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Charlotte Mason’s approach to mathematics is so brilliant and very unique. And a big part of it is something called “mental math.” What is that? What does it look like? That’s what we want to focus on in today’s conversation with Richele Baburina.
Sonya: Now for those who that’s a new term, possibly, or those who just need some clarification, what is mental math?
Richele: So if you’ll remember, we have a little rhyme: “new, review, and mental math too.” These are the three components of Charlotte Mason math lessons, and mental math stands on its own, even though at this point during arithmetic, our lessons are largely oral. And in any math lesson, our students are going to expend a lot of mental activity. So, how does mental math stand on its own? Well this is a 5-minute time, set apart, where all of the manipulatives, or everyday concrete objects, are put away, and we’re going to engage the child in lively, rapid questions that are within his scope of learning.
Sonya: Okay, you said “rapid.” How rapid?
Richele: “Rapid” is definitely relative. The mental math time is going to increase a student’s ability to rapidly answer questions, but that’s going to progress as the child progresses in his learning.
Sonya: So as in everything, we teach the child and go at his pace, but it’s a gentle, lean-on-the-elephant type thing.
Richele: You can watch your child, just as you would when giving a dictation lesson. You can add in pauses, you can slow down, and you can give the child the time he needs to think and answer the question.
Sonya: Good, okay. So why are we doing this? What’s the purpose? I can see the benefits, as you said. He’s gaining some mental speed where he can calculate more quickly over time and at his own pace, but what else? What’s the purpose of this? I’m sure there are others, because Charlotte Mason usually had like 25 purposes for everything she did.
Richele: Right. Because these are methods that lay on top of principles in the math lesson, and in any lesson, we remember that Charlotte Mason favored the living math lesson for its ability to nurture good habits in our children. That’s one of the top reasons for mental math. There are mental habits, such as attention. That’s one of the big three in habits. We want careful execution, and some abstract thinking is going on here.
Sonya: Oh yes, because they don’t have the concrete manipulatives anymore.
Richele: Yes, it’s a good stepping stone between that concrete lesson going toward abstract thinking. And then she said that mental habits are going to lead the child into moral habits, which we might not think about in correlation to a math lesson, but independent honest work and accuracy are two of these moral habits.
Sonya: Yes. That makes total sense, and even in a math lesson, for the teacher, that can elevate this 5-minute mental math time. It elevates it in your head; it’s not just, “Oh, here we go again, let’s do it.” There’s a real purpose to it.
Richele: Yes. Charlotte said that these habits are going to stay with the child throughout his or her life.
Sonya: So you said it’s part of the lesson. Talk a little more about those specifics. When are we doing this? Does it have to be at the beginning of the lesson? At the end of the lesson? Another time? Does it always have to be at the same time as the lesson? Do we have to be sitting in our little chairs? Talk about the details here. Let’s get the nitty-gritty.
Richele: All right, so this can be given anytime during the lesson when you see that your child’s attention is waning, or maybe she seems to be getting tired, and so we have that option, since a change is as good as a break sometimes. We can switch to the five minutes of mental math and freshen the child up.
Sonya: So it would be, “Okay let’s just set that aside for a few minutes, and we’re going to do this now,” and give her that little boost of energy. Because it’s the rapid that makes your adrenaline go.
Richele: So it is a change, or it can be given at the end of your math lesson as a kind of grand finale.
Sonya: I love that.
Richele: Yes, a fun way to end the math lesson is with mental math. Now, if you’ve already lost your child before the time of the math lesson is up, then you can save it for another time, or you can give more mental math at any time throughout the day. It can be during a walk, it can be around the dinner table; it can be while you’re running errands or while you’re in the car. This five minutes of mental math can be given at different points.
Sonya: I remember you talking about, at some point, your kids were doing mental math with each other. It wasn’t all teacher-initiated.
Richele: Right. So as teachers, we can have our book that has the mental math included, but it’s a great idea to have your child make up his or her own questions and pose them to you. If you have multiple students, then they can pose questions to one another.
Sonya: Which is what my grandkids do. You’ve seen the little video with, I think she was six at the time, they were six and four at that time; they’re running around the kitchen island, and one of them dashes into the pantry and the one running around the island gives the mental math problem, and the one in the pantry opens the door and pops out and gives the answer. It’s just part of their play.
Richele: Right. It’s so wonderful.
Sonya: It was fun. All right, so a lot of people are going to be saying, “Yes, but what does it look like?” So now, these are always questions within the student’s scope. These are review. Things that he has already mastered the concepts of, and he’s just working on the memorization, I guess you would say, recalling those facts quickly. Right?
Richele: Yes. It is within the student’s scope, and so you could be actually doing much more complex work in your new section of the math lesson, but your mental math should be within his ability as you slowly climb up that hill or that mountain. We could be using smaller numbers rather than larger numbers so your student could be doing long multiplication, but his mental math might not include long multiplication.
Sonya: Clarify for me, because we’ve got our big three: new, review, and mental math too. Mental math is a type of review, but what I’m hearing, and clarify this if I’m wrong, okay, is we have our new concept, like if we’re working on long division, the review is going to be closer to that new concept. It’ll be just one step behind. “Remember, we were doing this, and that leads to this,” whereas the mental math can be anything back to the first book.
Richele: Yes. We don’t want our child to be bored during the time of mental math, but it can be anytime. So reviewing multiplication tables, reviewing addition and subtraction, and it’s done in a little bit more lively way than if they were doing, say, some written work.
Sonya: And it’s not just drill, where I give six times seven, nine times four and so on. It is much more engaging than that, which is where we want the demonstration to come in, if I have the guts to do this. Which book are you pulling these things from?
Richele: I have pulled mainly from book 3, because I want to give you all an idea of what a student, perhaps third grade student, will be working with in mental math and just what his abilities are at this point.
Sonya: Okay. I think I can do third grade.
Richele: All right, we’ll see.
Sonya: Do you usually start a timer when you’re doing it? Or do you just keep an eye on the clock? How does that work?
Richele: If we’re outside, or in the car, believe me, this can go on for much longer than five minutes.
Sonya: Do you let it?
Richele: Yes, as long as the children are engaged, we’ll just keep going for it. I remember; there’s a Parents’ Review article where a parent talked about how her husband said no more mental math around the dinner table, because the children weren’t actually eating their food. They were just having fun.
Sonya: That is so fun.
Richele: During the lesson, we’ll set a timer for five minutes. And I think it will surprise you at how long five minutes of mental math actually is. Okay, so I’ll set my timer. Ready?
Sonya: Can I peek at the, no, I won’t peek. I won’t peek. [laughs] And this might give our listeners a good opportunity to see what you do when somebody gets a mental math problem wrong. We’ll see how this works.
Richele: Martin has 4 apple trees, 2 peach trees and 3 pear trees. How many fruit trees has he?
Sonya: He has 9 trees.
Richele: Cossette picked 7 pink roses and 7 yellow roses. How many roses has she?
Richele: Nick and his brother each check 6 books out from the library. How many books were checked out in all?
Sonya: 12 books. Now let me ask this. You can pause if you want to. Am I supposed to be giving the whole equation?
Richele: At this point, you don’t. You can just give the answer. It’s usually in the earlier years with addition and subtraction, when they’re first learning what that even means, that we want them to give the full answer. It will help them retain their facts.
Sonya: Okay, thank you.
Richele: Lucy is 8 years old, and her brother is 2 years older. How old is Lucy’s brother?
Richele: After paying 5 cents for a gumball, Abram has 20 cents left. How many cents had he at first?
Sonya: Oh that’s a good one. 25 cents.
Richele: 9 is how many more than 4?
Richele: 6 added to what number makes 10?
Richele: 8 added to what number makes 13?
Richele: 10 is how many more than 2?
Richele: Lydia rode her bike 12 miles in April and double that amount in May. How many miles did she ride in May?
Sonya: 24 miles.
Richele: If you bike 8 miles in an hour, how many miles can you bike in 3 hours?
Richele: How many gum balls at 5 cents each can we purchase for 30 cents?
Richele: How many 4s in 12?
Richele: How many inches make a foot?
Richele: If you divide a foot in half, how long will each half be?
Sonya: 6 inches.
Richele: What is 1 foot take away 5 inches?
Sonya: 7 inches.
Richele: Good. How many inches added to 3 inches make a foot?
Richele: If you subtract 4 inches from a foot, how many inches remain?
Richele: How many half inches are there in 1 inch?
Richele: How many half inches in 3 inches?
Richele: How many inches in a foot and a half?
Sonya: Ooh, 18.
Richele: If you had 12 inches of ribbon, and you cut it into 3 equal parts, how long will each part be?
Sonya: 4 inches.
Richele: How many 2-inch pieces can you cut from 1 foot of ribbon?
Richele: Carl caught 7 fish a day for 4 days. How many fish did he catch in all?
Richele: 2 pepper plants each contain 8 peppers. How many peppers all together?
Richele: I see we can move on to something a little more challenging.
Sonya: Oh now, don’t assume, keep it within the student’s scope here! [laughs]
Richele: An artist had 19 paintings and sold 7 of them, how many had she left?
Sonya: 8, no, 19 minus 7 is 12. 12.
Richele: Rachel had 20 dollars. She gave 5 dollars to her brother and spent 4 dollars. How much had she left?
Sonya: 11 dollars.
Richele: Liam has 23 miniature figures. He’s painted 12 of them. How many has he left to paint?
Richele: Now we can move to some abstract, or pure number. What is 3 taken from 5?
Richele: 3 taken from 12?
Richele: 3 taken from 77?
Richele: 3 taken from 34?
Richele: From 29?
Richele: From 48?
Richele: From 91?
Richele: If there are 8 crayons in a box, how many crayons in 5 boxes?
Richele: How many legs have 3 kittens?
Richele: How many legs have 7 kittens?
Richele: How many legs have 10 kittens?
Richele: How many legs have 8 kittens?
Richele: How many ears have 6 dogs?
Richele: 2 boys?
Richele: How many ears have 3 dogs and 4 children?
Sonya: Oh, goodness! This is nice. 14.
Richele: How many ears have 5 girls and 4 boys?
Sonya: 18. The two part-ers, these are so good.
Richele: What is 5 taken 6 times?
Richele: 5 taken 8 times?
Richele: What is 7 taken 6 times? [alarm goes off]
Sonya: 42. And that’s my time, yay, saved by the bell! So I love how those were just multiplication, division, addition, subtraction, but they really were engaging, and especially those two part-ers. I assume you wouldn’t do the two part-ers for the younger grades, but up into third grade, they are getting there.
Richele: In third grade they will be there, and we didn’t even get to fractions. You’ll be doing mental fraction work in third grade as well.
Sonya: Yeah. We did a little of it when we were taking half inches and such, but it was just that gentle introduction that Charlotte’s so good at.
Richele: And it really kept you on your toes.
Sonya: It did; it did. About, I’d say maybe about the 4-minute mark, my brain was kind of like, “Oh this is getting hard. It’s okay. It’s okay. We’re almost done; hang in there.” So I’m not saying it energized me, but it did keep me on my toes. It helped with perseverance and focus, trying to pay full attention. I will say, we’re doing this in the morning, if we had done this after supper tonight, it would have taken me twice as long to answer each question.
Richele: It probably wouldn’t have been that fun.
Sonya: Yeah, so this is great. Thank you for this demonstration. It’s not something that I grew up doing in my education. We had timed worksheet drills to review our facts, and it was just pure number on those worksheets. But this is so much more engaging. I can see how it’s building a relationship here too.
Richele: Yes. It’s building a child’s relationship with the parent as well as a relationship with numbers.
Sonya: If it’s, “here’s your worksheet.” setting the timer, and walking away, there’s no relationship going on there. So this is fun; this is good.
Richele: You can also see just how much it builds those good habits. One of my favorite habits that Charlotte Mason mentions is steadfast thinking, and mental math is really good at building that steadfastness. Even with how you persevered, you stayed steadfast.
Sonya: Yes and holding those numbers in your brain, it all plays into it. So many great habits in a lively, interesting, and engaging way. It’s building relationships with five minutes a day. You can do this all the way up through 12th grade, right?
Richele: Right, we can use a definite oral component, no matter what the complexity or the branch of mathematics the child is studying.
Sonya: Where do people find these mental math equations and ideas?
Richele: So we have them throughout the Charlotte Mason Elementary Arithmetic Series, but you can get good at it. Whichever textbook you’re using, you can think, “Oh these could actually be given orally. All of these questions could be given orally.” Some textbooks do have them built in, even in trigonometry or algebra, they’ll have an oral component built in.
Sonya: I love how in the Charlotte Mason Elementary Arithmetic Series that you wrote, you have notes in there, like, “If you don’t get through all of these in the lesson, or if your student has already passed this and you’re ready to move on, just bookmark this page and come back and use it for mental math.” That makes total sense.
Richele: Yes. And if your children have already learned their math facts, you can bookmark those questions from the table work and use those for mental math as well.
Sonya: I’ve been doing it where I’ll use those questions, but I change it up. Rather than how many kitten ears, I would say, “How many kitten feet?” Or, “How many tails?” So you can just tweak one word here or there or tweak the numbers and reuse them as needed.
Richele: When you twist and turn these questions, then it makes it even more fun. The child doesn’t know what’s coming.
Sonya: Yes. You don’t want to reuse the same ones every time. Great. Thanks so much for helping us with mental math. Next time I’m going to ask you the questions, okay?
Sonya: Thank you.