ECT Interviews: Douglas H. Clements, Ph.D. On Math, Music, and More
- Grades: Early Childhood, Infant, PreK–K, 1–2
EARLY CHILDHOOD TODAY: Do you see a connection between music and math?
Douglas Clements: Any kind of rhythm is setting children up to understand patterns, and mathematics is filled with all kinds of patterns. That doesn't mean that music equals mathematics, but the two are connected. Research tells us that preschoolers deal with patterns all the time. In fact, some mathematicians have even defined mathematics as the study of the patterns of number in space.
ECT: Does music have anything to do with learning how to count?
Clements: You know, most children who learn to add and subtract start by using a simple strategy called "counting all." So, if you start by saying to a child "If you had four apples and then you got three more, how many would you have?" They'll take four apples, then they'll count those again, and again. One thing that happens between 5 and 6 years of age is that they'll now say, 4, 5, 6, 7. They've already gone up to 4, and now they'll just count on and avoid the repetition of going back and counting from the beginning. Lots of children do that because they have singsong type patterns to rely on-rhythmic patterns. They discover that if they have one more of something, they can just say the next number. The musical pattern helps them move from counting all to counting on.
ECT: How important is it to teach counting as a skill in early childhood?
Clements: Counting itself as a process is obviously of critical importance. But children don't just count. They know numbers in a variety of ways. There are precursors to numerical understanding that children can do at a very young age. For example, research tells us that by 6 to 12 months of age, children can recognize small groups of numbers without counting. If you show them pictures beginning with a set of three stars, then three circles, then three triangles, they will soon become bored. However, when you shift gears and show them pictures of four stars, four circles, and four triangles, they become interested again. This renewed interest shows that, at some low level, children can understand numbers in a way other than just by counting.
Another study involved hiding small groups of pennies under paper. By 2 or 3 years of age, children can reconstruct these piles of pennies even if they don't know the number words. In addition, by 3 and 4 years of age, children can do simple addition and subtraction problems using counting strategies. Not just by rote counting, but by doing some very simple reasoning.
I also want to mention the importance of reinforcing spatial and geometric concepts. Children live in a spatial world and have lots of experiences and knowledge already, but also lots of potential we can enhance if we work with them as they move around the classroom, putting things together, making designs, and the like.
ECT: How can teachers use learning centers to build math skills?
Clements: When it comes to developing mathematical skills, the younger the children are, the less we need to interfere. There's nothing to lose and everything to gain by putting on your "math glasses" as you watch children involved in activities all around the room. Try to understand what is really going on and then ask questions or offer objects that will help children see the math behind the activity.
ECT: Are there special kinds of math materials you would recommend to our readers?
Clements: It's a hard question because good teachers can use all kinds of materials and use them well. What we have seen from practice is that water tables, sand tables, and unit blocks are very useful. Blocks contain such a wealth of geometric relationships. Recent High Scope studies show that most teachers, most of the time, manage children, so we need more help in the classroom. We want to be certain that we don't get so caught up in managing that we miss opportunities to help children learn.
Douglas H. Clements, Ph.D., is Professor of Mathematics and Computer Education at The State University of New York at Buffalo. He has conducted research and published widely in areas including the early development of mathematical ideas. Dr. Clements was a member of the writing team for the recent national Council of Teachers of Mathematics report, which, for the first time, includes math standards for pre-K through grade 2.