“Why do I teach math to students? I teach math so that students might love the Creator of math. But I also teach math so that I will love God and love my children more” (Leigh Bortins, The Conversation, 127).
The thing I love most about math is that I don’t have to have all the answers. As a Challenge B tutor and working with my own child on high school math, I have learned that being a know-it-all takes away the joy of discovery. In fact, it’s even more fun when I don’t have every answer. I only have to have good questions and a desire to see beauty at work.
Approaching math this way is sort of like going on a hiking expedition. You have an endpoint in mind, but you aren’t sure what you will encounter along the way or exactly how you will get there. It’s the adventure of the trail that makes it a true experience. In this day and age, it feels like every answer is only a Google search or a Siri voice question away. The Classical Conversations approach encourages a space for students to truly grapple with questions and inspires a curiosity to discover the answers for themselves. We make room for the Holy Spirit to show up by fostering the ability for students to think deeply about a problem.
In high school, I remember starting every single day of my sophomore year in terror. Geometry was my first class of the day. We would spend thirty minutes in a lecture style format where we were told exactly how we should work the problems. Then we were marched to the chalkboard, where we were to work the problems exactly as our teacher had stated, with only the steps given. I was terrified of being wrong every single day. Even if I got it right, I felt wrong anyway.
What I love to see in the Challenge seminar is how each student thinks differently about solving math problems. Some like to draw a table to solve a problem, others draw pictures, some work out every detail, and others simply solve it in their head. But the beautiful thing is they are not wrong; plus, they get to learn new ways of doing things from their peers. They get to see the beauty and creativity of math from the Creator at work, right in their midst.
As we walk through Leigh Bortins’ book, The Conversation, it’s a perfect reminder that the struggle of discovery is worthy too. We have been using the five canons of rhetoric as our basis for discussion and working through each subject for high school studies. If you need a refresher on the five canons, read the previous article called “Drawing Out the Wonder” here.
In Mrs. Bortins’ discussions in Chapter Seven on math, she states that she doesn’t walk through the five canons of rhetoric intentionally, but as a natural way of categorizing communication.
“The beauty of using math for conversations is that the problems are short and sweet. A math conversation can take fifteen seconds or fifteen minutes to complete, compared to a science text, which may take fifteen weeks to study or a novel, which may take a few days to read,” Mrs. Bortins said. “We can practice the five canons quickly with each math problem” (130).
Putting the Five Canons of Rhetoric to Work with Math
Let’s look at how you might approach the subject of math at home with the five canons.
Invention – What possible approaches are there?
Invention is always looking into the big pot of ideas and drawing from them. When looking at a math problem, you might invite your students to write out all they know about the problem or gather all the possible ways to solve it. Invite them to share what they see when they look at the problem and clarify what solution the problem is asking for.
Arrangement – In what order should this problem be solved?
Arrangement falls naturally with the steps in which the problem might be solved. Encourage them to think of other ways of arranging as well—perhaps with a table, a picture, or playing with ways to simplify the process. Some ideas might include solving first in their head and then checking their steps to see if the answer is reasonable.
Elocution – How will you best explain the solution to this problem?
It takes one set of abilities to solve a math problem, and quite another set to explain that solution to others. When students communicate how they solved a problem, either in class or at home, it’s a great lesson in being able to articulate ideas concisely and clearly. What are the best words, laws, phrases, or tools to share how the problem was solved? How can your student tell the story of the solution?
Memory – What similar math problems have you solved before?
Math lessons typically build upon themselves. With that in mind, challenge your student to consider what other relationships exist in concepts they have already studied. A simple idea might be to ask if this math problem reminds them of others they have solved before. Encourage them to see the patterns and connectedness in their learning.
Delivery – Can you articulate what you have learned?
When considering delivery, encourage your student to write out the solution neatly and legibly. Invite them to explain each step back to you and share what they have learned from working through the problem.
Celebrate the Beauty of Math
Everyone’s mind works uniquely in the way they approach math. For me, I have to solve everything methodically and write down every step. My son visualizes the problem in his head and talks through a “guess” at the answer before he even solves it. Usually he is right, and it surprises me that he can simply work through it mentally first. What’s striking to me about math is that there are many ways to arrive at the solution, but usually only one right answer. Our Creator, in His perfect design of the universe put truth, beauty and goodness everywhere—even in math.
Read Along in The Conversation
Read Chapter Seven – “Math”
- What were your experiences with math when you were a student?
- What is your perspective on “having all the answers”?
- How can you foster a great conversation about math with your student?
- Where do you see beauty in math?
- How can you help inspire your student to see the Creator at work in math?