Posts Tagged ‘mathematics’

What We Study and Why: Mathematics

Dear Reader,

This is part of an ongoing series in search of a reformed philosophy theology of education. You can find all the posts here.

Last time, we wrapped up the section of this series on practical details. You can find that summary post here. Today I’d like to begin a new sub-series on individual subjects. I have argued that the teacher’s attitude is paramount and so a large part of what we are doing here is just to frame each subject rightly. Whether you are a homeschooling parent or employed in a school setting, you may find yourself having to teach subjects that just don’t thrill you (what on earth does grammar have to do with the kingdom of God?). While we will touch on some practical details as well (why teach pagan myths? does everyone need calculus?), the main goal of this part of the series is just to show why we teach each subject.

There are a couple of big ideas behind what we are doing here, including: All truth is God’s truth; In education we lay before our students the things of God, primarily His general revelation which comes to us in many forms; and The purpose of education in the life of the believer is for the transforming of his (fallen) mind. (If you are just dropping in, I do recommend reading some of what has come before; see this summary post on the theory behind it all.)

With these goals and ideas in mind, we will ask for each of the subjects we address: Why do we study it? How does it point is to God? How does God reveal Himself or His truth through this subject? In answering these questions, we will look at Scripture whenever possible but we will also look at quotes from many other sources.

Finding God in Mathematics

Let’s jump right in then to mathematics. Most would agree that some level of math instruction is necessary. Beyond the basics, there tend to be two camps — those who see no need to go beyond the basics and those who find pleasure and meaning in higher mathematics. The problem is that there is a gap — we don’t convey the beauty of math when we are teaching the basics and so those who do not naturally enjoy it drop it as soon as possible and never get to the part where it seems to expand and take on a wider significance. The solution is to show that math is lovely even at the lower levels (that’s where the teacher’s attitude comes in again). So if you have lost to joy of math, or never had it, here are some quotes to inspire you:

The laws of mathematics point us to the Law of God:

“We take strong ground when we appeal to the beauty and truth of Mathematics; that, as Ruskin points out, two and two make four and cannot conceivably make five, is an inevitable law. It is a great thing to be brought into the presence of a law, of a whole system of laws, that exist without our concurrence,––that two straight lines cannot enclose a space is a fact which we can perceive, state, and act upon but cannot in any wise alter, should give to children the sense of limitation which is wholesome for all of us, and inspire that sursum corda which we should hear in all natural law.” (Charlotte Mason, Towards a Philosophy of Education, pp. 230-31)

Mathematics conveys eternity:

“But education should be a science of proportion, and any one subject that assumes undue importance does so at the expense of other subjects which a child’s mind should deal with. Arithmetic, Mathematics, are exceedingly easy to examine upon and so long as education is regulated by examinations so long shall we have teaching, directed not to awaken a sense of awe in contemplating a self-existing science, but rather to secure exactness and ingenuity in the treatment of problems.” (Ibid., p. 231; emphasis added)

Math underlies the universe. It may even be called the langauge of God:

“Mathematics is the language in which God has written the universe.”  —Galileo Galilei

Math is the foundation of many other fields, both sciences and arts. Its beauty can be seen even by non-Christian authors:

“Mathematical analysis and computer modeling are revealing to us that the shapes and processes we encounter in nature — the way that plants grow, the way that mountains erode or rivers flow, the way that snowflakes or islands achieve their shapes, the way that light plays on a surface, the way the milk folds and spins into your coffee as yo stir it, the way that laughter sweeps through a crowd of people — all these things in their seemingly magical complexity can be described by the interaction of mathematical processes that are, if anything, even more magical in their simplicity.

….

“The things by which our emotions can be moved — the shape of a flower or a Grecian urn, the way a baby grows, the way the wind brushes across your face, the way clouds move, their shapes, the way light dances on water, or daffodils flutter in the breeze, the way in which the person you love moves their head, the way their hair follows that movement, the curve described by the dying fall of the last chord of a piece of music — all these things can be described by the complex flow of numbers.

“That’s not a reduction of it, that’s the beauty of it.” [Douglas Adams, Dirk Gently’s Holistic Detective Agency (New York: Pocket Books, 1988) pp. 182, 184]

That’s all fine, you say, I am inspired but I am still teaching long division to cranky eight-year-olds. A couple of thoughts: I argued recently that when educating we must be careful not to provoke children. Math is a field in which it is very easy to provoke. It tends to come with a lot of repetition. I do think we should all learn to do long division without a calculator. But if I have ten such problems to do, I get my calculator. Why should we ask a second grader to do so many at once? Sometimes more is less (how’s that for a math concept?).

There is a certain progression to math; one can’t do algebra before learning to count. But that doesn’t mean the beauty of math needs to wait until high school or beyond. There are resources which are accessible at younger ages but which either introduce concepts usually reserved for later or give more of a big picture understanding of math, bringing out its complexity and elegance. (I will add a brief bibliography of some we have used at the end of this post.)

Lastly, there is the elephant in the room question: When will I ever use this? And its corollary (there’s a nice math word): Why do I need to learn calculus anyway? As for the first question, I reject the premise. Our approach to education is not utilitarian. Whether we will use upper level math has nothing to do with anything. The end we have in view is not the balancing of checkbooks or even being able to do advanced physics (for which I hear math is useful) but to bring glory to God which we do by learning about Him as He has revealed Himself through creation, and (as the quotes above are meant to show) mathematics is an integral part of that creation.

As for the second question, not everyone needs to learn calculus. We are finite people and time and energy spent on one subject come at the expense of another. So while I do think it is good to learn these things, beyond a certain point we must recognize that we are different — indeed unique, individual — people and that we don’t all have to learn the same things (see this post on core curriculum). So perhaps you don’t have to learn calculus.

I’d like to end with a plea — as I work on this section of the series, I am giving you my best ideas and resources but I could use some help. Please reply to this post or contact me if you can help with any of the following:

  • What questions do you have about teaching (insert subject here)?
  • Do you have good quotes about math, or any other subject, that you have run across, particularly about why we teach them and how they point us to God and/or teach us about Him and His creation?
  • Any favorite resources? Since math was our topic this week, feel free to add in the comments your favorite big-picture math resources.

Nebby

A Brief Math Bibliography

Life of Fred Math by Stanley Schmidt (Polka Dot Publishing) — You may have heard of this alternative math curriculum. It takes a narrative approach and follows the life of 5-year-old math professor Fred. Though the author says the elementary books can be used as a stand-alone math curriculum, I was always hesitant to do so. They do, however, make a lovely supplement to whatever else you may be using. The stories and such may be overly silly for some but my kids always loved them. The elementary series is a collection of thin books with short chapters. It is easy to add in one chapter a week. Ages 10 and up could breeze through them pretty quickly. The upside of these books is that they introduce concepts that usually don’t come up until later such as set theory.

Here’s Looking at Euclid by Alex Bellos

The Number Mysteries by Marcus du Sautoy

Thinking in Numbers by Daniel Tammet

These three books are all of a type. They are roughly middle school level books (and up) that have relatively short chapters which disuss math concepts like pi, prime numbers, and how people in Iceland count.  I am sure there are many other such books out there; these are just a few we have used.

 

 

 

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