Teaching a Love of Mathematics

A few weeks ago, NCTM President Linda M. Gojak posted her final message as president entitled “A Reflection on 25 Years in Mathematics Education.” You can follow the link to read the article in its entirety. In this message Gojak outlines from her perspective what the mathematics education community has accomplished over the last 25 years and what challenges still need to be addressed. I will let you determine for yourself how much you agree with her assessments. What I am most interested in is her closing remark:

B. F. Skinner famously said, “We shouldn’t teach great books; we should teach a love of reading. Knowing the contents of a few works of literature is a trivial achievement. Being inclined to go on reading is a great achievement.” With apologies to Skinner, as mathematics educators we might say, “We should not just teach mathematics, we should teach a love of mathematics. Knowing the content of some mathematics is a trivial achievement. Being inclined to see the beauty in mathematics and to go on doing mathematics are great achievements.”

We should teach a love of mathematics.

Knowing the content of some mathematics is a trivial achievement.

I agree with both of these statements, as I believe the majority of math educators would. However, these two statements get to the heart of the issue with the state of mathematics education today: while the majority of educators would agree on the sentiments of these two statements, both statements run contradictory to the current system of mathematical standards and assessments.

If we really believe that our goal as educators is to teach a love of mathematics (which I should note is a very different thing than saying every student has to love math) then we as a community of educators need to actually determine how to go about doing so. Because trust me, focusing on core standards/higher order thinking/critical reasoning/whatever you want to call increased cognitive demands, will not influence people’s affections. The issue is much more complex than that. We are talking about teaching love, beauty, truth to human beings created in the image of God.

I will have a lot more to say on this issue in the coming weeks/months/years as this is essentially the focus of my dissertation research. For now I will leave you to contemplate Gojak’s closing remark and consider why the underlying sentiment of the remark does not appear anywhere else in her summary of math education’s “accomplishments” and challenges.

2 + 2 = Jesus?

April 19, 2014 2 comments
I think I understand the author's intentions... but that is just an awful title.

I think I understand the author’s intentions… but that is just an awful title.

Whenever I talk about my passion for the integration of Christian faith and the study of mathematics, the typical response is one of confusion. I can tell immediately that the listener is going to a place in their head where they envision the arithmetic lessons from elementary school somehow combined with the Bible stories from Sunday school – where the answer to every question (even 2+2) was always “Jesus.” When the listener can no longer contain the awkwardness of this mental image they eventually blurt out something along the lines of “How can 2 + 2 = 4 (or insert other trivial math problem) be Christian?”

Where the Question Originates

In a weird way this reasoning process and questioning makes sense to me. It makes sense because in my years as a math major/tutor/teacher/Ph.D. student whenever I might have occasion to interact with the general public on the issue of what it is I do, the one inquiring of me would typically respond by boasting in their ignorance – “You’re a math teacher? That’s great. I was never any good at math.” I’m quite certain no other profession receives that response. “You’re a dentist? That’s great. I never floss… You’re a lawyer? That’s great. I steal my neighbor’s newspaper everyday.” Um, I just met you, but thank you for that confession.

Though other professions may not get as blatant of a response as math teachers, I do think there is a social tendency of politeness to try and interact as best you can with whomever you may be speaking. This tendency causes people to revert back to their earliest point of connection with the subject at hand. So I may not be a dentist or a lawyer but I do have a shared experience of extra years of schooling for my profession (plus I also brush my teeth…and have seen a lot of “Law & Order.” A lot). For mathematics, the earliest shared experience that the average person feels comfortable reverting back to is arithmetic. Occasionally someone may have had calculus and remembers a bit even though they “don’t use it anymore” or someone may mention their experience of geometry (since that is one of the specific subjects that I teach). But in general, a common baseline across America is Math = Arithmetic.

I also believe, from my years of experience as a Christian, that the baseline across America is Christianity = something roughly akin to the rigid Sunday school classroom experience. Maybe this is because the number of those who leave the church as they grow older is heartbreakingly large, leading to a large population who only experienced Christianity as a child in Sunday school, I don’t know. Regardless I think there is a general impression that we Christians are those who read the Bible and believe that Jesus is the answer to every question, without question.  Who fed the 5,000? Jesus. Who saved the animals on the ark? Jesus. Who discovered America? Jesus. Perhaps this is an overly dramatized rendering of the general perception of Christians, but I do believe that by in large we aren’t viewed as very academically sound thinkers.

Put together the general societal experience with mathematics and the general societal view of Christianity and it isn’t hard to see where the question “How can 2 + 2 = 4 be Christian?” My ultimate response to this question is the following: it’s a bad question. You may have had a teacher that told you there are no bad questions. They were being polite. There are bad questions and there are two things specifically that make this a bad question: 1) it misunderstands the nature of mathematics as arithmetical calculations and 2) it misunderstands the gospel of Christianity as an intellectual endeavor.

Responding to the Question – Math is More than Calculations

With the dental/legal analogy above I have already hinted at the fallacy of associating an entire field of study with one basic component of that field. There is obviously more that goes into being a dentist than brushing teeth and there is obviously more that goes into being a lawyer than emulating Sam Waterston. I don’t think any honest person would believe that all there is to math is arithmetic. I do think that a lot of honest people believe that all there is to math is calculations – so like arithmetic, just more complicated.

This couldn’t be further from the truth. I am personally at a point as a student where I can’t remember the last math class I was in where they asked me to do calculations. And while I certainly do teach calculation methods to my high school students, I would be a horrible math teacher if my only concern for them was that they be able to memorize algorithms for completing calculations and solving equations. In fact, if that was the job description then I would be in a different profession (youngest general manager in Atlanta Braves history).

The vast majority of my time as a math teacher is spent trying to get students to think logically/rationally/creatively/independently – not algorithmically. I want them to be able to solve problems like sustainable energy, human trafficking or world hunger – problems whose solutions are not numbers that can be arrived at by way of a memorized formula or a graphing calculator. They need math to solve those problems and any other problem of importance that they can imagine. It is my job (and my passion) to get them to see that. Math is everywhere. Math is pervasively engrained in the both the physical and social structure of the world around us and it is equally as pervasive in rational processes of the human mind as we attempt to explore, understand, appreciate, and communicate knowledge of anything around us. Math is more than calculations.

Responding to the Question – Christianity is More than Thinking

Christianity is always more than thinking, but never less.

- Neil Tomba, Senior Pastor, Northwest Bible Church, Dallas, TX

Christianity is more than thinking; it is more than an intellectual endeavor. Christianity is more than learning new facts and being able to give new answers/responses to the questions of the world. The gospel is transformative of the whole person, not just of the intellect. Beyond that, the gospel of Jesus Christ is transformative of all of creation. When rightly understood, the gospel is a message about the redemption of something that is broken – broken people in a broken world – not just fixing our mental understanding to be correct. Sin is a horrible thing. It is much more than wrongful actions that we commit. Sin seeps down into our souls, perverting our intentions, decaying our physical body, and spreading through all humanity into the creation we were designed to oversee. Sin is not a thing that we do, sin is a thing that we are. Sin is pervasive.

“But where sin abounded, grace abounded all the more” (Romans 5:20). In other words, if sin is pervasive then grace is not only pervasive but also prevalent, permeating, extensive, all-inclusive, boundless, unrestricted, and inescapable. The gospel changes everything about us to the core of our being in more ways than we can even comprehend. To think that applying Christian faith to mathematics implies there is a “Christian” way of computing calculations and a “non-Christian” is to vastly underestimate the message of the gospel.

In sum, I believe my students need math to solve any meaningful problem that they will encounter in life. I also believe that the greatest problem that they will encounter is that of their own sin nature. It is only by experiencing the full grace of God that my students will ever have a proper perspective on themselves and the world around them. Through this lens, deep beyond the surface level of life, is where I hope my students will explore the integration of mathematics with their Christian faith.

I believe that this is how mathematics is done Christianly. Though it is admittedly a longer answer anyone I may be exchanging introductions with would be expecting. Maybe their response can now be “Um, I just met you, but thank you for that confession.”

Good Friday

(This is a copy if a previous post, but appropriate for today).

Courtesy of the Association of Christians in the Mathematical Sciences:

Salvador Dali’s painting Corpus Hypercubus (1954) is a fascinating visual representation of a mathematical metaphor for the theological mystery of crucifixion.

Corpus Hypercubus, Salvador Dali (1954)

Many people are familiar with how to unfold a cube from three dimensions into two as shown in the figures below. Some of the edges of the cube are separated so that the resulting collection of squares can be unfolded into a planar shape. The resulting diagram is called a “net” for the cube. The net is not unique but one common net resembles a cross.

Dali painted the cross in Corpus Hypercubus as a hypercube unfolded into 3-dimensional space. The hypercube consists of eight three-dimensional cubes for hyperfaces. Each hyperface is attached along a two-dimensional square face to six of the other hyperfaces. Just as one can unfold a cube, one can also unfold a hypercube into the shape depicted in Dali’s painting.

Using the analogy of a (mysterious) higher-dimensional object unfolded into three dimensions, Dali depicts the theological mystery of the crucifixion as an event that originated in a higher plane of existence and then unfolded into the world that we perceive. With this understanding, Corpus Hypercubus communicates the idea that though one can discuss the necessity of the Jesus’ sacrifice for salvation or study theological ramifications of the cross, one can only do so by analogy because human nature simply cannot perceive the scope of God’s plan.

More from the ACMS:

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