Gene I. Maeroff on the small miracles of learning math

Sharon Griffin's comments about an aligned approach to math during the preK-3 years resonate with what I learned during field visits for my most recent book. She speaks of "counting words" and linking these words to quantities "that give them meaning." People frequently speak of the miracle of learning to read, but isn't it also something of a miracle that small children gradually learn that numbers are representations and that a number attached to an object one time it is counted might be different the next time it is counted, when the order of the objects changes

I was fascinated when I visited Joyce Goubeaud's class at Ashby School in north-central Massachusetts to watch this veteran teacher help a group of preschoolers learn that numbers have names and that a sense of order prevails-4 follows 3, for example, and never comes before 3. Like a guide on a mountain trail, she led her tiny charges gingerly through the permutations of the number 5, having them sit in a line facing her and then switch positions each time after they counted off, demonstrating concretely that 5 remained 5 even if two of the children were in different places.

Griffin also mentions the need for children to grow familiar with patterns. Natalie Charbonneau at Ronald McNair Elementary School in Montgomery County, Md., held her prekindergartners rapt as they sat on a carpet in front of her as she-on the edge of the seat on a rocker-showed them strips of paper, challenging them to turn up their thumbs when the succession of green and purple boxes changed.

Of all the subjects, math surely has a sequential nature that makes teaching and learning during the years from prekindergarten through the third grade an experience during which one lesson builds on another. Certain manipulations prepare young learners to perform ever more complex tasks as their knowledge grows. The alignment of standards, curriculum, instruction, and assessment is crucial within and across grades from pre-kindergarten through the early grades to make this happen in an orderly and productive way.

Delays in knowledge of which Griffin speaks are more readily commented upon and addressed in reading than in math. One reason that I and others call for greater emphasis on the years from preK through third grade is that skills in both reading and math must be imparted and reinforced to build a firm foundation during this period if there is any hope of improving outcomes at the upper grades.

I am impressed by what I saw of Singapore math-fewer topics, more depth, more problem-solving, and greater understanding. This approach, gaining support across the country, holds promise for the kind of approach Griffin seems to favor. I wrote in my book about American researchers who observed math instruction in China. They concluded that American classrooms could be bolstered by imitating the Chinese and prodding students to discuss what they are thinking and doing as they solve math problems. "Let's let them talk about what's happening," urges Griffin. Perfect.

Math is a language, a method of communication. Some students will end up communicating better in math than others, but all of them need the opportunity during the early years to learn the language that will allow them to participate in the conversation.

Gene I. Maeroff's latest book, Building Blocks: Making Children Successful in the Early Years of School, was published in fall 2006 by Palgrave Macmillan. He is a senior fellow at Teachers College, Columbia University.