What Is Mastery-based Learning?

What Is Mastery-based Learning?

Guest Gretchen Roe from Demme Learning says that math is like death and taxes: you don't get away from either one. She urges parents not to shortchange kids in their math instruction by claim they're just not a math-family.  

Learn how a mastery-based curriculum is student-centric, allowing a child to work at the pace they need to fully comprehend the skills (instead of the curriculum determining the length of lessons and how quickly you work through them). Find out why manipulatives are key to learning math and why some kids discard them too soon. Are your math lessons too long? Discover the ideal length of a daily math lesson. The day-to-day math we encounter as adults mostly comes to us in the form of word problems.

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Podcast Transcript

Janna Koch (00:36): Welcome to Homeschool Your Way. I'm Janna Koch, your host and BookShark's community manager. In the homeschooling community, much like any community, there are words thrown around with an assumption that everyone knows and understands the meaning. I, for one, hate when I don't know what a word means, because if I don't understand the term, how can I give my two cents? If you don't know, by now, I'll just come out and say it. I love to let people know what I'm thinking about in almost everything.

Janna Koch (01:09): Mastery-based learning may be one of those words. You may have heard the term, but can't quite give your two cents yet. I'm here to help. I've invited Gretchen Roe, a veteran mom who happens to have a degree in psychology and child development and has spent the last 19 years in positions of homeschool advocacy, serving on a variety of nonprofit boards. Plus, she is a sales representative for Demme Learning, one of BookShark's partners in math and spelling. She will help us master the idea of mastery-based learning and equip you to give your two cents about it.

Janna Koch (01:47): First, a homeschool hack. Keep it simple. If you're feeling overwhelmed with your homeschool or with life in general, ask yourself, “Are these tasks serving my why?” If you don't have a homeschool why listen to the episode [42] we did with Candace Kelly explaining the need for a why, or write down why you chose a homeschool in the first place. As you look at that to-do list, make sure it aligns with your why. My homeschool why has always been to foster the love of learning in my girls.

Janna Koch (02:20): There are times when I realize I'm doing just the opposite. If I allow the list or the curriculum to dictate my time, am I really fostering joyful learning? To be honest, I'm usually killing their desire to learn anything. So, keep it simple. Let your why fuel your day, not the list. If you have a hack you'd like to share, please go to bookshark.com/podcast and leave a comment.

Janna Koch (02:49): Gretchen, thank you so much for being here.

Gretchen Roe (02:51): Oh, it's my very great pleasure to have the time to spend with you today.

Janna Koch (02:55): Now I know you and your history, but for those who don't know, why don't you go ahead and share a little bit about yourself and talk about what's keeping you passionate about homeschool, after all these years.

Gretchen Roe (03:08): I had no intention of homeschooling. In fact, I had no intention of having children. We have six and we homeschooled 21 years. Four of them graduated homeschool from high school. And then our fifth was homeschooled to high school and our caboose was homeschooled to middle school. And it was the most joyful 21 years of my life. And I wouldn't have traded it for anything. I have worked in the homeschool community and positions of homeschool advocacy now for 15 years. And I love the fact that we have the ability to guide our children to adulthood in all aspects. And so, I continue to be as excited today about the homeschooling journey, even though it's not one that I'm taking right now. I just enjoy walking alongside other parents as they take that journey.

Janna Koch (03:57): So, how long have you professionally been involved with homeschooling?

Gretchen Roe (04:02): I became a homeschooler overnight in the middle of an academic year, when a teacher told my third grader, she didn't need to memorize her multiplication tables. And I said, "Nope, that's a wrong answer." Something's got to be better out there. And I really only intended to homeschool her from March to June. And it became a glorious adventure that didn't end for a long time. And she turned 36 yesterday, so I think we did okay.

Janna Koch (04:31): Now how about your partnership with Demme Learning?

Gretchen Roe (04:36): I have known Steve [Demme, founder of Demme Learning] for 15 years. We spoke on a homeschool circuit together and a little over eight years ago, they asked me if I wanted to come aboard professionally. And I said, I wondered when you would ask me to do that because I loved the product. It was a complete game changer for me. When I came to work for Demme Learning, it was Math-U-See and they had just launched Spelling You See.


Gretchen Roe (05:01): The end of the pool, where the language arts happens, is my favorite end of the pool to swim in, and so I was really excited to see Spelling You See come aboard. But Math-U-See was a huge game changer for me. I'm not a confident mathematician. I think math is spelled with four letters for a reason, but I loved the fact that Math-U-See made it possible to educate my kids. So four of my kids are Math-U-See kids, and I never looked back. It's been amazing.

Janna Koch (05:33): Well for those who don't know, BookShark partners with Math-U-See Demme Learning, we also use their Spelling You See in our program

Math-U-See Products

Janna Koch (05:44): Gretchen, a lot of parents ask me when I talk about Math-U-See, “What is a mastery-based type of learning?” And it definitely is not the type of learning that I had in traditional school or even in my homeschool years. So, it was very unique to me as I became aware of your product and started using it in my home with my children. So, could you just walk us through this philosophy of what this actually means and what it will look like for parents?

Gretchen Roe (06:15): Sure, absolutely. So, there's two kinds of ways to teach mathematics instruction. One is incremental, that's the one, most of us are familiar with. Someone pre-determines how many times you will see an individual concept, and so perhaps they present that concept three times and then it falls out of rotation or sequence. The challenge with that kind of learning is if you're not solid in your understanding, then your understanding is incomplete. And there's no way to assess that incompleteness as you go further.

Gretchen Roe (06:50): And because math is sequential and cumulative, it becomes really essential for us to get it right. And that is one of the reasons that I love a mastery-based program. At Math-U-See, we say we are student-paced. So. As a student can demonstrate their understanding to a parent or an instructor, they can move forward in the curricula. They're not bound by a predetermined number of math problems per se, and that makes a tremendous amount of difference.

Janna Koch (07:22): It does. Now, when you found out about Math-U-See and fell in love with this program, what differences did you see in your children as you started using it?

Gretchen Roe (07:33): One of the things I think that's really important is my background is in child development and child psychology. I actually was enrolled in a PhD program when I found out I was expecting my eldest son and so he's my PhD, but I love the fact that I can bring more than one sense to the table. Not all of us play on a level field, as far as our understanding, we all have different gifts, but if I can teach a student in as many modalities as possible, it makes it possible for a student to learn. So, I can teach a gifted learner, I can teach a struggling learner and they can all have a level playing field because they are bringing their talents to the table in as many ways is possible.

Janna Koch (08:22): Now I was a family who came into the program later on. So, my daughter was 12 when we started using Math-U-See, because I started to notice that other programs just weren't cutting it for us. And by that, I mean, it was taking over an hour and a half and there were tears every day. And so I thought, not only is she miserable, but I'm miserable as her mom to see her struggling. And I'm also miserable as the teacher, going “I don't know how to say it a different way. This is how I learned it.” I was unwilling in a sense to learn a new way of teaching because it works for me, why doesn't it work for her? And it worked for her two older sisters, which is really what threw me for a loop as a homeschool parent. Why this last one is this not working for? What am I doing differently? And we've talked about this in the past.

Janna Koch (09:07): So, when she came into it, she's not using the manipulatives a lot of the times. And part of me is like, well, if you're going to do it, you need to do it right and yet she is seamlessly moved into the program and working through it beautifully. So, the type-A in me that's struggling with there's manipulatives for a reason, you must use them. I can't be the only parent that appreciates your program and yet uses it and adjusts it to my child.

Gretchen Roe (09:38): Sure, and isn't that a definition of homeschooling, we adjust to meet the needs of our child. The truth is in a Math-U-See experience, the manipulatives hold a very special place. And the place that they hold is they allow a student to bring as many senses to the table as necessary to fully understand and grasp a concept. And the other thing that the manipulatives allow us to do is to take a concept that a student understands and give them the resources or the tools to teach that concept back to a parent. If they don't have the language to do that. At 12, both our daughters, because I came into Math-U-See at the pre-algebra level. So, my daughter was 13 and they pretty much have a well developed language resource at that point, but a six year old, maybe not. So, that's where the manipulatives help us in that process.

Gretchen Roe (10:35): You're not going to walk around with plastic blocks in your pocket. As Steve says, the blocks serve a tool to allow us to step along a continuum from the concrete understanding of the initial exploration to representational understanding what do you know in your head to the abstract end of the equation, which is really those Arabic numerals that we force kids to understand math. And so they serve as a tool to help a student facilitate their understanding. And they're a tool as long as they're necessary.

Gretchen Roe (11:09): Just like you said, if your daughter is getting the concepts and teaching them back to you and not needing the manipulatives, then she's moved beyond them. I do have to say sometimes I encounter older students who stepped away from the manipulatives because manipulatives… “We don't need no stinking manipulatives.” And the truth is they shouldn't have, because they didn't have that full conceptual understanding that really allows us to put it in our heads. And what the manipulatives do is they allow us to put that learning into our long term memory in the proper place. So, it can be retrieved later. That really is the goal of the manipulative experience.

Janna Koch (13:14): Well, what about parents who say my child is artistic? My child is a writer. My child is, and math isn't their strong suit. And so, we're really not pushing math or we're really not looking to change for them to just get through it, to just get by, because we know that they're not a math person, we are not math people. And I've been guilty of myself as saying it, but as I've matured and grown older, I understand that is so not true.

Janna Koch (13:47): So, you were explaining that in your younger years, your child psychology and so math wasn't necessarily your thing. But now you've been working with this company for eight years and you're very passionate about math. So, help me understand as a parent who maybe I shouldn't worry about my child really understands algebra or not, why we need these higher types of learning in these processes in order to make it a better experience as adults.

Gretchen Roe (14:20): Sure. The truth is math is like death and taxes, you don't get away from either one. And we have developed a culture here in the US of thinking that math literacy is not a necessary skill set, and because of that payday loan companies thrive. It's up to us to keep the doors open for our kids mathematically. And I would've taken that argument to the wall with you 15 years ago with the kid who brought me to Matthew, see, she's now 30. And she was 13 when we found our way here. And we had been through two different curricula and really struggled. And I said, those very same things, well math just isn't her thing. She's my daughter, blah, blah, blah. But the truth is as parents, our goal is to keep as many doors open as possible for our kids. We don't know what the future holds for our kids.

Gretchen Roe (15:17): And if we make suppositions, we narrow their ability to be flexible. And if I've learned anything since 2020, it is that flexibility is a great sign of intelligence, so we need to keep those doorways open for our kids. And as a matter of fact, we have this misapprehension that if you are artistic and you're creative, you're not mathy, and that's not really true, Leonardo da Vinci comes to mind. And I think the important thing is we don't know what the future holds for our kids. So why would we start narrowing the pathways? Let's keep the doors open wide and regardless where they choose to go academically, they have the wherewithal to be successful. I'm glad I kept the doors open for that particular child because that non-mathematical artsy kid is a research biologist today. And if I'd closed doors on her, she wouldn't view where she is today.

Janna Koch (16:24): My daughters were in their guidance counselor's offices and he was explaining that they didn't have to continue on to a higher level of math anymore. They'd accomplished what they needed to according to the standards, and so they were like, yeah, free ride, we're done. And I loudly interjected and reminded them that the reason they needed a parent there for these sessions is because I am the voice of reason. And I said that very thing. I said, "You don't know your interests are going to change. You could read one book, you could hear one lecture and it could change your life and the trajectory of what you want to do. Do not shut that door by saying, “I'm not going to take college algebra now because I've completed what I need to complete." And we'll see, jury is still out if that was helpful or not. But I think the other thing is, as a society, I have noticed that we tend, I'll speak for myself, tend to take the easy way out, the path of least resistance.

Janna Koch (17:22): So, if something is a challenge in a fixed mindset, well, then I don't want to do it because I don't know how it's going to turn out or if I'm going to do it well, but with a growth mindset, it goes, this is something I've never learned. As you were talking, I was thinking I've never done calculus. I think maybe I might just pick up some Cal. I want to, if I'm sitting here teaching this to my children, I want to be demonstrating to them as well. That's what they'll be like, why you only did mathematical investigations when you went to college and your master's degree had no math, which actually is not true because there was some finance and business and statistics that I had to take. So, you have to know how to do those higher processes of math, but I don't want them to limit themselves.

 Gretchen Roe (18:08): Well, I chose my college degree based on what I thought was the least amount of math necessary to get a degree, looking down through the course catalog, not realizing I'd have to have two years of psychological statistics. And then I made it worse on myself, I split those two years by a seven years, summer vacation. So, you don't know what the future will hold. And I always say to parents, what are your students' plans? And parents are like, well, he is a 13 year old boy. Great. That's awesome. Let's keep the doors open then because we don't know what he wants. And kids' desires change as they age. And I think mathematical literacy is as important as book literacy and it's part of our educational process. And we, as parents, are obligated to teach our children to be self-sufficient in society. And that means we have to have mathematical literacy.

Janna Koch (19:09): I have never heard the term mathematical literacy before, and I think-

Gretchen Roe (19:12): It might have just made it up, but you know what?

Janna Koch (19:15): I think it's beautiful.

Gretchen Roe (19:15): It's very relevant. So I always am impressed with my own lack of mathematical literacy. When I sit down every year and I'm like, oh, taxes, I got to do this. How does this work? Because if you don't do something with frequency, you don't remember it. And here's a tip, here's another reason why mastery in mathematics is so important. In our world, mastery is demonstrated by teaching someone else what you know. And isn't that the highest form of proving knowledge is to be able to explain to someone else why you know this particular thing works.

What is mastery-based learning?What is mastery-based learning?

 Janna Koch (20:01): Unfortunately, I think we have seen in our society a lack of mastery in so many things, because people don't know why they do things or why they don't know what they know, right? And so, I think as homeschool parents, it's another privilege of ours to be like, hey, here is a very serious topic that is relevant and current in our society. Let's talk about it. How do you feel about it? Well, what are your friends saying about it? Okay. What do you think about what they're saying? It was one of my favorite things about being a parent, really, is being able to walk with my children through these hard things in life, and then seeing, okay, we don't have all the answers.

Janna Koch (20:43): Nobody has all the answers, but let's work the process at each step of the way so that we can gain a confidence in what we do believe, the decisions that we do make. And I think math is a perfect example of that. Like you said, if you don't know, and you're making financial decisions, I mean, we live in a country, we have so much freedom. We're able to choose how we spend our money. If you don't understand how money works, how adding and subtracting and multiplying, and God forbid, even like you were saying compound interest in all of these things, you're going to be lost.

Gretchen Roe (21:20): Sure. Well, I think back I mentioned, my eldest daughter just turned 36 when she was 19 years old, she got a $53,000 SBA loan and opened her own coffee shop. And at that point in time, she had a little old ancient mercurial cash register that sometimes worked and sometimes didn't and she found that she could only hire homeschool kids to work in the coffee shop. And the reason was because when the cash register went on, the fritz, most kids couldn't calculate the change in their heads to know what change to give back. And so she very quickly learned that her staff was going to be homeschoolers because they could do that mental math. And so much of mental math is not part of the mathematical experience anymore. I'm glad it's part of Math-U-See.

Janna Koch (22:13): I am too. I think one of the biggest things that annoys my teenage daughters even now is I will say, okay, what are they going to give you back and change? Don't look at them. And of course my twins are 16 and they'll be like, stop it. You're embarrassing us. And I'm like, I'd rather embarrass you now with the safety net of me standing right here than when you have a job, like you're saying, and something goes wrong and you can't count it back to somebody. And then you know that anxiety, how that feels when you just don't know what to do in the situation. It's like, wow, as your mom, it's my job to help you avoid situations like this by embarrassing you now so that you have the skills later. Might be the title of my next book, I'm here to embarrass you now.

Gretchen Roe (22:57): I like that book. That's a good one. We could probably co-write that.

Janna Koch (23:00): Mm-hmm. Mm-hmm.

Gretchen Roe (23:02): My husband always says our goal is to raise kids who have character who are not characters, so we'll see.

Janna Koch (23:10): Yeah, well ...

Gretchen Roe (23:10): Boat's still out on the caboose and the train. We'll see.

Janna Koch (23:15): It is fun to look at all of the different ones and their different personalities and how you think you're parenting the same, but then birth order and different, multiple intelligences in different ways just really affect all of that, which is what makes us so unique and beautiful. And that is part of also expressing to our children that everyone is unique and has beauty. Let's find it. What is beautiful about this? And I feel the same way about education. We love to read in this house. We love to discuss, we are all talkers, but where's their beauty in math. Let's talk about it. Oh my gosh, there's patterns. There's patterns all out in the world in nature and in math and math is just kind of mimicking that and it's helping us understand it. So let's look at it that way instead of, oh my gosh, I have to now do my math.

Gretchen Roe (24:03): Right. Well, and I think part of that is anybody who was raised in a public school environment remembers an hour or gosh, my son has a friend who is in a block schedule classroom situation. And her math is a 90 minute experience in a day. And you don't love things that linger painfully for you. So, I think in some ways parents have to revisit their own math experiences and maybe shed some of that stuff, so we can help our kids be successful. At Math-U-See, we say, "If you're in our Greek series, the colored books back here, you're looking at 15 minutes a day, because your child has an attention span of their age, plus two to three minutes for new material. And so if you're spending an hour a day doing math, you have 15 minutes of quality instruction in 45 minutes of obedience."

Janna Koch (25:05): Mm-hmm.

Gretchen Roe (25:07): And that makes a tremendous difference for kids.

Janna Koch (25:09): Yeah. And for a parent, maybe even going a step further and translating it and saying, well, now you have 45 minutes of exercise of something that you actually despise, right? We're not talking about paddle boarding, because if you told me I had 45 minutes paddleboarding, I'd be out there in a heartbeat. You couldn't give me back off. But if you told me I had 45 minutes of running, how could I possibly psych myself up to do that? It just isn't possible. And I think we do forget that even in that 45 minutes, like you said of obedience, that is exercise to them of something that doesn't come naturally is not on the top of their list of boy, I want to sit here and do something for 45 minutes that I don't necessarily like, but gosh, darn it, I'm going-

Gretchen Roe (25:53): Well, there's a corollary to that as well because as parents, if we're not fond of something, we look to shuttle it off. And I often have conversations with parents who will say to me at what age can my child do math all by themselves? And I annoy them when I say, well it depends because every child is different and mathematics is a language. You can't learn it in a vacuum. And frankly you can't learn it from a computer because a computer's a tool. It's not a teacher. So you got to be able to engage with someone in order to test your understanding and make sure that it's solid and be able to move that forward.

Gretchen Roe (26:38): And that was one of the things that impressed me so much about Math-U-See is, yeah, a mastery math program sounded like a great idea, but he didn't realize how understanding the process of mastery would translate into all of my kids' other academics. Because if you talk yourself through something and you say, all right, what do I know? And you walk yourself through that process, that habit of learning to walk yourself through math then goes into your science and goes into your language arts and your history and those other things, and we become a more well rounded learner.

Janna Koch (27:18): Mm-hmm. I think that circles us back to Leonardo da Vinci, like what the Renaissance man, right. He was the epitome-

Gretchen Roe (27:26): That's right.

Janna Koch (27:26): ... of being well rounded. And yet unlike Leonardo, I say I'm the jack of all trades master of none, but it has suited me. It has suited me just fine in my endeavors in life. But I do love the idea of having mastery in all areas. Just like you, just like what I caught onto that word you said literacy. If we could look at math as a type of literacy as parents, then that would translate to our children as, okay, this isn't just numbers, and we have to memorize and we just have to get through it.

Janna Koch (28:04): How can we start writing a story with math? And yes, you'll use numbers because as a kid word problems were like, ugh, please. Not the word problems. They never made sense to me. I don't know who the author of these were, but I'm thinking maybe another book we might collaborate on is getting a fiction writer to start writing our word problem, so that we can make them engaging with students, but that they can actually see that there's two languages being woven together is math-

Gretchen Roe (28:36): Right.

Janna Koch (28:36): ... and vocabulary and certain structure.

Gretchen Roe (28:39): Well, the hard part in most endeavors, when I talk to parents who are like, ah, yeah, I hate work. My kids are great on computational math, but they hate word problems. When math comes to us as adults, it's a word problem.

Janna Koch (28:52): Mm-hmm.

Gretchen Roe (28:52): So, we have to give our kids a degree of facility. And one of the things that we say at Math-U-See is the word problems are where you prove your application and understanding.

Janna Koch (29:04): Mm-hmm.

Gretchen Roe (29:04): Because if you can take the conceptual understanding you developed in the worksheets and then apply it in the word problems, then you really have both sides of that mathematical coin.

Janna Koch (29:15): Yeah. And then their literacy would be even higher. So, [inaudible 00:29:20].

Gretchen Roe (29:19): Absolutely.

Janna Koch (29:22): I love [inaudible 00:29:23]. One more thing Gretchen, before we go, what would you like to say to a parent who is maybe struggling with several things, deciding whether or not homeschool has actually worked for them, really struggling with the idea of, are we going to re-up again next year? And maybe this is all coming from a place of, I'm not seeing the results that I set out to see. So, if you had a parent come into your booth and or call you on the phone, what would be your best words of advice for them for those things?

Gretchen Roe (29:56): Don't read other people's highlight reels. We all are involved in some sort of homeschooling endeavor where there's the child who has every kudo and accolade going on. And we've got the child at home who couldn't find their shoes to go to the homeschool co-op in the first place. And the truth of the matter is your journey is your journey and it is equally valuable, and this is a hard job. You're going to invest a lot of time and blood and sweat and tears. And you don't see the return on your investment right away. But it doesn't mean you're not making a tremendously good investment, but you are fully capable and equipped to teach your children and figure out what worked this year and celebrate that because it's a marathon, not a sprint.

Janna Koch (30:54): Yeah, man. And nobody wants to run a marathon, Gretchen.

Gretchen Roe (31:00): I know it. I know, but you find yourself there, you know what our kids are going to grow up. So do you want to influence them or do you want somebody else to influence them?

Janna Koch (31:08): Yeah. Well, good advice coming from a mother who has seen it from start to finish and is now helping other parents as they are along their journeys.

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