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The Mission of Mathematics

joshwilkerson1 Comment

In August I gave a talk at a professional development training for teachers at Regents School of Austin on integrating a Christian perspective into the teaching of mathematics. The mission statement of our school says (in part) that we are teach children to know, love, and cherish that which is true, good, and beautiful. My goal in my presentation was to tie in what I see as the mission of math education with the mission of our school. I outlined how math was beautiful and how math was true, but my real focus was on discussing how math is good. For a lot of students (many of whom are now teachers) their experience in a math classroom was by no means good. I believe for these people it can be easier to give intellectual assent to the fact that math is beautiful (Fibonacci sequences, golden ratios, etc.) and that math is true (2+2=4, am I right?), but what we need to grasp as distinctly Christian math educators is how deeply good mathematics is – that it is an inherently virtuous activity that can be undertaken by anyone.

Below you will find a video of the presentation as well as the PowerPoint slides. If you are interested in further reading, I shared some similar thoughts when I wrote about God, Math, and Order.

Enjoy.


mission math

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.

Education: An Act of Justice or an Act of Grace?

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It has been a while since my last post. Ph.D. work, conference, and family have all kept me busy throughout the summer. I should hopefully have a few posts over the next few weeks that summarize the conferences that I have attend, the progress I have made in my Ph.D. research, and some general thoughts I have considered this summer. This post falls in the latter category. Enjoy.

I have written here before that education is inherently value-laden. If you are an educator then it is not a question of “are you teaching values?” but rather “which values are you teaching?” In this vein of thinking it can also be argued that education is inherently religious if it instills within us some sense of values and some sense of faith. Now, those values and the object(s) of that faith could vary greatly depending on the educational institution, but the fact is they are always there. This is why for centuries the work of education was undertaken by explicitly religious institutions and it is only fairly recently in society’s history that the state has taken on this endeavor (Wilson). So for everyone who feels that there is something wrong with our current state/system of education, I would argue that the root issue is primarily a religious one.

Every pedagogy assumes an anthropology (Smith). Before you can teach human beings you have to have some understanding of what human beings are. Ultimately I believe this is the reason for the existence of standardized testing (at least in America). The state approaches education from the perspective that all human beings are essentially good. It is simply a matter of providing education equally for all that will result in well-trained, productive citizens who contribute to the good of society. From this perspective, education is an act of justice. It is a citizen’s right to be educated. If the educational system is an administration of justice on the part of the state then it will inextricably be tied to universal standards that students and educators are required to meet. I mean, isn’t that how the justice system works? It sets standards in place that apply equally to everyone in a blanket approach and expects every individual to live up to those standards. There are also consequences when the standard isn’t met. Fail to meet the justice standard in society and go to jail. Fail to meet the standard in school and get remediation or don’t move to the next grade level or don’t graduate. As long as the state is in control of education, expect standardized testing to always be a part of the educational process.

What is the alternative? Maybe, just maybe, human beings aren’t inherently good. Maybe they are inherently evil and no amount of knowledge is going to save them from that. If we adopt this (Christian) anthropology then education will not be seen as an act of justice, as a right of the citizens, but rather as an act of grace. Education can be viewed as an act of grace that missionally reaches out to engage the lost mind. Grace doesn’t set a standard for you to meet. In fact, grace realizes that you can’t meet THE standard. So then the focus of education shifts from universal standards to individual and communal transformation. Results aren’t measured in knowledge gained but rather in affections formed.

My thoughts are still developing on this topic, but for now I can leave you with this fact: as a Christian educator (be it in an explicitly Christian setting or even when I was in public school), I care less about what my students know, and more about what my students love. This is the purpose of education.

Some books that I have been reading that have influenced my thinking on this issue:

– Desiring the Kingdom: Worship, Worldview, and Cultural Formation, by James K.A. Smith.

– The Case for Classical Christian Education, by Douglas Wilson.