Teaching Resources

What If Learning

joshwilkerson1 Comment

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

joshwilkerson5 Comments

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.

How to Fall in Love with Math

joshwilkerson1 Comment

I’ve written before about the need to focus on the affective side of learning mathematics. It is a topic I am quite passionate about and it is the focus of my Ph.D. research in math education. I feel strongly enough about it that when people ask me what I teach I don’t respond with “I teach math,” or “I teach geometry,” or “I teach statistics.” Rather, I respond with “I teach math appreciation.” I think that is a much more apt description of our calling as math educators. We love math and the majority of students do not. Our goal is not to simply transfer our intellectual knowledge to the students, but to infect them with out enthusiasm.

I have been encouraged to see a recent publication come to my attention that address this matter. It was a New York Times article titled “How to Fall in Love with Math.” While I don’t necessarily agree with the conclusion of the article, that the solution to the problem is to be found in technology, it is nice to see the problem of mathematical affections being raised in the first place. I also enjoyed the opening of the article where the author clearly states what every math educator knows that nobody else does: when people say things like “do the math” they reveal that the public perception is that mathematics and arithmetic are the same thing. In reality arithmetic is an extremely small subset of mathematics. Mathematics as a discipline has something much grander than simply addition and multiplication that propels it forward. As the author states:

As a mathematician, I can attest that my field is really about ideas above anything else. Ideas that inform our existence, that permeate our universe and beyond, that can surprise and enthrall.