Mathematics in the Preschool
Clements, Douglas H., Teaching Children Mathematics
Anyone who is pushing arithmetic onto preschoolers is wrong. Do not hurry children. No math in preschool!"
"What else is preschool for if teachers do not get children ready for school? They should teach the children basic skills and how to sit and listen."
Principles and Standards for School Mathematics identifies a new age band that includes preschoolers for the first time (NCTM 2000). What mathematics instruction is appropriate for these young children? The two speakers have different opinions. I think that each is a little bit right and a little bit wrong.
High-quality teaching in mathematics is about challenge and joy, not imposition and pressure. Good early childhood mathematics is broader and deeper than mere practice in counting and adding. It includes debating which child is bigger and drawing maps to the "treasure" buried outside. Quality mathematics instruction includes providing loads of unit blocks, along with loads of time to use them; asking children to get just enough pencils for everyone in the group; and challenging children to estimate and check how many steps are required to walk to the playground (see fig. 1).
Much of our world can be better understood with mathematics. Preschool is a good time for children to become interested in counting, sorting, building shapes, finding patterns, measuring, and estimating. Quality preschool mathematics is not elementary arithmetic pushed onto younger children. Instead, it invites children to experience mathematics as they play in, describe, and think about their world.
Do We Really Need Preschool Mathematics?
We need preschool mathematics for four reasons.
First, preschoolers already experience curricula that include only a small amount of mathematics--and usually that content is anemic. We should improve this situation.
Second, many of these children, especially those from minority and low-income groups, later experience considerable difficulty in school mathematics. Recent curriculum development projects have shown that the gap between these and other children can be narrowed. We should address these equity issues.
Third, preschoolers possess informal mathematical abilities and enjoy using them. Before they enter school, many children develop number and geometry abilities that range from counting objects accurately, to finding one's way through the environment, to making shapes. Children use mathematical ideas in everyday life and develop informal mathematical knowledge that is surprisingly complex and sophisticated. Neglecting to nurture such interests would be an educational shame.
For example, five-year-old Chris is making shapes with a simplified version of Logo software. He has been typing R (for rectangle), then two numbers for the lengths of the sides. This time he chooses 9 and 9. He sees a square and laughs. A nearby adult asks, "Now, what do the two 9s mean for the rectangle?" Chris replies, "I don't know, now! Maybe I'll name this a square rectangle!" Chris uses his invented terminology repeatedly on succeeding days. Similarly, with the concept of number, children as young as three years old understand the basic principles of counting, even as they work to polish their skills.
Finally, although recent research on the brain has less to tell us about education than some suppose, it offers three general messages: (1) Preschoolers' brains undergo significant development, (2) preschoolers' experience and learning affect the structure and organization of their brains, and (3) preschoolers' brains grow most as the result of complex activities, not from simple skill learning.
Consider Alex, who just turned five and whose brother, Paul, is three years old. She wandered into the room and made an announcement:
Alex. When Paul is six, I'll be eight; when Paul is nine, I'll be eleven; when Paul is twelve, I'll be fourteen... [she continues until Paul will be eighteen and she will be twenty]. …