How to Fall in Love with Math…Again

A few posts back I shared an article titled: “How to Fall in Love with Math.” As I’ve stated many times, I am quite passionate about the need to focus on affective learning in mathematics. I have since come across a few additional articles in the same vein and I thought I would share them here with a few brief quotes.

The first article is titled “Finding the Beauty in Math.” Here are some interesting quotes:

Cornell Math Professor and New York Times columnist Steven Strogatz, author of The Joy of x, said much of middle and high school math curriculum (which covers not basic arithmetic, but higher math) doesn’t appeal to students’ hearts, instead offering answers to questions that kids would never ask — which he calls “the definition of boredom.”

“When people want to learn about music, they’ve reacted to it, they love it and naturally want to learn more about it. They have their own questions,” Strogatz said. When introducing higher math to a group of curious young students, he suggests first “showing them math’s greatest hits” and allowing them to become fascinated; students then naturally come up with their own questions. Suri was on the right track, Strogatz said, when he suggested students learn something like the origin of numbers — because the first step is falling in love with the mathematical ideas behind the formulas and procedures.

Strogatz acknowledges that grasping the concepts of higher math can pave the way to many wonderful careers — many in the popular and highly needed STEM fields. But rationalizing to students that math improves reasoning skills or that “you’ll need it in the real world” are two strategies doomed to fail, he said, because they not-so-subtly suggest that math isn’t worth learning for its own sake, but parallels something more akin to “mental push-ups.”

“Have you ever asked why you need music?” Strogatz said. “You don’t need music. It’s nice to know about music. Why do you need to look at Picasso?” Perhaps when presented first as the story of how the universe works, math can become beautiful.

The article also states that “Grabbing students’ hearts, however, is only the first step to falling in love with math.” I’m just glad someone recognizes that grabbing hearts (as opposed to minds) is actually THE first step. Much of math education today seems to ignore this route.

A second article (which is actually referenced in the one above) is titled “How Do You Spark a Love of Math in Kids?” After discussing improving student self-efficacy the author goes on to state:

A second element critical to switching students onto math is the value they attach to the subject. Parents and teachers can foster the sense that math is an important and relevant body of knowledge by demonstrating the usefulness of math in the real world, and by making themselves positive role models for valuing math. In fact, parents’ own interest in math is another important component Martin and his coauthors identified.

I both agree and disagree with this comment. I agree that parents (and teachers of other subjects) need to be positive math role models for students. Too often I’ll have conversations with parents who want their child to do well in math class but they have no idea how to help them because they “were never very good at math” or simply they “aren’t a math person.” Comments like this to irreparable harm to the psyche of our math students. I disagree with the quote in that it outright contradicts the ideas brought up by Strogatz above. Namely that

Rationalizing to students that math improves reasoning skills or that “you’ll need it in the real world” are two strategies doomed to fail, he said, because they not-so-subtly suggest that math isn’t worth learning for its own sake, but parallels something more akin to “mental push-ups.”

To read more about how math is worth learning for its own sake, and not simply its utility I suggest my post on Mathematical Affections.

What If Learning

Last week I attended the Kuyers Institute Conference on “Virtues, Vices, and Teaching.” The focus of the conference was on pedagogical practices that instill virtue in students. The big question addressed in the sessions was “how do we as educators build the character of our students (focusing more on who students become rather than what students learn) while still being faithful to the content of our discipline?” It was a great conference and I’m still processing many of the ideas. There was an entire session of papers that focused specifically on this issue in math education. Hopefully I will be able to cajole the authors of those papers to share their ideas here. For now, I would like to share one resource that was presented at the conference: the website www.whatiflearning.com.

From the website, here is a summary of this new resource:

This site is for teachers who want their classrooms to be places with a Christian ethos or atmosphere, whatever the subject or age group they teach. It explores what teaching and learning might look like when rooted in Christian faith, hope, and love. It does this by offering over 100 concrete examples of creative classroom work and an approach that enables teachers to develop their own examples. “What if Learning” is a “distinctively Christian” approach developed by an international partnership of teachers from Australia, the UK, and the USA. It is based on the premise that a Christian understanding of life makes a difference in what happens in classrooms. Its aim is to equip teachers like you to develop their distinctively Christian teaching and learning strategies for their own classrooms.

I still need to explore this resource in more detail, but from everything that I have seen thus far, I am quite impressed. On the website’s Examples Page there are 10 concrete examples of what it looks like to teach math from a distinctly Christian perspective. Here are the titles of those 10 lessons with link to their content:

A shortcut link to these lessons will be included under the resource tab as well as the link side bar on the right.

The Myth of Critical Thinking in Mathematics

One of the most touted reasons for the necessity of every student undertaking mathematics courses in school (regardless of their ability or interest level in the subject) is that math teaches students critical thinking skills. I hate to burst bubbles here (actually I don’t) but this claim is completely and utterly false. Critical thinking in mathematics is a myth.

To “think critically” is by definition “to be critical of thoughts” or in other words “to critique ideas” as they arise rather than accepting or rejecting them blindly. Critical thinking means thinking rationally and reasoning through arguments with care and consideration of the options on the table. This, of course, sounds all well and good until we as educators stop and actually consider the reality of the situation in the math classroom. 

A critique can only be meaningful if you already have a standard by which to judge something. I can’t critique an argument as “true” unless I know what it means for something to be “true.” I can’t critique a painting as “beautiful” unless I know hat it means to be “beautiful.” I can’t critique an act of charity as “good” unless I know what it means to be “good.”

There is an underlying standard of judgment that is being instilled in students (whether knowingly or unknowingly) and this is the root of what is occurring in mathematics classrooms. The way in which students implement their “critical thinking skills” upon the completion of their mathematics courses is simply a symptom of a deeper reality that is being formed within them. That reality can be formed from a Christian perspective where it is God who sets the absolute standards for Truth, Beauty and Goodness, or it can be formed by very humanistic standards of relative truth, subjective beauty, and goodness defined by utility.

I submit to you that there is an opportunity present before us as math educators to impact the very standards by which students judge their thinking. This is the goal we should ultimately be aiming for. Don’t settle for simply teaching “critical thinking” skills.

They are just a myth.