The Regents Podcast: Cultivating Affections for Math

The Regents Podcast is aimed to think about and equip how we practice that which is true, good, and beautiful in a 21st century context. The podcast gives Regents School of Austin a format to share with our community and beyond the amazing stories happening on our campus, and help equip parents shepherding their children’s hearts.

I was recently a guest on the podcast, invited to speak about the Regents math program. You can listen to the podcast here.

Podcast summary:

Dr. Josh Wilkerson, author of the God & Math blog, explains what it means to “think Christianly” about math. Along the way, he discusses how to pursue the true, good, and beautiful in a math education and how to deal with the phrase: “I am just not a math person.”

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The Text of Mathematics

Which of these is most similar to a math textbook?

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Image result for bible commentary

This past summer I was challenged by Jacob Mohler to consider the difference between a ‘text’ and a ‘textbook.’ The text is the original foundation and the textbook is (unsurprisingly as the name suggests) a book about the text. The Bible is a text. A Bible commentary is a textbook.

How would you classify the following? Text or textbook?

Image result for geometry jacobsImage result for calculus larsonImage result for algebra forrester

Clearly these would be classified as textbooks. The question then arises: what is the text of mathematics? And perhaps more importantly, how are we engaging students with the text of mathematics?

A Christian cannot fully grow in their walk with the Lord by only ever engaging Bible commentaries – they have to spend time in the text, in the inspired word of God. If all we are ever giving our math students are the equivalent of commentaries, are we doing them a disservice? What is the text of mathematics that students need to engage with?

What the text of mathematics is NOT: I don’t think the answer to the question lies in teaching from original sources in mathematics, for instance using Euclid’s Elements in a geometry course. While Euclid offers a more ancient view of geometry, I’m not sure he offers the original view of geometry – he doesn’t even offer an always correct  view of geometry. I would still consider Euclid’s Elements a textbook. What makes the Bible different from Bible commentaries is not merely its age.

I would argue that there is no written, scriptural equivalent for mathematics. Rather, I believe the text of mathematics is this: the text is the teacher.

If we keep with the Bible versus Bible commentary analogy, I think there are actually two ways people can interact with the Bible. One way is certainly to sit down and read it. Another way people interact with the Bible (the text) is through their interactions with believers who have allowed the text (and in reality the creator and savior God behind the text) to transform their lives.

Preach the Gospel at all times. If necessary, use words. ~ St. Francis of Assisi

This quote from St. Francis speaks to the transformative power of the Gospel on the lives that we lead (not just the acquisition of new knowledge). Jesus says “By this all people will know that you are my disciples, if you have love for one another” (John 13:35). The way we live as Christians matters. It should point people to God. It should reveal to them in our actions what the text says in its words. Jesus was the “Word became flesh” (John 1:14) and that is our calling as Christians as well.

So then how do our math students interact with the text of mathematics? Through their interactions with their teacher.

I’ll often define my job as a “math appreciation teacher” rather than just a math teacher. Content delivery is only part of my job. In fact, as a new department chair I challenged my teachers that they weren’t hired for their ability to deliver content. In our technological age the reality is that students can get content from Khan Academy 9or any similar venue). The real job that my teachers were hired for is cultivating mathematical affections. Interacting with students in such a way that students see a noticeable difference in the affections/attitudes/dispositions of their teacher towards mathematics – that’s the real job.

The Gospel is more than content knowledge. Math is more than content knowledge. The affections (or lack thereof) in teachers play a much larger role in students’ experience of mathematics than I think people tend to credit. I challenge my teachers that they are the text of mathematics.

Teach math at all times. If necessary, explain content.

 

The definition of a “math person”

It has been awhile since I have posted here. My new responsibilities as the math department chair have taken up quite a bit of my time – but I am certainly relishing the opportunity to put into practice many of the ideas I have espoused here on GodandMath over the years. One of my responsibilities has been hosting a series of math talks for parents. This has been a great way for me to meet more families in our school community and to have a platform to explain our department’s philosophy of math education. This post is a summary of that philosophy that I have been sharing with parents.

Our department’s number one aim is to cultivate the mathematical affections of students – a phrase I have written about numerous times here. Essentially, the aim is to provide students a meaningful experience of mathematics that solidifies their appreciation of the discipline regardless of their future studies or career trajectories. This goal is in contrast to the prevailing attitude of society towards their mathematics education, summed up in the phrase “I’m not a math person.”

I start these parent meetings by asking who in the audience has ever said or thought “I’m not a math person”? I then ask for a few brave volunteers to explain what they mean by that. Without fail (whether in these parents meetings or in any context when someone admits to me that they aren’t a math person – which always seems to happen whenever you tell someone you’re a math teacher) there explanation falls somewhere along the lines of: I couldn’t remember all the rules, I wasn’t good at memorizing multiples, I never completed the problems fast enough, etc. Basically reiterating the prevailing view of society that to be a math person is to be efficient and accurate in computation and factual recall.

My typical response to people is “Yeah, I hate that stuff too. But I’m still a math person. What you’re describing isn’t how I see math. Can I show you how I see math?”

Our goal is to give students a very different impression of mathematics than what society has. We want to take away from students this go-to opt-out phrase of “Well, I’m not getting it, I’m just not a math person.” Mathematics, true mathematics, is inviting and uplifting for everyone.

How we as a department aim to cultivate students’ mathematical affections is through developing problem solvers. Below is a working summary of how our department defines problem solving (written to the student).

Defining Problem Solving: [1]

 Problem solving has been defined as what to do when you don’t know what to do. In some of your math classes, you probably learned about mathematical ideas by first working on an example and then practicing with an exercise. An exercise asks you to repeat a method you learned from a similar example. A problem is usually more complex than an exercise, so it is harder to solve because you don’t have a preconceived notion about how to solve it.

Problem Solving Expectations:

  1. Perseverance: Humility paired with confidence. Grit. In this class you will be asked to solve some tough problems. You will be able to solve most of them by being persistent and by talking with other students. When you come across an especially difficult problem, don’t give up. You may find that sometimes your first approach to a problem doesn’t work. When this happens, don’t be afraid to abandon the approach and try something else. Be persistent. If you get frustrated with a problem, put it aside and come back to it later. But don’t give up on the problem.
  2. Collaboration: You will be expected to talk to your classmates! Your teacher will ask you to get help from one another.
  3. Communication: In addition to working with your classmates, reading the book, and learning from your teacher, you will also be expected to communicate about your work and your mathematical thinking. You will do this by presenting your solutions to the entire class and by writing up complete solutions to problems. You will do presentations and write-ups, because talking and writing allow you to show your thinking. These communication processes will further develop your thinking skills.
  4. Grace: When you work with other students, you are free to make conjectures, ask questions, make mistakes, and express your ideas and opinions. You don’t have to worry about being criticized for your thoughts or your wrong answers.
  5. Service: Your growth in your math educational journey is not just about you. If the big problems of this world (curing disease, ending hunger, ending human trafficking, addressing sustainability, etc.) are going to be solved then mathematics will play a central role in their solution. If you are going to truly become a problem-solver then there has to be action taken.

At this point, after having explain our departmental goals and philosophy, I return to my original question.

“Ok, so you may not be a math person. But do you believe in the value of perseverance? Do you think collaborating in community and communicating ideas well are important skills? Do you believe in showing others grace and receiving grace yourself? I should hope so in our Christian community. Do you believe that we are called to serve others and put their needs before our own? If you said ‘yes’ to any of these, then congratulations, you’re a math person!

 

[1] Adapted from Johnson, K. & Herr, T. Problem Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures, 2nd Ed., Key Curriculum Press, 2001.