– Mathematics helps us see the order and beauty of God’s creation and thus of God Himself. Hence, mathematics derives its purpose, meaning, and value from God. Discussion of these themes can be a legitimate and valuable part of mathematics education.
– Teachers should enjoy mathematics, receive it gladly and thankfully as God’s gift, and cultivate a classroom climate in which students enjoy it and want to do it. Educational materials should support teachers in doing this.
– Teachers need to show students explicitly how mathematics fits into our God-given stewardship of the earth and into the building of human communities. For example, teachers need to explain ways that people have used mathematics to advance principles such as justice, responsible stewardship, and community building as well as ways that people have misused mathematics.
– For much of the twentieth century, an abstract approach devoid of context dominated mathematics. By contrast, a Christian approach says that mathematics is not autonomous but rather is an aspect of an interconnected creation. Thus, teaching needs to be contextual—it needs to establish clear connections with other subjects and with the practicalities of life.
– We as Christians do not despise the physical and glorify the mental and abstract. Rather, we value our bodies as God’s creation. Thus, teachers should, as much as possible, use teaching methods that actively engage students’ minds and bodies by means such as using manipulatives and having students collect and analyze data.
– Teachers need to discuss in their classes how the surrounding cultures view mathematics and how a Christian perspective differs. For example, until fairly recently, the United States and Western Europe overemphasized human reason. Now these cultures have swung in the other direction, tending to undervalue reason and overemphasize intuition. Asian, South American, African, and Western countries tend to value mathematics solely for its economic benefits, without considering that pursuing economic gain apart from a broader framework of godly service can be harmful.
– Students often think of mathematics simply as recipes for how to do problems. Teachers need to foster an attitude of deeper reflection on what mathematics can and cannot do for human beings, on the wonder of this gift from God, and on what its order and beauty tell us about God and His creation.
I attended my first ACMS conference a few weeks ago at Westmont College in Santa Barbara, CA. I had a blast. I was able to present a paper, hear some great talks, and meet/fellowship with some great mathematicians who are solid believers in their faith. Too many great moments to share them all, but here are a few thoughts/quotes from the meetings:
1. Texas needs to find a way to hijack California’s weather.
2. I have a great, beautiful, supportive, loving wife, and for this I am extremely blessed.
3. Art Benjamin is an entertaining teacher which is great to see in a mathematician. I’m sure people who have always hated the subject pay more attention when he is talking.
4. My magic square (Hint on what makes it so magic, 35):
5. He left his Father’s throne above So free, so infinite his grace! Emptied himself of all but love, And bled for Adam’s helpless race. ‘Tis mercy all, immense and free, For O my God, it found out me!
6. This earth belongs to God…
7. It is amazing to see how such different branches of mathematics can work together in ways never before thought. The example of combinatorial proofs of trigonometric identities was very cool to see.
8. Building on 6, why would we want to find different proofs for stuff we have already proved? “The proofs we have may establish truth, but they don’t necessarily establish insight.” This quote sticks with me as an educator.
9. 2, 3, 5, 8, who do we appreciate? Fibonacci!
10. Paper by Jason Wilson of Biola University: The Divine mind is impressed on the world such that the secular mind recognizes it and seeks to use it for gain. The Biblical mind not only obtains a deeper understanding of it but is even beckoned to become a partaker of it. Notice the juxtaposition of wisdom in Proverbs 8 with Jesus in John 1:1-14.
11. I was pushed to really consider for what purposes I would use a math biography in my lessons – just to present ideas, or to bring out more in the life of the mathematician/believer.
12. The more we are able to recognize our weakness, the more we are able to practice true dependence on God.
15. In different cultures the goal wasn’t to convince you of the proof mathematically, but rather to give you different types of understanding – there was no “naturally” correct way of doing things.
16. When missionaries entered these cultures they brought their math with them, thinking a way to convert people to Christianity was to show them the superiority and power of the math and science that Christianity produced… perhaps this is not the best way of thinking 🙂
17. Are mathematical ideas universal, as evidenced in different cultures reaching similar results independently? Or is this just evidence of our shared humanity?
18. Mike Stob of Calvin College convinced me I need to use “R” next year with my AP Stat class.
19. Talithia Williams of Harvey Mudd College gave a great (and much needed) presentation on making students aware of the misapplication of statistics in American life. A great example is in how pharmaceuticals are now peddled directly to the consumer, yet since we don’t know the actual data from the studies, it is hard to know when to take a risk on certain medication. This might make a good stats-and-society project for students.
20. “Who we are mathematically is not who we always were, or who we will always be.”
21. Often models we use in the classroom are not accurately presenting the ways the material was learned at the time of its inception.
22. Some cultures preserved their mathematical ideas and passed them down in poems and songs – I’ve found these to be effective teaching tools in the past, I need more of them.
23. Wigner – in looking at the effectiveness of mathematics, the miracle is not in the connection of math with science, but in the math itself.
24. It was great to hear Bob Brabenec of Wheaton give a talk. I’ve mentioned his work on this blog on more than one occasion. It was interesting to hear him delineate between doing philosophy of mathematics and thinking philosophically about mathematics. I myself have realized that I probably fit more in the latter category.
25. Mark Colgan of Taylor University gave a great talk on encouraging students to connect topics in Calculus with Biblical ideas by using weekly reflection papers. Though I may not follow his model exactly, I very much like the idea of introducing reflection papers into my curriculum.
26. David Stucki of Otterbeing University gave a great talk on teaching students the concept of infinity. I wish I could have focused on it more and taken more notes, but my talk was right after his. He did list some great resources which I hope to contact him about and share here.
27. Mathematics Through the Eyes of Faith is due out in August. I got an advanced copy of it and it looks great! It really addresses some of the key issues in Mathematics and the Christian Faith. Do mathematical concepts point beyond themselves to a higher reality? Can the idea of chance be reconciled with God’s sovereignty? How do we account for mathematics being so effective in describing the world? How does giving people the capacity to do mathematics fit into God’s purposes for humanity? Should be a great read. I look forward to reviewing it.
28. In trying to describe the beauty and wonder of mathematics to a broader audience it is very difficult to “describe the mathematics simply without simplifying the problem,” which is where the beauty lies.
29. There was something wonderful about being in a room full of academic colleagues and being able to all worship the Lord together.
30. I hope I don’t have to wait two more years to this again.
I'm in there, but I'm half hidden. You can try to find me, but I think I made Waldo proud.
For my philosophy of mathematics course I am reading the book Thinking About Mathematics, by Stewart Shapiro. It is an excellent read and I highly recommend it. I hope to give this book a fuller treatment on this blog sometime over the summer.
In the meantime, I just finished reading Shapiro’s chapter on Formalism and he makes a telling editorial comment on the use of calculators in math education. Below are a few excerpts from the chapter (emphasis added).
The various philosophies that go by the name of ‘formalism’ pursue a claim that the essence of mathematics is the manipulation of characters. A list of the allowed characters and allowed rules all but exhausts what there is to say about a given branch of mathematics. According to the formalist then, mathematics is not, or need not be, about anything, or anything beyond typographical characters and rules for manipulating them.
For better or worse, much elementary arithmetic is taught as a series of blind techniques, with little or no indication of what the techniques do, or why they work. How many schoolteachers could explain the rules for long division, let alone the algorithm for taking square roots, in terms other than the execution of a routine?
The advent of calculators may increase the tendency toward formalism. If there is a question of justifying or making sense of, the workings of the calculator, it is for an engineer (or a physicist), not a teacher or student of elementary mathematics. Is there a real need to assign ‘meaning’ to the button-pushing?
We hear (or used to hear) complaints that calculators ruin the younger generation’s ability to think, or at least their ability to do mathematics. It seems to me that if the basic algorithms and routines are taught by rote, with no attempt to explain what they do or why they work, then the children might as well use calculators.
GOD & MATH: Thinking Christianly About Math Education 