
Latest Devlin Article
Posted:
Jun 10, 2010 3:41 AM


Keith Devlin wrote this month regarding a topic that comes up often in this discussion, that the teaching of mathematics is too procedural and does not have enough "real life" problems.
http://www.maa.org/devlin/devlin_06_10.html
He goes on to say that this has been proven in studies but the powers that be force the curriculum to be rote and lacking in application. I am not sure where he is getting his material because there are some serious validity issues in his statements.
1. I have reviewed many texts this last year and the only text that I have come across that could be considered rote and procedural was published in 1909! In fact, if this were so widespread a problem (rote instruction) then why isn't Devlin (or others that make this claim) holding up several texts to prove his point? I'll tell you why, because the point is false. It is a myth repeated so often that people take it for granted and believe it even though examples of such texts don't even exist and haven't existed for some time, probably even before said people were born. Even if Devlin searched high and low and found such a text, I could produce a dozen current texts that are jam packed with examples of applied math.
2. He states that people don't believe the studies that this helps kids learn math better. Well, as I said, texts have had these applicable examples for decades now and we know the standing of our scores in TIMSS. What is there too believe or not believe? It's right there in front of us. Of course, he states that it takes a knowledgeable teacher to teach math via application rather than via rote procedure, and I agree, but he states it in a half truth sort of way. He implies that teaching with examples doesn't work because the teachers don't know math. The fact is, even if you start with definition and lead to example OR start with example and lead to definition (the Keith way), you need to know the subject to pull it off. Yes, if you do not understand math then you will probably only be able to regurgitate the steps for your students and not pull it all together. But the current curriculums are packed with examples. Examples we got. It's the actual mathematical reasoning and language that we are missing.
3. Another reason that people don't buy this (as if the first falsity isn't enough) is that we are familiar with successful math kids (yes they are out there) and they know the math. They show up in the various clubs or competitions (and math rings) and they are adorable to watch as they eagerly set out to solve the problems they are challenged with. And they do all of this without even warming up on "real life" examples. And there were more than likely real life examples in their teaching (since they abound in curriculums anyways). But what they have that other students do not (other than ability) is that they have an authentic mathematical understanding. They are PAST the example stage and own the math now. And these kids and the problems they solve don't resemble what we see in many classes, with or without nice applicable examples.
4. We have people like Dy/Dan showing movies of water bottles (that never even get to the math) to middle and high school age students. He claims that students learn better when shown real life examples of math (except for some unknown reason he never actually gets to the math). And this is a big reason why people (correctly) don't buy this. They don't understand that if this is so successful then why the hell are you still doing it by high school? When using this approach do the kids ever get the math? You would think not if you based everything on Dy/Dan. I have never seen a math teacher talk so much and do so much without doing any math. In my opinion Dy/Dan is somewhat of a fraud in this business. I don't think he belongs teaching a math class and is more interested in self promotion, as witnessed by his "other" home page I posted here recently.
But Devlin was not (I hope) writing with Dy/Dan in mind. And maybe Devlin should check him out and realize what some people think of when he says "make math real". What Devlin doesn't touch on is how bad some of these curriculums have become when they focus on activities AND these activities become excuses to avoid the math rather than conquer it. This goes beyond teachers not being up to the task. Yes there are bad teachers, but they PASSED the very same math classes the students are in now. If you don't stop that then even if you replaced the current teachers (if that were even possible), you would have a fresh batch of poor teachers tomorrow. We lack (entirely in some cases) authenticity. If that is not fixed then even if there is a valid reform, you will never be able to implement it.
I challenge Devlin on two counts. First, show me a curriculum (in the last 20 years) devoid of these real life examples. And secondly, after he exhausts himself looking for those, find out how many curriculums use real life examples AND lead into what we would call mathematics. I mean the reasoned and abstract part that requires no example, just an interested brain. He is going to find that there are very few and he is going to find why there is so much push back on all of these ideas. It isn't the ideas, seriously, it is how they are implemented. For some odd reason, each and every one of these reforms was accompanied by a dumbing down factor. AP Calculus has lowered the cut scores so much that now they have to eliminate the guessing penalty in order to stop failing half the kids. Why even make a test with 4 times the number of problems necessary to pass? And AP Calculus is one of the better examples. When Achieve gave the algebra test to students last year they gave to students that had taken algebra and passed. Yet less than 15% passed the Achieve test.
Good examples are in the texts and have been for some time. But you won't see their effect on teaching math until you put the math back into the curriculum.

