Conference Material

It's no accident that in planning the agenda for this meeting, Ruth Parker has been strategically placed after the sessions that focused on the importance of the discipline and the stages of change that we go through and on student assessment and before the session on policy. Ruth is a strong believer that, and these are her words, "the most useful and meaningful kinds of assessment tasks are those that ask children to engage with essential and relevant mathematics. Tasks that reveal students' real understanding of mathematical ideas, as well as their dispositions towards mathematics. And tasks that provide teachers, parents, and other educational decision makers with information needed to make appropriate ongoing instructional decisions."

She is also a strong believer that the mathematics and science education communities must work to educate parents and the public as we change the ways we teach and the ways that students learn. Ruth brings to this work a long and rich set of experiences as a classroom teacher, a professional development leader, a consultant, a writer, and a speaker. She is, in my opinion, without peer in her leadership and thoughtfulness about surrounding parents and the public in the context of K-12 mathematics education. I am absolutely delighted to put you in the very capable hands of Dr. Ruth Parker.

Parker: Thank you, Diane. Now I'm going to be more nervous about living up to the expectation that you set. It's good to be here with you this afternoon and especially to be asked to address the issue of working with parents and the public since it is my passion and it's the area that I have been focusing my work for the last four years. I have become absolutely convinced that the dreams that many of us have and the work that we've been doing for many, many years to get higher quality mathematics and science classrooms happening for children cannot happen on a broad scale until we have a public that shares our vision. In order to accomplish this, all of us in this room and others within the mathematics and science community need to focus strategic thinking on how best to position those of us who are deeply knowledgeable about the issues in mathematics and science education to work strategically with our parents and public.

I'm struggling some because I think I could probably do justice to this subject if we had a day to talk about it. And we have an hour and 45 minutes. Susan Elko has twisted my arm to make sure that some of that time is devoted to you folks dialoging with each other around the issues. So I'm going to try to honor that. Although it will be a challenging task.

In handouts that you have, I have spent just a couple of pages building a rationale for why we need to work with parents and the public; why that's essential. What I didn't say in that hand out is that from my experiences working with parents, and I've worked literally with thousands of parents in districts all over the country, I find parents and the public to be our easiest audience to bring on board as allies in this work to reform mathematics and science education. I spend most of my time these days doing similar talks with parents and with teachers and administrators. With teachers and administrators, although they're enthusiastic about the ideas, they're concerned because they have to confront the enormity and the complexity of the task we're asking them to do--restructuring the content of what they're teaching; restructuring how they assess whether children are learning; restructuring their learning environment. And for parents, all they really have to do is to hear the ideas and say, "Well, I never thought of it. But of course it needs to happen. And how do we make it happen?"

I would suggest that parents have a very loud policy voice when it comes to schools and districts. If we can bring them on board as our allies, they can have a huge impact on moving the system forward.

I am pretty convinced that there's a need for two kinds of work with parents and the public. One that we are fairly familiar with. Which is the kind of work that can only be done by leaders who live within a community and build the sense of trust over time and provide the opportunities to learn over time. Family Math kinds of experiences fit into this category. But there's a second level of work that I think needs to be happening that can best be done and perhaps only be done by people or entities external to any educational system that is working on mathematics restructuring.

It's this second category of work with parents and the public that I want to focus on today. The kind of work that must be done by leaders in mathematics and science education. When it comes to large group sessions that are really paradigm shifting sessions, we're into a new realm that many of us haven't had opportunities to become comfortable with.

In getting started, I need to let you know a couple of things. As I'm talking today, all of my experience is as a mathematics educator and I'm very aware that many of you are here with science projects. I suspect that often when I'm saying mathematics, you could substitute the word science and be addressing very similar issues. But my perspective will be from the mathematics community.

This talk, I should also let you know, is not a result of my studying the field of engaging with parents and the public. It's coming almost entirely from my personal experiences working around the country with parents and the public and it's filtered through my own belief systems. So I would invite and indeed welcome you to challenge any of these assumptions. Or to challenge any of the ideas that I'm sharing with you today.

I want to do three things this afternoon. I want to focus on the content of the mathematics sessions that I have been sharing with parents and the public. I want to share some of the lessons learned -- some of them the hard way. And I want to provide opportunity for dialogue. Both opportunities for you to dialogue with each other and to interact with me.

How many of you have actually been to a session that I've done for parents and the public over the last two or three years? It looks like about a fourth of you maybe and so three-fourths haven't. That's part of my dilemma. I wish we had that as a common base to talk from. But what I've chosen to do, and I'll have to apologize to those of you who have been with me before, is to take some pieces of those talks and to do them with you in order to illustrate points or issues that I think are issues that we need to look at.

In planning sessions for the public, I have some guiding principles that I consider. And they're probably obvious, but they also have deep parallels to what we've been trying to do in terms of learning with children in the classroom. One is that whether we are in a hands on family math night or in a large public session, parents and the public need to be actively engaged as learners during the session. They will filter our ideas through their own experiences and through their opportunities to reflect purposely on those experiences.

Secondly, when we're thinking about working with parents, we have got to be very aware that we need to provide information that can be understood at a variety of levels. When you are working with the public, you may have a neuro-physicist in the audience, or someone who knows, in my case, much more mathematics than I will ever know. And you are also almost certain to have math injured or math phobic parents in the audience. So one challenge is to provide experiences that allow access in to all of the participants who are coming -- experiences that can be understood at a variety of different levels. All participants come with questions and concerns and issues. And the sessions that we provide for them have to have opportunities to have those issues confronted or addressed.

I want to take three pieces of a talk that I've done with parents and teachers in many regions of the country and ask you to examine these experiences through a couple of filters for about the next 20 minutes. And then we'll stop and you'll talk about what we've done.

With regard to content, the first question I ask myself when planning a session for parents is, "What do I want these people to leave understanding?" I have planned sessions for parents that are largely designed to confront the myths that have been fairly well established. In fact, myths that I would suggest have become conventional wisdom in terms of how a segment of our public thinks about mathematics education. By the way, those myths are listed in your handout, so you don't have to write the myths down.

But I am going to look at the first three myths and I'm going to ask you to filter them through three things. I'd like to ask you to experience a little bit of a public session and look at the interaction between, first of all, the opportunity for active learning through direct experiences and, secondly, the giving of important information. And as a constructivist, that feels a little hard to say -- the giving of important information. And third, the reflecting on experiences in ways that are purposely designed to help dismantle the myths.

Now the first three myths that I want to address are myths one, two, and three in your handout. The first one being that problem solving is important, but it only belongs in the curriculum after basic skills have been memorized. And the second myth is that the anti-reform movement in mathematics is a back to basics movement made necessary because mathematics reform efforts have neglected basic skills. And the third myth that I want to address is the myth that the new National Science Foundation funded mathematics programs are fuzzy, devoid of substantive content, and lacking in the basics.

And I would suggest to you that these are fairly well established myths. Or I probably don't even need to have that conversation with you. You're well aware of it. So let me move on to a brief look at public sessions through those filters.

So first, problem solving is important, but it only belongs in the curriculum after basic skills have been memorized. Now I have to set this in a context. This is actually a piece of the second level talk that I've been doing with parents. And the talk is really built to confront the notion of we don't care about basic skills anymore. And I take the issue of knowing multiplication facts and the importance of having fluency with multiplication facts and the session is built around that.

So before the experience that I'm going to do with you, parents have seen work from two documents. The first one is a book by Marilyn Burns called Math by All Means: Multiplication. And the second one is a book called A Collection of Math Lessons that looks at building rectangles for multiplication, analyzing the data through rectangles, using those rectangles to build the multiplication table, and then searching for lots of patterns that show up in the multiplication table. We also use a zero to 99 chart and have looked at patterns in multiples of threes and multiples of nine.

And we basically have built a case for what does it mean to teach for understanding and what does it mean to teach in a way where mathematics is consistently presented as a search for patterns and relationships. This is actually one of the last experiences that parents have in that session. And it's a story about a boy I don't know, Brian Frankle, who was a third grader. I heard about Brian Frankle when his teacher, Eva Piper, wrote to a colleague of mine, Mary Jane Smith. And Mary Jane put it out over a list serve and told Brian's story.

Eva Piper said that when her third graders came to her, they came not knowing their addition facts. And so she decided that early in the year she was going to spend several weeks getting them fluent with the addition facts, believing that that was important to building the foundation that they would be using in mathematics throughout the rest of the year. So she started by putting up an addition table and asking children to search for patterns in the table. That was their assignment and everyday they did a search. After several days of this searching for patterns, she started to focus on strategies.

She first had them focus on their doubles until they knew seven and seven and six and six and eight and eight and four and four and three and three and nine and nine. And when they were comfortable with doubles, she put those aside. And then she had them focus on doubles plus or minus one. So that they looked at, if they already know seven and seven, then seven and eight is really easy and six seven is really easy. And they looked at all of their doubles plus or minus one and they put those aside.

And then she taught them a strategy that she called the sharing method for addition. The sharing methods works if you're adding numbers that have a difference of two. So she had children build a tower of seven blocks and a tower of nine blocks and take one off the tower of nine, and put it on the seven. So that they realized that it was just the doubles in between and they already knew their doubles. So knowing their doubles, they now know seven and nine and six and eight and three and five and all of those. So they put those aside and they went on to other strategies.

Well, I heard about Brian Frankle late in the year when Eva Piper had just moved these third graders into a look at multiplication. And again, she started by giving children a multiplication table and asking them to search for patterns. And Brian Frankle came in one morning, about three days into this search for patterns, and said, "Teacher, I found a sharing method for multiplication." And her teacher said to Mary Jane, not to Brian, I didn't know there was one. But said to Brian, "Well, how does it work?" And he said, "Just like with addition." He said, "It works with numbers that are apart by two" (or that have a difference of two).

So if you want to multiply seven times nine, Brian says you take the number in the middle, which is what? Eight? You multiply it by itself. Which is what? 64. You subtract one. Which is what? Is that seven times nine? Well, Eva said to Brian, "Brian, is that always going to work?" And Brian said, "Try it." So let's try it. If we wanted to multiply three times five and we wanted to use Brian's method, what would we do? Four times four. 16 minus one. 15. Is that three times five? Ahh, but is it always going to work?

Now as soon as you ask the question is it always going to work, you have created a great context for drill. But drill where children are motivated because they want to test whether a pattern's going to hold true or not. What about 19 times 21? Could you do 20 times 20 mentally? What do you get? 400 minus one? 399. Did it work? Well, we don't know, but we have now created a great context for caring about two digit by two digit multiplication. Again, because we want to test out whether an idea is going to work or not. Now some of you are not going to hear anything I have to say in the next few minutes because you're testing Brian's idea.

But what struck me when I heard about Brian is that Brian wasn't in a classroom where the teacher thought, okay, Brian, that's a really interesting pattern, but your real job is to memorize your multiplication facts. So let's get busy with that. And Brian also wasn't in a classroom where the teacher believed what I hear commonly discussed in the national debate about mathematics education. And that is that problem solving might be important, but it doesn't belong in the curriculum until kids have memorized their basic facts.

I think if Brian was in a classroom where the teacher believed that, I don't think he would have invented the sharing method for multiplication. His classmates wouldn't have known about it. I wouldn't have known about it. I didn't know there was a sharing method for multiplication until I heard Brian's story. Brian was fortunate enough to be a classroom where the teacher understood that everything we teach, everything we teach including the basics, needs to be taught in a way that is consistent with the message that mathematics is a sense making process. And everything we teach, including the basics, needs to be taught in a way that is consistent with the message that mathematics is about a search for patterns and relationships and order in the world around us.

Now what I now know that I didn't know before was wouldn't it have been wonderful if Brian's teacher was comfortable enough with mathematics to be able to ask Brian, "Brian, do you think it only works with numbers that have a difference of two?" Now I'm going to leave that for you to explore, but I'd suggest it's a wonderful investigation. By the way, what Brian saw when he was looking for patterns is he looked at this diagonal and he noticed that in every case we had a four and we had a three and a three. A nine and an eight and an eight. A 16 and 15 and 15. A 25 and 24 and 24. And because of his experiences in searching for patterns all year long, he didn't think it was there for no reason at all. He wanted to know why and went into a search for why it was happening.

Okay, I'm a little worried that you're going to feel as fractured as I am because we're now leaving that piece of the parent talk and we're going someplace else. We're moving to a piece of the talk with parents that happened in the same session but before Brian's story. This is an experience that I built in to address myth two: The anti-reform movement in mathematics is a back to basics movement necessary because mathematics reform efforts have neglected basic skills.

And again, we have already spent in this session about an hour building and understanding multiplication in many contexts. And then I addressed the issue of drill. And I say that one of the questions that I'm often asked is, "Is drill important?" And my response to that is, "Absolutely." No matter what it is we're trying to learn to do, it's doing lots of it that causes us to be able to do it with ease. But it is important that we understand what drill will and won't do. Drill will not teach a concept. It will reinforce a concept that has been taught. All the drill in the world will not teach a concept. I think I taught for years believing drill would teach. I taught for years thinking, "If I just give them one more page, surely they'll get it." Well, I now understand that that's not where getting it comes from. I would suggest that with mathematics, drill needs to be embedded in contexts that are meaningful and engaging and that ask children to behave in mathematically important ways and that give the message again that mathematics is a sense making process.