Conference Material

Engaging Parents and the Public

This is Moe. Moe is a child who came to us as a fifth grader having said, "No, thank you" to mathematics. It wasn't his thing. But he did some kind of interesting things the second time around. And, again, I don't know if you can see all of this. But if you think for a minute about the thinking about fractions that Moe had to do to solve this, first of all, he had to measure precisely to divide up his square. And then he had to find the area of each of the regions, compare that to the area of the square to find a fractional relationship. There's a lot of thinking about fractions that went into just Moe's.

This is James'. And James was a typical learner, an average student in mathematics, if we want to label children. I like to get the labels off of children. Until this unit. When James decided maybe math's okay after all. Now I wish I had time to have you look at whether this one-twelfth is or is not one-twelfth of James' square. There's some very interesting thinking that goes into that one. But as a teacher, I was delighted. Because finally I had curriculum that helped my children develop an understanding of fractions and that did it in a context where they were also finding the area of two dimensional geometric shapes.

And I was especially delighted that they were learning fractions in a context where they were also measuring and measuring precisely. The reason I was delighted with that was because earlier in the year I had asked these children to build a three dimensional scale model of the classroom with doors and windows cut out. And as they went about measuring, I was horrified by what I saw. It was as if nobody had ever asked these fifth graders to measure anything real in their lives.

I had children who took a yardstick to measure the length of the room. But every time they moved the yardstick, they had a three or four inch gap or overlap and didn't seem to think it mattered. I had a group of four children come up to me and ask if they could go to the custodian to get a tape measure because "That’s what real builders would do." So I sent them to the custodian. When they came back, they had one student hold the tape at the corner. He held it about three inches from the corner (who needs precision when we're measuring?). When they got to the other side, they held it up like this, with a huge bow in it, and wrote down the number at their finger as if that was the length of the wall. I couldn't believe what I was seeing. I had children who took a trundle wheel - do you know what those are? It has a wheel on the end that will click off meters as it rolls. And they said, "This will be easy. We'll just use the trundle wheel." So they just went click, click, click, ran into a table and went click, click, click. And I thought, "My gosh, these are 5th grade students who don't seem to understand that if you want to measure a distance between two points, it's important to stay in a straight line." So I was delighted that they were learning fractions in a context where they were also measuring and measuring precisely.

But here's what concerns me a lot today. A lot. Teachers are being asked to teach programs that look this different. And they're being asked to do it as part of a profession that doesn't seem to recognize that teachers need to be learners of mathematics in order to be powerful teachers of mathematics. And they're being asked to teach programs that ask them to work very, very hard. You can't do this change easily. To work very, very hard at the very time that nearly any day you can pick up a newspaper or you can pick up a magazine, or you can get on the internet and read scathing things about these new programs in mathematics -- these National Science Foundation funded programs -- scathing things about them; often written by columnists who have never taught either children or mathematics; sometimes written by university professors, some of whom have taught mathematics but most of whom have not taught children.

And I want to ask you to consider for just a moment, if you were on your district's textbook selection committee and you were responsible for selecting the next textbook for your district and you knew that whatever you selected was likely to be the only mathematics that any child in school today is likely to get because we typically only select every six to seven years. And if what you saw when you looked at this textbook that I just showed you student work from was pages that look like this, followed by pages that look like this. What do you think you'd conclude about this new program for mathematics? Pretty empty?

Q: It's empty and devoid of substance.

Parker: Certainly devoid of substance. They haven't dealt with the basics, have they? I don't see skills development here. I certainly don't see any drill. This is a fifth grade textbook. We all know fractions are important in fifth grade. I don't see fractions in this book, do you? What are they trying to do to our children?

It's going to take an extremely rare individual who, removed from actually teaching these programs to real children in real classrooms, is going to be able to look at a page that looks like this and in that page see not only the potential for Moe or James or Shelly. You didn't meet Shelly. Parents have met Shelly earlier in the talk. She's an artist. This doesn't quite do it justice.

Do you remember Matthew's first one? This is Matthew's second one. Matthew is ten years old. Now how would you like to be the classroom teacher who gets to face ten year old Matthew everyday in math? He gives you a code to help you. He lets you know that small pink is 1/288, etc. Now as Matthew's teacher, I learned very quickly that if I were going to challenge his ideas, I’d better double check my own. Because invariably I'd made the mistake trying to figure this out. He was doing just fine.

In selecting the textbook that is going to influence your child's mathematics future, I think it's critical that we find ways to have people who are both comfortable enough with mathematics and knowledgeable enough about children that they can look at a page that looks like this and in that page ask two very important questions. The first question is, "Is the mathematics presented in an open enough way so that it allows access in to all children?" Can a child who came to me really struggling with mathematics still have a way to measure and say something like there's two halves, there's two fourths, there's two eighths.

And as importantly, we need to be able to look at a page that looks like that and ask the second question. And the second question is, "Is the mathematics presented in a robust enough way so that even those children who are going to go on to take mathematics much, much farther than I may be able to take them myself as a teacher, is it presented in a way where those children don't have a lid on their thinking?" Does it allow for the Matthews in the classroom? And if we can't answer yes to both of those, that it allows access in to all children and it keeps the lid on the thinking of no child, then I think we have to say, "It is not good enough." Because as mathematics educators, we are responsible, I believe, for keeping all children on the edge of their understandings, always pushing to extend the boundaries of what's known.

I'm going to pull you out of that piece of the parent talk again and I'm going to ask you to spend just about ten minutes, which won't be enough or satisfying, dialoging with each other. And one of the things I'd like you to talk about is, having looked at those three pieces very briefly, what did you notice about the interaction between the three areas -- actively engaging parents as learners through direct experiences, giving important information, and reflections that are designed to purposely dismantle the myths about mathematics? So go ahead and spend a little bit of time talking to each other, if you would, at this point. [Break for discussion]

I've had more than one question about this. Actually that was a big request. Could we pull back together again? I apologize. You were in the middle of a big thought.

On your handout, you have my e-mail address. And if you really care about this, I will send you one. But if you look at how it's set up, we basically have all the factors from one through nine. And all the possible products for those factors put in sequential order on a six by six grid. Now you might have younger children and you only want to work with smaller facts. Well, change the game and have zero through six as possible factors. And either use a smaller grid or put the products in twice, it doesn't matter.

When my fifth graders came to me, they were not fluent with addition. So I set up the game as an addition game with the factors one through twelve and all of the possible addends put in. So they were just practicing things like seven plus eight, but it was engaging because of the strategizing that went on in the game. When they got really good at that, I changed the game again so it had six through 19 as all the possible addends. So they were just doing lots of drill with addition. But I'd be happy to send you a copy of this if you'd like.