# Early Childhood Today Interviews Dr. Herb Ginsburg on Math Education for Young Children

Amelia Swabb, ECT Associate Editor: Can you tell us about your preschool math curriculum, Big Math for Little Kids?

Dr. Herb Ginsburg: Big Math for Little Kids was developed 5 or 6 years ago, with Carole Greenes at Boston University and Robert Balfanz at Johns Hopkins. We developed it as a complete math curriculum for four and five year old children – when I say complete, we meant it in two senses. First, it covers a lot of topics in mathematics – not only number, but shape, operations on number, pattern, measurement, and space. Second, it was designed to be used all year long, and we have an activity to do at least once a day throughout the whole year. They’re not boring activities and they’re not textbook activities, they are fun activities for kids to do, but there is a plan and there is intentional teaching. Topics and activities are designed in a sequence, and the teacher goes through them one at a time – the idea is that when a child goes through a set of activities, they are then ready for the next set of activities. The program is not heavily scripted, it relies on teachers to improvise and make sure that the kids are having fun but it is a curriculum in the sense of a planned organized set of activities.

Amelia Swabb: What are some important milestones in the development of mathematical thinking skills in the early years?

Dr. Ginsburg: We know that at four years of age, kids really like to count. They like to say the counting words. And there are roughly three levels of counting that they can learn how to do. The first level is where they have to memorize the numbers from about 1 – 12. Then the next level is learning the numbers 13 – 19, and kids know that the numbers from 13 – 19 are weird so we make a special case for them and we call them the “yucky teens” so that kids will understand they are a little unusual!  The third level is counting from 20 upwards where it’s very regular, very rule governed. And what we believe is that kids, when they do that counting, are really exploring the first regular pattern that they see in mathematics. The pattern is why you go from 20, which is like two tens, to 30, three tens, 40, four tens, 50, five tens and so on. The tens have a pattern and after each ten you add 1, 2, 3, 4, 5, 6, 7, 8, 9. So the three levels of counting are very different: the first is memorization, the second level is memorizing but also recognizing there are some strange rules involved, and the third is a real mathematical pattern – base ten. And we encourage even the four year olds to count up to 100 because that helps them get into patterns in a deep way.

Another example is in shapes. Very early on, young children know the names of the simple shapes, like circle, square, and triangle, and they can see the difference between them – even three-year-olds can do this. The really difficult thing for them is if you take a triangle, for example, and you make it tall and skinny. Or if you make it lopsided and slightly weird looking. When you make one like that, they say it’s not a triangle. So what they have to learn, is to really analyze triangles. It’s not a question of seeing them, it’s not a question of naming them; it’s a question of analyzing them. So we know that developmentally, that’s the progression: it’s easy to see the shape, that’s first, then they name them, that’s second, but third they analyze and really realize, “Oh, a triangle has three sides and the sides don’t have to be the same.”

Amelia Swabb: Can you give us a very practical example of how a teacher can support the development of these skills?

Dr. Ginsburg: So our activities start simply, but after a short while, we get into that analysis issue. So we do things like put shapes of different kinds in a bag – circles, triangles, squares, rectangles, but also different looking ones, which we call nonstandard. And the kids close their eyes and have to reach in the bag and pick out a triangle, and say why it is a triangle. That’s a really fun activity for the kids and it forces them to think about and analyze what it is.

Amelia Swabb: What is the most effective way for early childhood teachers to teach math in their classrooms?

Dr. Ginsburg: The philosophy in early childhood up until recently has been that teachers should always teach math in the context of everyday activities. For example, during snack time, you have a child put out a cookie on each plate to do one-to-one correspondence. Or you say during block play, “What shape are you using? Is this shape bigger than this?” Or when children line up, you ask, “Who is first? Second? Third?” That’s a very standard nursery school routine. And those things are fine, and very useful, and teachers can continue to do that. But there are some arguments that these are not enough. One argument is, this exploits teachable moments – the kid is doing something and the teacher pounces on them and says, “Oh wow, that’s very interesting, now try to make a square.” Another argument is that the teachable moment is just very hard to do. You’ve got 20 kids, you just can’t do it all the time with all of them. It’s not a viable strategy for really helping kids on a systematic basis.
Therefore, what is needed is a more planful approach on the part of teachers. It’s great to integrate math into every activity, but you’ve got to have a plan for doing it. So the early childhood education field is recommending more and more that teachers should use a curriculum. Big Math for Little Kids is just one example. High Scope and Creative Curriculum are both producing new math curriculums right now. There is definitely a trend toward saying children really enjoy math, they can benefit from it, so teachers, you really ought to think about using a curriculum! And it’s fine to pick from several, or combine them. I know there are teachers doing Creative Curriculum in New York City and also doing Big Math activities.

Amelia Swabb: You've been a proponent of the "clinical interview" method to help teachers understand their students' mathematical thinking. Can you describe this method for us?

Dr. Ginsburg: The clinical interview method should be used more often in early childhood. Let me preface this with the fact that early childhood educators have relied a lot on observations. The clinical interview starts with that, with something you see the child is doing, then you ask questions like “How did you do that? Why are you doing that? What’s going on here? Tell me more about it. What are you thinking about?” So it’s very simple. The clinical interview method is sort of flexible questioning of individual children to try to find out what is the thinking that is producing the behavior that you see at the time.

I know that in a classroom you can’t do that all the time. But you still can do a lot of “partial” clinical interviews. Or don’t even think of it as a clinical interview, think of it as part of your teaching. When you introduce a triangle or a rectangle, you say “What are these called? How are they different from each other? Why do you think they are different from each other?” One kid might say one thing, one might say another, but as they say things, you have to try to get more out of them. And what happens is that you are using language in very important ways within the mathematics. That’s why we say math is also a literacy activity. Particularly if you use the clinical interview. If you just watch the kid, you’ll learn a lot but you won’t get the child to express his knowledge. And the process of putting knowledge into words is a really important thing. And for teachers to help kids put ideas into words, express themselves clearly through the clinical interview method or any other method – that is a key part of math education. It’s learning to think and talk and express and use language to share ideas and explain their thinking. So the clinical interview really stresses the language functions of math learning.

Herbert P. Ginsburg is a Jacob H. Schiff Foundations Professor of Psychology & Education and currently teaches courses in Development of Mathematical Thinking for early childhood teachers at Teachers College, Columbia University. He has interests in intellectual development, mathematics education, testing and assessment, and professional development for early childhood teachers. He has helped develop a math curriculum, Big Math for Little Kids, and is also involved in the Video Interactions for Teaching and Learning (VITAL) Project, supported in part by a National Science Foundations (NSF) grant.

• Subjects:
Real-World Math, Early Math, Learning and Cognitive Development, Educational Standards, Teacher Training and Continuing Education

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