing I think that’s important to address here is sometimes we look at our child and we think, “You should be, and you can fill in that blank.” And that should is such– is the dangerous word in that sentence because your child is exactly where they are. And I have if I had a quarter for every conversation I’ve had with a mom who’s either been in gamma 23 or somewhere in delta, going, “Oh my goodness! We’re never going to get out of this.” The truth of the matter is, you’re looking at two things here. You’re looking at your child understanding mathematically, and you’re looking at their developmental capacity catching up there. And often what we find is if we’ll spend the time, and we’ll keep our anxiety out of the equation, our kids will begin to blossom. And I have talked to countless families over the years where I’ve had this conversation, and they’ve been pulling their hair out at a conference. And they come back the next year, and they’ll say, “We did two and a half levels of Math-U-See. And I cannot believe that that actually happened.” And what happened was you kept the anxiety away from your child, and you just said, “I understand you are where you are, and we’ll get as far as we need to go.” And then your child was able to mature into the understanding of being able to do that.

Gretchen Roe: 00:29:46.201
Now, we’ve answered this lady’s question. But if you all are sitting in our audience or listening to us on the podcast or watching this as a recorded webinar, and you’re like, “Yeah, but I’m not there,” that’s when picking up the phone, calling us, joining us on live chat and having a deeper conversation because everyone who answers the phone at Demme Learning is adept at asking more questions. And there may be some things in that process that you haven’t considered, and that’s where the value of a conversation becomes paramount. So I think that’s really important. Abby, I want to go back.

Abby Franco: 00:30:23.984
Yeah.

Gretchen Roe: 00:30:24.491
You said something about use the manipulatives on the word problems. And I know that there’s a bunch of parents in the audience going, “Why?” Because I hate word problems.” The truth of the matter is, and I was that parent, my kids would say, “Mom, I need your help with a word problem, and I would go, “Oh, I hate word problems.” Model that in front of them, which is absolutely not the way we would like you to behave. But can you talk about why Math-U-See’s word problems are a little bit different and to your advantage?

Abby Franco: 00:30:55.614
Yes. So you have to keep in mind that math, whether it’s just a math equation or a word problem, it is abstract. Point blank math is abstract. The blocks, the intention of the manipulatives is to take it from the abstract to the concrete. And so even in those word problems, I feel like they’re even more abstract, especially if you have students who struggle with any sort of reading or anything like that. That’s a whole other level of anxiety they might carry. And so taking the manipulatives and using them to represent what they know, what’s important in the word problem, will help them organize the information in the word problem that they’re going to need. A lot of times that’s the issue is that they can’t collect the important information from the word problem to know what even– where to even begin. But if you can use the blocks to kind of, “Okay, I’m using this to represent this number in this word problem. Now I can move on.” Kind of set that one aside. I’ve modeled it. Now I can move on to the next piece of information. Rather than thinking like, “Okay, I’m in my mind. I need that three. I need that seven. I need the word more. I need the word less.” They’re getting to organize it as they go modeling it with the blocks. And so you’re breaking it down into that step of the building. Then once they have it built, they can write what’s appropriate. They can write whatever mathematical symbols are needed to go with it. And then you can go into the talking about it, answering the word problem that’s asked. So it just gives it a more of a step-by-step approach rather than a very daunting, abstract situation that they’re having to face.

Gretchen Roe: 00:32:41.256
Right. And very often the reason word we get off on the wrong foot with word problems is when you mix math and words, we start to freak out and your children will start grabbing the words before they know what’s really being asked of them. So the really important thing that you can do as a parent is come alongside them and ask them to read that word problem and have a conversation. “Okay, what are they asking us to do here?” “I don’t know.” “I don’t know either. Let’s read this again and see if we can figure that out.” That’s where your value as the parental instructor or the classroom teacher is paramount because you’re there in a collaborative capacity for them. And it’s huge. And it really is huge. Lisa, you said something about working longer is not necessarily effective. And I wish I’d known– I wish I’d known this lesson 30-plus years ago. But anyway, could you elaborate, please?

Lisa Chimento: 00:33:39.202
Yeah, it’s hard to sometimes hear parents have been struggling with their children and they call up finally frustrated and they’ve been working at it for over an hour. And at that point, I almost want to just say, “Okay, then I’ll call you back tomorrow and we’ll talk about this because you’ve already worked too long.” There’s a general rule of thumb here that we offer parents, and that is that you can add two or three minutes to your child’s age. And that’s really the optimal amount of time that they have to understand and retain what they’re learning, especially for new material. And so when you go past that, you’ve crossed a neurological threshold for them. And even if you have a very willing and compliant child, who’s willing to sit and continue to work, to be able to take that and take it into the next day and remember it is going to be very difficult because it’s just too much. Their brain just can’t hold it all. So I like to say to parents small bites over more sittings is more effective for both understanding and retention than trying to gobble up a lot of material in a single sitting. They’ve already become mentally fatigued. They’re going to make more errors now, and they’re not going to be able to remember what you’re trying to get them to learn. So put it away. And then anxiety, of course, always enters that situation when it’s gone on too long. And then learning just has completely stopped. So put it away, go do something else, bring that anxiety level down, and save it for tomorrow. The other thing is you’re giving their brain an opportunity to sort and organize that information better. And when you come back the next day and look at it, they’re coming back with something they didn’t have the day before behind them to help bring better understanding.

Gretchen Roe: 00:35:29.230
Abby, you said something that I thought was really fascinating when we talked last week, and that was about the value of the manipulatives with kids with limited verbal skills. So can you elaborate on that a little bit? Because I know statistically there are parents here who are joining us, who are struggling with that. And I know that there are classroom teachers who have that kind of challenge as well.

Abby Franco: 00:35:53.685
Absolutely. So you’ve heard us mention several times this build-right-say method. And that method is the way we encourage concepts to be taught to the students, as well as a way for them to demonstrate mastery back to us. So that’s the building with the manipulatives, that’s the writing the numerical symbols, and then saying what they’re doing, and then saying their answer at the end. And so you may be working with a student who is limited verbally, or maybe they’re limited on how they can write. And so you can take the steps of the build-right-say method and use them in a way that is applicable to your student to allow them to show mastery again at where they’re at. Mastery, by and large, is performing where they are at. And so if that means they are nonverbal and they can only build and they can only write, then that is their way of demonstrating mastery to you. If they cannot write, then maybe they can just tell you what to do. And they can demonstrate by describing to you, they’re saying maybe you can build for them, whatever it may be. And that’s a great way to use that build-right-say method still in the context of what they’re able to do.

Gretchen Roe: 00:37:10.041
And I think that that’s something that’s really a valuable idea because the idea of mastery is not limited to mathematics. And if you can learn how to explain what you’re doing, you can translate that across every academic discipline. And that is the definition of lifelong learning. We have another question here today that I think is really helpful. And I think I’m going to let each of you answer this, because Abby, I want you to answer this as if a classroom instructor were asking. Allow your younger student to just keep going level by level if they are well beyond their expected grade level, or do you slow them down a bit? And the irony of it is Abby and I talked about this a little bit yesterday afternoon because we have an interview on our website with a young lady who finished Algebra 1 in the first time. I don’t think she was quite eight yet. It’s worth finding the interview. In fact, I’ll include it in the show notes. Her name is Grey Carson. But can you talk about that a little bit, Abby?

Abby Franco: 00:38:25.985
Yeah, so from a teacher standpoint, I would say– or no matter what you’re doing, I would never want to slow down a student from where they’re performing. You’d want to, of course, make sure you’re still following that zip, don’t skip. You don’t want to just fly through material that you think they’re already good to go with because, I think Lisa made a great point earlier, it does build. So if they don’t have the proper foundation of seeing the previous things, they may start to struggle at some point, even if they seem to be flying. But I would say if you’re implementing the curriculum with fidelity and your student is showing mastery at maybe a quicker pace than what you expected or what you’ve seen in the past, then I would go with that personally. I would allow them just to make sure they’re still showing that mastery, whether it be through the teach back, whether it be through modeling with any– you could model with markers. I have a set of markers that I use to demonstrate the block colors. So that’s a way that they could show you. As long as they’re showing that mastery with each concept, I think you should feel free to continue to let them continue with the levels that they’re going through.

Gretchen Roe: 00:39:40.405
Lisa, do you have anything to add?

Lisa Chimento: 00:39:42.565
Yeah, I totally agree with that. And for parents who are homeschooling, you have this unique opportunity to really become a student of your children. You know them better than anyone else on earth. So be watchful as long as emotionally and maturity-wise, they are able to do that work without getting totally overwhelmed or stressed, then let them go because if you don’t, then they’re going to be bored, and bored kids is not a good idea. So yeah, let them go. Let them move at their pace. Make sure that there isn’t an emotional or anxiety issue creeping in here.

Lisa Chimento: 00:40:22.055
And even for parents, I’m going to say be ready because you might have a child who is flying through certain levels and then hits a level where things slow down and you aren’t expecting that. Be ready. They might have to slow down then and that’s okay. Both of you might need to get used to that idea, and that’s okay because things will become more complex. The steps will get longer. Things will become more abstract. It might take a little longer than it has previously, so just be watchful.

Gretchen Roe: 00:40:53.827
And I think that that is really good advice from both these ladies. We have answered so many of the questions that were asked of us, but I have one that I want to ask of you all. Does repetition equate with mastery? [laughter] I’ll let you guys duke it out for who gets to answer that one. Abby’s laughing, so I’ll let Abby answer.

Abby Franco: 00:41:19.950
Lisa can go for it. She unmuted first, so I’ll let her– [laughter] hear her answer and then add anything else.

Lisa Chimento: 00:41:25.741
So I think this really kind of is the dividing line between what we call a spiral approach and– a spiral approach and a mastery approach because a spiral– I think the thing that most people put forward for spiral is that, oh, it does a lot of review. Here’s the thing to keep in mind that review literally means seeing it again, and seeing it again is only effective if they learned it the first time around because if they’re only seeing it again, it’s not reinforcing learned material. And the cumulative review, if you will, that Math-U-See incorporates is actually reinforcing learned material. If they mastered it as they went along, then they have that opportunity to reinforce it, and in that case, the review, if you will, is helping to imprint it into long-term memory even better. So that is effective review, to see something multiple times one year and then again the next year and then the next year, and if the child still doesn’t understand it, it’s really not benefiting them.

Gretchen Roe: 00:42:35.189
Right. And the further you go, the more difficult it is to assess where the holes are.

Lisa Chimento: 00:42:39.888
Exactly. And you’ve now begun building higher-level content that depends on understanding of that earlier content, so you’ve created a gap, and that’s what we don’t want to see happen.

Gretchen Roe: 00:42:53.986
Right. So Abby, as a high school math teacher, what were some of the things you wish the younger students had known before they were high schoolers? I’m looking for you to encourage the parents who are, as my German father said, the mitten drinnen of sitting there with their kids with addition and multiplication and division and those kinds of things. What are the things you wish kids had spent enough time on so that they really understood by the time they got to high school?

Abby Franco: 00:43:25.447
Well, you just said them all. It was by and large, my students were lacking their basic number reasoning or basic number understanding with those math facts, so they lacked that single-digit edition math facts. A lot of them had to rely on a calculator to know what the answer was a lot of times, especially multiplication, those multiplication facts, as well as division. That was always a difficult one. So I would say spend the time to achieve mastery in those, even if you feel like you’re spending a little bit longer, even if you have multiple kids, if one kid is slower than the other that’s okay. You’re allowing them to show their level of mastery. And if that takes a little bit longer, I would say take the time because once they get into algebra, geometry, where they’re now incorporating letters, and then they’re not only needing to learn these new– factoring of polynomials, that’s something we also show with the blocks, which is cool. But if they don’t have those skills of addition, subtraction, multiplication, and division, they’re going to struggle. And so that’s one thing I always wish– that and comparing numbers was another thing that– comparing values of numbers, especially those decimal values when you get into zeta, the values of fractions, comparing those, that was something that they lacked as well, which just makes it difficult the higher that you get. So spending the time on things that seem like they should be quick really will benefit your student as they get older.

Gretchen Roe: 00:45:03.251
Right. One of the things I want you to think about is if you’ve ever seen those little, wooden race cars that have a rubber band in it and you know if you wind the rubber band up, the car will go further, think of the time that you’re investing in those computational facts as winding that rubber band because it makes a difference. Lisa, I want you to talk about another place where we know it makes a difference because we have talked countless parents off the ledge, and that is fractions. And what happens when we’ve used these things so very effectively? And then we get to fractions. Why do the wheels sometimes blow off the wagon?

Lisa Chimento: 00:45:47.689
Yeah, fractions is that first place where math starts getting quite abstract. We’re dealing with numbers that are less than one, so you can’t see them. And even programs that do use manipulatives tend to not have any resource for fractions. But the fraction overlays that are used in Math-U-See are powerful tools because we want students to be able to see concretely what they’re doing, why they’re doing it. And I have this conversation with folks on social media all the time, and they’re like, “My kids don’t need the manipulatives because they can do mental math.” The manipulatives are there, even for kids who can do mental math, because we don’t want them to just learn the processes, the procedures, for solving on paper. We want them to understand the why behind it, and the manipulatives show them the why. It connects all the different aspects of fractions. It connects fractions to division. And it connects fractions to decimals that come afterwards. So those manipulatives are powerful tools. And what we have found and what research is bearing out is that when students gain a solid understanding of fractions, they are more successful in algebra later. And when kids are assessed in algebra who are struggling, almost 100% of the time, the area that is causing the problem is fractions. So take the time in fractions. And even if your children are reluctant or resistant to use the manipulatives, let them know, “These are going to do something in your brain that just solving on paper isn’t going to do.” And you don’t have to make them use them for every single problem but have them teach back at least one problem a day using those manipulatives with their fractions. And it’s going to make such a big difference. They will learn more efficient ways. They’ll learn the formulas. They’ll learn the tips and tricks. But if they forget the tips and tricks and know what they’re doing, they’ll still be able to make it work.

Gretchen Roe: 00:47:51.388
Yes. Abby, do you have something to add to that?

Abby Franco: 00:47:53.750
Yeah, I was going to say I actually recently did a training for some teachers. And when I did the training on the fraction portion using the fraction overlays, my most common response whenever I do that training, not just that one is, “Wow, I wish I had had this when I was learning fractions,” from teachers, from professionals who have gone through school to be an educator. And so I would just want to encourage you, parents, if you are maybe apprehensive about using the fraction overlays just because of maybe how you feel about fractions. I did have a teacher who had been through the fraction training before. And it wasn’t till her second time hearing it to where she was like, “Wow, it is really clicking.” So take the time to allow yourself to learn it as well and to allow yourself to get used to using those fraction overlays. There are a lot of correlations to the integer block kit, which make it easier to use. So keep that in mind as well. But I will say just give yourself some grace, give yourself some time to– because you may have never learned fractions this way. You may have never learned concepts with the manipulatives before in this way. And so if that’s something you are nervous about, take the time yourself, dive into the instruction manual, dive into the videos to allow yourself to learn how to use those manipulatives to help your students, especially with those fractions because I feel like those are extremely, extremely powerful for concretely modeling fractions for your students.

Gretchen Roe: 00:49:30.167
I want you all as parents to think about this. Up to the fraction level, when your children have multiplied something– when they’ve multiplied two numbers together, they’ve gotten a bigger something. And when you multiply two fractions together, you got a smaller something. And it’s antithetical to everything you’ve taught them to this point in time. So if they can see that, then they can understand it. We have a great question here, ladies. And I’m going to address this to both of you because I think you’ll have different answers. What if your kids refused to use the blocks? And my answer to that was, “You don’t have to use the blocks on the review pages, but I anticipate that you will use the manipulatives to teach to me that you understand. And as soon as you teach it to me, you’re done. You don’t have to use them anymore.” But that was the purpose of the manipulatives in our household. Abby, what do you say to that? Because I’m sure that you have classroom teachers who are like, “My kids don’t want to touch these things.”

Abby Franco: 00:50:36.997
Absolutely. So I would say the best way is to model it. Model it first. Maybe they’re scared to use them. Maybe they’re embarrassed if they don’t know what to do. So I would say first try modeling it for them and see if that changes their attitude. If it doesn’t, I would say make it a point system. Make some sort of game out of it. “Okay, if you can show me this one with the manipulatives, we can do five minutes of something you like to do, whatever it may be.” It can be something that seems silly to us, but it may mean a lot to them and help them feel like, “Oh, this isn’t a chore that I’m forced to be doing. This is something that–” And they may realize that eventually it will help them. They may not, [laughter] but that’s okay. But I would just encourage them by first showing them that you can use them, how to use them, and then allowing them to get some sort of buy-in to use them.

Gretchen Roe: 00:51:35.491
Incentive.

Abby Franco: 00:51:36.479
Incentive. Yes.

Lisa Chimento: 00:51:36.564
Sure. Sure.

Gretchen Roe: 00:51:38.340
Lisa?

Lisa Chimento: 00:51:39.660
Oh, I like those ideas. And I also want to just remind everybody of something that Abby said earlier on when we were talking about the gamma lesson on multi-digit multiplication. And her question to teachers and parents of, were you using the manipulatives for the preceding lessons? Because a lot of families who their kids are just flying through and they don’t really touch the blocks in those earlier lessons of gamma, then they get to the multi-digit multiplication and they’re stuck. So there is a method to this. There is a reason for using them even for concepts that seem very simple and we don’t need them for those things.

Lisa Chimento: 00:52:17.614
Well, you might need them so that you understand how to use them later in more difficult concepts. And so use them at least once. And you can say to your student, listen, you don’t have to use them for all of the problems, but I am going to ask you to be able to teach it back to me. So get some practice using it beforehand so that you can demonstrate back to me. And that will give me the signal that it’s time to move on to the next lesson. If I don’t get that teach back from you with the manipulatives, then we can’t move on.

Lisa Chimento: 00:52:49.979
So I mean, that’s my way, but I think maybe Abby’s ways is a little more– is going to be more appealing to the student.

Gretchen Roe: 00:52:58.092
And see, my way was, I spent the money on the manipulatives. You’re going to use them with the program. But I will say this, it wasn’t until I saw Math-U-See’s methodology of multiple-digit multiplication that I understood why you put that zero in the second line of multiplication. I had a third grade teacher when I said, why do you want me to put a zero here? Her reply was because I said so.

Abby Franco: 00:53:27.469
Yes.

Gretchen Roe: 00:53:28.372
And I forevermore thought, well, because Mrs. Strunk said so, I have to put a zero there. But honestly, I was probably 38 years old when I found my way to Mat-U-See and realized that there was a reason for that zero being there. So if you are like me, well, this is the way I did it. My kids can just learn the same way. I want you to suspend that thinking for perhaps a hot minute and think there might be an easier way for you to help your students be mathematically successful. And let me explain how that comes back to bless you later.

Gretchen Roe: 00:54:09.541
I was an algebra two and I’m through kind of gal. I never wanted to go beyond algebra two. And I have two kids who went all the way through Steve’s upper level, all the way through calculus, did calculus in college. I’ve got one kid who does it for fun. I think he’s crazy, but he looks like me. So I know I gave birth to him. And when my youngest son was a senior in high school, he was working on a very complex calculus problem, five, six pages. Obviously not something one is going to get through without showing one’s work. And he came stomping into my office and plunked the papers down on my desk and said, I need your help with this calculus problem.

Gretchen Roe: 00:54:53.803
And prayer is real [laughter] because I started praying. I thought, I have no idea what I’m going to say to this kid. And I said, all right, show me what you’re doing. So he said, all right, here’s what I have to do. This is– and he’s explaining step by step. And all of a sudden he goes, “Oh, oh, I forgot to do–” whatever it was. I don’t even remember. But he said, thanks, mom. I appreciate your help. Ladies, I did absolutely zero to help this kid. I just sat and listened. But he had learned the process of build right, say he was speaking himself through the problem. And that’s how he found his own error. And that is invaluable. He is now an electrician’s apprentice and he came home last night from work and he’s laughing and he goes, I used build right say at work today. And I thought, how did that happen? And he said, “Well, I’ve been taught this process”. And he said, “I was stepping myself through the process and the end game wasn’t working. So I decided I would talk my way through the process he said, “I realized I had forgotten– there were five steps and I had forgotten step number four.” And because he had talked his way through the process, he was able to do that. So what we want to do is help you understand it’s not just for now, it’s for always. You’re creating a lifelong learner. Lisa, what were you going to say about that?

Lisa Chimento: 00:56:24.311
No, I absolutely agree. And I think a lot of parents, when they see the manipulatives, they give their kids the manipulatives and they let them build and build and build and build. And they’re forgetting that there are three parts to build, right, say. Writing that material down in their own hand is hugely effective, especially for long-term retention. There’s some kind of magical connection between you writing things and your brain storing it in long-term memory. So don’t leave that off. And the verbalizing, like you just explained, is so important. So especially for those kids who are reluctant to using the blocks, let them know this is one of three things that you’re not just building. We need to build it and write it and say it. And when you can do that for me, well, they don’t even realize how much it’s benefited them, but it’s doing double duty because it’s also showing you that they have indeed mastered the material.

Gretchen Roe: 00:57:20.722
And there’s a percentage of you who have children who are allergic to pencils. They don’t want to use them in any way, shape, or form. And that doesn’t mean you can’t engage in the right process. You can sit with your student and say, you tell me what to write and I will be your scribe. So it doesn’t mean that just because your child doesn’t want to put a pencil on a piece of paper, they get a pass on doing that part of the process. Ladies, this time has gone so quickly. I cannot believe it. The information you all have shared has encouraged me. I hope it’s encouraged the parents who have asked questions online. What would you say in closing to our families? Abby, I’ll let you go first.

Abby Franco: 00:58:06.106
Yeah, I would just say keep going. You have the resources, just get into them, use them to your advantage and use those manipulatives. Those are important. Those are a big part of it. They’ll help them see the math. That’s why it’s called Math-U-See so that you can see it and keep going with that. But just encourage you, take the time for yourself to get into it if you’re still a little hesitant, but your students will benefit from it in the long run.

Gretchen Roe: 00:58:39.115
Absolutely. Lisa?

Lisa Chimento: 00:58:41.296
Yeah, I just want to say, if you are struggling with any part of this, if you have questions along the way, we are here to support you. We’re not just here to provide you with materials. We have these materials for you because we know them and we know how they will benefit your student. And we believe in them. And we are here to support you. Whether you are a classroom teacher or a parent whose kids are in school, or a parent who is homeschooling, or a grandparent who is homeschooling, a tutor, whoever you are, please give us a call. We’ve got toll-free numbers that are available on the website, and we are here to help you in any way we can.

Gretchen Roe: 00:59:20.778
Absolutely. One of the things I think is beneficial is to recognize that you didn’t get here overnight and you’re not going to get out of here overnight. So anticipate that it will take a little bit of time. We have a good question here, which is, do you have a fraction overlay training for parents? And indeed, we do. It’s called the epsilon level. And it’s the videos and the instruction manual together. And here’s something that sometimes parents miss. Because you didn’t really need the instructional materials in alpha and maybe beta. You think maybe you don’t need to crack the books except for the answers in gamma and beyond. But as the math becomes more complex, Steve can’t impart everything that you need to know in those videos. And that’s why being able to use the textbook and the videos together gives you the complete instruction. And I think that that is really important. I want to thank all of you for joining us today. Thank you all for being here. Thank you all for your positive comments. I will share them with the team when we conclude. And this has been a joyful experience.

Gretchen Roe: 01:00:38.929
I think you see why I enjoy working so much with these ladies, because, man, they are something special. This is Gretchen Roe for The Demme Learning Show. I want to thank you all again for joining us. You can access the show notes and find a recording at demmelearning.com/show or on our YouTube channel. Be sure to rate, review, follow, or subscribe wherever you may be hearing this, especially if you enjoyed it. Have a joyful afternoon, everyone. And we’ll look forward to joining you over a cup of coffee in your living room sometime soon. Take care.

Lisa Chimento: 01:01:11.460
Bye.

Abby Franco: 01:01:12.347
Bye, everyone.

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