Transcript: Are We Teaching Our Kids Fuzzy Math?
This partial transcript from Hannity & Colmes, April 17, 2001 was provided by the Federal Document Clearing House. Click here to order last night's entire transcript.
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HANNITY: And in our "One-onZOne" segment tonight, a new trend in the way math is taught has quietly crept into some schools without the consent of parents. The so-called constructivist math downplays the use of basic techniques, like long division, which proponents say dampen children's enthusiasm, and emphasizes underlying concepts, and students are encouraged to feel good about their answers, which only have to be reasonable, not necessarily correct. So are we teaching our kids fuzzy math?
And joining me now from Chicago is Dr. David Fiekes. He's an associate professor at Purdue University North Central and an advocate for this new math. I'm not a mathematician, but one plus one -- I guess one could say a reasonable answer is three? I can feel good about three. It's not necessarily the answer. There's only one answer to one plus one, right? Right, Doctor?
DR. DAVID FIEKES, PURDUE UNIVERSITY NORTH CENTRAL: Yes, but...
HANNITY: Yes, but?
FIEKES: I would -- let me explain. Let's take three plus four equals seven. If I ask you, "What's three plus four?" you would say?
FIEKES: Seven. And I would say, "How do you know that?"
HANNITY: I got a gold star.
FIEKES: Yeah. Good job. How do you know that?
HANNITY: I know that.
FIEKES: As a...
HANNITY: Go ahead.
FIEKES: Go -- go ahead.
HANNITY: No, no. Go ahead. Finish your point.
FIEKES: As an adult, you memorize that. You think, "Well, I have that memorized." But if we ask a child, "What is three plus four?" a child will tell me -- he'll count out three objects, and he'll count out four objects, and then he'll put them all together, and he'll count out seven objects. So, for a young child, say a first grader, it's a counting activity. Later on, when children become a little bit more sophisticated in their thinking, they think, "Well, three plus three is six, and I know that." They start to memorize that. And then later, they realize, "Well, three plus four -- that's one more. So three plus four has to be seven," and that's -- constructivist viewpoints look at how children learn. So if a child would come to me and say, "Three plus four is eight," from the old transmission perspective, you would just simply say, "You're wrong. It's seven." But from a constructivist perspective, I would tell him how -- I would ask him "How did you know that three plus four is eight? Explain to me your thinking." So I can look at his thinking process, rather than just looking at the correct answer.
HANNITY: Well, I don't have a -- I don't have a problem if you explain to the student, Doctor, that three plus four does not equal eight, it equals seven, as long as you explain that to them, and then you can work through the process, "Well, let me teach you a better way to do this or a way to come up -- or little tricks of the trade." I'm -- it doesn't matter how you get there, but this -- this notion or this idea that we don't want to offend kids or we don't' want to tell them they're wrong or that there could be a reasonable answer to a mathematical ques -- equation -- there's no reasonable answer. Three plus four is seven. Eight is not the right answer, and I don't -- what's wrong with telling them, "OK. Let me help you. Let me teach you a new method of getting there, but it's the wrong answer."
FIEKES: That's not how they learn, though. That's not how they're learning that three plus four is seven.
HANNITY: That's how I learned, and I know how much three plus four is.
FIEKES: Yes, but I would say that's not how you learned. I would say, when you were a young child, you counted those things out until it made sense to you, and we're -- you're looking at this as an adult. You and I both know that three plus four is seven.
HANNITY: I've got to tell you...
FIEKES: That young child does not know that...
HANNITY: But what...
FIEKES: ... until they work problem for themselves...
FIEKES: ... and work out that example.
HANNITY: But when we tell them -- look, I've learned more, Doctor, from the mistakes I've made in my life, and I've made a number of them. What is so wrong with telling people if you're -- I work with -- my son's only 2-1/2, and -- we do reading, and we do letters, and I'll say, "What's this?" and he'll say, "It's an A," and it's really an O, and I'll say, "No, no, no. That's an O, and this is what an A looks like." I've tell him he's wrong and tell him what's right. Am I doing that wrong by your estimation?
FIEKES: Not in terms of basic things like, "This is an O, and this is an A," but in terms of mathematical concepts -- see, we look at information. Yes, we have to tell children information. Yes, you know, "This is your phone number. This is -- these are the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and that's the order they go in."
HANNITY: I -- all right. We -- we've got to take a...
FIEKES: But in terms...
HANNITY: Is it that you're afraid to hurt their feelings? We'll ask you that question on the other side. We'll take a quick break, and we'll talk more about...
HANNITY: ... about constructivist math, what we're calling fuzzy math, on the other side of the break on HANNITY & COLMES.
HANNITY: As we continue with Dr. David Fiekes -- Dr. Fiekes, from "The New York Post," let me put in what they said. "The so-called constructivist programs minimize use of algorithms, long division, and other basic equations in favor of students working in groups and discovering their own answers and reading passages." My point here is there's a fear for you to tell students they got it wrong, and I don't understand that, and I don't think a lot of people at home will understand that.
FIEKES: Well, I try to tell teachers -- I work with a lot of teachers in local elementary schools, and I suggest to them to try to be not -- as non-evaluative as possible and let children -- it doesn't mean we don't want children to come up with the right answers. In constructivist viewpoints, we want children to learn addition, subtraction, multiplication, and division. We want them to know their facts just like everyone does. But the question is how do they learn their facts? Simply telling them they're wrong does not help children learn their facts. When we examine their thinking process and how they go about constructing...
HANNITY: I don't have a problem analyzing how they get to an answer, but if...
HANNITY: ... you don't tell them they're wrong, they'll nev -- they'll think it's right, and you've got to...
HANNITY: You've got to point out in the case of math, four plus three equals seven, and that's the right answer. Eight does not count. There's no such thing as a reasonable answer. I find this -- look, I learned the old-fashioned way, and I turned out OK, and I know a lot of other people did, and I -- I just have a hard time understanding this unwillingness -- we see it on the ball field. Parents don't want to keep score because they're afraid they'll hurt kids' feelings if they lose the soccer game. I don't understand that thinking.
FIEKES: Well, returning to math -- math is a neat subject because math will not let you come up with wrong answers. If it's a sense-making activity and kids are truly thinking about mathematics -- if a child in a second-grade class or a first-grade class says that three plus four is eight, other students will disagree with him, and other students will even -- you can point this out by counting out three cubes and four cubes.
HANNITY: But -- but...
FIEKES: But that's how they figure it out.
HANNITY: But we've got to tell them there's only one right answer. There's only one right answer.
FIEKES: But, in life, there isn't only one right answer.
HANNITY: But, in math, there is, sir. In math...
FIEKES: Not in all math.
HANNITY: ... four plus three is seven. One plus one does not equal three.
FIEKES: In higher math -- as we get higher and higher in math, we find that there's not just one right answer. There can be many answers to the same problem.
HANNITY: Well, I hope the guy that figures out -- writes your check every week doesn't use your system of math because, if they come to a reasonable number that's lower than what you anticipate, I don't think he'd be too happy.
FIEKES: If it's not a valid number, I won't accept it. If someone writes the wrong number, I won't accept it.
HANNITY: Are you going to call him and tell him that's you're wrong?
HANNITY: Are you going to call him and say, "You're wrong. That's not the right answer!"
FIEKES: I'm going to -- I'm going to call and say, "I disagree," and that's the premise I would use with children, say, "I disagree."
HANNITY: So, in other words, there's a right answer. You get a certain amount of money. There's a right mathematical answer to what you get paid.
FIEKES: There's a viable -- I don't like the word "reasonable." We use the word "viable" answer, and if -- if it's...
HANNITY: It's not -- there's no viable. Four plus four is eight, and four plus three is seven, and one plus one means we're out of time. But thank you very much.
FIEKES: Thank you.
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