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4th Grade Math Unit Parent Overview Handouts

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Redefining What it Means to Be Good At Math

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Redefining What it Means to Be Good At Math

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Redefining What It Means to Be Good at Math

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Why is Math different now? by Dr. Raj Shah

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Sara VanDerWerf

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What is Math? -  for Parents, Grandparents & anyone else supporting their student in mathematics

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Ann Elise: Well, first of all, we need to define fluency. We need to be all on the same page of what fluency means. So in my presentations I ask people, "What words come to mind when you think about being fluent with your math facts?" And, overwhelmingly, people will put words like 'speed.' Speed, fast, automaticity, all words about speed. And then occasionally, I'll get 'accuracy,' right, because kids can give the right answer but then be wrong. Right? So we want to have the accuracy as well as it being, I call it relatively speedy, because it's the least of the four things I want to talk about. But there are two more pieces of fluency, which is crosstalk.

Jon Orr: Today we speak with Ann Elise Record. Ann Elise is a seasoned educator with a career spanning over two decades of elementary classroom experience. These days, she's a K-5 math coach who works with districts on developing strategies to increase students' fact fluency as well as how to use manipulatives in the classroom.

Kyle Pearce: Stick around as we'll discuss effective strategies to help students build their fact fluency, how to help students with the progression from additive thinking to multiplicative thinking, and, how can we help students with concepts that hold them back from their learning?

Jon Orr: Let's do this, Kyle.

Kyle Pearce: Welcome to the Making Math Moments That Matter Podcast, I'm Kyle Pearce from tapintoteenminds.com.

Jon Orr: And I'm Jon Orr, from mrorrisageek.com. We are two math teachers who, together...

Kyle Pearce: With you, the community of Math Moment-Makers worldwide who want to build and deliver math lessons that spark curiosity...

Jon Orr: Fuel sense-making...

Kyle Pearce: And ignite your teacher action. Are you ready, Jon, to dive in to this awesome conversation with a dear, dear math friend?

Jon Orr: Mm-hmm (affirmative), mm-hmm (affirmative), of course, Kyle. We are honored to bring Ann Elise Record onto this show as we've been looking forward to this conversation.

Kyle Pearce: All right, but before we dive in here, Jon, we want to make sure that you folks at home have taken the time to explore some of our most recent full units of problem-based math lessons.

Jon Orr: Right, right. We've been busy adding full units to our Make Math Moments website. And last episode here, we shared some details about our six day unit called the Wooly Worm Race that was created to help educators address teaching fractions, decimals, and percentages conceptually.

Kyle Pearce: Well, we've also tossed in some more context, rich, problem-based math lesson fun with our unit called Snack Time, where students explore the tapintoteenminds.com classic three-act math task called Cheese and Crackers, to use partitive division to partition and distribute slices of cheese to a specified number of crackers.

Jon Orr: That's definitely a classic I've used with my class, and now I'm set up with a whole unit of connected math talks. Sense-making prompts, purposeful practice, and summative assessments, all scraped from my web browser by visiting our test page at makemathmoments.com/tasks.

Kyle Pearce: Yes, it's super exciting, Jon. We hope to see you over at makemathmoments.com/tasks, so that you can run one of these awesome problem-based units in your classroom today.

Jon Orr: All right, enough from us. Let's get on with our great, great, great, great conversation with Ann Elise.
Hey there, Ann Elise, welcome to the Making Math Moments That Matter podcast. As always, we are super excited to chat with someone we've met, someone we know... How are you doing today?

Ann Elise: I'm doing great, doing fabulous.

Jon Orr: Awesome stuff, awesome stuff. Well, we know you quite well, but maybe there's a few Math Moment-Makers out there who aren't as familiar with Ann Elise Record. Can you help us out? Let's learn a little more about yourself. What's your role in education and how did you get to that part in your learning journey?

Ann Elise: Sure. Currently I'm a consultant. So currently I work for myself out of my home and I was traveling around a lot and working in schools and districts, and also presenting around the country for the Bureau of Education and Research. But then once we had the shutdown, I've been working from home. But I had gone to get to, my undergraduate degree was in sociology. So I was not certified or able to teach. And so I got back to school, once our kids were becoming of school age, I went back to school and got my master's in order to teach. And then I taught grade five for 13 years. And then a math coach position opened up in my district, and so I became the math coach K five.
And that was really the start of my journey to truly understand the trajectories of the learning and progressions of kids from the early numeracy on up, and all those connections. But also at that time, I taught some pre-service college classes, the math methods, I helped people, tutored them to help pass the Praxis test, because I've experienced in this role, working with so many different populations of people. And I've seen the anxiety and the stress and the phobias, firsthand, of people.
And I didn't have that growing up. When I grew up, I could answer things quickly and accurately, so I felt good about myself. But to have seen the phobia up close for a variety of people, it was surprising to me how many of the college kids were terrified of math going into teach elementary. And it just became a passion of mine, the more that I learned, why I wanted to share with people. And my husband got a new job two hours south of where we had been living. And then I'm like, "Well, what am I going to do now?" There weren't any math coaching positions. I loved working with the teachers, and the kids, and everyone. And that's when my two close friends and mentors, Dr. Nicki Newton and Christina Tondevold, said, "Well, why don't you go off on your own?" And that's what I did. So my life has been completely different these last few years, doing this new part of my life.

Jon Orr: Yeah. And I think you've brought up a huge point about math anxiety being a huge thing, and I think still is for so many people, and I'm wondering, what suggestions can you give our listeners right now, and teachers, that can help reduce that anxiety? If you've been recognizing it's a problem in your past, in your career, now I'm wondering, I guess, two things. One is, what can we do now to help kids, and even teachers, reduce some of that math anxiety? But then I'm also wondering about, what did Ann Elise look like as a early teacher? Did you recognize that right from the get-go, that we've got this math anxiety, and it's something that you've been using in your career right from the start? Or is that a progression that built up over time? And so those are, I guess, two things to talk about.

Ann Elise: Yes, okay. So first of all, when I think back to when I first began teaching, so I think we all know what we know at the time and we don't know what we don't know. And so, in my master's program to teach, the only class that I had to take that involved math to become certified K eight was math and literature. So it was a literacy-based math class. So I came out certified K eight, really being no more qualified to understand early numeracy than I was to teach an eighth grade math class. I think the assumption was that you'll be given a textbook of whatever district hires you, and you follow the textbook. So that's what I did. I became the grade five teacher, we had a textbook, I was very procedural in my teaching. It's all that I knew when I grew up learning math. It was a very procedural, rote procedure. There was no open tasks. There was no talking about our thinking or having any kind of flexibility of thought.
And so I gave time test to my classroom, all 13 years I was in the classroom. And over the course of that time, I know I did concrete and pictorial things, but it was leading toward the algorithm. I didn't do flexibility with number sense, I was trying to show them why the algorithms worked. I didn't know anything else. So it definitely was not in play the first many years that I was teaching. But as I learned more, and we had a consultant come to our district that showed me how to teach math in a visual way, that was totally new to me. I had no idea that you could teach math visually, like pattern blocks, refractions. It was a mind-blowing thing to me. I had never seen it before.
So it's been, certainly, I call it a journey because I think we're all on journeys. We as educators, as well as the kiddos, right? As we get to find out where we are on that journey, and then you continue and when, Dr. Maya Angelou says, "When you know more, you do better." And that's exactly what I believe and I've been living, that, I know the more that I learn, the more I realize I have to learn. This is a never-ending process. And so, I think we need, I need to send the message to people, I want to let the people know that there is so much more to mathematics and connections and a beautiful journey to it, so far beyond rote memorization and procedures. Because I think that when we think about giving kids worksheets that are just 20 kill and drill things, that's not going to be encouraging a love of math, nor will it build the flexibility of thought that we need to build our number sense and to develop the confidence to try harder problems.
The idea of the growth mindset messages of Jo Boaler from Stanford, the fact that our brains have the way of growing new parts. There is no such thing as a math brain, but think what happens is people have gone on their journey, and I truly believe time tests have begun, well, research is out there that proves it, but, that it's the start of math anxiety. Kids think that because they're not fast at the math, and they're not good at math, and it begins disassociating themselves from the idea that they can be a mathematician. And then it gets harder over the course of the year, as if we're only doing procedures and formulas. That's the only way they've been exposed to thinking and algorithms... Algorithms take lots of steps. And I think, I'm like, a three digit by two digit multiplication problem, that's a lot of calculational work.
But until we explore these things in more flexible ways, it can make it much easier. And I find that my consulting work, the more that I share these ideas, and that they're seeing the math in a different way. Even the parents, I have my districts do math nights, because I want to talk to the parents. It's huge we get the parents involved. And by the end of that 30 minutes, the parents are like, "Oh my gosh, this is a whole new world to me. That's why my child was doing that this morning." Literally they've said to me, "We were arguing with my child this morning about eight plus six. We just told her, 'It's 14.' She's like, 'But no, mom, that's not the way I was supposed to do it.'" And the parents were like, "But now we know why, and we totally get it. We've seen the future impact of that work."
And so, the whole anxiety piece comes from, not the math, but the feeling of insecurity and embarrassment and humiliation people have felt growing up, that they were not a math person, as if it takes some extra kind of brain to be good at math. And it's not true. We all can grow those parts of our brains, and in fun and engaging ways. I want our students to have no bad stories of math growing up. In all my consulting, I would say probably 80% of the people that I meet tell me the most awful, traumatic math journeys of their lives. It's just always negative. They're always about 20% like, "Oh, it was good. It was fun. I loved it." It's like, "Well, you're like me then, because I got my answers correct, I was able to get them done fast, so I thought I was good." But it wasn't until I really began this deep journey that I realized I didn't have any understanding of mathematics, so I didn't see connections to topics within the math. But now the more that I learn, the more I'm like, "Oh my gosh, that connects to that. And throughout the grade levels, even, it's a beautiful thing, to finally see those connections.

Kyle Pearce: Yeah. Well, and we love asking about these things because I worry that when teachers and educators who are at that place in their own journey where they feel like maybe they don't feel comfortable with the content, or they maybe remember their own math anxiety that they had as a student, or they just think plain out that they're doing it wrong and they see someone like yourself, Ann Elise, or Jon and I, and we are so into thinking about how mathematics develops, and thinking about the conceptual connections, all of those pieces. But yet, most of us, most of us didn't have that same experience growing up. And many of us, as you just mentioned, and it's great to hear, that, many of us actually taught it the way we were taught. And it's okay if that's where someone is as they're listening. So I think that is such a huge message for people to see that it takes time.
And I immediately connected when you were describing how you were teaching very procedurally and you were trying to help kids to understand why the procedure works, which I think is part of that trajectory. If you learned procedurally, you tend to teach procedurally, and then hopefully over time you start to see that, "Oh, connections are important." But then what we do, it seems like for me, anyway, I started to still teach the procedures, but then I tried to explain them afterwards. Instead, now we're realizing, "Oh, we really need to start with kids making meaning, and making sense first, and then working towards and allowing those student-generated algorithms to start popping out and helping them to make their connections so that we can essentially get more efficient along the way, but not with the end goal just being an algorithm or a procedure, right?

Ann Elise: Absolutely, 100%. And in fact, the more learning that I'm doing, I've been trying to work on my own knowledge of middle school mathematics, in terms of the conceptual understanding. I can get right answers, I help people pass the Praxis test. That's not the issue of getting right answers. It's, I want to get the connections that I missed first time around. And so I've been doing a lot of work on that. And the more of the work that I'm doing, I am doing mental math or ratio tables and things of using chunks of numbers that are nothing to do with the algorithm. And I'm getting easy answers really quickly, I'm breaking apart numbers in ways I never had done before, and it's just a matter over time. I do a lot of Pam Harris' Math Strat Chat every week, and inaudible Academy. I took a class with Pam Harris on proportional reasoning, that is just like, I'm learning these ways of thinking about it. When I learned it the first time, I had no idea of those connections, I was just following procedures. And it's just a beautiful extension to what I already know as a foundation of understanding K five, and to extend that to that middle school level.

Kyle Pearce: I love that. And it's actually ironic that, nowadays you'll see, both in your messaging and so many others who come on our show and obviously Jon and I, who, we do not believe, like math fluency is not speed. Yet, when we actually start to help kids become more flexible in their thinking, and start to play with different strategies, and really just give them the freedom to think and use critical thinking in order to reason and solve through problems along a trajectory, along a progression, what I end up seeing is actually kids end up becoming more quick with their math facts than kids who are memorizing the procedure. It's actually mind-blowing when you're saying ,"No, no, we're..." It's not about speed, but then the end goal ends up oftentimes becoming speed anyway, which isn't the holy grail, it's just like a symptom of having flexibility and fluency with number. And I'm hearing that in your voice, I hear that in your message.
So before we dive deeper into fact fluency, because we have a lot of questions for you, we know your connections with Christina Tondevold, as well as Nicki Newton. We know you're big into that, and we'll be diving into those questions, but before we let it get out of hand here and we dive too deep, we've got to hear about a math moment from your past. So you've described a few things about how you began teaching, how you taught for a while, also, a bit about your experience learning in the classroom as a student, but is there a moment that pops out in your mind? It could be defining, maybe it's something that, like a celebratory moment, or it could be one that maybe you remember, and it's one of those memories that you sort of wish you didn't remember. What's a math moment that pops out in your mind that you're willing to share with our audience?

Ann Elise: First of all, I'm just so happy to be able to share you my math moment, because I've been listening to your podcast forever. And I walk my dog listening to it. Whenever you ask your guests, I'm like, "Oh, I would tell this story if I was ever inaudible them." When I became math coach, K five, before I began that part of my job, I took a one-week class with Dr. Mahesh Sharma, on, really, it was K eight type content. And it was the first time I saw the connection between grade levels of things I could do at a lower grade level that affected what came up. It was my eye-opening to that kind of procedure. Well, we did the area model of multiplication, and he loves Cuisenaire rods, they're my favorite math manipulative. I think they're the key to helping our kids move past the counting phase of reasoning and into strategic, additive thinking, multiplicative reasoning.
inaudible we had these Cuisenaire rods and we built area models of basic facts. So in the third grade content, right? Well, over the course of that week, we kept using the area model to do double digit by double digit, or to do decimals by decimals, or mixed numbers by, like the same area model, I was able to use with harder content. Well then he said, "We get to division, and we're using the area model to do division," which I had never, ever thought of before. And we were doing it concurrently with the Cuisenaire rods. And he put on the board 'X squared plus five X plus four.' That's the exact problem that he gave. And he wanted us to divide it by X plus one. Now, I remember my brain saying, "I'm out." I took calculus in high school and again in college, it wasn't like, I really thought I did well with math. But, it had been decades since I had done that before.
So I'm like, "Okay, well I'm out. I'm not even going to attempt this." But then he said, "Try doing the same thinking we've been doing with the division for the area model. Can you make a rectangle that is X plus one by something?" And within 20 seconds, I built the area model, I knew the answer was X plus four, and I could explain to you why. And that was my moment that I went, "Oh my gosh, a model that I can show the thinking with the kids in third grade, can follow them through their entire math journey, and the math journey will make sense." It's not just getting a right answer. And I was sold on the whole idea of, "Wow, this is just a learning progression." And the more that I see that, the more that I know, it's all about that journey.
My husband has been working from home since the shutdown in March, and he says, and after doing a lot of trainings online, he's like, "Hon, you say the word 'journey' all of the time." I'm like, "I know, but it is true." We're all on a journey, right?

Jon Orr: Yeah, yeah, for sure. And I'm glad you brought up the area model because we love using it, we love talking about it, and we think it's...

Kyle Pearce: Didn't we just talk about it last night, Jon?

Jon Orr: Yeah. I was just going to bring that up, Kyle. Kyle and I talked about it last night, but I just had a recent discussion with a friend who couldn't see this new math, and why did their son or daughter have to learn this diagram or this way of multiplying? And when I can show her how to multiply, and get done in 30 seconds, and he referenced that Facebook post that we've all seen crosstalk...

Ann Elise: Oh my gosh, I know...

Jon Orr: Somebody being done in 30 seconds, and then twiddling their thumbs for the rest of the time and...

Ann Elise: Yup, exactly.

Jon Orr: Versus somebody who's drawing the area model. And we had this long conversation about that, and that was exactly what I referenced, Ann Elise, is that this model can carry forward, whereas this algorithm works in this one instance, and... We use it in high school and, listeners of this show know I'm a high school math teacher, and I just helped model my students this morning. And yesterday with completing the square, using the area model, and completing the square for a grade 10 student can be tough. And some teachers think it's one of those procedures you just got to show kids. "They just got to memorize this procedure." And it's hard to explain why it works unless you use a square to model it. And the area model works perfectly. And I love how it carries forward from there. And I really like how you referenced, both Kyle and you referenced that, by using these models, kids can get that fluency.

Kyle Pearce: I was sold on the area model from high school and then downwards. Whereas you went from an area model from lower elementary upwards, because I was sold downwards, because after using the area model to help kids complete the square in high school, they're completing the square in their heads. They didn't have to draw anything, they didn't have to write anything, because they could actually imagine the square and what the dimensions of the square would be. And so that they could write the vertex form of a parabola or quadratic expression, so it is a great tool, and I know that we'll talk about many other things.

Jon Orr: And I'm being a high school teacher and still trying to learn more about elementary math. I know Kyle's been on a journey for that for the last few years, but I don't get a lot of experience into the elementary math unless I do that on my own, or I talk to fantastic teachers like yourself. So I'm really hoping for this episode and the remainder of this episode to be a master class in fluency, and a master class that I can learn from, and all our teachers can learn from. So if we just think about diving into early mathematics in particular, and if we could help educators and parents learn effective strategies to help their children and students with fact fluency, let's think about some practical suggestions, some tips that we can help our teachers with on fact fluency at an early age.

Ann Elise: Well, first of all, we need to define fluency. We need to be all on the same page of what fluency means. So in my presentations I ask people, "What words come to mind when you think about being fluent with your math facts?" And, overwhelmingly, people will put words like 'speed.' Speed, fast, automaticity, all words about speed. And then occasionally, I'll get 'accuracy,' right, because kids can give the right answer but then be wrong. Right? So we want to have the accuracy as well as it being, I call it relatively speedy, because it's the least of the four things I want to talk about. But there are two more pieces of fluency, which is flexibility and efficiency. Those are the four pillars of math fact fluency. And I want to honor the fact, also, that there may be some of our students that are not ever going to fast, but they are using gray strategies and number sense.
I have to mention to you right off the bat, that, a lot of my consulting work has been focusing around what's called a math running record. It was a protocol designed by Dr. Nicki Newton. She did 10 years of research on math affluency, and created this interview protocol for us to talk to our kids about their thinking. I believe it is the key to transform schools and districts and the mathematical journey for our kids, because it's looking for that flexibility of thought. And if we explore flexibility with our different operations with the kiddos, it'll set a foundation for thinking that will then apply to the actual grade level content we're trying to teach. Without having to go to algorithms, they'll become much more efficient problem-solvers, and with their fluency, with the calculations, because they're using strategies and number relationships, which will build their number sense.
It's the start of everything. I've found it's been my key to educate people on early numeracy, because myself, having gotten, honestly, a master's degree, certified K eight, I had no idea the world of early numeracy, until I took a course from Dr. Sharma, that whole beginning of that journey. But then I also took the Number Sense 101 course with Christina Tondevold. And that was like, "Oh my gosh, what is this world?" And then Dr. Nicki as well, and it filled in more information. And then I just continued to learn about the early numeracy. So I want us to think, first of all, about that, there are developmental journeys our kids go through. Typically what our kids do for math inaudible journey is they begin counting on their fingers, right? Fingers are very important for the brain, very important for kids to do that.
But there's also something called finger agnosia, which is the discrimination of the fingers, but not finger counting. So the idea that the kids are going to start by counting, they usually count all, our youngest kiddos. If you ask them three plus two, in a context, I like putting all the fluency work in context, but you ask them three plus two, they put out three fingers and two fingers, and they would count them all, starting at one. Then kids developed to count on. So they may have all five fingers up, but they know this hand has three, and it's four or five. That progresses to head counting on. So the three isn't even out anymore, they might finger count four or five, or then, in their head, go, "four or five."
Then we have a whole section of derived facts. And that's typically the phase people skip. They tend to go, "Okay, you're counting on." So kids are counting on their fingers when they do their teen sums, because how else do you count on eight without keeping track on your fingers? And then we tell them, "Memorize them. I want you to play games with all the math facts, I want you to memorize these." As the kids are waiting for numbers to pop in their brain, when you ask them the questions, so that they don't know what it is. If they don't know what the answer is, that nothing pops in their head, what do they do? They count on their fingers, which is their comfort level, to find out what the sum is. And then when you think about a double digit addition problem, where we have raised to put the algorithm in front of the kids so soon in their journey, they're usually grade one, I find, a lot. Well, within the algorithm, it's just single digit basic facts. And in each of those basic facts, they're counting on their fingers. So they're in a counting phase of reasoning, within the context of addition problem.
I love this work of Pam Harris on the development of mathematical reasoning. That image of her graphic that she has, to go from the counting phase into additive thinking, and then by grade three, the multiplicative reasoning, before the proportional, and then the functional, the whole K-12 journey. So when I try to think about the math the kids are doing, what phase of reasoning is it? And the algorithms, adding and subtracting, are usually, kids are counting, they're counting on their fingers. So how can we get that? Well, we can work on the flexibility of thought. The idea that I could ask kids what's eight plus five, and that the kids could break apart that five and give two to the eight to make a 10, and then I can rename eight plus five as 10 plus three. That's a lot easier for my brain.
So the heart of that addition of breaking apart numbers and putting them back together in flexible ways will be the key, because I can then forward that to 48 plus five, or 98 plus five, or 98 plus 25. I can take two from it to make a 100, so 100 plus 23. It progresses all the way through their journey, including to fractions. Adding four fifths and three-fifths... Rather than adding numerators, keep denominators the same, uh oh, it feels weird, this large number on top, right? Break apart the three fifths and give one fifth to the four fifths and rename it as a whole plus two-fifths. It just will affect everything down their journey, starting with the basic facts.
So the Math Running Record allows us, when we're interviewing our kids, to be aware of that learning journey. Because there are codes for that. This is all based on Carpenter and Moser's research, inaudible research of the developmental trajectories, that the kiddos, we ask them sets of facts as a benchmark inaudible question for each of the set of facts. So you find which set of facts are causing a super slowdown, inaccuracies, or inefficient strategies, like just counting on. And then within that zone, where are they on that trajectory of the having no strategy to even try it, the counting all, the counting on, the head counting, the derived strategies, and the automaticity. Because we can't take kids from counting all to automaticity in one step, that's not how kids learn and develop. So it's a protocol that allows us to learn about the expertise needed for early numeracy. It's a brilliant protocol, and it's been a lot of my consulting work, because Dr. Nicki is just brilliant and she's so prolific, and she just talks about all different areas of mathematics. But I've latched on to this Math Running Record of the fluency piece, because I really feel it's my gateway to get people to understand, teachers and the parents, to understand the foundations of the operations, and to build the fluency through flexibility. And it alters everything, because it applies to every other content that you're doing.

Kyle Pearce: I love how you reference, even, how, we jump the gun on the memorization of those derived facts, right? They're not really memorizing derived facts or memorizing facts, when we skip all of these parts, and composing and decomposing number is so important. And I'm hearing that in what you're saying here, and this idea of equivalence pops out. And as you're working with young kids and, my son, who's an SK and my daughter who's in grade two, I get to have fun with these things, by playing with numbers and using strategies and seeing the strategies that they're using. And it really is pretty magical when you see them thinking.
And I just had this, I guess, a bit of a sad moment there, reflecting, as you had mentioned, like a student who's sitting there trying to bring up a fact that they've tried to memorize, but now it's like they're recalling facts they haven't derived themselves, so they don't have a connection. They also don't have a path to help them get out of a jam. And we talk about that a lot on this podcast and it continues to cause more and more problems down the road, because if students don't have a understanding of how they got to where they are, which I think many of us are like, as adults, many of us are like that, right? Those adults, like Jon, you had mentioned that friend who was thinking of the algorithm like, "I can multiply two digit by two digit numbers, no problem." But could they do it any other way? Or if they forgot one step of that algorithm, well, how are they going to get themself out of that jam?
And this is happening to so many young children, because I think for so long, we've made them take that leap, and the students who had the memory, the ability to memorize a little more easily or fluently than some other students, they were rewarded in the schooling system, but not necessarily rewarded with any sort of extra reasoning skills in mathematics. They just got the big gold star, and that was about it. Jon always references his puffy stickers that he used to get as a child. So I love that you're referencing this trajectory. And when this episode comes out, it'll be a few weeks after we had Doug Clements on, and his work.

Ann Elise: Oh, my goodness.

Kyle Pearce: Yeah, how fantastic.

Ann Elise: Clements and Sarama, they're just like the king and queen of early numeracy.

Kyle Pearce: Exactly. She was stuck out of town and we wanted to have both on the show.

Ann Elise: Oh, my goodness.

Kyle Pearce: I'm telling you right now, hearing you and your passion about this trajectory, it's so, so critical. And again, I know Nicki Newton thinks so highly, as well, of Doug Clements and Julie Sarama, and...

Ann Elise: Absolutely.

Kyle Pearce: It really all does come back full circle. So whether you're sitting at home right now, and you're thinking to yourself, "Maybe this episode isn't for me, I'm a middle school teacher, or I'm a high school teacher..." I hope that people are seeing the connections, and you brought up Pam Harris and the development of mathematical reasoning that, way down the road in high school, some of our students that are struggling the most, their struggles began way down here in this area where we didn't help them make those connections and really start to use reasoning to get themself through number fluency. And that's really hindered them.
And it makes me think, "What do we do?" Do you have any thoughts, if someone's sitting there thinking, and maybe I have a vision of a specific student in their class, and they're like, "Oh, this student is really struggling." What might be a get started tip for someone who, maybe this is a new idea for them, what are you going to say to them? Where might they begin? Might it be PD of some type, or might it be just a website to get them going? What are your thoughts on that?

Ann Elise: Well, I typically go right back to the Math Running Record, honestly, because it's going to help you understand where each child is on their journeys. You can develop instructional response derived for the kid, and then to get a sense of where all of your kiddos are. Because typically what I find, I'm training districts to implement this and then to do the next steps of how we explore fluency with our kids, in concrete, pictorial, and abstract ways. That's what our book is about. Dr. Nicki, Dr. Alison Mello, and I collaborated on a book about fluency doesn't just happen with addition and subtraction. So the idea that, now I know where I need to begin working with each kid, what can I do then to explore these concretely pictorial and abstract, and develop this fluency program for my kiddos?
So the Math Running Record, I have a Math Running Record Facebook group that I began close to three years ago now, because Dr. Nicki, she's doing so much all the time. I said, "Yo, do you mind if I make a group, of a support group for those of us that are really going in depth of implementing these?" She's like, "Oh, go right ahead." So there are videos in there of she and I talking for an hour about Running Records, and I have a whole Padlet of resources for the group that has all kinds of information, great resources on fluency as well. So it's a wealth of knowledge in one place that you can learn all about this. And I'm always right there. A lot of my time is online, providing advice to people within Facebook, because it's a great platform to be able to share things like that. And so a lot of my life is being in there, and providing advice, and guiding people along.
inaudible beginning a book study starting next Monday, but I know this will not be out in time for that, but all the information in the book study is going to be within the Facebook group. So no matter when anyone joins the group, it'll be there for you. So you can see the posting, and the questions, and the comments, and all. Because until we understand that trajectory of learning, and, then you can't really be looking for that, right? We've got to know, "Oh, that child is counting on. They're counting all." Now, what I want to make sure I'm clear about a derived strategy. So, for example, one really important fact for me is when I get to the progression, the beginning of the progression, say to add zero, and add one to numbers, and then counting on within five, and then within 10... But then I'm going to get you teen numbers, you have the doubles, and then doubles plus one.
So when I ask kids five plus six, most kids tell me that they know it's an 11, because five and five is 10, and one more is an 11. So it's a derived fact. The using a fact that they know to figure out one that they don't know. But the very next question in part two gives them more problems in that zone. The very next question is six plus seven. And that's where I can tell the kids who have begun using strategies, and breaking apart numbers in flexible ways, versus the counting on, because the kids will count on six from the seven. So the very same student that tells me five and five is 10, one more makes an 11, so they know five plus six makes an 11, will count on their fingers, six, higher than the seven. So I can tell that there's no strategy thought there.
So for that kiddo, I'd want them to go on to explore what doubles plus one is. And I would show them like a rekenrek. So a rekenrek is a tool that, one version of the tool, you can have two rows of 10, and the beads are color-coded in each five. So I can slide six beads over and seven down in the bottom row, so kids can see that amount of the 13. And I'll ask them, "What do you see? How do you know?" And some kids will count all the beads. So I know they're in a counting all phase, some count on the six from the sevens, they're in counting on, but other kids will say, "Well, I'm seeing five and five red, and that's 10. And then I see one white and two white, that's three. So I see ten plus three, which is a 13." But other kids say, "Well, I see six and six is 12, and one more makes 13." Other kids say, "I see seven and seven is 14, I take away one is 13." And still other kids say, "Take three from the six and make a 10 with the seven. So it's 10 plus three."
So I'm aware of all these different look fors to then develop my own instructional response with them. Because the kiddo that tells me that six plus seven is 13, because they could break apart that six to be a 10 and a three? They go to the end, they do all their math facts, and do whatever strategies they want with any of the addition math facts. But the kiddos that are counting on their fingers at that point? They go to just having visuals, to see the quantities, and describe what flexible ways can we get to that total, and make it easier for our brain. So that's where I find it's a great place to begin the journey.

Kyle Pearce: Right? And, forgive me, I'm not an elementary school teacher, haven't had experience working, other than with my own kids, talking about numeracy at that level... I'm wondering, if I'm a teacher who wants to have that interaction, that lesson with my students, and, what do I do beforehand? How do I prepare for that? We often talk about, that preparation is so important. Another quote that we've used from Tom Schimmer is that you want to plan with precision, so that you can proceed with great flexibility. In that preparation, we can't underestimate that. So I'm wondering, what does a teacher do to help prepare so that when they get in a conversation like that, they know to look for those strategies, and they know, "If I have that strategy, I'm going to push them this way." What would you suggest the teacher can do to help get ready for something like that?

Ann Elise: Well, I think it's a matter of us building our own knowledge about that. Dr. Nicki has a class, an online class, on her site. I've also, on my Padlet, have created videos for each of the strategies, and how we can explore them with math tools. And there's no cost to any of this. The protocols to interview the kids are free, there's no cost to the Running Records. But really it's a matter of us learning what we're looking for, right? And so how do we do that? Well, her Math Running Record book describes all the four operations, and the thought behind each of the operations, and the strategies.
And then our book we've written so far, the addition/subtraction, we are currently working on a multiplication and division book to go along with it. But that's a matter of learning about it, the matter of just building our own... Christina Tondevold, building our math minds, so we can then build the math minds of the kids, right? Because if you don't know what you're looking for... I ask people all the time, when kids are counting. You put eight objects in front of a student and ask them to count - what are you looking for? And very basically I always hear about one-to-one correspondence, and saying the numbers in the correct order, and that's pretty much it.
Well, Clements and Sarama has 20 levels of counting, right? So their site, learningtrajectories.org, I send all my participants to that site, because it is the most wealth of information about, from birth to grade three, of early numeracy and mathematics. But until you know there are 20 things you could be looking for with counting, you're going to look for one-to-one correspondence and if they say it in the right order, right? So it's a journey.

Kyle Pearce: I know. And I love that response because I think that's where the content knowledge piece is so important. And I think in mathematics, I mean, in education in general, oftentimes teachers, we have this drive to find new pedagogical moves. And while they are important, and they are a huge part of how you're going to organize and run your lessons, the content knowledge is key because if you don't have that, then it doesn't matter how hard you try to prepare, you're underprepared, because that look for is not there. Being able to notice and name, and then being able to, essentially, once you've noticed and named what a student has done, to know what comes next. And Jon and I are constantly talking about that with our igniting the next moves piece of the framework, which is this idea of really understanding that trajectory of math learning that students travel down. And that's something that we continue to try to do, and, clearly, you are also an advocate for that, continuing to try to grow your own math mind as well.
And we're just thrilled that we've got some great ideas and some great links to share. We're going to definitely get that Facebook group up there in the resource page. We'll throw in learningtrajectories.org, which is a great resource. And we'll also grab some of those Running Records links, as well as to the book, so... I'm wondering, before we wrap up though, is there anywhere that the Math Moment-Makers can learn more about you specifically in your work, some of which that you've already mentioned here, but where can they find more about you and get connected?

Ann Elise: Sure. I have a webpage, anneliserecord.com. You can check that out, and check out all the different offerings and things I have for you there. And honestly, I have found that connection in the Facebook community because I was living in Northern New Hampshire for over 20 years, and I found this amazing collection of people online. So they're just brilliant and generous and kind. And so, I began in Twitter a little bit, and then in Facebook, creating communities of people willing to learn. So I run a Facebook group of my own called Elementary Math with Ann Elise, and that's any math topic, K five is on the table, anything you want to talk about to give advice and all.
And then I facilitate the Math Running Records one. We have over 13,000 people in there right now. And so that group is focused on fluency. So that's the fluency piece. So the Elementary Math with Ann Elise is that, anything, like fractions or any other topic on mathematics, but the Math Running Records is that fluency one. So joining in those groups or following me on Facebook... I have a growth mindset tree as my picture, because that's my math profile on Facebook. So I only share math things there. So if you follow me there on Facebook, you could continue learning about me.
And I also have a newsletter that I do because I know and respect the fact that people may not want to be on Facebook or social media, so they can subscribe to my newsletter, and I send it out but once every week or two, with all the links and the great things that I come along.

Kyle Pearce: Awesome stuff, thanks for sharing that. We'll make sure that all of that is in the show notes page for this particular episode. Ann Elise, we want to thank you for taking time out of your day to share your expertise with us and our listeners. And we hope you enjoy the rest of your day. And we really appreciate talking to you and hopefully we can catch you at a face-to-face conference sometime in the future.

Ann Elise: Let's hope, absolutely. Thank you so much for having me, I really appreciate it.

Kyle Pearce: Thanks so much, we'll talk to you soon.

Ann Elise: Okay, take care.

Kyle Pearce: It was awesome to finally welcome Ann Elise onto the show to chat with us about her amazing efforts in conceptualizing mathematics.

Jon Orr: Hopefully this conversation has inspired you to dive into your next math class using a problem-based approach.

Kyle Pearce: Right? So be sure to check out the Wooly Worm Race, the Snack Time unit, or any of the other problem-based units that are available for you to dive into right now over at makemathmoments.com/tasks.

Jon Orr: Absolutely, Kyle. Get on over to makemathmoments.com/tasks to run one of these awesome problem-based units in your class today.

Kyle Pearce: In order to ensure you don't miss out on new episodes, make sure that you smash that subscribe button on Apple Podcasts or on your favorite podcast platform. And, did you know that these episodes are also on our YouTube channel? And you know what, Jon? We've been doing a lot of these YouTube lives lately, so be sure...

Jon Orr: Yeah, we're getting ready...

Kyle Pearce: To subscribe over on YouTube, because we got some pretty cool little tricks up our sleeve that we're hoping to do each and every week.

Jon Orr: Yeah, we've got some new stuff coming. Also, if you're liking what you're hearing, please share the podcast with a colleague, help us reach our wider audience by leaving a review on Apple Podcasts, and tweet us over at Make Math Moments on Twitter, or Instagram, or on Facebook.

Kyle Pearce: Show notes and links to resources, including full transcripts that can be downloaded or read right from the web for this episode, and all the other episodes can be found over at makemathmoments.com/episode113. Again, that's makemathmoments.com/episode113. Well, my friends, until next time, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us...and a big high five for you.

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Episode #113: Fluency Doesn't Just Happen - An Interview with Ann Elise Record - Make Math Moments

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Today we speak with Ann Elise Record. Ann Elise is a seasoned educator with a career spanning over two decades of elementary classroom experience. These days she's a K-5 math coach who works with districts on developing strategies to increase students' fact fluency as well as how to use manipulatives in the classroom.

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Dr. Hilary Kreisburg Dumovic and Dr. Matthew Beyranevand

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Adding Parents to the Equation | Facebook

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In this group, we aim to help parents better understand how math is taught today at the early education level (preschool - grade 5) and why the way we teach math is different than how we learned it....

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KY Center for Math - TONS of amazing games

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KY Center for Math - TONS of amazing games

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Due to school firewalls and security restrictions, students may not be able to access resources directly from this site. To give a student access, please first save a copy of the resource to a teacher-owned Google account, then connect the student to the teacher-owned copy. See the video tutorial on "How to share Google files with students" for more information.

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Due to school firewalls and security restrictions, students may not be able to access resources directly from this site. To give a student access, please first save a copy of the resource to a teacher-owned Google account, then connect the student to the teacher-owned copy.

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Parent advice from Stanford Professor Jo Boaler

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Parent advice from Stanford Professor Jo Boaler

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Padlet shared by Sue O'Connell for exploring math through literatures grades 3-5

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Padlet shared by Sue O'Connell for exploring math through literatures grades 3-5

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Get a daily email featuring the latest talk, plus a quick mix of trending content.

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Dan Finkel: 5 ways to share math with kids

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Mathematics is not about following rules, it's about playing-and exploring, fighting, looking for clues, and sometimes even breaking things, according to Dan Finkel. In this playful, inspiring talk, the founder of Math for Love offers teachers and parents alike a five-step guide to sharing the beauty and playfulness of mathematical thinking with children.

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Kids Math Talk - a podcast for Teachers and Parents  Interview with California Early Math Symposium creators

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Kids Math Talk - a podcast for Teachers and Parents  Interview with California Early Math Symposium creators

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Advocating for Early Math with Carolyn Pfister and Lisa Grant

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Register for the Early Math Symposium happening June 25, 2021 Desiree Harrison 0:00 Looking for some professional learning opportunities this summer? One focused on children ages 0 to 8 years is happening on June 25, 2021 - The Early Math Symposium. Tickets are absolutely free and there is a great lineup of speakers and breakout sessions.

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Looney Math

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Same But Different is a powerful routine for use in math classrooms. The images can be used for teaching a way of thinking: grayscale thinking, categorical thinking; helping students to build a network of ideas and an approach for learning and thinking about mathematics.

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Math is Figureoutable Parent Group (search within Facebook)

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Math is Figureoutable Parent Group (search within Facebook)

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by Pam Harris

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Download PDF Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts By Jo Boaler, Professor of Mathematics Education, co-founder youcubed With the help of Cathy Williams, […]

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Build Math Minds Podcast on Math Running Records

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Build Math Minds Podcast on Math Running Records

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Do you like to draw? If you're great at it, you can get paid to draw as your job! Look at Jim Paillot, who draws the pictures or "illustrations" in the Bedtime Math books, dozens of My Weird School books, and many others.

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Dr icki Newton and I joined podcast host Melissa Milner to create a List of 10 favorite math daily routines. Such fun!

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The Teacher As...Top Ten episodes are a new addition to the podcast. Dr. Nicki Newton and Ann Elise Record collaborate to create one top ten list of math routines. The collaboration gets a bit intense when the two disagree as they get closer to the top five picks. These math educators have so much to share in this episode.

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030: The Teacher As...Top Ten Math Routines with Dr. Nicki Newton and Ann Elise Record - The Teacher As...

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The Teacher As...Top Ten episodes are a new addition to the podcast. Dr. Nicki Newton and Ann Elise Record collaborate to create one top ten list of math routines. The collaboration gets a bit intense when the two disagree as they get closer to th...

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Watch our weekly Facebook Live Show on Wednesdays at 7:30pm eastern. Sign into our group at www.facebook.com/groups/pibeforedinner

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Helpful tips for parents of math-averse children

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Skip to Content

In these times of uncertainty, youcubed is here to help students at home continue to explore and learn maths in rich and creative ways. We are collecting here modified versions of our tasks to be more home-friendly, as well as some new explorations designed for learners at home.

Please help us distribute these to anyone who might use them and share your students' work with our community using the hashtag #YoucubedAtHome in social media.

HIGH SCHOOL TEACHERS: learn to teach our data science course this fall in ten 2-hour, online, afternoon (Pacific) sessions! More info here

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In these times of uncertainty, youcubed is here to help students at home continue to explore and learn maths in rich and creative ways. We are collecting here modified versions of our tasks to be more home-friendly, as well as some new explorations designed for learners at home.

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Various game options with Tiny Polka Dot cards from @mathforlove

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Various game options with Tiny Polka Dot cards from @mathforlove

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Tiny Polka Dot is absolutely fantastic. It gives J a structure that he enjoys exploring, and when he tires of the Match 7 game, we will move on to Match 8, Match 9, or any of the dozens of games and iterations we can create from these cards.

These cards are going to be part of our playtime for years to come.

Kent Haines, The Process Column

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Tiny Polka Dot is absolutely fantastic. It gives J a structure that he enjoys exploring, and when he tires of the Match 7 game, we will move on to Match 8, Match 9, or any of the dozens of games and iterations we can create from these cards.

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Build Math Minds Podcast. Host Christina Tondevold interviews Cathy Palkovic about when her students determined how many cards were in 6 boxes of hundreds of decks of cards. Wow!

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Build Math Minds Podcast. Host Christina Tondevold interviews Cathy Palkovic about when her students determined how many cards were in 6 boxes of hundreds of decks of cards. Wow!

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Episode 60: Building Self-Reliance in Math

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Welcome, fellow recovering traditionalist, to episode 60. Today is an interview with third-grade teacher, Cathy Palkovic, and a theme of our conversation is about building self-reliance in math. Christina - In this interview with Cathy, we get into it all kinds of things, from what her distance learning looks like to Math Running Records, to how her third-graders solved 898 x 52 and they did it without any guidance from her.

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Parents know that we need to read 20 minutes a day with our kids.

But teaching math to your kids doesn't have to be intimidating. It can be fun. Just as children say goodnight to the moon, they can say hello to numbers, shapes and measurement.

Talking Math with Your Kids provides ideas and products that get children and caregivers talking about math with creativity and joy.

Whether you're reading books on the couch, cooking dinner, running errands, or scheduling your day, opportunities for math talk abound.

This website collects research about, and examples of, math talk with children. Each post offers suggestions for adapting the examples for your own children, interests, and lives.

Enjoy and let me know how those conversations are going in your home. Use the contact form to ask questions, send feedback or to send along a conversation for highlighting on this site.
Thanks for reading. Read more about Christopher

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Parents know that we need to read 20 minutes a day with our kids. But teaching math to your kids doesn't have to be intimidating. It can be fun. Just as children say goodnight to the moon, they can say hello to numbers, shapes and measurement.

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California Mathematics Council

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A great place for parents to start supporting their children's mathematics learning is Math at Home, short parent guides to mathematics education. These booklets were written expressly for parents and guardians of Pre-K and K-12th grade children. Each booklet contains straight-forward information, practical suggestions, and resources for families who wish to better understand the importance of mathematics and the role they can play in helping children learn this critical subject.
The California Mathematics Council wants you to share the Pre-K and K-12 Math at Home resources with parents, guardians, and families!
The Math at Home parent guides to mathematics education are available in editions for Pre-K or K-12 in either English or Spanish.
Click on any of the Math at Home cover images below to view or download individual articles from that parent booklet.
To download a FREE complete copy of that Math at Home parent guide click on the links below the cover.

The California Mathematics Council grants permission to share these files with parents, guardians, and educators-all other uses require expressed permission.

Math at Home parent guides to mathematics education low cost paper booklets are available for purchase. To order booklets for use in your school or organization, click here:

CMC hopes you will use these tools in your work with English and Spanish speaking parents so they might in turn work with their children to help them to enjoy, appreciate, and understand mathematics.

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A great place for parents to start supporting their children's mathematics learning is Math at Home, short parent guides to mathematics education. These booklets were written expressly for parents and guardians of Pre-K and K-12th grade children.

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The Top 3 Facts Every Parent Needs to Know About Today's Math

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Math at Home

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What Happened to Math: Understanding the Shifts in Math and How to Help Support Your Child's Learning

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What Happened to Math Class? Understanding the Shifts in Mathematics Teaching and How to Support Your Child's Learning

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I recently facilitated an information session for parents and educators to help them understand the changes in mathematics education. 

Visit http://mathleadership.org/what-happened-to-math-class/ to access resources that support this session and to see the video broken into chapters. 

To get updates on new videos and resources, follow me here: https://twitter.com/MikeFlynn55

If you would like to learn more about these ideas, you can get my book, Beyond Answers: Exploring Mathematical Practices with Young Children: https://www.stenhouse.com/content/beyond-answers

If you would like me to come to your school, district, or organization to work with your teacher, contact me at mflynn@mtholyoke.edu

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Illustrative Math Suggestions for Caregivers

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Illustrative Math Suggestions for Caregivers

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Links to Math Resources for Caregivers - IM CERTIFIED® BLOG

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Here is a collection of links the content team here at IM has used with our own students and kids to start mathematical conversations, play math games together, explore new topics, come up with projects, and have fun. There are also some cool links to other education stuff, like virtual museum tours…

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Washington Post Article Explaining Why We are Exploring Math the Way We Are Now.

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Washington Post Article Explaining Why We are Exploring Math the Way We Are Now.

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Student work posted in an elementary school before the pandemic shows the "partial product" method of solving a multiplication problem, one of many methods students have learned with Common Core. (Jackie Mader/Hechinger Report)

Allonda Hawkins said the way her children are expected to do math is "100 percent different" from the way she learned.

"There are terms that I've never heard before, like arrays. It's very foreign to me and it's hard to teach," said the 38-year-old real estate agent from Winston-Salem, N.C.

The mother of four children, ages 5 to 11, often turns to YouTube for explanations and recruits her fifth-grader to help the younger children. Hawkins said she's catching on more now that she can eavesdrop on her kids' online classes, but she still is frustrated that she doesn't have more guidance.

Parents across the country are getting an up-close look at math instruction - and, like Hawkins, they don't always know what to make of it. But with about half of American kids still learning at home as of Feb. 21 (either all virtually or in hybrid programs), it's time for parents to get up to speed.

Experts say it's important for parents to know the basic ideas behind the current methods if they are going to help their kids. Positive parental help could make the difference between students being excited about math or falling behind during the pandemic, said Jennifer Bay-Williams, co-author of "Elementary and Middle School Mathematics: Teaching Developmentally" and professor of education at the University of Louisville.

The new approach is actually not all that new. It's grounded in research going back more than 30 years and is reflected in the Common Core State Standards, which are used in 41 states. (And most states now follow standards with the same principles, even if they don't call them Common Core.) Instead of memorizing procedures to solve problems, kids are asked to think through various ways to arrive at an answer and then explain their strategies. While some parents believe these methods are just a more complicated way of teaching math, they are designed to promote a deeper understanding of the subject and help students make lasting connections.

Kids' math skills have taken a hit during the pandemic. Here's how parents can help.

"There's not just one way to solve a problem," said Megan Burton, president of the Association of Mathematics Teacher Educators and associate professor of elementary education at Auburn University in Alabama. To fully grasp deeper mathematical concepts, "students need to think about what makes sense and build on what they learn."

Making sense of problems and persevering in solving them is the top priority, said Bay-Williams.

When watching a kid struggle to complete a math problem, "it's very tempting for a parent to want to get in there and rescue the child, which doesn't always help in the long run," Burton said. Research is clear that allowing kids to experience a "productive struggle" - wrestling with an idea or pondering a new concept - pays off in children's math ability.

In Common Core, math students are asked to look at numbers and think about the amounts they represent. For instance, 100 can be thought of as 100 ones, or a bundle of 10 units of 10, or "10 tens." And 127 can be thought of as a bundle of 12 units of 10 and seven ones, or "12 tens and 7 ones," or even "10 tens and 27 ones."

Students are asked to use the idea that numbers can be represented differently when problem-solving, too. Take 4 x 27. Traditionally, a student would line up the numbers vertically, multiply 4 x 7, carry the 2, then multiply ... well, most adults remember the procedure. (The answer is 108.)

Now, kids are encouraged to think: Wait a minute, that's really just 4 x 25, which is 100, plus 4 x 2, which is 8. If I add the two products together, I get 108.

"That works pretty slick and makes more sense," said DeAnn Huinker, professor of mathematics education at the University of Wisconsin at Milwaukee and director of the university's Center for Mathematics and Science Education Research. "I can do that in my head, write down a couple of partial products and add it up."

Huinker advocates redefining math success: "It's not being able to tell me the answer to three times five within a heartbeat. Rather, being successful means: 'I understand what three times five is.' "

For some students, it might help to use a number line to see the relationship between numbers. If a student is given the problem 12 minus 7, the student can start at 7, jump to 10 (that's 3), and then jump to 12 (that's 2), so the difference is 3 plus 2, or 5. Ten in this example is known as a "benchmark number," said Huinker, and students are encouraged to use benchmarks to move toward more efficient and meaningful computation strategies.

An array, which flummoxed Hawkins, is a model that students can use to master multiplication. It's essentially a grid. Students can plot out 5 x 6 by coloring in five rows of six or six columns of five. Count the total number of squares and you've got the answer: 30. Break the grid apart into sections, and you can see three sets of 10. The visual representation can also help kids understand area and measurement and can plant the seed for connections that will help in later math.

This is why it's so hard to help with your kids' math homework

In China Grove, N.C., Millbridge Elementary School hosted a webinar last fall for teachers to explain math expectations to parents and tamp down pressure for perfection with homework.

"We honor and value mistakes, because mistakes are how we learn," said Abby Covington, a mathematical instructional coach at the school.

In time, students will learn to do the traditional approaches to solving problems their parents were taught, but Covington said the idea is to build a proper foundation: "I tell parents we are going to get there ... that's our ultimate goal, we're just not in a race."

To help demonstrate the value of the new flexible approach, Mathew Felton-Koestler, associate professor in the department of teacher education at Ohio University, produces videos for parents such as "What's Wrong With Carrying the One?"

"People worry that if we are focused on these different strategies, kids aren't going to be good at doing computations.," Felton-Koestler said. "That doesn't turn out to be true. They end up being just as good - and much better at higher-order type tasks."

Some parents of older kids are finally seeing the long-term benefits of all that early focus on how to think about math. Despite having an MBA, Michelle Majdoch, 46, of Coral Springs, Fla., said she was initially confused by her kids' math homework with the story problems and drawing to show their work.

But now that her children are in fourth, fifth, 10th and 12th grades, she gets it. Having to learn three ways to do a problem in the early grades made each of her kids discover the methods that made the most sense to them. These days, her high school daughters are doing well in Algebra 2 and pre-calculus.

Michele Alley, who has two elementary-schoolers, isn't there yet. She and her older child, Cora, who is attending third grade from a spare bedroom in the family's home in Monticello, Ky., often disagree about how to do math homework.

If it's something Cora understands, she follows her teacher's directions. But if her daughter gets stuck, Alley said, she doesn't know how to help other than to demonstrate the way she learned it in the 1990s - working through the problem by writing out the equation on paper.

In Alley's district, Bell Elementary hosts math nights for families twice a year to help bridge the home-school divide, and in October pivoted to a drive-through event on a Saturday morning. It drew 300 people, said Jamie Reagan, a first-grade math intervention teacher at Bell. Teachers gave out bags with math games and information on math standards in "layman's terms," said Reagan.

Reagan also regularly provides math packets with cards, counters and other materials for her students. Still, teachers here expect many students will likely not meet grade-level expectations when they are assessed later this spring.

Meanwhile, parents can help by pointing out math in daily life. Bay-Williams, the author of a book on teaching math to kids, said parents should trust their intuition about what ends up being importantthis year.

"Take a deep breath," she advised parents. "Kids are resilient, they are learning things at home ... that are going to serve them in other ways."
This story about teaching math was produced by Follow More reading: For high school athletes, sports during the pandemic caused grief. Here's how parents can help. A teacher's pandemic dilemma: Struggling students and a state-mandated test on the horizon 7 strategies for parents who hit the pandemic wall On Parenting on Facebook and join our discussion group here to talk about parenting and work. Sign up here for our weekly newsletter. the Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Hechinger newsletter.

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Confused by your kid's math homework? Here's how it all adds up.

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Elementary students are taught math in ways that can make parents' heads spin, but there are good reasons for the new methods.

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The site also offers expert insights into how to spark your child's interest in math and promote positive math attitudes. You also can share your experiences with other families and ask questions of our math learning team. Explore the links below to get started and keep our guiding principles in mind - Math is a Process, Math is Everywhere, and Math is Social.

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Need a way to get students more excited about building math skills? A deck of playing cards might just be the answer. These math card games work for little ones and older kids alike, and they're all free to learn and play. Draw a few to add to your winning math class hand today!

1. Match to make eleven

Lay out three rows of three cards each, face up. Then check to see if you can find any two cards that add up to eleven. If so, remove those cards and set aside. Replace them with new cards from the deck. Continue until you run out of cards or can't make any more matches.

Learn more: Game Rules

2. Race to 100

Flip a card and add its value to your running total. First person to reach 100 without going over wins! (Remove face cards for younger players; use these values for older kids: Jack-11, Queen-12, King-13, Ace-0.)

Learn more: 123Homeschool4Me

3. Play a game of 21

In Vegas, they call this one "Blackjack," but it makes a great learning game for kids too (no need to place bets). Not only do they practice their addition skills, but they'll also get a little practice at thinking logically and calculating the odds.

Learn more: Planning With Kids

4. Try pyramid solitaire alone or in teams

Some versions of solitaire are really just sneaky math card games, and pyramid is one of them. Try to find cards that add up to 10 as you clear your pyramid row by row. Learn how to play at the link below.

Learn more: Multiplication.com

5. Flip and add one or subtract one!

There are a few versions of this basic addition and subtraction game. We like this one: Remove the face cards from the deck. Flip a card. If it's red, add one and say the amount out loud. If it's black, subtract one. Get it right? You get to keep the card!

Learn more: Plus One Minus One/Creative Family Fun

6. Go fish for pairs that make 10

Your students probably already know how to play Go Fish, but in this version, they're fishing for pairs that add up to 10. Have them ask: "I have a 2. Do you have an 8 to make 10?" Change aces to 1 for this game and leave face cards out entirely.

Learn more: Go Fish/The First Grade Roundup

7. Calculate the gain or loss

Each player starts with 15 points. Player one flips a card (remove face cards or assign them point values first). If the card is black, they add it to their total. If it's red, they subtract it. Highest point total when all the cards are gone wins! Get a free printable worksheet to use with this game at the link.

Learn more: Guided Math

8. Practice counting on with cards

Remove the face cards for this one, and grab a die. Players flip a card and roll the die. Starting with the number on the card, they "count on" using the number on the die. For instance, if the player flips a 7 and rolls a 4, they would say, "Seven... eight, nine, ten, eleven." If they get it correct, they keep the card.

Learn more: Creative Family Fun

9. Turnover and multiply (or add)

This one is so simple! Have students pair up. One person flips two cards from the deck. The first student to multiply (or add, depending on what you want to practice) them correctly and call out the answer wins and takes both cards. Play continues until all the cards are gone, and the winner is the one with the most cards.

Learn more: Turnover/Top Notch Teaching

10. Try for a total of 10

Play this math card game alone or as a team. Lay out 20 cards on the table (leave out face cards or change them to equal 0, while aces equal 1). Kids remove sets of cards that add up to 10, ultimately trying to remove all the cards from the table. It's harder than you think!

Learn more: Total of 10/The First Grade Roundup

11. Practice number sequencing with "builder's paradise"

Simple math card games can help kids learn how to put numbers in order. To play builder's paradise, discard the face cards and lay out the 4 sevens in a deck side by side. In each round, players work to add the next higher or lower number in each suit, trying to be the first to get rid of all their cards. Get the full how-to at the link below.

Learn more: Builder's Paradise/Math Geek Mama

12. Add decimals to "make a buck"

Draw, swap, and discard to make a hand that equals $1. Learn what face cards equal and get all the rules at the link.

Learn more: Make a Buck/Math Geek Mama

13. Declare a fraction war

War is one of the original math card games, but this version adds a fraction aspect. Students deal two cards, a numerator and denominator, then determine whose fraction is the largest. The winner keeps all four cards, and play continues until the cards are gone. ( Click here for more fun and free fraction games.)

Learn more: Math File Folder Games

14. Learn numbers with card bingo

Remove the face cards and have each student lay out a 4 x 4 playing "board" of cards. The remaining cards (or another deck) are placed face down, and a caller flips over a card. Any player who has that number on their board turns the card face down. Play continues until one player has a row flipped over horizontally, vertically, or diagonally and calls "Bingo!"

Learn more: Card Bingo/Top Notch Teaching

15. Play a game of "I Spy"

Lay out cards on the table, then take turns giving clues. "I spy two cards that add up to 12." Differentiate for younger kids with options like, "I spy a card that's less than 4," or for older ones: "I spy two cards that are factors of 12."

Learn more: Susan Jones' Teaching

16. Use order of operations to get to 24

Math card games aren't just for little kids; even adults will find this one a bit tricky. Each player is dealt four cards, then uses the order-of-operations rules to try to make a number as close to 24 as possible. Simple but challenging!

Learn more: Learn With Math Games

17. Take a gamble with triple-digit dare

Each player gets three cards and privately determines the highest three-digit number they can make (you can use decimals or not, depending on age). Then, each player has a turn to stick with the cards they have, swap with one from the deck, or steal one of the other player's. All players then lay down their best number to see who wins. See more at the link below.

Learn more: Math Coach's Corner

18. Deal and round to tens to win

Each player deals two cards and lays them on the board. Then, round to the nearest ten to find the winner of that hand.

Learn more: Adventures in Third Grade

19. Find a way to make 10

One of the terrific things about math card games is that many of them can be customized for various concepts and skill levels. The original goal of this game was to look at the cards you're dealt to find ones that add up to 10, but it can be changed to 15, 20, or any number you choose. You can also add to the difficulty by allowing addition and subtraction (for example, you could use 8+4=12 and 12-2=10). Get the rules and free printable mats at the link below.

Learn more: Mama.Papa.Bubba

20. Use Close Call to practice two-digit addition or subtraction

The best math card games are simple at heart. To play Close Call, each player deals themselves four cards, then determines how to arrange them so they make two two-digit numbers that add up as close as possible to 100 without going over. For a subtraction version, work to get as close to zero as possible. Learn how to play at the link.

Learn more: Close Call/Math Geek Mama

21. Let card color indicate negative or positive

In this game, red cards are negative integers, while black cards are positive. Students attempt to play pairs of cards that total 6 or -6. You can change the goal number as needed.

Learn more: Filing the Frame With Learning

22. Take a trip around the card spiral to practice math facts

You'll need a pair of dice for this math card game. Lay cards out randomly in a spiral formation as shown, and set a marker for each player on the center card. Player one rolls the dice then moves their piece that number of spaces shown. They then must multiply (or add or subtract, depending on preferences) the card number by the number on the dice. If they get the answer correct, they stay where they are. If not, they return to their original card. Play continues until one player reaches the end.

Learn more: My Baba

23. Flip to make a prime number

Flip two cards. If you can add, subtract, or multiply them to make a prime number (use one or all of these operations), you get to keep them.

Learn more: Flip for Prime/Games4Learning

24. Be the fastest in the race to pi

In this game, kids work to lay out the digits of pi in order. It's a simple draw-and-play game, but will help familiarize students with this important number. You can write out the digits first or see who knows them from memory. Find out how to play at the link below.

Learn more: Race to Pi/Math Geek Mama

25. Pick three to make number sentences

Flip any three cards. If you can use them to form a valid number sentence (8-3=5), you keep the cards!

Learn more: Number Sentences/Games4Learning

26. Do some basic fast facts practice

Give your flashcards a rest and practice facts with math card games instead. Simply lay down two cards from the deck (remove the face cards first) and add, subtract, or multiply them. Kids can work on this alone, or you can make it a contest to see who can call out the correct answer first.

Learn more: Math Facts/Top Notch Teaching

27. Challenge them to beat the teacher

Practice place value by drawing cards and trying to build the largest number possible. Kids play against the teacher to see who wins! Get the rules at the link below. ( Find more fun place value activities here.)

Learn more: The Teaching Love Fest/TpT

28. Read minds to figure out the correct numbers

Two students draw a card from the deck without looking and hold it up to their forehead facing out. A third student mentally multiplies the numbers and gives them the product. The students then must figure out what number each is holding. You can do this with addition and subtraction too. You'll find this game along with dozens of other math card games in the free printable book at the link below.

Learn more: Acing Math (PDF)

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28 Card Games That Will Turn Your Students Into Math Aces

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Need a way to get students more excited about building math skills? A deck of playing cards might just be the answer. These math card games work for little ones and older kids alike, and they're all free to learn and play. Draw a few to add to your winning math class hand today!

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Math Resources for Parents and Families | ST Math

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Help your child succeed with this collection of math resources for parents and families. Includes research-based tips, articles and activities for deeper learning.

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Model your word problems with Thinking Blocks! Only at MathPlayground.com.

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Marilyn Burns blog

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Games shared by Jennifer Bay-Williams in her NCTM session on including parents

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Games shared by Jennifer Bay-Williams in her NCTM session on including parents

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NCTM100 Engaging Families in Fact Fluency with JBayWilliams

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all 3 versions

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Share your videos with friends, family, and the world

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TONS of games that can be played at home modeled by a father and daughter

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TONS of games that can be played at home modeled by a father and daughter

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With so many families grappling with the effects of COVID-19 and trying to provide quality home-schooling for their children, I decided to share some of my favourite maths games. All of the games have been selected because they are filled with rich learning opportunities, do not require very much in terms of resources and are both fun and easy to play.

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Double Digit Addition

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Gamewright - Zeus on the Loose - A Card Game of Mythic Proportions
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Gamewright - Zeus on the Loose - A Card Game of Mythic Proportions

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Amazon.com: Gamewright - Zeus on the Loose - A Card Game of Mythic Proportions : Staff: Office Products

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Upper Elementary

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Sum It Up! Sums of Fractions, Decimals, Integers

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These classroom-tested sets include everything you need to play three different games. In each game, players place tiles in a row on the board horizontally or vertically - just be sure they all add up to the target number forthat game. Earn points based o

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Theresa Wills games including card games virtually

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Theresa Wills games including card games virtually

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Games - Where THERE'S A WILLS, there's a way

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Synchronous Online Teaching Strategies and all material on this website by Theresa Wills is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Based on a work at theresawills.com. Permissions beyond the scope of this license may be available at theresawills.com/permissions.

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Reckon Math: Board Games for Early Mathematics

This site provides a systematic, step-by-step program of more than 300 two-player math games and more than 50 activities to focus students' attention on mathematical concepts. These resources aren't just for practicing, they are for learning.

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Reckon Math: Board Games for Early Mathematics This site provides a systematic, step-by-step program of more than 300 two-player math games and more than 50 activities to focus students' attention on mathematical concepts. These resources aren't just for practicing, they are for learning.

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🥳 Welcome to your new favorite math game! Salute is a low-prep, high-power game for building fact fluency (+ or x)! It builds understanding of part-part-whole and the relationship between operations. Watch to learn how to play! #MathGames #iTeachMath #Math #mtbos #Math4All

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🥳 Welcome to your new favorite math game! Salute is a low-prep, high-power game for building fact fluency (+ or x)! It builds understanding of part-part-whole and the relationship between operations. Watch to learn how to play! #MathGames #iTeachMath #Math #mtbos #Math4All https://t.co/k9SYLqYZQe

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🥳 Welcome to your new favorite math game! Salute is a low-prep, high-power game for building fact fluency (+ or x)! It builds understanding of part-part-whole and the relationship between operations. Watch to learn how to play! #MathGames #iTeachMath #Math #mtbos #Math4All pic.twitter.com/k9SYLqYZQe
— All Learners Network (@AllLearnersMath) February 9, 2022

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🥳 Welcome to your new favorite math game! Salute is a low-prep, high-power game for building fact fluency (+ or x)! It builds understanding of part-part-whole and the relationship between operations. Watch to learn how to play! #MathGames #iTeachMath #Math #mtbos #Math4All https://t.co/k9SYLqYZQe

# data[].attributes.attachment_link.metadata.attachment_props.original_text
🥳 Welcome to your new favorite math game! Salute is a low-prep, high-power game for building fact fluency (+ or x)! It builds understanding of part-part-whole and the relationship between operations. Watch to learn how to play! #MathGames #iTeachMath #Math #mtbos #Math4All https://t.co/k9SYLqYZQe

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🥳 Welcome to your new favorite math game! Salute is a low-prep, high-power game for building fact fluency (+ or x)! It builds understanding of part-part-whole and the relationship between operations. Watch to learn how to play! #MathGames #iTeachMath #Math #mtbos #Math4All

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KY Center for Math Family Games Resource Page - Printables and Suggested ones for purchase

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KY Center for Math Family Games Resource Page - Printables and Suggested ones for purchase

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Reckon Math: Board Games for Early Mathematics

This site provides a systematic, step-by-step program of more than 300 two-player math games and more than 50 activities to focus students' attention on mathematical concepts. These resources aren't just for practicing, they are for learning.

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Reckon Math: Board Games for Early Mathematics This site provides a systematic, step-by-step program of more than 300 two-player math games and more than 50 activities to focus students' attention on mathematical concepts. These resources aren't just for practicing, they are for learning.

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Our flagship game, nerdle, was inspired by Wordle and a passion for math. It challenges you to find the hidden calculation in just six guesses. In the wider nerdleverse, you'll roam an entire galaxy of puzzles, including number-based crosswords, anagrams, and so much more. Whether you're a math enthusiast or just looking for a daily brain workout, the nerdleverse has something special for you. Join us and let your mind explore the wonders of the nerdleverse!

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Nerdle - guess the solution in 6 tries - try classic, mini, speed and pro

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10 Books to Spark a Love of Math in Kids of All Ages - MindShift

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The committee also looks for books touching on a range of interests. "A lot of kids don't think of themselves as math people, but the intention of the award is to help kids understand that math is for everybody," says Bohl. Below are 10 books on the Mathical list, including this year's winners.

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Graham Fletcher blog and video

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Question: If you memorizeyour basic math facts have you learned them?

The term from memory is used twice in the K-5 math standards, and they continue to be the most misunderstood words I encounter each day. The term "from memory" does not suggest that students mindlessly their basic facts the way we were taught.

Here's my first stab at an Ignite Talk explaining the difference between from memory and memorization that I recently shared with some teachers and administrators.

Here's the link to the Prezi

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From Memory and Memorization: There IS a Difference

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Question: If you memorize your basic math facts have you learned them? The term from memory is used twice in the K-5 math standards, and they continue to be the most misunderstood words I encounter...

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Build Math Mind's Page of Video Resources

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Build Math Mind's Page of Video Resources

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Build Math Minds Elementary Math Trainings

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Free trainings for teaching mathematics, whether at home or at school.

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Steve Wyborney's  free Multiplication Course for Students and Parents on Youtube

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Steve Wyborney's  free Multiplication Course for Students and Parents on Youtube

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math "steve wyborney" "number sense" multiplication teaching elementary

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Share your videos with friends, family, and the world

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The Story of Maths 1 of 4 The Language of the Universe

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FogStone Isle Game - Use student Gmail account

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FogStone Isle Game - Use student Gmail account

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The Progression of Fractions (Meaning, Equivalence, & Comparison)

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This book illustrates what is wrong with math education. It uses badly executed pictures (that look like drawn by a 7 years old) silly texts (that look like composed by a 9 years old) to try to - supposedly - describe what math is about. I purchased it to use with my middle school students (ages 11-13) - but it insults their intelligence. I was then thinking to use it with my 7 years old granddaughter - but it is too silly even for her. Thanks Heavens, Amazon has a pretty flexible return policy and the Purolator drop off box is close by.
PS: To make my day even more disappointing, when I tried to find an envelope where I could fit this book to return it, I found out the format of the book to be quite tricky to be fitted inside normal large size envelopes.

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I'm Trying To Love Math [Bethany Barton] on Amazon.com. *FREE* shipping on qualifying offers. I'm Trying To Love Math

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After touring a German submarine in the early 1940s, young Raye set her sights on becoming an engineer. Little did she know sexism and racial inequality would challenge that dream every step of the way, even keeping her greatest career accomplishment a secret for decades. Through it all, the gifted mathematician persisted―finally gaining her well-deserved title in history: a pioneer who changed the course of ship design forever.

The Girl With a Mind for Math: The Story of Raye Montague is the third book in a riveting educational series about the inspiring lives of amazing scientists. In addition to the illustrated rhyming tale, you'll find a complete biography, fun facts, a colorful timeline of events, and even a note from Montague herself!

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The Girl With a Mind For Math: The Story of Raye Montague (Amazing Scientists)

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The Girl With a Mind For Math: The Story of Raye Montague (Amazing Scientists) [Finley Mosca, Julia, Rieley, Daniel] on Amazon.com. *FREE* shipping on qualifying offers. The Girl With a Mind For Math: The Story of Raye Montague (Amazing Scientists)

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Math makes the world go around. An educational book that will give you surprising answers to everyday math challenges. will not only change your child's perception of numbers but give them the skills and understanding to apply the principles in their everyday life!

This book unpacks how math is an essential part of our everyday life in ways that you never thought of. Full of crazy facts, magic tricks, and mathematical brainteasers and beautiful illustrations show you that math is interesting, fun, and not intimidating at all!

Inspire your children with numbers and help bring mathematical explanations to life with this engaging educational book. Expand their knowledge in the complexity of understanding math by using simple illustrative examples.

This educational book explains the point of:

- Numbers and counting
- Shapes and measuring
- Patterns and sequences
- Probability and logic
- Data and statistics

To make these topics more exciting and impactful, the book is full of great puzzles, awesome games, and interesting facts that will break barriers in their understanding. "Try it out" examples give mathematical explanations that are simple and easy to grasp.

Ever wondered where math originated from? This fantastic educational book unpacks all the curious questions that your child has about math including intriguing historical stories that explore the often-surprising origins of math that we use in our daily lives.

Learn about how the formation of number sequences began, to the origins of trigonometry, and find out how to become a trillionaire! Math in our daily lives is used in many things that might not even seem that obvious.

Math Controls Just About Everything What's The Point Of Math?

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What's the Point of Math? (DK What's the Point of?)

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What's the Point of Math? (DK What's the Point of?) [DK] on Amazon.com. *FREE* shipping on qualifying offers. What's the Point of Math? (DK What's the Point of?)

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Find the clues and lift the flaps on this mathematical mystery!

Join Molly as she ventures into a curious world where nothing is quite as it seems. A trail of clues leads from scene to scene, presenting Molly with a number of challenges. But who is leaving the clues, and where will they lead? This interactive mystery shows math isn't just about numbers-it's about imagination! An explorative and creative approach to the world of mathematics.

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Molly and the Mathematical Mysteries: Ten Interactive Adventures in Mathematical Wonderland

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Molly and the Mathematical Mysteries: Ten Interactive Adventures in Mathematical Wonderland [Cheng, Eugenia, Artymoska, Aleksandra] on Amazon.com. *FREE* shipping on qualifying offers. Molly and the Mathematical Mysteries: Ten Interactive Adventures in Mathematical Wonderland

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This gripping mystery, spiked with math clues, follows quirky outcasts Lady Di and Tom Jones as they try to save their woebegone island community. In their trailer park next to the Folsom Energy Plant, people have started to vanish, and no one seems to care. At first the kids barely notice the disappearances themselves-until their beloved math tutor, Mrs. Clarke, is abducted too. Mrs. Clarke has left them clues to her whereabouts in the form of equations that lead them all over the trailer park, through hidden tunnels under nearby "Mount Trashmore," and into the Folsom Energy Plant itself, where Lady Di and Tom Jones and a gang of other misfits uncover the sordid truth about what's really happening on their island.
Readers "will be swept up in the fast talk and exciting action" ( Booklist ) of this "inheritor of The Westing Game " ( Kirkus ) that is sure to make math lovers of even the most determined number-phobes.

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Island of the Unknowns: A Mystery [Carey, Benedict] on Amazon.com. *FREE* shipping on qualifying offers. Island of the Unknowns: A Mystery

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Practice addition, multiplication, fractions and algebraic reasoning with our popular math games. Discover fun learning games kids love to play.

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Separate being fast from begin good at math

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Separate being fast from begin good at math

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Get to know Spotify for Podcasters, the free, all-in-one podcast platform for every creator.

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Hey, parents and teachers, welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris.

Kim Montague:

And I'm Kim Montague.

And to introduce us just a little: we teach math teachers. In this podcast, we help teachers refine their math teaching so that more students are more successful.

Kim Montague:

But in this week's episode, we're talking directly to you, parents. We know you have questions, so we decided to make a few episodes just for parents. So, welcome!

Yeah, thank you so much for joining us. You are so important. Your child is so important. You might be listening today because someone recommended this podcast to you. We are so grateful that you're joining us for the next few minutes. We've decided to tackle the really difficult conversation around why math instruction has changed. Why does it look so different? You might have seen The Incredibles movie, Incredibles 2, where there's this great scene where the dad is trying to help his son with his homework and he's excited and frustrated. "Math is math! You can't change math!" Some of you have seen that scene. I love that movie. Maybe you've felt that way as well. So what is going on with this new math? Why does it look so different than maybe what you were used to?

Kim Montague:

Yeah, we hear you because we're parents, and we're also teachers. We get calls from friends who are frustrated and trying to help their students. So we're aware that you want to be supportive to your kids and to your kids' teachers. We're also aware that you may feel frustration about math looking so different these days. So let's talk about that.

Yeah, and let me just say, we are so grateful that you care about your student's education. We want you to be involved. We love the fact that you're listening. Thank you so much for caring about you and your kids and how that's all going. And both Kim, you and I just said that math look so different. And we said new math. But let's actually do a little history about math and math instruction that you might find helpful, parents. I'm going to keep this super brief. But I want to give you a glimpse of the 'what' and help you understand the 'why'.

Kim Montague:

Yeah, the 'why' is so important for you to understand. That it's not actually 'new math' that's going on. What's maybe new is that what we're actually asking of kids is more than ever before, because we can. If you would briefly think back to the way you and I were taught how to add numbers. So parents, we would have been told to line them up underneath each other, and then add in columns starting from right to left. And that's a way that adding can be done.

Right. But it's not the only way. Like- and that might blow your mind just a little bit that there are other ways. It's not the definition of doing math is to do those steps. Like for example, let's take subtraction. Same thing. We were sort of taught to line the numbers up, borrow when needed, etc. However, there are other ways to subtract. So for example, Kim, how might you find, say 36 minus 19?

Kim Montague:

Oh, okay. So for 36 minus 19, I would actually think about 36 minus 20. And I know 36 minus 20 is 16. But I actually subtracted too much, just one too much. So instead of 16 then my answer would be 17.

Bam. And we kind of call that an Over Subtraction strategy. Now parents you might be thinking, Okay, well, that's actually what I would do. But, you know, that's not the way the teacher showed me. So on the paper, I might have done all the crossey-outies and borrowing and what they now call regrouping. You might have sort of done what the teacher said. But in your head, you were doing what Kim did. Well, to be clear, I wasn't. I was just dutifully doing what my teacher told me to do. So the math that we were taught was a way. Procedures. Steps. Where you line them up to add or multiply or you do that house top division. That gave many people the sense that procedures, that that procedure was the only way. When in reality, those procedures were only one way to get answers. And you might find it interesting that that one way is not actually typically the way that mathematicians solve those problems. Or sort of mathy people like engineers, that they do more like what Kim did, where they use relationships to solve problems. So the procedural way, the step by step way to get answers is a way to get answers. But what it doesn't do is help you understand numbers or mathematical relationships. Or how to reason better, how to solve problems, like Kim just did.

Kim Montague:

Yeah, some of you may use your intuition and relationships to solve problems when you're in the store or maybe other areas of your life. But some people don't. Why is that?

So a little history. Would you consider that I think that today's generation of parents and their parents were actually taught very similarly. That arithmetic is procedures: line the numbers up, get the answers. But the older generation actually had to use math to survive. What I mean by that is grandparents were calculating the same way in school, lining them up doing the procedures, but that they learned relationships in life, because they had to. They didn't have technology. So they counted back when they were getting changed. They had to pay bills and keep their checkbook current, unlike many of us today. All without technology. They didn't have cash registers, or, for sure, not calculators, or spreadsheets, none of that stuff was around. They had to reason about numbers to survive. But consider the next generation, the parents of today's students. For the most part, that generation was still taught math as steps and procedures to get answers in school. But now they have less real experience in life because they had technology. So my generation and younger were taught the same way. But they actually owned less Real Math, because we could just pick up a calculator, punch it into a cash register, use a spreadsheet on a computer, all of those things were sort of available to us. And because of that, we were kind of less in the experience of having to mess with numbers and figure out relationships. Let me give you a quick example. During the university, I had a couple of months over Christmas, where I worked in a drugstore. And if you - so a little bit more history about me. I was the quintessential, I memorized the steps, I did the procedures, I got answers. I was not doing what we now call "Real Math". I was not doing what we advocate now that teachers do with students to help them really understand math. So you might relate to this, that as that sort of non math person, even though I was doing a lot of fake math, and I was working in the drugstore, when I would ring people up and use the cash register, and I would say okay, you owe me blank. And every once a while people would hand me a $20 bill and a nickel. And I'd be like, whatever weirdo and I would just type that in. And I never noticed that they would be getting back an even set of bills. Because they had already thought about the fact that if they gave me that extra nickel, I wouldn't give them back all those cents, I would just give them back that even bill. But I hadn't thought about that. I would just dutifully type it in, I would look at them like they were odd for giving me that extra nickel, or the extra penny, or whatever it was. I would look at them like, whatever. And I would just type it in, never realizing. I mean, it's embarrassing now for me to think about the fact that I was so not numerically powerful at all, that I would just, you know, like hand them back the bill and not even know why they had given me that change. Similarly, not too long ago, I was in a small drugstore. And I had just a few things. And I got up to the checkout line. And as I got up there, the power went out. There were big windows in the front of the store so we could sort of still see what was happening. But there was no power. Very fascinating to me that both the sort of clerk there that was checking us out and then the manager who came over - the power's out - would not let us check out. Because they were convinced we couldn't figure out what we owed. And I said, "No, no, no, we can add this up. We have the prices right here. We can add these numbers up." And then the manager goes, "But we can't figure out sales tax." I was like, "No, we actually can." Like we - and nope, they were not hearing it. You could tell they were both very nervous. And they were both not going to have us be able to check out. What I'm suggesting is that we have a generation of people who because we were never sort of put in this position that we had to figure that stuff out.

Kim Montague:

Right.

We kind of can't. Sometimes we say that the kids these days are really tech savvy. I think kids today are tech dependent. So that's noteworthy, it's noteworthy that we kind of might have a generation of people who because they weren't kind of forced or highly encouraged to deal with relationships among numbers, all they have are these procedures and a step by step instructions that they got in school. So parents, I invite you to lean into the possibility that today's parents might not understand what teachers are trying to do with math these days. Because that generation never built the mental relationships to be able to recognize them in today's math teaching. Math to that generation was largely devoid of meaning and so that generation might not recognize the meaning that can be in Real Math. So we're suggesting it's not just about getting answers. Today, we have technology, we have calculators that can get answers. When we were in school, I would suggest all those steps and procedures are about getting answers. But today, technology can get those answers. So we don't need that anymore. Now, we need people who can solve problems by reasoning. Teachers today are trying to help your students, not just Google to find answers. But we want to help students, we want to create students who can create the Google of the future. Right? Not just Google to get answers. So let's create Google, not just ask Siri or Alexa for facts, but be able to use those facts to create new products and services. And frankly, to innovate. Facts are everywhere. Whatever. We can get those just on the computer, we type them in, and we can ask Siri or Alexa. We want to help your students use those facts. Now, this conversation could be a little tricky. We are not interested in bashing teachers.

Kim Montague:

Right.

But the reality is that much of implementation of what we would hope for in math teaching today is not actually what any of us sort of wishes it could be.

Kim Montague:

Right. And so as we're supporting teachers, let's remember that they also grew up in the same system, where step by step procedures were also the norm, right?

For them as well.

Kim Montague:

Right. So maybe what you're seeing isn't as fine tuned as we all wish it could be. But the math behind it is solid. And we're so grateful for teachers who are willing to learn and grow along with their students, as we all work to get better at this fascinating work of raising kids who are better and better at mathematizing.

So today, we hope we've helped give you a glimpse of why things might seem so different to you in math teaching. We tried to give you a brief understanding of how math isn't just about getting an answer.

Kim Montague:

Yeah. And next week, we're going to be talking more about how math instruction maybe looks so different, why you're seeing things on your papers. What's all this picture drawing? So stay tuned for more to help parents understand what we're trying to do.

So thanks for listening in. Teachers, thank you for recommending this podcast to your parents who are interested to understand why math instruction needed to change. We've got a few more episodes planned to help you, parents, so tuned in to help make more sense out of today's math teaching because Math is Figure-Out-Able!

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