Conference Material

Engaging Parents and the Public

Now, the reality is that some of you are not going to hear anything I have to say in wrapping up because, quite frankly, you care more about the turkey problem right now than anything I have to say. But trust me on this one, the turkey problem is not nearly as important as what it has to teach us. So if you would do whatever you have to do to come back together. And it might mean that you actually have to turn your paper over. But if you have to do that, would you do that, please?

I apologize for interrupting you prematurely. Because in terms of the learning potential, what's going on right now in the classroom is the most important opportunity for learning to happen. For a variety of reasons. I've given you a somewhat messy problem to think about. You've done your own thinking about it. We're in varying stages of understanding or not understanding. But as you're talking to each other, some important things are happening in the room.

One of the things that's happening in places in the room is some of you are finding, as you're sharing your thinking with your small group, those holes in your thinking that kind of slipped right by unnoticed when you were thinking alone, have come right to the foreground where they have to be confronted. Children need to talk mathematics while they're learning mathematics. And one of the reasons they do is because when you're thinking alone silently, it is very easy not to notice what you don't fully understand. But when we have to defend our thinking or explaining our thinking to others, those incomplete understandings do come to the foreground.

Another thing that's happening different places in the classroom right now, is some of us didn't have any way to think about the turkey problem. And now you're getting to hear a variety of different ways to think about it. But as a teacher, I don't know whether you're all getting good advice out there or not. So if the mathematics of the turkey problem is important, then I have a responsibility as a teacher to process the problem with the whole class in a way that will help us all deepen our understanding of the mathematics. What I would do in the classroom at this point is ask students if anyone was willing to come up and defend why their answer makes sense. And we'd look at different ways of doing that.

I don't have time to do that right now. But before we move on, I want to share with you just a couple of things that my students did with the turkey problem. Actually first I want to share with you what the high school math teachers tend to do with it. If they can solve it. And I don't see them solving it any more frequently than the rest of us, by the way. But they tend to set up ratios. Did any of you set up a ratio? Now as an ex-middle school teacher, it doesn't make me happy that about three of you set up a ratio. I worked really hard to get you to understand ratios.

One of the ratios they set up is they say something like three slices is to a third of a pound as some number of slices is to a quarter of a pound. Does that look familiar now? What do they do to solve it? They cross-multiply and they get three-fourths is equal to one-third. Why do they cross-multiply? It works. What do they do next? They solve for x. So if we divide by a third, these will cancel and we get x is equal to three-fourths divided by a third. What do they do next? They invert and multiply and they get three times three-fourths or three over one times three-fourths. Why do they invert and multiply? And then when we multiply, we get nine divided by four is equal to x.

That's not what my students did. Now in fairness to you folks, I should have told you that Kathy and I on the way home were in hysterics. Now in our defense, I was driving a car and didn't have paper and pencil, my hands were on the wheel. It was in Bay area traffic in California, which is scary to begin with. But I was so confused. I knew I had 1/12 too much because I made equivalent fractions. But then I couldn't figure out whether it was 1/12 of the three slices or 1/12 of the whole pound. And there was no way to sort that out and pay attention to traffic.

Kathy and I had a little argument about whether we had to deal with 1/12 or 3/36. And we actually argued before we said, "Oh my gosh, they're the same thing." So I was a little surprised when I gave it to my students. Especially with the first child who came up and said, "Well, Ms. Parker, I just thought about it. I knew that if three slices was a third of a pound, nine slices would be a pound. And if that's a pound, what's a half a pound? If that's a half a pound, what's a quarter of a pound?" Now at times like this, it's really hard not to be humbled by a ten year old.

And I had other children who said, "Well, I just thought about it too, Ms. Parker. I knew that three slices were a third of a pound. So I knew nine slices were a pound. And if you could eat a quarter of a pound, I knew I had to divide that by four." So here we have a 5th grader, who by just thinking about it, starts where those of us who set up our ratio get to after we've done this. We discover that we have to divide nine by four. And I have other children who said, "Well, I knew this was a third of a pound, so I drew a pound. And I knew you could eat a quarter of a pound, so I divided it into quarters. So you can eat a slice, a half a slice and a half a slice makes two slices, and a quarter of the one in the middle makes two and a quarter."

And I had other children who said, "I also drew a pound and I knew that if you could eat a quarter of a pound, I had to put them into four groups somehow. So I started putting them into groups. But when I had four groups, there was one left over. I had to divide it into four pieces and give a piece to each group." I have seen children solve the turkey problem a dozen different ways.

Now I didn't give you the turkey problem because it's an important life problem. It's not. As mathematics problems go, it is a very trivial problem. Part of what caused me to go into the classroom every single day saying, "Ruth, even if you don't have support, you have got to do something different," was that I knew that nowhere in life are these children going to encounter mathematics that looks the way it looks in a traditional textbook. They're just not. Life doesn't present you with neatly set up problems that have one right solution path and an answer book to tell you if you're right or not.

Math in the real world looks more like how are we going to finance a house? Something I've personally wished there were an answer book to. Math in the real world looks more like the question I asked myself every single day walking into Monroe Junior High School in Seattle, Washington. And that question was, "Ruth, are you raising a generation of kids who will keep the Social Security system afloat?" It's a serious question. We have a vested interest in the answer to that question. They're going to be our guardians in no time.

And yet from where I sit, the answer to that question looks pretty darn bleak. Because every single day in Monroe Junior High School, I saw class after class after class of kids who, if I gave them a page in the textbook, they did it happily. If I gave them a ditto sheet of problems, they did it happily. If I gave them a problem that asked them to think, they'd spend three or four or five, maybe ten minutes at the very outside stretch, before saying, "Just tell me what to do and I'll do it." Or, "It's impossible." And I found that frightening.

The message we've given children in this country, that speed is important in mathematics, is a very debilitating message. Timed tests are a common practice in spite of evidence that they're a leading contributor to math anxiety. And a child who's math anxious doesn't choose to do math. They choose to avoid math. We do timed tests in spite of the fact that any mathematician out there will tell you that speed is not what's important in mathematics. Persistence is the mainstay of mathematician's endeavors.

Now I didn't give you this problem because it's important mathematically. I gave it to you because I think it illustrates the critical breakdown that happens all over this nation – and we see it on every national and every international assessment of mathematics that we do. What we continue to see is that children in this country are pretty good at adding, subtracting, multiplying, and dividing. They can do those things proficiently. They cannot use those skills to solve even simple problems.

Now you're the survivors in this game called school. I don't have any doubt about it. You wouldn't be here today if you weren't one of the survivors. And to be here today, you have all literally done hundreds of pages of computing with fractions. Would you agree with that? Hundreds of pages. I don't have a doubt in my mind that had I, when you walked in the door, given you all a sheet of problems to do that looked like this (2/3 ¸ 3/5), every one of you would have gotten 100%. Or very close to it. Do you agree with that?

Well, I have bad news for you. And the bad news I have is those hundreds of pages of computing with fractions, by, "Our's is not reason why, just invert and multiply", did not serve many of us here today when it came to using an understanding of fractions to make sense of what we now see should have been a pretty simple problem to think about. And that's the critical breakdown. Do we want kids who can add, subtract, multiply, and divide, deal with fractions, decimals, and percent with confidence and competence? Absolutely. But mathematical competence doesn't come from memorizing recipes you don't understand. Not in today's technological world it doesn't.

Recently when I've been doing parent sessions, some of the parents have come with an article that they have downloaded off the Internet from a site called Mathematically Correct. The article is about me, and it's titled, "A New New Math Educrat Exposed". And it is subtitled, "Where's the Beef in the Turkey Problem?" By the way, I am still saying this in my talk with parents. So we're still in the parent talk. And the author of the article made two main points. The first one was that in doing the turkey problem with the public, I'm using trickery unbecoming of a professional.

There was no trickery here. This was a problem that actually happened to me and I was curious to see what my students would do with it. And the other thing that they said was that I was making fun of ratios. Now if what you heard me doing was making fun of ratio, then I have miscommunicated. I've been an advocate for a very long time of ratio and proportional reasoning being one of the big ideas that needs to permeate our middle grades; 6th, 7th, and 8th grade. Proportional reasoning is very important to how mathematics is put to work in the world.

So my intent was not to make fun of ratios. My intent was to say if you could take me through how to solve this once I set it up for you, but if you couldn't take a situation and recognize it as a ratio situation and set it up for yourself and then solve it, then your mathematics education has ill prepared you for today's word. Because in the world of work today, this will be done by an inexpensive machine. Or an expensive machine. But what we are in urgent need of is people who understand mathematics well enough to tell the machines what to do, and people who understand numbers well enough to translate whether what's coming out of the machines is reasonable or not.

Okay, I have to pull myself back out of that piece. My purpose in doing this piece was I really wanted them to walk away knowing that they have not been well served. Their mathematics education did not well prepare them for today's technological world. Oh, yikes. Well, we're going to do it. I'll blame it on you because you didn't come in to start on time. But we'll be out very close to four.

Myth: The NCTM standards based practices taking place in classrooms across the nation are the reason why American students are outperformed by students in other countries. I have been recently asking a question that is not my idea. I first saw it from Richard Cerchi in San Francisco. Well, let me just ask you the same thing that I've been asking communities all over the country. First of all, think about how many schools you have in your district. And I know that varies a lot.

But think for just a moment what percent of those schools would say about themselves, not that we would say it about them, what percent of the schools in your district would say about themselves, "We really took the NCTM standards seriously. We all read them as a staff, we talked about what it's asking us to do, we talked about where we are now, we set goals. We purposely came back together to see if we were making progress and, if we weren't, we talked about what we were going to do to make progress. And if we weren't making progress, we asked what we were going to do to hold ourselves accountable. We really have worked hard." You cannot align with the NCTM standards without hard work. What percent of the schools in your district would say, "Yes, we've really worked hard to implement the standards?"

Do you know what the most frequent response I get around the country is? Any idea? Zero. And I say, wait a minute, be generous. Be generous. And they say maybe two. And I say be generous. Maybe five. Oh, come on, be generous. Would 10% be generous? And they usually say, yeah, it would be really generous. And I say, well, let's be real generous. Let's say 20%. Would that be generous for your schools? I know you're working with schools that have been working hard. 20% generous? Well, we can afford to be generous.

Well, let me ask you this. If you and I, pretty knowledgeable folks, visited one of these schools, the schools that have really worked hard, on a day when they didn't know we were coming, but we actually happened to be there for math period in every single classroom and we go through the school, what percent of those classrooms would we go in and watch a math lesson and walk out the door and say, "Wow, that was exciting. We just saw the NCTM standards come to life in that classroom."? What percent of the classrooms?

Any idea what the most frequent response I get around the country is? 5% usually. And I say be generous and they say maybe 10%. I say 10% is generous? And they say yeah. And I say, well, then 20% would be generous? And they all say, yeah, it would be really generous. One out of five classrooms. And I say, well, we can afford to be really generous. So you're telling me that when we are very generous, by both measures and I did hear you say we're being very generous by both measures, we have maybe this percent of the classrooms in this country that have aligned with the NCTM standards. And I have to ask, well, why is it these classrooms that get blamed for those people at Burger King who can't make change?