Glasnost, Perestroika and Graphing Calculators (John Dewey)
This is the eighth in a series of articles from an ed school student working towards certification as a math teacher. Click for his first, second, third, fourth, fifth and sixth and seventh columns. As always, he prefers to remain anonymous. -ed.
After last week’s missive quoting from Dr. Cangelosi’s textbook, I expected he would have left a comment expressing his eternal gratefulness for the exposure I gave his book. But he lives in Utah, where the state legislature there recently adopted a resolution that calls for the Utah State Board of Education to give Utah’s math standards an overhaul. That may have him worried and I’m sure that’s why he hasn’t written.
From what I see and hear in ed school, Dr. Cangelosi doesn’t have a thing to worry about. The milieu-controlled ed school environment of discovery/inquiry based/NCTM-standards-based/constructivist-based/brain-based/knowledge-based/critical thinking-based/ and higher order thinking skills-based learning is ever expanding.
Indicative of this brave new world is a comment that Mr. NCTM left on a lesson plan I turned in—an assignment that called for a lesson which made use of technology.
My lesson plan had students explore the graphs of quadratic equations using graphing calculators. I borrowed heavily from exercises in a math book by Gelfand on functions and graphs. In one of Gelfand’s non-calculator based exercises, he asks the students to graph y = x2, and then y = 5x2 and asks “What scale unit would have to be taken along the axes in order that the curve for y = x2 could serve as a graph of the function y = 5x2?” Students are to provide a rule linking the shape of curve to the x coefficient, based on their answer to the scale unit question. Mr. NCTM wrote in the margin: “This is just the kind of ‘discovery’ learning that you have rebelled against.”
His comment reminded me of the movies made in the Cold War era in which a staunch Soviet leader says to the American hero: “Perhaps, comrade, we are not so far apart as we thought.” I believe what he saw in my lesson plan was my clever camouflaging of what is called “scaffolding” as “discovery”. Scaffolding refers to the providing of information and knowledge to allow students to apply such knowledge to a new situation or problem. So perhaps in this sense he is correct that we are not so far apart. But in other areas, despite the optimistic nature of his remark, I do not feel we are really as close to glasnost as he would like me to believe. Perhaps he sees my clever camouflage as a chink in the armor on the way to get me to see things the NCTM way.
His view of me as a dissident in need of enlightenment comes from things I say in class, most recently in a class discussion on the role of graphing calculators in math education. The discussion started in the usual manner: get in small groups. In my group was the fellow with whom I had an argument about state standards the first class and which I talked about here. I’ve grown to like him; he’s very young and full of opinions and enjoys being contrarian. For many people in their twenties being contrarian is a quest for identity until marriage, work and humility take over, and not necessarily in that order. In any event, for this young man none of these things have yet kicked in.
Mr. NCTM facilitated the classroom discussion. While we are not Luddites in our class, and can appreciate the value of graphing calculators in teaching, we also saw problems. After several minutes the whiteboard was filled with issues including overdependence, obscuration of concept, and interference with conceptual mastery. After some discussion of the pros and cons of graphing calculators, Mr. NCTM decided to change tack on us and asked: “Do you think they are introduced too early?” (They are introduced as early as kindergarten in some programs.)
Our answers were going in the direction of “yes”, until my young contrarian friend spoke up and said, to Mr. NCTM’s obvious delight, that he really couldn’t see what was the cognitive value of teaching students the procedure for multiplying 36 x 7 when calculators were available. I was unable to keep my mouth shut. “Don’t you think that students need an understanding of basic procedures and that place value is an important concept?” “Why?” he remarked and went on to the uselessness of learning long division at which I drew the line and said “How can you say that? Don’t you think the distributive property is worth talking about?”
“Who cares?” he pointed out.
Mr. NCTM was enjoying this debate immensely. Dialogues such as these apparently feed into his fantasy that he’s actually teaching in a real grad school in a real program.
Mr. NCTM took over and allowed that there was some value in teaching the long division algorithm and perhaps some value in multiplication algorithms, but after that, it is just so much tedium. “There are some who feel there should be no pencil and paper calculators in classrooms at all; you either do it in your head using estimation or you use the calculator. It breaks my heart when I see kids writing down 32 divided by 2 and solving it as a long division problem.” It breaks my heart too. Students used to be required to practice problems such as these until they could do it in their head as he would like to see. Such problems used to be called “short division”. Apparently, Mr. NCTM sees long division as causing this problem, not the calculator.
“Let’s put it this way,” Mr. NCTM said. “If I saw a student who was not able to perform the division problem of 168,514 divided by 384, that would not be a reason for me to hold him back from taking algebra.” Well, if it were me, I would first want to know why he couldn’t do the division problem and then what else he couldn’t do.
Which tells me that Mr. NCTM and I are a long way from perestroika.
From the gulag of math teaching methods, I remain,
Faithfully yours,
John Dewey
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“If his purpose, however, were what it appears to be here, to show that he is an expert on questions of teaching and learning mathematics, I’d have to ask him why he’s spending his or someone else’s money on tuition and not getting paid instead to provide true enlightenment. After all, he makes it clear that he has nothing to learn from Mr. NCTM: maybe he should apply for his job.”
The way I understand it, Mr. Dewey is in ed school to get certification to teach. One can be an accomplished and degreed mathematician and still not be allowed to teach without certification, e.g Frank Wang.
Seems like “Mr. Dewey” takes a lot of pleasure “outsmarting” Mr. NCTM. But of course, we only have “Dewey’s” word as to how these exchanges go. How trustworthy is our reporter? Well, he doesn’t post under his own name, for starters. And so granting him the benefit of the doubt that he’s the hands-down winner of these duels and perhaps the hero of the majority his fellow education students is simply more than I’m willing to do. Frankly, I find the tone of Dewey’s blog sophomoric, a rigged game by a “clever lad” who is very much in love with his own brilliance.
Not much new here, really, except for the amazing chutzpah of calling himself “John Dewey.” Obviously, he’s anything but.
Of course it’s disappointing when students abuse technology to do what they should likely be able to do in their heads. But if so doing keeps some kids “in the game” and still open to learning mathematics, that seems not so awful. Kids can be taught to use technology appropriately. That includes paper and pencil which, after all, comprise technology as well. It’s always easy to find the most extreme opposing views when creating straw people to defeat. It’s a bit harder to win against a knowledgeable, intelligent, and flexible opponent who is actually more interested in finding things out than in waging ideological warfare via a blog. If “Mr. Dewey” were a student in one of my classes, I would welcome his raising interesting questions and objections to anything, if it were done in the spirit of learning and inquiry. If his purpose, however, were what it appears to be here, to show that he is an expert on questions of teaching and learning mathematics, I’d have to ask him why he’s spending his or someone else’s money on tuition and not getting paid instead to provide true enlightenment. After all, he makes it clear that he has nothing to learn from Mr. NCTM: maybe he should apply for his job.
I’m sure Mr. Dewey will have a host of smug and devasting retorts to offer. What I wonder is if he’ll ever be open to learning anything about teaching mathematics to kids who probably are vastly different from him and who might need a kind of teaching on occasion that he’s not yet willing or able to deliver?
Oh, boo hoo.
I can’t apologize for calling someone a “best-selling ghost writer,” because that’s a COMPLIMENT, you twit.
And, rest assured, she’s a big girl. She can take care of herself.
Your mission here, Mr. Dewey, is becoming painfully clear (and sad)–parrot the lines you see in the so-called anti-establishment blogs, and voila, you’re a revolutionary.
Yet one important characteristic separates your meandering missives from those sites who set themselves against the status quo . . .
They at least try to know what they’re talking about.
I remain faithfully yours,
Mr. Person
Disagreeing with someone’s opinion is fine. Name calling and personal attacks are not. I am disappointed in your behavior.
“What say the rest of you?”
I say that graphing calculators make excellent graduation presents: for undergraduates majoring in the sciences or engineering.
There isn’t a single course in the K–12, undergraduate, or graduate mathematics curriculum where a calculator is absolutely necessary.
“How can you say that? Don’t you think the distributive property is worth talking about?”
“Who cares?” he pointed out.
This is why parents need to be the deciders.
It’s time for educators to become true professionals.
A professional offers professional counsel.
The client makes the decision.
It shouldn’t be up to a 25 year old contrarian to decide whether the distributive property is or is not worth talking about with other people’s children.
If I want my child taught the distributive property – and I do – that decision should be up to me.
–So says a best-selling ghost-writer who has the time and the money (or at least the money) to offer up a biased (and ageist) opinion. [We are just talking about school here; such inflammatory rhetoric is unjustified.]
What say the rest of you?
Oh wait. That’s right. You can’t answer.
“How can you say that? Don’t you think the distributive property is worth talking about?”
“Who cares?” he pointed out.
This is why parents need to be the deciders.
It’s time for educators to become true professionals.
A professional offers professional counsel.
The client makes the decision.
It shouldn’t be up to a 25 year old contrarian to decide whether the distributive property is or is not worth talking about with other people’s children.
If I want my child taught the distributive property – and I do – that decision should be up to me.