What Is Charlotte Mason Practical Geometry?

I don’t know if you have heard about the topic for today, “practical geometry.” You’ve probably heard about half of it, “geometry.” I had heard about that, but I wasn’t quite sure what practical geometry was. Today we want to talk about practical geometry and the place that it had in a Charlotte Mason education. Joining me is Dr. Julie Ryle and Tabitha Wirges, authors of the new Charlotte Mason Practical Geometry course.

Sonya: We’re so excited about that. First off, “practical geometry,” what is that? 

Tabitha: It’s practical! (laughs)

Sonya: That’s why I’m asking, because my geometry course was formulas and proofs and it was all writing things down that went right over my head. The worst grade I had in all of my high school math was in geometry, and it was like, “There’s nothing ‘practical’ about this.” 

Julie: And that’s not an uncommon experience. 

Tabitha: That was actually my experience too. I did well in it, but it was my least favorite math. 

Sonya: Yes, so what is “practical geometry”? 

Tabitha: It’s fun geometry! 

Julie: This is geometry you would start in the later elementary or early middle school years. And it gives students a taste of geometry before we get to writing proofs and having to use complex formulas. It’s all using tools, hands-on. So we’re using a ruler and a compass, and students get experience with these tools. It’s a lot of fun. 

Tabitha: It uses the ancient tools that civilizations have been using for thousands of years, and we are continuing to use these same practical tools, so that’s the “practical” part of it. 

It uses the ancient tools that civilizations have been using for thousands of years.

Sonya: Okay, now it makes sense. 

Tabitha: It’s practical because the ancient Egyptians used this in order to build the pyramids and many of the other buildings that they had. The Babylonians would have used the same thing, and the ancient Greeks as well. So that makes it practical. It’s the things you can use when you’re building structures outdoors. We’re still using those, but we’ve made them smaller so that we can use them on our tables. 

Sonya: We don’t have to go outside and actually build a pyramid. 

Tabitha: (laughs) Right, exactly.

Sonya: So, what are the benefits of it? You mentioned we’re doing this before we get to the proof-based geometry. Why should those older elementary- to middle-school-aged kids do something like this? 

Tabitha: Well, this is hands-on; it’s concrete. Charlotte Mason started almost every subject this way, with the concrete, but especially with math. She’d start off with manipulatives and things that you can actually touch and handle, so that you know that when you’re adding two plus two, it makes four because there’s four in front of you. It’s not abstract. Those geometry concepts, those formulas that you’re talking about, those are abstract. That’s abstract thinking. So we ask, “Well, why is that the formula for the circumference of a circle? Where did pi come from?” That’s what practical geometry gives them. For something like alternate interior angles, this is why they are equal. Because we’re actually going to build them and measure them with our geometry tools and find out that they are the same. And with our book, they do more than just build them and measure them with the tools. They actually take little pieces of paper, and rotating them, they see how they end up being the same. 

Charlotte Mason started almost every subject with the concrete, but especially with math. She’d start off with things that you can actually touch and handle, so that you know that when you’re adding two plus two, it makes four because there’s four in front of you. It’s not abstract.

Julie: That’s an exercise my students have loved. We actually take little strips of cardboard and use a brad and move the strips of cardboard. You can see the angles keeping the same measure as each other and it’s very practical and hands-on. 

Sonya: Yes. So you talk about Charlotte Mason and hands-on approaches, especially in math and discovery-based learning. Talk about some of the research you’ve done. I’m assuming you have done Charlotte Mason research to put together this course, and I know you have, but let’s share some of that with our readers. 

Julie: Sure. So, a book that Charlotte actually had in her own programs, with her PNEU [Parents’ National Education Union] programs, was called Lessons in Experimental and Practical Geometry. It was written by two mathematicians, Hall and Stevens. It’s now over 100 years old. 

Tabitha: They wrote it because they had a geometry book, actually, and they realized that they had a lot of students who didn’t understand these concrete-based foundational ideas. And so, they said, “Well, it’d be really nice if there was this precursor to geometry that was practical and that they would understand why the angles of a triangle can only be 180 degrees. That’s just the only way that this could even work if you added them all up.” So they put that together, this precursor book. It was meant to stand alone. You could do geometry without it, but they found it very helpful for students if they had done it beforehand. Irene Stephens, who did a lot of Charlotte Mason’s research when it came to math and helped her and guided her in great ways to learn math and explore with math and make math living, suggested it to Charlotte Mason as a tool to use for parents in the PNEU schools. 

Julie: So, about five years ago, Tabitha and I were both at a Charlotte Mason homeschool conference together. And Richele Baburina was there, and she was speaking on math and what Charlotte used in her schools. And that was my first introduction to the Hall and Stevens book. And yours? 

Tabitha: Mine was a little bit before that, not much, still from Richele, though. She would have been the one that introduced me to it. And I had been perusing through it in the archives online and got really excited about it. So I had seen it a little bit. As I said before, my early experience with geometry was just rather dull. 

Sonya: But you both have degrees in mathematics. 

Julie: Yes, I actually have a doctorate in Math, and I’ve taught at the collegiate level and the high school and middle school level.

Sonya: But you’d never seen this book? 

Julie: I’d seen geometry used as we use it in modern day, at a high school level, but had never seen this book before. And when I saw it I got so ecstatic. I was just thrilled with it. And it was actually the perfect timing. I had a daughter who was entering sixth grade at the time, and she was just at the right age. She was at about that fifth grade math, and so she was at the right age for me to go home and try it with her. So I took this book home, and at that time we actually schooled one day a week with another Charlotte Mason family, and so I had three late elementary-to-middle school girls, and I was working through this book with them. And they really enjoyed it. We did it once a week together, and their mom actually really enjoyed going through it too. She’s a scientist, and she went through this book with us, and she was doing the hands-on work as well and enjoying it. She has a little bit of math phobia and she was quite intrigued by this book. 

Tabitha: Which is a little bewildering to us because she is so good at science. She’s amazing at science, and math is the language of the sciences. 

Julie: Yes, but if you have that math phobia, you know what that feels like. 

Tabitha: It’s hard to break past that, even if you know you have to use it sometimes. 

Julie: She was so intrigued by these lessons, but I realized that this wasn’t something she could take home and implement in her own home with her children. 

Sonya: Because of the way it was written. 

Julie: Yes, because of the way it was written. Hall and Stevens wrote it for a math teacher to use in a classroom setting. 

Sonya: Oh, sure, yes. 

Julie: And so this was written in a way that the directions were not clear. You had to understand what they meant. 

Sonya: They were assuming the teacher would know how to teach this “shorthand,” if you will. 

Julie: And Charlotte didn’t teach straight through from lesson one through the book. She kind of hopped around, went through some of the precursory material, and then came back to the beginning, and went through again. So it wasn’t clear to a homeschool mom how they should best use this book. 

Tabitha: Yeah, I used it in a similar way. Not long after that conference, that next fall, I was using it in a Charlotte Mason private school setting. I had a classroom full of middle-schoolers, actually, but they had not had practical geometry yet. We were going to do that one day a week because that was a great precursor. I was just super excited about it, and anything that gets us excited about math carries over to students. But it was also good for them to learn that before they came into a formal geometry study.

And so, I started doing it within a classroom, and I was going through the same things that Julie was talking about. I was having to redo all the lessons and tweak them for myself. And I wasn’t the only middle school teacher. We actually shared it, where we each did different subjects for the middle-schoolers, so they could go to the different rooms and rotate, like they would have done in a public school setting. That way, we could hone in on our skills.

But I realized that I would not have been able to hand that book over to one of the other teachers and say, “Here, use this for your students.” I would have had to take them through an entire lesson, like, “Okay, for this lesson, do this, this, and this. And then say this, and then do this exercise, and don’t finish it off, because you’ll do that next year,” and I wouldn’t be able to hand it off.

I also ran into a lot of issues; I have a lot of homeschool friends, and one of them started her own business. She’s a court reporter now. She’s very intelligent; she can do all kinds of things. She has math phobia, though, and especially if she hasn’t seen it, she’s got to see it written out. If I just tell her, “This is how this works,” she’s going to be like, “What are you saying?” on top of the math phobia that she has. So there was no way that I was going to be able to hand that book over to her.

I was so excited about it. I think every person should go through practical geometry. But there is no way I could hand it to anybody else, and so, that’s where it blossomed that we wanted to do the book for everyone. 

Sonya: Tell the story, then, of how you got sucked into rewriting this book so homeschoolers can use it very easily and practically, as you say. I’d love to hear this story. 

Julie: We had people asking for some help in this realm, and so we batted around a few ideas—Do we write a solutions manual? Do we write just a teachers guide that they could use with the Hall and Stevens original book, telling them what exercises to use? Do we make a series of videos? We had tossed around a few ideas. We were both at a very busy point in our lives with young children and teaching. 

Tabitha: We just tossed these ideas around for a year or two, actually, before we were finally like, “Okay, this needs to happen. Parents need to have this.” And actually, that point happened when the world shut down in 2020, and nobody could go anywhere. 

Sonya: How convenient! That just aligned so beautifully. (laughs) 

Tabitha: Yes, so, towards May of 2020, we were chatting around with different moms. We couldn’t go places, but we wanted to be able to have practical geometry. So the world shut down, and we decided that we would write a book. 

Julie: We had been in contact with Richele as she was writing her Elementary Arithmetic Series and we were thrilled to be able to partner with her and bring that together with her materials. And so, of course, then we got to partner with Simply Charlotte Mason and bring this to the table. And as we began rewriting it, we realized that there were a lot of things that we wanted to update and change. 

Tabitha: At first, we just were going to rearrange it in the way that we had been using it with our students and with our children, but as we jumped into it, we realized it needed a completely different format. 

Sonya: It’s about 100 years old, right? 

Julie: Yes, and some of the math terminology is very different, the terms mean different things in the math world today than they did in that book. If you learn them that way, it’s not going to translate to your high school math. So it kind of grew. We were updating terminology, we were rearranging lessons, and then we were like… 

Tabitha: “I would introduce this this way…” 

Julie: And we got some other older geometry texts and took some inspiration from there and built, I think, a good series. 

Tabitha: We also based it off Charlotte Mason’s lessons, in the way that a math lesson should go, where you start off with review, and then you explore the idea, and then you narrate it. We didn’t want parents to have to figure that out as they opened it up to get going. We wanted them to be able to be like, “Okay, we’re ready to go.” We wanted students to be able to have this accessible to them. This is their knowledge that they’re taking in, and so, they could own it for themselves. So, it’s written neutrally to students and parents, so both can take it and learn it and enjoy it.

Julie and Tabitha’s Charlotte Mason Practical Geometry is now available. Enjoyable lessons in practical geometry that introduce important skills and concepts through hands-on exploration.

Sonya: I love how you created the videos to go with it. Not a video for every lesson, but some of the constructions and the tips that are in there are just a lot easier to grasp for some people if they can see it being done, rather than just reading it and looking at the illustrations. Different learners are going to grab it in different ways, so I love the video component that you added to it. Just to help parents be able to… 

Tabitha: Visualize, right. “Oh, that’s how you turn the compass,” and, “Oh, I hold the ruler over here.” I’m going to be honest, there are some constructions where I even have to work through it for a second and go, “Right, I need the ruler over here and the set square there.” I have to be doing it before I can actually say, “Okay, this is how you should hold it. It just makes it so much easier to be able to see it. 

Julie: It was very important for us that this was something that could be opened and used in your home and not something that you purchase with the best intentions and put on your shelf. I’ve done that; I have many books like that in my home. We wanted it to be something that is usable by everyone. 

Tabitha: We also didn’t want you to have to go find more help from somewhere else, where you have to take the time to go look for that information. I’ve been there. That takes time from my homeschool day that I could be spending with my children. 

Julie: And it means the lesson is just not going to happen, right? 

Tabitha: Yes, exactly, so this way, it’s easy. It’s right there, you can just go look at it real quickly, and then you can continue on with the lesson. 

Sonya: And this is used in conjunction with Charlotte Mason Elementary Arithmetic Series. How do you recommend this new course, the Charlotte Mason Practical Geometry course, be used? 

Tabitha: We suggest that you use the Elementary Arithmetic four days a week, and that you do the Practical Geometry lessons one day a week. 

Sonya: Starting in which book?

Tabitha: Book 5. 

Sonya: Book 5. So, we’re not doing this from the first book? 

Tabitha: Not from the first book. 

Sonya: You have talked about middle school. 

Tabitha: Yes, we started using it with students around the time they were in middle school, just because that’s when we found it. 

Sonya: Yes, perfect timing. 

Tabitha: But it’s never too late. You can use it anytime!

Julie: If a student has not gone through Practical Geometry, it would be great to pick this up and use it with a seventh or eighth grader before they get to high school geometry. But it is designed to go with Charlotte Mason Elementary Arithmetic, Book 5, so that’s the arithmetic level they need to be at before they can start doing the math that’s in Practical Geometry

Sonya: Oh, okay. That’s why, because they have to have, what, fractions? I assume… well, they’ve been learning about using a ruler and measurements and everything, and that’s going to come into play as well.

Tabitha: Exactly. They need to know how to use a ruler and read a ruler. 

Sonya: And they’ve been doing the conversions between inches and centimeters and meters; metric and US Standard measurements. You use both of those? 

Julie: We do. We use both in the course. We give them experience with both. We go back and forth between the two, so they use both sides of the ruler. 

Sonya: So, it’s used along with Charlotte Mason Elementary Arithmetic, Book 5. How? 

Julie: We do Book 5 four days a week, and so Practical Geometry will be done one day a week. A lot of families view this as their kind of “fun math.” It gives the brain a break and lets you focus on something else. And this might be something that your student is especially successful at, to give them that boost in confidence. 

Tabitha: A lot of times you’ll have a chance to use what you’ve been learning in your arithmetic studies. You can actually use it on these geometry lessons, and so that gets really fun too. So maybe you’ve been practicing adding fractions, and you’re going to come over here and add some fractions together, but you’re going to draw them. So you can have some fun with that. Also, say you’re in your arithmetic studies, and you get to multiplying fractions and that just gets too hard, or you’re subtracting fractions and that gets too hard, and you just need to take a break from your arithmetic studies, or you’re at a wall where you need to keep practicing that particular thing, so in order to take a break from that, you can keep reviewing that for part of your lesson, and then do a few practical geometry lessons. Maybe you do more than one that week for a couple of weeks, while your student catches up on that fraction lesson and gets it under his belt. 

Julie: You could even do the entire course in 36 school days, if that’s what you choose to do. It could be, if you hit a wall in your arithmetic study, sometimes it is best to pivot. You still want to be reviewing that arithmetic concept where you were stuck at. 

Sonya: Which you could do with mental math. 

Julie: Exactly. So that could be your mental math lesson, and if your student just needs a break, we want to respect his personhood. If that’s what he needs at that time, then we can step back and use Practical Geometry in that way. There are many ways it could be used. 

Tabitha: I’ve done that with a couple of my own kids, actually, where they get stuck. Long division is usually the place that we get stuck at, and so we just cycle through, and we keep moving forward in their math lessons. We either cycle over to practical geometry, or I’ve even gone ahead and gone into fractions as we continue to review the long division at the very basic level of manipulatives. We keep having math every single day, but we cycle over to these other things. And Practical Geometry is just a really great one. You’ll be amazed how far they come forward in this concept that seems so hard as you give their brain a break and do other things. It also prevents not liking math. There’s nothing worse to take all of the fire out of something than to just keep pushing it when it’s too hard. 

Sonya: Yeah, drill and kill. 

Julie: Yes, it also could be used as a summer math. If you’re schooling year round and you wanted to do something a little bit different so that it felt fun for summer, it could be used in that way. 

Sonya: Lots of different ways to use it, and I like how you’re bringing to life that idea Charlotte talked about, that sometimes, a change is as good as a break. And I like how you said, for some people who think that they don’t like math or aren’t good at math, here’s a different type to try. And it’s like how with art, someone might say, “I’m not good at art,” but all she’s tried is pencil sketching. “Try pastels. You might be good at that.” 

Tabitha: I think of it like reading, too. You’ll have people that will say they don’t like reading. I’m like, “Well, maybe we just haven’t found the right type of book.” 

Sonya: Yeah, “What are you reading?” That might make a huge difference. Yeah, that’s great. Well, we’re so excited about this course. I know it’s going to be of huge benefit to so many people, and keep writing, okay? Can you give us more like this? 

Julie: (laughs) We’ll try. 

Sonya: Just, you know, in your spare time. Just write, that’d be great. Thanks so much.


  1. So excited for this! Plan on using it with my middle and high schooler (who’s taking Geometry right now!). Wish I would’ve had something like this sooner. Keep the upper level math resources coming!

  2. Thank you for this discussion. Is practical geometry only for lower grades or is it challenging enough as a high school course

    • Practical Geometry is designed to be used in upper elementary or middle school and would not be a complete geometry course for high school. A high school student could use Practical Geometry as an introduction to the study of geometry, but that student would need further study and resources to complete a high school level geometry course.

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