Getting Started with Charlotte Mason Math

I’m excited to introduce to you today a new regular contributor to The Simply Charlotte Mason Blog. She’s longtime friend of mine, a dear friend of mine, and she might be familiar to some of you too. Today I want to introduce to you Richele Baburina.

Sonya: Richele, I am so excited to have you joining me on the podcast.

Richele: Thank you. I’m really excited to join as well.

Sonya: You’ll be regularly contributing solo things as well as conversations. It’s going to be fun. So today, let’s just kick it off with a conversation. I know many people know you as the Charlotte Mason Math Lady, but there is so much more to your wisdom and your knowledge. I’m excited that you’ll be able to share about that in the coming weeks and months, but today we’re going to start with math.

So what we want to talk about today is some people might be new to Charlotte Mason math, and it’s different from the way many of us were taught math. So let’s talk about how people can get started with a Charlotte Mason approach to mathematics. What do they need to keep in mind?

Richele: One of the things that happens is that people think that Charlotte Mason math is different from the way she taught other subjects, but some of the things that we’re going to go through today I want people to be reading and thinking about. They already know a lot of these methods because they’re the same methods that run like threads throughout her other subjects.

Sonya: So the big difference is that she didn’t use living books for math.

Richele: Correct.

Sonya: So that, like you said, it’s easy for us to say, “Oh, then this is completely separate. This is completely different.” But I like how you said there are so many other similarities. Even though it’s not a living-book approach, there’s a living component to it.

Richele: There’s a living component to it, and even though she didn’t use picture books or a story narrative to teach math, she recognized that the language of math was living.

Sonya: Yes. Let’s talk about what to expect and some of those areas that we might be able to make some connections with other methods that she used. Where should we start?

Richele: Whenever I’m thinking about things like this, I think about the three educational keys of atmosphere, discipline, and life. So part of the atmosphere of a math lesson is that it’s a short lesson, and you’ll recognize this too with all of her other subjects. These are short, concentrated lessons.

Sonya: So many of us grew up with hour-long math lessons, and we feel like, because we were taught this way, you have got to drill it and kill it. And so that’s what most of the hour is: it’s all this drilling and killing. So how would you reassure the parent who says, “But if I don’t do a long math lesson, my child’s not going to learn math.”

Richele: Think about it, perhaps for yourself. If you have two hours to complete a project, you might tend to dawdle or get distracted. But if you have say, 20 to 30 minutes to complete a project, you’re going to stay focused and give your attention to that project. So the short math lessons, in the early years, they’re building to about 15 minutes, and then we include 5 minutes of mental math, which we’ll talk about later. Even in high school, those lessons never expand beyond 30 minutes.

Sonya: So the short lessons that, as you said, are a staple of the Charlotte Mason method across the board, and we need to apply that to math too. As hard as it may seem, it does work.

Richele: The child is actually learning more by being able to fix his attention for that 20 or 30 minutes than up to two hours. I’ve heard people say they’re giving their high schoolers two hours with a math lesson.

Sonya: Oh, wow.

Richele: You can just imagine that they really aren’t learning a lot past the first 30 minutes anyhow.

Sonya: The brain can only take so much.

Richele: Right. Our children are expending great mental effort during this time, so we need them to stay fresh, which brings me to the second point on getting started, and that’s when we schedule the child’s math lesson. We want to schedule their math lessons when they’re at their freshest. Traditionally in Charlotte Mason’s schools, math was the second lesson of the day following Bible. Unless the child was learning to read, the he might have a short 10-minute reading lesson following Bible and then go into the math lesson. But this works. 

The beauty of homeschooling is that we get to choose what’s right for our family and for our children. This worked great for one of my children. This boy was up and at ’em at 5:30 every morning, raring to go, so we had his math lesson right away. Now, my other child was a bit of a sleepyhead, and he wasn’t mentally awake until later on in the day. Again, just because Charlotte Mason scheduled it second, doesn’t mean you have to, but it is a good thing to try, a good precedent to follow.

Sonya: Yeah, it’s a good principle to keep in mind, when your child is fresh. Let’s talk about the subjects that came before and after it as well. It is a big part of the scheduling, using different parts of the brain as you progress through your day. I like how she did Bible first, because that’s dealing with words, and then it’s using a different part of the brain and dealing with numbers next.

Richele: Yes. So then following the math lesson, which part of the brain or body would we like to use? Something different. It could be something like even a play break for your younger child. You could have composer study or a picture study. What’s really interesting is that, in Charlotte Mason schools, a lot of times they would have a handicraft or handwriting following the math lesson, and that’s because Charlotte Mason math lessons have a large oral component to them.

Sonya: So often when we think of math, we think worksheets. If the child is writing all of these answers on the worksheet, you would not follow it with a handwriting lesson. That doesn’t make sense. What grades are we talking about when we say younger years?

Richele: As your child is learning to read and to write, that’s when the larger part of the math lesson is an oral lesson. So it can be dependent on the child. But we’re talking about up to fourth grade. In fourth grade, we see a lot more writing happening in the math lesson, but we are slowly building. We have numeration and notation. Our children are learning to read math and write math as they go along, but it is a slow, gradual build. We never want the writing to overshadow the ideas of the math lesson. That’s another reason that they’re largely oral. 

Now we’ve headed into another component of getting started with Charlotte Mason math, and that is oral work and incorporating oral work into the lesson no matter what age the child is. Even in high school, our students still have an oral component to the math lesson.

Sonya: That’s just like narration.

Richele: Yes. I’m glad you picked up on that because that is what we want to think about. These are methods we see throughout a Charlotte Mason education. If you think about our early years, we are reading to our children, and they are narrating back to us orally.

Through that is the process of assimilation, where they are digesting this knowledge and then they are giving it back. That’s how it becomes a part of us is when we give that narration. So with our children, we are giving a lot of oral work, and they are taking that in. They are processing it. What do they have to do next? If we’re narrating a history book, they’re thinking what happens next in the same way our children are thinking, “What process is next?”

Sonya: I noticed a lot of times in the math books that you wrote, we help the child discover how to figure out an answer, and then we have them later on tell us as they work through it; they are narrating what they are doing.

So it’s not just, “Here, show me that you can follow the formula.” It is, “Explain to me what you’re doing and why and how it works,” just to make sure they’ve got the grasp of the why behind the how.

Richele: We’re building those roadways in the brain that way as well when we’re doing that and when our children are doing that. You can see, by incorporating oral work, that the child can get through a lot more during his math lesson than if he were having to read and write everything himself.

Sonya: Yeah, especially in those early years when reading is not natural yet for many children. It’s asking them to do too many things in the lesson. It’s like, “Practice your decoding skills, and practice your fine motor skills, and understand the math concept.” Let’s just get rid of those obstacles, focus on the math concept, and we’ll work on handwriting during the handwriting lesson later or reading during the reading lesson.

Richele: In all of the Charlotte Mason subjects, the focus is on the ideas. When we take out those two mechanical processes of reading and writing for our younger children, they’re able to focus on the ideas.

Sonya: Now, when we talked about the child explaining how they are doing things, I have in my head a picture of my youngest using the play money, and the objects to do that process. Talk a little bit about those everyday objects we’re using, the manipulatives, if you want to call them that.

Richele: Charlotte Mason was actually quite unique in this approach of using concrete objects, but they were everyday objects. We hear people talk about whether or not a math curriculum is manipulative-based. Charlotte Mason went beyond the manipulative-based approach. She wanted to use the child’s natural environment, so there was nothing that was scientifically-based to ignite all of the senses and stimulate their senses.

Sonya: Specialized particular-shaped things that are only used for the math lessons that you don’t see in everyday life.

Richele: This is across the board in Charlotte Mason’s philosophy of education. She didn’t think that you had to come up with a specialized child environment for them. They learn best in their natural environment, their home environment. So everything that the child uses are things that you can find around the house or out in nature, but you’re going to want to have a good variety of them, and we’ll talk about why that is. First of all, we’re going to gather our everyday objects.

Sonya: We had buttons and beads, and we used coins. We’ve used little toy animals. We’ve used food sometimes, like little gluten-free Cheerio-type things, and craft sticks. A plethora.

Richele: Right. Anything that you have in your home that can be gathered together. Game pieces. Fridays were chocolate chips, and that was reserved just for Friday because otherwise you’re going to want those chocolate chips every day.

Sonya: You’re like the best math mom ever.

Richele: Well, that’s when you want to do your division and your sharing exercises on Friday with the chocolate chips.

Sonya: There you go.

Richele: These everyday objects were just a part of the math lesson, and they didn’t continue all the way through; a child can give them up when he is ready to. Because for one, if the child doesn’t need them, they’ll begin to get bored with them, so we don’t want to chain them to using manipulatives. But also they’ll get bored if you’re always using the same manipulatives. So change up those everyday objects. If we use buttons for two days, then let’s go to dry beans the next day. Money is one of the most important of the daily objects that we use, and that’s because the money is able to give a lot of ideas. The main idea that money gives is place value, because we have a decimalized money system. It’s very easy to learn place value when we’re working with dollars, dimes, and pennies because we’ve got our units, our tens, and our hundreds.

Sonya: 10 pennies in a dime. 10 dimes in a dollar.

Richele: Then as the child progresses, we can add in $10 bills and $100 bills, and that’s where your game pieces come in really handy.

Sonya: And playing different games. The games are not part of the math lesson itself. We do not teach math through games, but they can certainly practice the math skills with games outside of the math lesson. It’s things like keeping their own score. Those types of ideas.

Richele: Even moving pieces back and forth. Or we played one called Aggravation. So you’ve got your two dice, and then you get to decide, and you can break those up and move different pieces. So we don’t play games during the math lesson. Charlotte Mason felt very strongly about that; the play way took the focus off the ideas, but certainly playing games outside of school is going to be really instrumental in solidifying certain math processes.

Sonya: We don’t want to put the focus of that game time on the math necessarily. It’s on the relationship-building, right?

Richele: Yes, so these are just your regular everyday games that you would have at home. It’s not a specific contrived math game.

Sonya: So if we’re not playing games during the math time, what is it we need to keep in mind that we are doing during the math time? I know you have mentioned, I’m going to call it a motto, a motto that you came up with that is so easy to remember. It helps me so much when I sit down to do math lessons with my youngest. It’s like, “Okay, I’ve got to remember these three things,” and it even rhymes so it’s easy to remember.

Richele: It’s “new, review, and mental math too.” This is not something that Charlotte Mason actually said herself. It’s something that I came up with as a reminder of what should be the components of our math lessons throughout the week. Some days we might not have all three in one day. We try to have mental math every day. 

Let’s begin with new. New is the newest concept, newest idea, newest math process that we’re working with. If it’s a day that we’re going to introduce something new, then that might take your whole 15 minutes of math class, and then we’ll have our five minutes of mental math either at the end of that. Or if the child is beginning, if his attention’s beginning to wane, or he’s getting worn out from math, then you can have that five minutes of mental math later. So that’s the new part. That new concept we’ll work on every single day of the week. 

Then we have review. Review in the younger grades, so say first and second grade, review is going to be a lot of our oral work again, covering the numbers that we’ve already covered. Then as we move on, we’re constantly going to be having some periodic review of concepts that we’ve had in the past.

Sonya: So the review doesn’t have to happen every day, but it does need to be included during the week.

Richele: Yes.

Sonya: All right, so new and then review.

Richele: New and review. For first and second grade, basically, we’re exploring numbers, we’re getting to know numbers, so we don’t have a lot of things to review, but we do have to keep building on the those skills. As we progress in math, then that’s where we have the periodic review of things like, “All right, we’ve learned prime numbers, now we need to go back and we should review long multiplication.”

Sonya: As they progress, there’s more and more that becomes review.

Richele: We want to habitualize these processes in our child’s brain along with the physical aspect—how to do a certain notation, for example. Now, how much review is needed per concept is going to depend on the child. So keep in mind that you want to have enough review that it’s going to solidify something they’ve already mastered, or build speed, or really make it internalized, or second nature.

Sonya: They just know how to do it. It doesn’t cause all the effort of decision. You’re almost making it a habit. It’s like you’re blazing a trail in the brain of “This is how I figure out this type of thing,” or “This is what six times seven is.”

Richele: Exactly. It’s going to be dependent on our children, again, so we watch. We want to give enough review that it becomes a habit in their brains but not so much that they become bored by it, and they start to loathe it.

Sonya: Okay, so that’s new and review. Talk a little bit about mental math.

Richele: It is funny because whenever we’re doing math, we are putting forth mental effort, but mental math is a specific activity that we do with our children that is free from manipulatives or those everyday concrete objects and free from pencil and paper.

Sonya: So it’s all done in the head.

Richele: It is all done in the head.

Sonya: Thus mental math. Okay, okay.

Richele: Yes. From grades one to six, we’re giving our children about five minutes of mental math a day, and it’s going to be lively, and it’s going to be engaging, and it’s also going to be challenging enough for them that they are really having to think and build good habits.

Sonya: Attention and accuracy.

Richele: Yes, promptness.

Sonya: I like how Charlotte talked about not every child is going to be able—well, putting it in my terms, this is not what Charlotte said—but not every child’s going to be a math whiz. But even the tortoise, she said, should be able to progress a little bit more with each time he does this or as he goes through this mental math. You want to challenge them, but not frustrate them.

Richele: Exactly. Sometimes that means that we might be working with larger numbers or more complex processes in the new section of our math lesson. The mental math might be using smaller numbers, but we might be adding more of them.

Sonya: Okay, so can you give an example of it? Go ahead. I’ll be the student. Be nice. We’re not going to do five whole minutes of it because it sounds small, but I know I’ve sat in workshop sessions that you’ve done where you walked us through five minutes of mental math. And by the time you’re about three minutes into it, everybody’s looking around like, “Aren’t we done yet?” Because it does take a lot of mental effort, as you said. So don’t give me a whole five minutes, but just give a a quick example of what you mean by mental math.

Richele: So with a child say in first grade, we’re going to use our word pictures and make an interesting example. So it could be two kittens are playing with two other kittens. How many ears are in all? So the child has to think. First of all, they’re excited by the image.

Sonya: I can see the kittens playing in my head.

Richele: But then they have to think about how many ears those four kittens would have.

Sonya: There are four kittens, and they each have two ears. So it would be eight ears. And then do I need to tell you how I came to that answer, or are we just going?

Richele: That one might be not the very beginning math lessons, but the child is always encouraged to give a full sentence because that is going to also habitualize the math facts in them. So in that case, you could say two plus two.

Sonya: Two plus two plus two plus two makes eight.

Richele: Then we move on to pure numbers, and we’ll give it just like dictation in this case. So, eight minus four.

Sonya: Eight minus four equals four.

Richele: Plus three.

Sonya: Plus three is seven.

Richele: Minus two.

Sonya: Minus two is five.

Richele: We’re going to build it, and the child doesn’t know it’s coming. So it’s really fixing her attention.

Sonya: And as she gets gradually into that, you could cut out where I’m saying what the answer is as we go.

Richele: Yes.

Sonya: So you could just say four plus three minus one plus 10 minus seven.

Richele: Exactly, so the child is just keeping these things in their mind.

Sonya: Oh, good examples.

Richele: And then we could, depending on what we’re doing in our math classes, do fractions. We could even do algebra. So it could be X plus three equals eight.

Sonya: So you should take mental math all the way through.

Richele: Historically. We see on the schedule that it ended in eighth grade. But then students had a time for reviewing things like Euclidean proofs. After they had proven something, then they would recite the proof back.

Sonya: Interesting. All right, so new and review, sometime during the week. We need to make sure we are covering all three: new, review, and mental math too. And the new and the mental math should be every day at some point. I’m narrating. And the mental math doesn’t have to be the last thing of the lesson. It can be, if it fits well there, but if you need to move it to a different part of the lesson to regain attention, or if you need to do it a different part of the day, you can. You have that freedom, correct?

Richele: Yes. Charlotte says that a change is as good as a rest. So if you see that your child’s attention is beginning to lag, then start that lively session of mental math. And if you have a child who begins to get fearful if something new is coming his way, you might start a math lesson if you’re going to introduce a new concept. Begin it with review, and then gradually go into this new section of math.

Sonya: So you’re starting a territory that they are well familiar with so they get comfortable and feel secure. Then you just take them one more step. That’s what I love about Charlotte Mason. It’s not throwing all these new concepts at them. It’s just taking them one more step.

Richele: Yes. She described it like going up the rungs of a ladder. Everything is built; you don’t want to skip a rung. Everything is slowly graduated lessons, again, at the child’s pace, which we can talk about. I’ll say one more thing about mental math, and that is that the mental math time is really great for solidifying the math facts.

Sonya: Like the addition subtraction tables and multiplication and division, those types of things.

Richele: Yes, but in a really fun and lively way. And this is something that all of the children, no matter the ages, can get involved in—giving mental math problems to one another, allowing your child to come up with his or her own problems, and posing them to you as the teacher as well.

Sonya: If you’re brave enough. Once they get into algebra, we might not do that. I love to see this.

Richele: You’ll learn alongside them. That would be good for them.

Sonya: So, let’s talk about the child’s pace, because I love how you talked about adjusting the scheduling to each child as an individual; we need to keep that same principle in mind with how quickly we progress in these lessons. Talk a little bit about how that concept is a constant.

Richele: Again, we see that it’s part of Charlotte’s philosophy of education is that we teach the child, and we don’t teach the textbook. So just because there’s something called lesson one in the textbook does not mean that that is one math lesson.

Sonya: That day, check it off, we did that.

Richele: Right, you must get through that math lesson.

Sonya: It’s not “even if it takes two hours, we will finish it today,”

Richele: Exactly. It depends on the concept. Some concepts a child will grasp very quickly, and then you can just make that part of her review, and other concepts might take quite a while to grasp. We never want to push or pull the child through something. We don’t want to base the progress on arbitrary standards or on her siblings. You know, one child might get a math concept quickly, and the next child might take a little longer to really understand or grasp that idea.

Sonya: I think that’s one reason it’s so important to do our math lessons one-on-one. Even if you have two children who are in the same grade level or the same age, to me, math lessons should be done separately so that you have the freedom to go at each child’s pace. What are your thoughts on that?

Richele: It depends on the children for one. I was able to give math lessons to my children together up to a certain point, until the older brother started looking over his shoulder, concerned that the younger brother was catching up to him and might possibly surpass him. If you’re able to give the attention to each child that he needs, then you can do that, but it might not work. Like I said, it might be just the mental math time or one child could be working on review if you’re having a number of children at the table at the same time. They can be working on review sections of their math while you’re giving oral work in one concept to another. But, you know, it can be a juggling act. It is really nice because the time that you’re giving one-on-one with each child might only be that that 10 minutes in the earlier years, first grade, second grade, third grade. Depending on their progress, you’ll want to be available to them throughout the math lesson, but as the child reaches around fourth grade, we’re going to give them a little more independent work, but we’re going to make sure that she doesn’t get off track.

That is one of the habits that Charlotte Mason talks about of the math lesson, the habit of working independently, but she doesn’t mean that you send your child off to another room to do the work. What she’s really talking about is that the child is doing the work, not the parent-teacher.

Sonya: That can be such a temptation, especially in math, but in really lots of subjects, to figuratively pull the child along. And I just see them, joining hands, and, “I’m going to keep walking. And I hope you can keep up, and if you can’t, just lean on me, and I’ll carry you the rest of the way.” And that’s doing our children such a disservice. But it’s easy to do when we see them struggling with a concept, it’s so tempting to jump in and give them the answer, because we don’t want them to have to struggle. We don’t want them to not keep up with others. It’s the comparison game.

Richele: I do think that fear is a strong part of that. As a parent, if your child isn’t able to understand something right away, you can start to get this feeling, and we want to start pulling him along or giving him the answer.

Sonya: Dropping hints.

Richele: And that’s what Charlotte Mason calls giving crutches. And she says we don’t give crutches in math; it’s in the child’s own power. He must go. And that’s like Charlotte telling us that the only true education is self-education. If we constantly give our children the answers, or we call an answer almost right and that’s good enough, that is a real disservice to them. It’s a beautiful thing to be able to allow your child the time he needs to process rather than thinking, “Okay, he’s not understanding it.” There’s an example I give. I was sitting at the table with my younger son, and he wasn’t working as quickly as I thought he should be, and I thought he just was not understanding it. So I was going to explain it a different way. So I started talking and talking and talking, this was with my son Luca, and slowly his hands went up and covered his ears, and he’s looking down, and then he says, “Mom, could you be quiet? I’m trying to think.” I was just smote by that, because I became that talky teacher who over-explains.

Sonya: I’ve heard you say before that if we hit that situation where the child’s not understanding something, we need to be careful of jumping to that conclusion, as you just told us. Perfect example. But if we do come to that conclusion legitimately, that the child is not understanding, rather than panic, all we need to do is take a step backwards because Charlotte’s approach is so gradated and gradual that we can just go back to something she does understand. It’s usually only one step back. I think of it as a running pass at it again. We’re going to gain some momentum, starting on the ground we know, and then see if we’re ready to take that step to the next idea again. So rather than panic, just take one step back.

Richele: Our children can feel when we are panicking because we really control the atmosphere of environment in our home as mothers. So yes, just one step back, sometimes two, but usually just one. Or just look at the example problems in front of you because one of those example problems might be the problem that sparks the idea for your child.

Sonya: Yes. Good word. We probably need to wrap up today because we could keep talking on this for a long time, but in future posts, I would love to have you address, as you said, the atmosphere of the math lessons and how that plays out and discipline. I love Charlotte’s approach to the discipline that is instilled in our math lessons and what our focus should be there. Then the life that is there, even though we’re not using living books, we mentioned it earlier that there are the living ideas given. So will you come back and talk about those things?

Richele: I really look forward to going more in depth on each of those.

Sonya: That would be great. Thanks so much.

Richele: Thank you.

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