[music]

Lisa Chimento: 00:00:00.000
So when an error does occur, here’s the situation. Are you just going to mark it wrong, give them a percentage, and move on? Well, what happened with the percentage that they got incorrect? They’re taking that wrong thinking with them to the next lesson. And now you’re just piling more information on top. Instead of doing that, let’s stop forward motion momentarily, and let’s take a look at that error and ask the student to go back to the problem they got wrong without giving them the correct answer and see if they can find the error themselves. [music]

Gretchen Roe: 00:00:39.182
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. Hi, everyone. My name is Gretchen Roe, and it’s my very great pleasure to welcome you today to this conversation about creating the skill sets for high school math success. We entertain this conversation so often in one-on-one conversations with families over the phone through live chat, through email exchanges at conferences, that we thought that there was merit in having an intentional conversation with you about what your student needs in order to be mathematically successful before they step into their high school years. And I have to be honest with you, what Lisa and I are going to talk about today are things that I did not think about with my two eldest children. It wasn’t until I found my way to Math-U-See that I realized there was a structure, an intention, to the way that mathematics is created. Being a hesitant math parent did not help me in that process. So I’m grateful for Math-U-See helping guide me toward that end. Today, I have the privilege of being joined by my wonderful colleague, Lisa Chimento. And I’m going to let Lisa introduce herself, and then we’ll get started. Lisa?

Lisa Chimento: 00:02:09.129
Hi, thanks, Gretchen. My name is Lisa Chimento. I am a Customer Success Consultant and Placement Specialist here at Demme Learning for about almost six years now, full time. Before then, I worked at homeschool conventions. And my husband and I have four children that we homeschooled all the way through graduation. They are now adults and out of the house. And it is a pleasure to be here today. I think that this is such an important topic, and I’m really excited to be able to talk with Gretchen about these things.

Gretchen Roe: 00:02:39.818
Absolutely. And my husband and I have six children. And as Lisa says, five are grown and flown. And the caboose in our train graduates high school in June. And so life takes yet another turn in our family. And I have been a placement consultant at Demme Learning for eight years. And then the last year, I have been our community relations coordinator. So it’s my very great pleasure to facilitate this conversation today because boy, do we have it a bunch of times. And toward that end, when you receive the show notes for this event, we’re going to include a video that Lisa and I did to answer the questions about what do you do when fractions are a struggle? Because fractions are really the gateway to higher mathematical understanding. And without having a parental’s perspective of why this is important, sometimes we miss the importance of understanding fractions. So we’re going to include that little video as part of the show notes for you all today. So look for that. But today, Lisa, in opening our conversation, what is the question question that parents ask you so often about why math when it gets to fractions and decimals and pre-algebra is different? What do you hear from parents?

Lisa Chimento: 00:04:14.980
Yeah. Sometimes we hear from them, then. Sometimes we don’t hear from them until a little later on. And then, unfortunately, things have already started to take a downward turn. And so they’re concerned about that. So we have to think about something. And Gretchen, you and I just were talking about this before we started, that when student starts work in fractions, they are no longer just working computational work. Before then, they’re dealing with the four operations, addition, subtraction, multiplication, division. And once they get on that roll, it feels like, “Okay. Good. Now we’re kind of coasting and we’re doing an easy ride here.” [laughter] But then when you start fractions, it’s another ball game. You are having to put all of those operations into play in a very different way. You’re working with numbers that are often less than one. They can’t see them. So you’re not dealing with things that you can see, touch, feel concretely generally. And it’s more abstract. You’re getting into some higher-level thinking. And so I think the thing to mention, first of all, and we’re going to go back through some of this, of course, but if you are at this place where you are teaching your children about fractions, this is not the place to let them go and work independently. This is the place for you to be beside them. Make sure that they are understanding what they are doing. There is a difference between having a good understanding of those underlying concepts versus just being able to be taught a tip or a trick to solve this equation on paper. That’s not going to stick with them. They will at some point forget the tips and tricks. And if you’re not there to remind them of what they are, then they won’t know what to do with those problems. So working with them through the fractions time will really pay off going forward. So make sure asking questions, asking them, why are you doing what you’re doing? Ask them to narrate a problem through to you and explain the steps as they go. And not just, “Well, somebody told me to flip the second fraction and multiply.” That’s not the reason why that’s the tip or trick. So that’s just an intro into some of the importance of fractions.

Gretchen Roe: 00:06:30.897
Right. And one of the things that we want to make sure that we are doing as parents is setting our kids up for success. And we talked about this actually last week in our webinar about, do you have a heart for math? Because sometimes as parents, when kids reach the age of 10, 11, 12, we want to foster that independence. So we leave them to their own devices a little bit. And this is the point in time where you need to be intentional about checking in with your student more frequently than perhaps you did when they were doing multiplication or division because you don’t want them to practice something in the wrong context and then have to undo that practice later. And Lisa, I think I said last week, I’m the parent who found so many things– with six kids, there’s only so much of you to go around. So it was easy for me to say, we’ll just check your work on Friday, and how discouraging that can be if you have worked all week and your work has been inaccurate. So you have a good suggestion, though, that you give to parents about checking in the beginning when they begin the process so that they’re comfortable and then circling back around the next day to make sure that they haven’t forgotten can you explain that in a little depth?

Lisa Chimento: 00:08:02.792
Yeah. And I think this also goes to the idea of how parents have been using the materials up to that point, and I see this a lot on social media. People will report, “Okay, on Monday, we do this. On Tuesday, we do that.” But remember, the goal here is mastery, not following a preset schedule. So the idea is if your student watches a new video lesson and you read the written lesson instruction and he goes, “Huh?” that’s not the time to go to the A page and start work in the workbook. He doesn’t know what he’s doing. You’d be wasting the page. So a better chance is put the work aside for the day. It didn’t click yet. Let his brain organize, sort that information, and then come back the next day and look at it with new eyes. He will be looking at it from a different point of view than he was the day before because now something else has been presented to him and his brain has received it. Let him go back over the video instruction, the written lesson instruction, and then talk it through. Work through those several sample problems that are available to you, explaining the why as you go through, and then let him try one. And then when you get to the workbook, the first workbook page, maybe have the parent work the first problem, narrating the steps as you go along, and then ask your student to do one doing the same thing. The ability to verbalize what they’re doing helps them to understand it better, and it lets you know whether or not they’re quite getting it. Because if they aren’t, it will become apparent to you immediately, and you’ll be able to go, “Okay, this was right. But wait a minute now, that’s not what he said there, remember? We’ve got to do this instead.” And that way you can do a correction right from the get-go and then the student won’t be practicing the wrong way.

Gretchen Roe: 00:09:56.703
Correct. And one of the things I think that’s very important to emphasize here is as parents, I know that I would have thought that the verbalization of the process became less important. And actually, what we know is it becomes more important, so don’t discount that. And you will have, particularly– and I know it sounds like we’re dissing boys here, but about the time fractions start, if you look at the statistics, girls are ahead mathematically than boys as far as the statistical process of understanding what they’re doing. And boys often are resistant to the language surrounding math and verbalizing it. Lisa, you also had talked about– I know we were very intentional in the way we designed the new Algebra 1 PSM mathematics program for Math-U-See in creating a mathematical notebook. But you say that starting at about the time you’re stepping into this more expanded thinking mathematically is a good time to do that. Will you talk a little bit about that?

Lisa Chimento: 00:11:14.819
Yeah. I’ve never thought of this. When I was homeschooling my kids, this just was not on my radar. But it’s – oh, God bless you – it’s become apparent to me, and I’m mentioning it more and more to parents and students as I’m supporting their high school work. And taking notes is so powerful in terms of long-term retention and better understanding. It’s a different way for your brain to receive information than just reading it. You are now active in that. Your hands are involved. Material is coming into your brain through different neural pathways, and there’s just something about writing that helps materials stick. And having the student do the writing, not mom. And I know that’s hard for some moms. You’re organized, you want things done just so. But having your student take those notes, whether they keep them in a notebook or on index cards, whatever, take those notes. The instruction manual, the way that it’s laid out in a very organized, systematic way, it has italicized and bold-faced words that give you a clue that these are important terms to learn because mathematical terminology is important as well. There is a glossary in the back of both the student workbook and the instruction manual that you can utilize to get proper definitions but– even just writing out formulas and some things. Now, if your student is doing some work in their workbook and you go and check it at the end of the day and you find out that an error occurred, that’s a perfect opportunity for that student to take out their notebook and write down what they’re learning as they’re correcting their own mistake. Because that’s something now that they need to commit to memory. They need to be able to remember, “Oh, the next time I encounter this situation, I have to remember to do it this way.” And so writing that note out is going to be meaningful to them and it will stick with them better.

Gretchen Roe: 00:13:14.915
Lisa, I remember– I’m having a memory of having a conversation with you about what you did with your own children about– I think it was long division where you had them right across the top of the page on every page that they did so that they would get an ingrained habit of being able to recall that. Can you talk a little bit about that?

Lisa Chimento: 00:13:38.044
Yeah, there were a couple of times through our journey that there were things that they were forgetting, things that were multi-step formulas. And so I would say to them, “Okay, I’m going to give this to you, and I want you to write it. And you can write it at the top of your page every morning before you start your work. And you’re permitted to refer to it.” And by the end of three weeks, they didn’t need to write it anymore because it was in them. For long division, we just created a series of icons to remember the steps for long division. First, you divide, then you multiply, then you subtract, you bring down the next number, go back up to the next one and start again. So we created little icons to do that. When we got to algebra one, for instance, they had to learn the slope intercept form of a line. And it was used throughout multiple lessons. And it became more and more important as they went on. And I realized after a few lessons, they just really didn’t have it. So I had them write that formula at the top of the page. And again, after about three weeks, they had it. They didn’t need to even look and refer to it anymore. So that kind of a thing really helps ingrain important information for them because they’re not only writing it, they’re not only seeing it, but they’re using it every day.

Gretchen Roe: 00:14:55.945
Right. And I think as parents, we need to remember that we’re seeking here to create mathematical independence. And not every child gets there on the same schedule. So here’s where it’s really important not to compare with what your friend’s kids are doing or what your sister-in-law’s kids are doing, however that is, your child is on a continuum that is of their own making. And we want to encourage you, don’t hurry the process. Don’t feel as though, “Oh my goodness, we should be here, and we’re only here.” And there is a valuable amount of training between here and there that needs to occur. And expediting it does not necessarily mean it’s going to be a more successful experience. So I think that’s an important thing for parents to take away. And a lot of our parents who join us use Math-U-See some parents do not, but in this context, I want to bring this up as far as Math-U-See. is concerned because I want you to get what you paid for. And Lisa, I want you to talk about why just using the videos from about the beginning of fractions forward is not going to serve you to accomplish the instruction the way you need it to be.

Lisa Chimento: 00:16:28.205
Right, because we talked about this point where, once they hit the fractions level, they’re no longer just doing computation. There’s a lot more involved in conceptual understanding. And so the video lessons are powerful. In them, Steve Demme is demonstrating. And whenever you can demonstrate something concretely for a child, it always helps them to understand better before they have to apply that thing abstractly. So that demonstration is really great, but he’s speaking in a very off-the-cuff way. He’s addressing students in front of him. When you use the instruction manual alongside it, you are getting the why behind the way it all works, and you’re also seeing it laid out in a very organized, systematic way. In addition, there is sometimes extra information in the instruction manual that was not discussed in the video lesson. So it’s really important that parents are using both resources; they are designed to work together. And so you want to make sure that you’re making the most of that because you’ll be more successful.

Gretchen Roe: 00:17:36.417
And with regard to that success and fostering that independence, I think it’s important for us as parents to be able to frame, “This is what I want you to do. And if you have questions, if you’re hesitant, I’d rather you ask me before you do it than have to unpack what you didn’t do correctly.” Lisa, you have talked about that a little bit, how that worked in your household. Can you elaborate?

Lisa Chimento: 00:18:11.290
Yeah. Yeah, and this was something that I remembered from my college days, that nobody was coming after me to ask me how I was doing. [laughter] Nobody was going to– if I wasn’t doing well on my work, nobody was coming over to me. No instructor was coming to me and saying, “How can we help? You seem to be struggling with something.” And it made me realize they needed to learn early on, while they were still at home and with me, that they needed to grow in responsibility for their education. It wasn’t going to happen overnight, but I wanted to encourage them to be able to say, “I don’t understand this,” so that if I have left them to do some independent work and they hit a roadblock, that they didn’t just pass it by and let it go and not mention it to me, but that they would come to me and say, “I’m not getting this,” and then I would know that they’re not ready to work on that independently yet. We’ll get there, but they still need some help with this, so that was important for me to do. And I let them know you’re going to need to be the one who initiates the conversation if you are struggling, if you have questions. If you want to know something that you don’t know now, it’s okay for you to ask.

Gretchen Roe: 00:19:25.577
And I think that’s a good thing to model for our kids, not just in mathematics but in everything that they do. We have to be intentional about teaching our children to be independent learners. We just can’t assume that that happens overnight, [laughter] and ta-da, you are now an independent learner, although I confess that there were times with my kids that I really wanted that to happen, as my Hispanic friend says, inmediamente. Right now, [laughter] right now. I want it done. So, Lisa, you had said that, particularly by the time we get to algebra, we should be ready to slow down. Can you talk a little bit about why? Now, as an aside, everybody, Lisa is one of our customer support representatives and customer success consultants who offers Algebra 1 support to families, so she has these conversations all the time. So you’re getting it from the best possible source here.

Lisa Chimento: 00:20:28.232
Yeah, every day, actually. People call if they get stuck on a problem or they’re not understanding something, and so I do have these same conversations every day. And I try to let them know, listen, if your kid’s been cruising along up until now and they’ve just been enjoying understanding math pretty easily, pretty quickly, and then they hit algebra and all of a sudden it’s like the brakes went on and whiplash, so it’s not unusual. This is typical, and this is something that needs to be mentioned and brought up and have a discussion with the student about because right at the same time when they should slow down is the time when they’re hitting a place in their own lives when they’re in a hurry. They just want to get through this and get on to the more important things in their lives. You’ve got teenagers and preteens and all kinds of things are happening in their bodies and in their brains and in their lives. And so the conversation really does need to happen ahead of time so that they know what to expect, that they’re not going to cruise through these lessons, that you’re not going to want to be skipping pages because they learned it quickly. There is a lot of content. It is much more abstract than what they’ve been doing up until this point. The problems can become extremely complex where you can have six or seven or eight steps to solve a single problem and all these different operations going on. Their brain is going to have to be able to jump back and forth from one operation to another and remember what order they need to come in. So it’s important to give them time to develop evaluation skills, critical thinking skills. That doesn’t happen overnight and it won’t happen if they race through this course. Let their brains have that time to develop and let the material do the work that it does so well in developing those skills. And it’s going to pay off big time, well beyond math, in their adult lives to be able to learn how to slow down, to think critically, evaluate a situation before they jump in and make a decision.

Gretchen Roe: 00:22:41.782
Absolutely. And Lisa, toward that end, can you talk a little bit about when it’s not working, more is not a better enterprise?

Lisa Chimento: 00:22:52.770
Yeah, and this one happens a lot too, and I think there’s two things connected here. One of them is what we mentioned already about jumping into workbook pages and letting them just get started, even if they don’t understand the material. That kind of wastes the work, wastes the page, and they’re not unlimited. Unfortunately, we don’t have the ability to give you unlimited access to worksheets. So if your student has worked through all of them without understanding what they’re doing, now they have no more worksheets to practice once they do get the correct understanding. So be careful that if they’re struggling, they’re not just, “Well, let’s do more of this, more of this, more of this.” First things first, if they’re making errors in their papers, stop and take a look at those errors. You want to analyze them and find out, okay, what’s going on here? Is there a pattern to the errors? If there is, let’s go find out what step that’s happening or what concept’s been missed to see what we need to review before we get started again. You you also want to check and find out, was this a careless error? Was it another careless error? And yet another careless error? That lets you know that students probably been racing through the work and not paying much attention, and maybe the time of day or their frame of mind when they were doing that work was not ideal. Maybe they were trying to get this math work done before they had some kind of an event going on that they really wanted to get to. That’s maybe not the best time. Maybe they’re like my kids when it’s almost lunchtime, and they’re hangry. You don’t want to give them math then because they just want to eat, so go feed them first and then come back when they’ve been well fed and they can look at this work without rushing through it. There’s a host of different reasons why those errors might have occurred. Take the time to find out what they are. This is a chance for you to study your student and find out what’s going on because just going on and just doing more won’t solve the issue.

Gretchen Roe: 00:25:00.765
Right. And Lisa, you speak eloquently about figuring out from the errors what is really happening. So can you talk a little bit about how you help a parent analyze the errors that are being made and what might be at the root cause of that?

Lisa Chimento: 00:25:20.195
Yeah. And this brings in another really great point that I think we’re going to have to hit anyway because you’re getting to this place – and really it may have occurred to you before we got to this place – where your kids maybe have been used to doing their work in their head, and they’re just whizzes at it. And there’s no work on the paper, and there’s just an answer. At this point, I could say really at the fractions point, they need to be showing all of their work, every step if you can get them to do that, and even if you can’t get them to do it for some of the things that come much more easily to them, at least show it in a couple of problems. So when an error does occur, here’s the situation. Are you just going to mark it wrong, give them a percentage, and move on? Well, what happened with the percentage that they got incorrect? They’re taking that wrong thinking with them to the next lesson, and now you’re just piling more information on top. Instead of doing that, let’s stop forward motion momentarily, and let’s take a look at that error and ask the student to go back to the problem they got wrong without giving them the correct answer and see if they can find the error themselves. So what happens now if they haven’t shown their work? They won’t know where the error happened, and so this is a reasoning. This is the rationale that you can bring to maybe a student who’s been fighting with you a bit on this. You need to show your work because there were multiple steps in this problem, but you don’t know where it went wrong. Maybe you got three of the four steps correct. We want to know that because then that’s reinforcement that you’re doing it the right way. But if there was a wrong step in that problem, we need to address it. We need to find out why it happened. Did you just forget it for the moment, or is that something you never really understood? Now we can go back. So having the student go back to their own work, take a look through the steps, and see if they can find out where it went wrong. If they can’t, you can do it with them, but along the way, there needs to be verbalization, there needs to be communication. And having that student narrate the steps as they go is a big piece of it. You can say, “What did you do here?” And they can tell you and you can say, “Why?” You can ask the question, “Why did you do that here?” And then they can explain, “Oh, because when you’re doing this thing, you’re supposed to do it this way.” If they don’t know the why, that’s an opportunity to go back and review the why because maybe that’s– sometimes they get it right just because they were lucky. They took a guess and they got it right, but that’s not going to help them going forward. You want to make sure they’re really understanding their work.

Gretchen Roe: 00:28:04.837
Absolutely. And the other thing that looking at their errors and looking where their errors occurs can reveal to you is sometimes parents will find themselves with a student in pre-algebra or Algebra 1 and all of a sudden it feels like their capacity for math has completely been obliterated. They can’t do it anymore. Usually, that’s a foundational skill set that’s weak. So Lisa, can you talk a little bit about that?

Lisa Chimento: 00:28:34.638
Yeah, and this is something that maybe you hadn’t considered and maybe you don’t want to think about but it’s so important. If you have a student who has gone for years and they’re doing higher level work, even in division, frankly, or fractions, and they are counting on their fingers, or they’re counting up in their head, or they’re using tally marks. I remember talking to one parent, she said he’s got tally marks all over his page. If they’re relying on a number chart or a calculator or when they’re doing multiplication computation, they’re skip-counting. That will get them a correct answer. But it’s really going to– it’s really going to pose as an obstacle. The harder the concepts become, the more complex the problems become, that counting, it’s not only going to slow them down but it interrupts their focus. They are forced to disengage from the problem they’re working on to go dig for that fact, get the fact, bring it back to their work, and try to re-engage. Where was I? I don’t remember what step I was on. They lose their place. It’s so exasperating. It really is. But we’ve mentioned this many, many times in our talks. It also burns up a lot of their brain battery, that interruption in and out, in and out of the problem. And the more steps you have in that problem that involve computation then there’s more interruption. And they’re becoming mentally fatigued very quickly. And I hear this from parents sometimes where they are saying that their kids are saying things like, “That’s it. I’m done. I’m too dumb. I can never learn math. This doesn’t make any sense. I’m never going to understand it.” And I have to tell you, I just don’t believe it’s true. I really don’t. I’ve talked to kids and I can see that they have understanding but their brain’s not free. The facts are getting in the way. So we have the ability to remedy that. And it means pausing forward motion for a short time, maybe a couple of weeks, maybe a couple of months. But what you want to do is make sure that you give them that foundational skill. Think of it like building, constructing a building. I say this all the time. Math is like constructing a building. Those foundational skills of fact mastery are like the foundation of a building. And if you discover that there are cracks in the foundation, the best thing you can do for your student is pause, halt forward motion, and get those cracks filled in and strengthen their foundation because then it gives them confidence.

Gretchen Roe: 00:31:18.846
Right. And I know that there’s somebody in the audience who’s going to watch this at some point in time and say, well, I did well in math and I didn’t have my facts memorized. But what you did have if you did well in math and you didn’t have a memorized fact set is an inordinate ability to stay engaged to the end of the problem. And we live in a more distracted world. So we have to provide our kids the tools to remain engaged with a math problem to the end. Lisa, we had so many great questions. But before I turn my attention to the questions, I want to ask you if you’ll elaborate on why, particularly in Math-U-See’s world, pre-algebra is not an optional experience.

Lisa Chimento: 00:32:08.512
Yeah, yeah. And Math-U-See, it’s not just like, “Okay, we’re gearing kids up for algebra and we’re giving them a little boost.” There are skills taught in pre-algebra that are absolutely necessary. They’re critical in order to be successful in Algebra One. We’re teaching negative numbers. We’re teaching order of operations. We’re teaching distributive property and greatest common factor and least common multiple and all of these different skills that are going to be so, so important for them to be able to now put into place when they get to Algebra One and they’re really doing that complex abstract work. So if you’re worried, and I think we probably need to address this, I know some parents are like, “Oh, well, they’re behind and they’re not going to be able to get– first of all, they are where they are. You can’t make them be somewhere else in their understanding. So pushing faster won’t make that happen better. Filling in the gaps, making sure that you are building concept upon concept very solidly and securely gives them stability in their understanding. It gives them a feeling of being equipped because every new lesson is a new challenge. You need to be fully equipped to take on those new challenges. And that way there’s confidence. So don’t skip pre-algebra. Even if you think, “Oh, no, we’re not going to be able to get through all the high school maths,” do the pre-algebra anyway. There are many strategies to getting through the high school maths. If you’re concerned about time, give us a call. We’ll talk you through it. We can help you build an individualized plan for that student to be successful.

Gretchen Roe: 00:33:45.919
Absolutely. And Lisa, I wonder if you could talk a little bit because now that we have the opportunity to offer parents two kinds of Algebra One experiences, I want to talk a little bit about how we evolved to offering two Algebra Ones. And I think it’s an important thing to recognize that we were looking to create an opportunity for kids to learn more independently. And if you want, I’ll put up the chart that you and I had talked about. And you can talk your way through that a little bit.

Lisa Chimento: 00:34:20.001
Yeah, sure, that’s a great idea. So if you’re not aware, we do now offer two different Algebra One courses. The original one with the brown cover that looks like this, if you already purchased it previously, we are now referring to this as our Legacy Algebra One. The new course has a different cover and it’s blue. And this is Algebra One, Principles of Secondary Mathematics. They are different in both content and format. So the chart will help give you just a quick rundown of some of those differences. So in terms of the format, the Legacy Algebra One follows the format of the other Math-U-See levels that you’ve used previously. There’s one video per lesson. The video is of Steve Demme standing in front of a whiteboard, addressing a room of students, and demonstrating with the manipulatives. The new format has multiple videos for each lesson. And it’s not of any one person’s face. You don’t see anyone, but you do see someone working and walking the student along through the work text, which now has additional information. The old workbooks were just practice problems. The new workbooks have instructional material embedded. There are sections in each lesson for note-taking. There are self-mastery checks. So there is a very different format. And the videos show someone guiding the student through the work text with voiceovers. In terms of standards, many of our homeschooling families live in states or they homeschool through charter schools that mandate certain content be included. The legacy course of Algebra 1 does not include all of that content. The new Algebra 1 does. We do include that content throughout other levels of Math-U-See Algebra 1, Algebra 2, Pre-Calculus, but it’s not all, that content isn’t all in the legacy Algebra 1, but it is in the new Algebra 1. So if you are homeschooling through a charter school, you no longer have to purchase supplemental material to be able to be aligned with your state’s standards there. With regard to lesson script, the legacy Algebra 1 has that information in the instruction manual. It doesn’t have it in the new material because all of that information is in the video lessons. Let’s see what else. In the legacy Algebra 1, Steve Demme does demonstrate certain of the lessons with the manipulatives. So they are included in the set material. It’s optional for new Algebra 1. And with regard to independent work, there is more of it promoted in the new Algebra 1 course where there is a great deal more independence available because of the depth of the video instruction. So students can do that. There is a readiness check for both courses. And so if you are considering either, please reach out to us. There is a readiness check on the store, the Demme Learning Store website in the Principles of Secondary Mathematics page. You can see that readiness check there. If you find that your student isn’t quite up to par, is missing some material, there are some bridge materials available there for you that will help fill in that gap if you’re going to the new Algebra 1.

Gretchen Roe: 00:38:06.941
Absolutely. And Lisa, I appreciate you being able to walk parents through that to understand. One of the things I think that is important to understand is whichever path forward that you choose, our goal is for you to create a student who is mathematically competent. And sometimes that seems like an insurmountable goal. If you’re like me, that math-hesitant parent, it feels like it’s a harder thing to do. So one of the outgrowths of the new Algebra 1 PSM product is for you to have more intentional instruction for your student along the way. And I think that you’ll find that to be a very helpful thing as you go along. I really liked this question because we have talked really about this, of what my student needs to be confident with high school math. And I think you succinctly answered it in saying they need a solid foundation. If there are gaps in that foundation before your student starts high school math, it would be a better experience for you to figure that out now than it is to get 7, 8, 10 lessons into either pre-algebra or Algebra 1, and then say, oh my goodness, we’re having a struggle. One of the things that is difficult for parents to grasp if they’re new to the philosophy of Math-U-See is that mastery element when it’s an older student. And I confess that I found my way to Math-U-See at pre-algebra. And it took me a while to understand that mastery element. So, Lisa, you had talked about the the practical tips to look out before a student starts Algebra I. And I want to reemphasize that teach back component. So can you explain to a parent why that particular tool is valuable in setting their student up for success?

Lisa Chimento: 00:40:24.268
Yeah, the teach back is such a great opportunity for both of you, actually, because it doesn’t just allow you to ascertain mastery, but it really helps the student to cement that material in their own brain so that they can retrieve it when they want it. The ability to communicate and verbalize to someone else what you understand really helps you to understand it even better. So one of the things that we encourage is, as I said before, if the student is not able to teach back some of that information before they even begin the workbook pages to practice it and become more adept and fluent with the material, then don’t move on to workbook pages. You can pick a few problems off of maybe that first page and work on them together. But having the student verbalize the steps as they go, I find this is really a neat thing when I’m talking to a student over the phone who got stuck on a problem. Fortunately, I can’t see their work. And so I have an excuse to be able to say, “Well, I’m going to need you to talk me through your steps.” And sometimes they feel awkward doing that, but the more they do this, the easier it will become. And you can model it for them first if they’re not sure what you’re looking for. But having them talk through the steps, and sometimes I’ll stop and go, “Okay, why did you do that?” And I can ask that question, and then they’ll answer it. But let them talk through the steps.

Lisa Chimento: 00:41:54.943
And sometimes they’ll say a step, and I know that that’s where the error happened. And I won’t say anything. I’ll just wait. You can kind of count one, two, three seconds go by, and then you hear, “Oh, I see what I did.” There is something about them having to talk out loud and hearing themselves say what they’re doing that they catch their own mistakes. Now, it doesn’t always happen, but when it does, it’s a beautiful thing. When it doesn’t happen, though, you can let them finish, and then you can go back and say, “Okay, let’s go back to this step here. There’s something going on here that’s not right. Why did you do this?” Then you can get into the heart of the matter. I explained this last week when we did our other webinar. I had been talking with a student and she was supposed to– she was isolating a variable to solve for that X. And in doing so, she had to move a number from one side of the equation to the other. And she had subtracted it from the left side of the equation, but she added it to the right side. She ended up with a positive number on the right side. And so I just went back and I said, “Okay, let’s go back to this step. How did you get that number over to the other side of the equation?” And she said, “Well, I subtracted it.” And then I just waited. And she heard herself say the word subtract. And I guess as she was doing this, she’s looking at her own page and she realizes she’s got a positive number on the right side. She caught her mistake. So those kinds of things can really, really help. And when they do it themselves versus you telling them what they did wrong, that sticks with them so much more. You know what I mean? If you’re just telling a student, “No, you did this wrong, it should have been like that,” they’re hearing it, but it’s not going to sit as well. When they have worked through it that way, it’s really going to stick with them.

Gretchen Roe: 00:43:47.776
It does. I think I have adequately portrayed myself as not the most confident math parent. But the truth is, last year, my son Owen was doing pre-calculus. And y’all there is no way if Gabriel and his [trump?] stood over here and said, “Just work through one pre-calc problem, [Gretchen?] and you’re in,” I probably wouldn’t be there. But he came rushing in with a fistful of papers. And he said, “Mom, I need your help with this problem.” And he slaps the papers down on my desk and he says– and I said, “Okay, explain to me what you’re doing.” No idea what he was doing, to be wholly honest. But he said, “Well, first you do this and then you do this.” And all of a sudden there’s a pause and he goes, “Oh, I understand.” And he left. I said absolutely nothing. The reason I tell you that is because I want parents to understand that if you teach your children properly, there comes a point in time where they take control of the reins and they can figure out what they’re doing. Lisa, we had a great question about a child who is 15 and behind, and will that hinder him in high school math? And I think it’s important for us to explain that– we’ve talked about every child’s path is different. But if the reason for their being behind is the fact that they don’t have their computational fact sets down, then we both want to encourage you to take a pause and figure that out.

Gretchen Roe: 00:45:39.015
And I will tell you all this story of a young lady I worked with before we had the AIM products that you see on the shelf behind me. She was failing. She had failed Algebra 1 twice. As a homeschool student, they’d used Algebra 1 in two different curricula offerings, and she’d failed it two times. And so her evaluator had recommended Math-U-See. And her mother called and said to me, “How is this going to be a different experience?” And part of the difference was we analyzed where her gaps were. It took us an entire year to fill those gaps. Now, she was almost 16 when we started to fill those gaps. No, she was almost 16 when we finished filling gaps. The gaps that we had to fill for her was, she didn’t have her computational facts. She counted for addition and subtraction. She skip counted for multiplication. She’d never gotten to a memorized multiplication fact set. She was very weak with fractions because she used a curricula that, instead of teaching one process of fractions to mastery, it juggled multiple concepts. And it didn’t give her enough practice in any one of those concepts to really feel confident.

Gretchen Roe: 00:47:08.022
So we took a whole year to fill all those gaps. And she ended up stepping into Algebra 1 at almost the age of 16, graduated high school a year and a half later in Florida, having finished pre-calc, and now has a college degree in mathematics education and teaches high school math. And the reason I tell you this story is because her mother felt that she would never be mathematically successful. And what she said to me when I checked in with her for the last time – which was about three years ago – she said, “You know what, Miss Gretchen?” she said, “There’s a lot of people out there like me who think that we can’t because we don’t have the right foundations.” And she said, “I feel like it’s my job to help them find the foundations. So I I said she taught high school math. She doesn’t. She teaches middle school math, which I think makes her extra brave. But the reason I tell you that story is because, as we’ve said already, every child’s journey is their own. And if your child’s journey is impeded because their foundation is weak, this would be the place to fix that. And this would be the time to do that. Lisa, the next question I have is about– and I thought this was an interesting conversation. It’s about when do you let a kid begin to use a calculator?

Lisa Chimento: 00:48:41.843
Oh, yeah, that’s a good question. There is a recommendation that we do make that they not use a calculator until they get to pre-algebra at the earliest and even then, not all the time. When they get to pre-algebra, they’re going to be encountering problems, like when they’re solving for finding the surface area of a solid figure. And there’s a lot of multiplication and division involved in this. And so we say, “Okay, that’s going to be cumbersome.” We want them to be learning the new concept. And if their brain is totally focused on all of these heavy-duty computations, then they’re really not going to be free to learn this new concept. In that case, go ahead and pull out the calculator but make sure that they’re not using it so regularly that they forget. And honest to goodness, if you’re an adult and you’re using a calculator all the time, stop and think to yourself, “How easy is it for you now to be able to recall a math fact that you haven’t done in a while without a calculator?” So math– it’s a language. It can be forgotten if it’s not used regularly. Make sure that they’re using it regularly. And then when they need the calculator to deal with those cumbersome problems, let them go ahead and use it.

Gretchen Roe: 00:50:00.607
Right. I laugh because I think back to my own middle school math teacher who said, “You’re not going to have a device in your pocket all the time to compute.” And I’m like, [laughter] “Well, okay, that is true, but.” However, there’s a point that I want to make. If you’re having to use a calculator or something like that to calculate computational facts, and you find yourself in a standardized test, be it the ACT or the SAT, there is not the time for you to use that calculator effectively to do computational math while you’re solving more complex math. They deliberately set that up so that you need to be able to figure out how to get to the endgame with some degree of expeditiousness. So I think it’s a larger context to say, not only when do you use the calculator, but why? And if you have a child who has come out of the public school where they have failed your student in teaching them foundational skill sets, and they’ve said, “Oh, just use the calculator,” they’re not serving them long-term. And it would be worth taking a time to pause and make sure that that happens. Lisa, we had one other question that I thought was really helpful and that had to do with a student who has special needs and how can we best prepare them for success. And so can we talk a little bit about knowing your child and knowing what those expectations should be and framing those expectations accurately?

Lisa Chimento: 00:51:56.154
Yeah. A lot of it is going to be dependent on where that child is going to be going. And I want to encourage parents sometimes we have a vision for our children, but it may not exactly be the vision that they’re going to walk in. They may surprise you. I had a really neat conversation with my son the other day, and we were talking about algebra. And he said to me he felt that algebra one was what a student needed to be able to be set for life, to be able to use math skills in life. Beyond that, maybe, probably not. You know what I mean? Unless they’re going into higher level coursework in college, if they want to go into engineering or a medical field or science or something where they would need higher level maths. But for the average person just living a regular life in a regular career, algebra one, I would think at a minimum. You can also take advantage of consumer math type of coursework too. And that will still count as a high school math. And it is very practical. And it will help with everyday things, budgeting and learning how to use money well and figure out a mortgage and maintain your home and your car and things like that. So I think that those things are important. But again, every child is different. And it would be– we would love to help. I love having the conversation with a parent and figuring out how can we create an individualized plan for this student. Your child is not like every other child, even if they don’t have special needs. They’re not all homogenous. We need to be able to look at these kids and say, “Let’s help them to learn at their pace, to keep them appropriately challenged for whatever their abilities are, and to keep them progressing. Progress is it. And be mindful also that learning doesn’t stop when they get out of high school. Even if they don’t go to college, learning will continue through the rest of their lives. And we have a gentleman who is part of– he’s been doing Math-U-See. on his own for years. He calls into us every now and again with questions. He’s a terrific guy. And he’s teaching himself the math that he never understood when he was in school. I think it’s a marvelous thing. So it’s never too late to learn. And then your student, even with special needs, if they’re not going into hired learning, they can be doing math throughout their lives. Give them the opportunity to learn. Give them the tools they need to continue learning themselves.

Gretchen Roe: 00:54:38.669
Absolutely. Probably the most practical level of Math-U-See would be Zeta because as adults, we deal in decimals percents all the time, right? And we need to have that understanding in order to think independently. And I think that that makes a practical application. Lisa, in these last five minutes before we conclude, what are your closing thoughts? And let me say as an aside before you share those, if any of you have questions, please don’t hesitate to ask them through the Q&A. I want to make sure that we answer your questions before we conclude today. So Lisa, what are your thoughts?

Lisa Chimento: 00:55:18.484
Yeah, I’m looking over some of the notes we took when we talked about this. One thing that we didn’t mention that I think is really important, we talked about a student showing their work. That is key, but also neatness and organization with their work. It’s really easy when they start going into those higher-level concepts where there are many steps to drop a negative sign, to miss an exponent, to miss something along the way. I like the way that Steve Demme does it on the board where he writes the equation and then each step comes below. And it sort of creates this inverted triangle so that you end up at the bottom with your answer. But what it allows the student to do is before they take each next step, they can glance quickly back up to the line above and make sure that they’ve got everything they need and then do the next step down. So keeping that work neat and organized. If there’s not enough room to do that in the space allotted on the workbook page, then they can do it in a notebook, on a piece of paper, whatever, but keep that work neat and organized. And going back in then to look at errors makes it so much easier to discover those errors. And that’s the other thing, really quickly. Errors, let’s talk about mistakes. Parents, if you are using Math-U-See and you are grading the workbook pages, I want to encourage you to consider laying that aside because that’s where learning is happening. It’s not expected and probably should not be expected that a student understands and can master something immediately. This is a learning process and they’re going to practice. And in that practice, mistakes will happen. So forget about grading their papers. If you want to lay a grade, lay it on the test. But for those workbook pages, this is the opportunity for them to make mistakes and learn from their mistakes. And we have the opportunity as adults to reframe the idea of a mistake as something, from something that is bad and should not be done and should be punished for to this is a great opportunity to learn something that we didn’t understand quite well enough. Let’s take this opportunity and really get it down. And it might need several times of doing that same area before it finally clicks. But we can reframe it. We can model how we respond to mistakes so that if you’ve got a kid who’s a little stressed about his own mistakes or you’ve got a perfectionist at home, because I think we probably all have at least one, then you can help that little perfectionist learn how to relax and see the value in the mistake. See the goal that can come out of a mistake by taking advantage of it and learning better.

Gretchen Roe: 00:58:10.037
Right. And I want to answer out loud. I answered this question in the chat, but it was, “What comes after AIM?” And if you have used AIM for addition and subtraction and you’ve used AIM for multiplication and you’re working with an older student, Lisa, what would be the next thing that they would need to assess?

Lisa Chimento: 00:58:29.251
Call us and let’s do an assessment. We’ve got diagnostic tools to help you determine where they should go, because not every student is going to go in the same place. It depends on their own conceptual understanding. So we want to figure out what that is. Where are you? We want to meet you there and then help you progress from that point.

Gretchen Roe: 00:58:47.839
And that doesn’t mean, I should also say, that doesn’t mean if you’ve gone through the two AIM products, then you pick it up, if you will, at gamma, you’re going to pick it up where your student’s learning ends. And that would be the important thing for us to make sure that you understand. Since every student is different, it’s important for us to make sure that we level the playing field, if you will. And Lisa, this is a good question and so I’m going to toss it to you since you provide so much algebra support. She says, “I teach a middle school class and a homeschool co-op. How do I help them all get ready for pre-algebra?” I have some opinions, but I’ll let you answer the question.

Lisa Chimento: 00:59:37.162
Well, I’ll tell you what, I think the best thing to do would be to give us a call and let’s have a conversation because I would have a few questions. I don’t have a pat answer for that. You probably have some better suggestions, Gretchen, but I would want to, I would want to dig a little deeper, find out how many kids we’re dealing with because they might indeed not all be in the same place, and do some assessing to find out where there may be any gaps, identify those gaps, and find some materials to fill in the gaps.

Gretchen Roe: 01:00:05.960
And having worked often with co-ops in my tenure here at Demme Learning, one of the things that’s important is to know where they’re coming from into your co-op pre-algebra class because not all math programs are created equal. And so you’ll have kids who might academically appear to be on the same level, but they haven’t had the same degree in depth of instruction. And so there may be– and I give this advice to co-op instructors all the time. If you’re going to teach a co-op beginning in September, I would say the time to start assessing those kids is March before that September. And the reason is because you want the playing field to be level when they begin in September. And there may be things that you require of those students’ parents to complete for them to be ready to do that come September.

Lisa Chimento: 01:01:01.840
That’s a great idea.

Gretchen Roe: 01:01:03.344
Lisa, we’re at the top of the hour. And I want to thank everyone who has joined us live. We had a bunch of you all today. So obviously, we have touched on something that’s really important. We’re going to be sending in the show notes, some follow-up things. I mentioned at the top of the hour that we were going to be sending you the link to the video that Lisa and I did about when fractions are a struggle. And I think that will give you some insight and depth. We’re also going to be sending you a link to a very special interview I did a couple of years ago with a young lady named Gray Carson. She talks about the value of doing a level of math more than once. And I think you’ll find that very interesting. And sometimes as parents, we’re not always the prophet in our children’s lands particularly as they reach high school. So I think you’ll find this an edifying conversation to be able to use in conversation with your children about what their mathematical goals are and to be very helpful. The last thing that will be included in our notes is our most popular blog post, the post that we wrote that you all reference more times than anybody else. And that’s about why we learn algebra. So look for that information in the follow-up notes. And thank you all for joining us today. It’s been our pleasure to share this time with you. And we’ll look forward to your joining us again in the future. Take care, everyone. And thank you.

Lisa Chimento: 01:02:35.446
Bye.

Gretchen Roe: 01:02:36.007
Bye-bye. 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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