Ask an Expert: Dr. Herbert Ginsburg, Teachers College
On this installment of our Ask an Expert interview series, Tiggly sat down with Prof. Herbert Ginsburg. Dr. Ginsburg is the Jacob H. Schiff Professor of Psychology and Education at Teachers College, Columbia University. His research interests include the development of early childhood mathematical thinking and the assessment of cognitive function.
Tiggly: Please tell our readers about yourself. What are your research interests?
Professor Ginsburg: I work with kids and study how they learn mathematics and how they think about it. I have also done work that tries to create materials that would help them think about and learn different mathematical ideas and that will help teachers understand how kids learn.
I developed a program called Big Math for Little Kids, some years ago, with Carol Greenes & Bob Balfanz. The program has been used in many schools in the US and other countries around the world: Bangladesh, Portugal and some other places.
It has also been used in South America in a radio show in Paraguay, where remote villages don’t have television, so the education people would broadcast a radio program every day designed to help teachers implement the big math activities. Isn’t that interesting? I never thought it would work! I’m very happy with that!
Over the last six or seven years, I’ve also been working on math software called MathemAntics. We say it’s math software “from 3 to 3″: that is, for 3-year-olds to third grade students.
Tiggly: When we are talking about mathematics for two or three year olds, what do we even mean by that? Is math relevant for that age?
Professor Ginsburg: Well, children at two and three definitely don’t do math in the same way adults do. Obviously, they don’t deal with written math and don’t deal with symbolic math. By “symbolic” I mean the signs we invented for addition, “+”, or subtraction, “-“ for example.
What they are doing is dealing with some very basic mathematical ideas that they are challenged with in their environment. For example, they may need to know when they can have more food, and what “more” involves, or if they can have the same amount of food as somebody else.
There are a lot of situations when they have to deal with more/ less/ same amounts of things. If they are reading a book about the three bears they need to know that one is the baby, the other is a middle-sized mother, and the other is the big father. So they need to learn something about the order of size.
These are very concrete things they are facing all the time. We call this everyday mathematical thinking. As children grow up, they are going to learn more about how they can describe these more exactly in words, and learn how to count, how to write symbols that relate to these ideas and so forth. The idea is that children start with informal math within their everyday activities, and then hopefully connect that to formal symbolic math as they grow.
Tiggly: You talk a lot about informal mathematics and synthesizing and connecting it to formal math — what do you mean by that?
Professor Ginsburg: What I mean is that if the child knows that the baby bear is smaller than the mother bear, and the mother bear is smaller than the father bear, that’s a very concrete situation and the child develops and everyday math to deal with it. Or if they have 2 candies, and their friend has 3, they will protest that that’s not fair! They want to have the same.
In doing so, the child is judging the differences, but then later on, when you are introducing ordinal numbers or ideas of relative size, the child has to realize that: “Oh, when we write that 1 is smaller than 2 (1 < 2), that is kind of like when I had 1 popsicle and my friend had 2, or when we write 5cm is less than 10cm, that is kind of like the baby bear was smaller than the mother bear.”
Tiggly: How can parents do that? Does reading a lot of stories to them or playing different activities on software help children connect their informal learning to formal?
Professor Ginsburg: I think what they can do, for example when reading a story to their kids, is to point out these math ideas very explicitly. Have the child talk about who is bigger than the other person. Parents can extend some of the problems like, “Well, we know that the mother bear is bigger than the baby bear, but is the father also bigger than the baby bear?”
When dealing with 2- and 3-year-olds, the parents are not going to spend a lot of time trying to introduce written symbols — they would probably do better not to at all! Some of the best things parents can do are really to talk about these concepts.
Making pictures can also help. Have the child make drawings of the 3 bears and talk about how some are bigger than others and so forth. There is software that also engages kids in problems like that, like arrange these objects, from smallest to biggest and so forth.
So yes, parents can encourage kids’ activity with software, but also just with objects around the house: “Oh, here is a salt shaker, what in the kitchen is bigger than the salt shaker?” The important thing is to talk about these ideas within the context of everyday life.
Tiggly: When you say parents should talk to their kids and ask them questions, it reminded us of your clinical interview technique. Is that something parents can do?
Professor Ginsburg: Absolutely! First, let me tell you about the clinical interview technique. The clinical interview is an attempt to learn as much as possible about the child’s thinking. The interviewer, parent, teacher, or researcher presents problems, asks questions, observes, listens, and then, in reaction to what the child says and does, revises the questions in order to clarify the problem or probe more deeply into the child’s reasoning.
It is really a flexible and easy conversation between the child and parent with the goal of finding out how the child arrives at the answer and how the child thinks.
For example, put five candies in front of yourself and five in front of your child, but more spread out. Then ask,”Who has more candies?” Ask to show how they know.
Clinical interviews can help us learn more about children’s thinking, but also help children reflect on their thoughts and use language. One thing we know, and that we need to make very clear to parents, is that early mathematics language is very important. It’s very important for kids to be able to describe in words what they are doing, what their idea are. It’s very important for parents to say in words what they want kids to understand. It’s also very important for parents to elaborate on the verbal descriptions in books, for example.
So, we know that children’s language is important, we know that adult language is important, we know that the more teachers talk about the math the better the kids do and so forth. Now one part of this could be clinical interview. And clinical interviewing usually asks the child “Why did you do this?”, or “Why did you think that one was bigger?”
Asking the child questions serves two purposes: one is to help the child talk more about what he’s doing and what his ideas are. The other is that it teaches the parent what the child is really thinking. Clinical interview is really perfect to do with kids of almost any age.
Tiggly: Can kids start thinking about addition or subtraction operations when they are young?
Professor Ginsburg: They can when they are young in some very simple ways. They need to learn, of course, at first that when you add something to something else you get a bigger amount, so very simple ideas like that are important. At the age of 3 or 4 they can learn to do some very simple counting in kinds of addition.
I thought you were going to ask about shapes though? And I think that yes, they can learn about shapes as well, and it’s very important for parents to talk about those shapes. Most kids will easily learn what a circle is, a square, a triangle — that’s not very difficult.
What they really need to know is why is this a triangle, and not a square, what makes this square different from that circle, and also this skinny thing is still a triangle.
So the kids need to think about the common variations that you see, and the more parents can help the kid and talk about those and try to figure out the rules for why is something a triangle or a circle, that’s the kind of learning they need to engage in early on.
Tiggly: Can you talk more about stories and how they can help kids with math? Part of it is language; part of it is contextualizing math concepts. Do you want to add anything more to what you said earlier for parents?
Professor Ginsburg: I would tell parents that almost every story has some mathematical ideas in it. It’s hard to think of a story that doesn’t.
There are stories about big things and small things, stories about people going to places and space and all kind of things. You find me a story that does not have a mathematical element and you will win a big prize.
In any event, I don’t want to exaggerate, and it’s clear that some books have more interesting math events in them than others, and I’m not talking about deliberately math books like counting books, but a lot of books that have classical stories, like the three bears, really have some important mathematical ideas at the heart of them.
So parents first of all ought to read to their kids in general, regardless of the math; it’s a good thing to do from a social, emotional perspective, as well as literacy. You are engaging in a fun activity with your child. That is very important. But also the math in the stories gives the parents or teacher the chance to introduce the math within an engaging context.
It should be an interesting context that helps the kid make explicit the mathematical thinking they engage in and help them talk about it, and then the other benefit is that the parents won’t be afraid about how to introduce math to the kid.
Many parents don’t know what to do so they buy these awful drill books in Wal-Mart, but that is not what we are talking about. Don’t do drills, don’t punish your kids — just enjoy the story and elaborate a bit on the mathematical ideas in the story. That sets a good foundation for kids’ learning in the future. It also sets a positive attitude toward math.
Tiggly: Growing up did you have a favorite game?
Professor Ginsburg: My favorite game was stick-ball. It was a big game for kids in New York City when I was growing up in the Bronx. You take a broomstick, you cut of the broom, so you have this big stick and then you have a rubber ball and essentially you play baseball along the street.
Tiggly: What game will you play with your kids or grandchildren, or with any 3 year olds?
Professor Ginsburg: This is not with 3 year olds, but for a little bit older: all my grandchildren play “Sorry!” with me. It’s a board game where everybody has a different color piece, and you role the dice and you can move a certain amount of spaces on the board but then under certain conditions you can nuke off somebody else’s piece and prevent them from winning, and then you say S-o-r-r-y!.