Yesterday, I posted [this article][bozo] about the bozo who didn’t like his college calculus course because it wasn’t Christian enough. One of the commenters pointed out that there’s actually a site online where a college professor from a Christian college actually has [a collection of “devotionals”][devotional] to be presented along with the lecture in a basic calculus course.
They’re sufficiently insane that I have to quote a couple of them. No comment that I could possibly make could add anything to the sheer goofiness of these.
For the lesson on “Function Operations”:
>**God’s Surgical Improvements of our Actions**
>
>Genesis 50:15-21, Romans 3:9-10, 21-24
>
>One of the more horrible images in the book of Genesis is that of Joseph being
>sold by his brothers into slavery. This type of hate turned into evil act is a
>common occurrence in our world, too. In the Genesis situation, though, we are
>given the gift of 20-20 hindsight because we know the end of the story. God
>used the brothers’ evil action to prevent starvation of the descendants of
>Abraham. Joseph says, “You intended to harm me, but God intended it for
>good. ..” [Gen. 50:20] In the same way, God makes our unrighteous actions
>righteous through Christ. He surgically improves our actions to his own
>purpose.
>
>This idea of twisting something from one form into another is what happens when
>function operations work on elementary functions. You can start with two
>ordinary benign functions, the reciprocal function 1/x and sin(x), say, and put
>them together. Depending on how you put them together, you can create
>something interesting and easily understood, like sin(x)/x, or something with
>wild behavior, like sin(1/x). Either way, you have twisted one object into
>something very different.
For the lesson on the Limit definition of the derivative:
>**Secant Lines and Sanctification**
>
>Ps. 119:33-40
>In differential calculus we study how a slope of a linear function can be
>generalized to the slope of a function whose graph is curved, creating the
>derivative of the original function. The definition of derivative uses a
>sequence of lines (secant lines) drawn through two points on a function that
>are approaching each other and a single point on the function curve. The
>derivative value or tangent line slope is defined to be the limiting slope
>value of this sequence of secant lines. (See the figures below.)
>
> Figure 1 : Secant line between 1 and 1.8
> Figure 2 : Secant line between 1 and 1.5
> Figure 3: Tangent line to f at x=1
>
>Once a person has been called to be a Christian, we are redeemed by Christ but
>not released from following the law of God. We are justified once but continue
>with the process of sanctification for the remainder of our lives. This
>sanctification process is like the limit process of the secant lines
>approaching the tangent line. There is one distinction between the concepts of
>sanctification and secant line limits, however. In the mathematical contexts,
>we accept results that are “sufficiently close,” results that are in an
>epsilon-neighborhood of the desired quantity. While in our quest for
>perfection, the “better” we get the further we realize we are from satisfying
>all aspects of the law.
Ok, just one more. This one just about had me rolling on the floor! For the lesson on the chain rule:
>**Chain Reactions**
>
> 1 Corin 5:16-21
>
>Once students have seen the chain rule for differentiation of composed
>functions, it is natural to extend the chain rule to nested functions, where
>there is more than two functions that are composed. Fun problems to
>investigate are ones that are repeated applications of the same function. Try
>differentiating tan(tan(tan(tan(tan x)))) or ln(ln(ln(ln(ln(ln x))))), for
>example. Working your way from the outside to the inside yields a derivative
>which is product chain of related functions.
>
>In a similar way, when we interact with other people there is a chain reaction
>to our behavior. Most people believe that abused children are more likely to
>become abusers themselves someday, for example. Less dramatic behavior also
>can have a reaction that extends beyond the initial engagement. A popular
>Warner Brothers film of 2000 “Pay it Forward” (based on a novel with the same
>name by Catherine Ryan Hyde) depicts how a chain of reactions to an initial act
>of kindness can change an entire community. Christians need to be specially
>mindful of this chain reaction, since we are ambassadors for Christ. Our
>verbal and nonverbal witness can yield unexpected results, especially under the
>influence of the Holy Spirit.
This, apparently, is how “real” Christians are supposed to teach math classes. I seriously wonder how they have time to actually cover the *math* in class if they spend time on this gibberish!
[bozo]: http://scienceblogs.com/goodmath/2006/08/math_is_bad_because_it_isnt_ch.php
[devotional]: http://www.trnty.edu/faculty/robbert/SRobbertWebFolder/ChristianityMath/Calculus.html#Chain
Good Math/Bad Math
The beauty of math; the humor of stupidity.
Bleh. Jehle was complaining about where the “Christian” was in “Christian math”. This seems to be the opposite; where is the “math” part of this? For example, in the first bit quoted in the article, the only math content I can see is that “sin(x) is not the same as sin(1/x)”, which should be pretty obvious to the student. The whole passage does nothing to illuminate the mathematical content that is being presented.
To be fair, do we know what his motivation is behind these things? There is a lot of flakey stuff done in “reform” Calculus classes to motivate students on the relevancy of Calculus (particularly for liberal arts students who are taking it as a terminal math course). Maybe he just knows his market and has found a successful way for his students to pay attention in class.
In her meditation on “Transformation under Christ,” Dr. Robbert says:
“Differentiation is an operator on functions that takes one functions and transforms it into another form. The new form is related to the old form–the derivative tells interesting information about how the original function behaves graphically–but it is a completely new function.”
Which makes me wonder whether e^x is going to Hell.
I don’t really want to start a discussion on “reform,” but it sounds like you hold a somewhat caricatured view of what reform math actually is (nothing wrong with that; I did too, until I learned more about it).
pg:
To be fair, these things aren’t the entire lessons. They’re insane, and they don’t belong in a math class, but they’re described as “devotionals” to be presented *alongside* the actual math lesson.
I have taught Calculus for many years and have several reform Calculus textbooks. My comment is not that it is all bad.
So. . . “reform calculus” is like the “New Math” but for older kids?
— Tom Lehrer
I don’t think this sort of thing is really representative of all of Christendom (using that word just to represent the complete set of people referring to themselves as “Christians”). At least, I’d hope not. 🙂
Fair enough.
I made the mistake of referring to the flaky texts being used at various schools around Seattle as “reform” (because they seemed new-ish), and was later corrected. I don’t actually know the calc reform books; I’ve only used Stewart for teaching calc.
(Apologies for the non-Christian digression.)
I am OK with these “devotionals” if they are presented to Christian math students in a religion class for example. It is really a reflection of faith using math as an entry. People do that all the same with real life situations. So why not with math?
I agree it is goofy. The same was also said about telling jokes in C# or transact-SQL – which I also do at some point in time. 🙂
MarkCC your being unfair and you are exposing your insularity.
As the other commentators mentioned adding devotionals to the lessons is one of many ways to motivate students who may not otherwise be motivated to learn Calculus. I don’t find that insane at all. Not everyone is a math geek like you or I and not everyone just loves the stuff for what it is.
Also, I don’t think the messages contained in the devotionals are particularly heinous. What’s wrong with encouraging students to always better themselves (sanctification)? Is it insane to point out that the individual student’s actions towards others have large and perhaps unintended impact?
For the right students, associating these allegories with the math concepts might help them to internalize them, the life lesson and the math.
The problem is that it’s a math class. It really all comes down to Mark’s concluding sentence: “I seriously wonder how they have time to actually cover the math in class if they spend time on this gibberish!”
on the internets, no one can hear your screams.
Reminds me of the recent Simpson’s episode Girls Just Want To Have Sums, when the elementary school is divided into a boy’s half and a girl’s half. Lisa’s new math teacher’s lesson begins, “How do numbers make you feel? What does a plus sign smell like? Is the number 7 odd, or just different?”
What a pathological waste. Goofy stuff indeed. Moses did’nt come down with anything like Euler’s equation from the mountain in addition to the other commandments – or did I miss somthing?
I checked the dictionary definition of a computer virus:
“a computer program or part of a computer program which can make copies of itself and is intended to prevent the computer from working normally”
… to conclude that these guys have badly infected boot sectors and they just try to spread the virus.