It has been said that scientists and mathematicians comprise a new priesthood. Our leaders, educators, and policy analysts are consumed with statistics for STEM (science and technology). How are our students doing in these critical subjects? The pressure to succeed in these areas causes us to make some critical errors. We focus too much on earning a credit instead of having students who spend enough time on the material to truly know it and, in turn, to love it. We put an “x” in the check box and move on before the children are ready. Secondly, we forget why we should pursue these subjects in the first place. As classical, Christian tutors and families, we want to turn the conversation so that we pursue these ideas because they lead us to a deeper understanding of who God is and how He has marvelously designed our world.
One of these errors was replicated in my own education. I made an A in AP Calculus my senior year in high school and was able to earn my college math credits before I set foot on the university campus, but this in no way signifies that I understood calculus. As my husband and I have discussed several times, we wish we had understood what we were doing. Instead of learning to memorize and apply formulas, I wish I had understood the amazing applications of calculus. I am excited for the opportunity to do it all over again. This time, I might just understand it!
I recently went with my daughters to an 1889 one-room schoolhouse. We spent the day precisely following the script of a school day in 1889. This was most illuminating for the families in my Classical Conversations community as we constantly juggle students of different ages. (It was equally delightful for the teacher, who is used to public school students. She was so happy to have an authentic day with children from ages six to thirteen).
My favorite part to watch was the instruction in math. For about thirty minutes, the young woman read story problems to the class. The youngest pupils were instructed to write as much of the problem as possible, even if they could only hear and write the numbers involved in the equation. When students finished as much of the problem as possible, they were to raise their slates above their heads silently so that the teacher could check their work while other students continued to puzzle out the math.
What did all of this accomplish? In contrast to a classroom in which students are all working through problems in the same grade-level workbook, these children in the one-room schoolhouse were learning to play with numbers. The youngest students received early exposure to math concepts they would encounter in full in the upcoming years. Some of the youngest students were able to accelerate by solving the advanced problems. Others worked on their listening and copying skills. Older students were encouraged to increase their speed to compete with their classmates.
Our Challenge math seminars function in much the same way. Every year in every class across the country, there will be a wide variety of abilities. Some students will be reviewing the curriculum they completed at home the year before. Other students will be previewing the curriculum they will complete at home the following year. Some students will be discussing the same curriculum that they are completing at home, but will be ahead or behind of the four lessons being discussed in class that week. Other students will be working on the assigned four lessons, but will be ahead or behind one another in their comprehension of the concepts.
The Classical Conversations math seminar occupies a unique position among educational options. We meet with students only thirty times each school year, for a total of thirty hours. This means that the bulk of the day-to-day instruction will occur in the home. Some students will be self-taught while others will be video-taught, parent-taught, or privately tutored at home throughout the week. Challenge directors work with parents to help them understand that the math seminar is only one component of their math education for the year.
As our Challenge tutors continue to grow in their dialectic and tutoring skills, they will move farther away from a push to cover weekly material and will move toward playing with numbers and meeting each of their students exactly where they are. This will take time and effort on the part of every tutor and every parent. As we grow and mature, our math seminars will not look very different from the other seminars because they will be focused on the discussion of ideas.
How can Challenge tutors begin the process? One way is to ask questions during every math session. Which of the four mathematical operations is being used? What kinds of numbers are being used? What terms need to be defined? For example, in my Challenge III chemistry class, we always start solving equations by asking the same basic questions. What are we being asked to find out? What are the “unknowns”? What are the “knowns”? What formula do we use? Do we need to rearrange the formula to solve for this variable? Are all of the known quantities in the correct units or do we need to convert them? Tutors use these questions to stimulate the students to really think about how to solve problems so they can learn how to solve any kind of problem.
In summary: classical, Christian educators should seek to give students a firm foundation in concepts so that they can progress to more complex concepts. Sometimes, this means slowing down, reviewing, and even repeating math rather than racing forward to check off boxes. We want to teach our students to be enchanted by numbers, so that they can fully worship God for the beauty and order of His creation by knowing the language in which it was written.
Caldecott, Stratford. Beauty for Truth’s Sake: On the Re-enchantment of Education.
Nickel, James. Mathematics: Is God Silent?