Alice P. Wakefield
Nov 1, 1997
Citations
0
Influential Citations
15
Citations
Journal
Phi Delta Kappan
Abstract
When children solve their own problems and are accountable for the consequences, they become more confident about their problem solving and more autonomous as well, Ms. Wakefield points out. So let the games begin! Just as children's disposition and ability to read benefit immeasurably from having had nursery rhymes and picture books read to them, so do children acquire a sense of number when they have early opportunities to think about "number in action." Families that provide opportunities for children to share a treat equally, to make intelligent guesses, and to play simple board and card games that require the players to count, add, subtract, and match are giving their children thinking challenges that develop their number sense. Children who come to school without this kind of previous experience encounter problems when math programs assume that mathematical relationships can be taught directly by the teacher in accordance with the curriculum rather than being constructed by each child according to his or her level of previous knowledge. Sometimes parents and teachers think that they are teaching children only when they are telling them directly how to do something, as with the rote learning of letters and numbers. However, children learn much more when they use letters and numbers to accomplish what they themselves want to do. The normal interactions of children at play (e.g., figuring out how many spaces to move a game piece according to the roll of the dice, what combination of cards adds up to 15, or what a "Chance" card requires) provide natural challenges that involve reading and numbers. The Role of Active Thinking Adults formed their understanding of counting and of adding and subtracting so long ago that it is hard to identify with the internal straggle young children face as they attempt to form these relationships for themselves. Many of us have experienced the difficulty of directing a young child to count the spaces around the game board - "peck, peck, peck." It seems so simple to us. But if the child has not formed a one-to-one correspondence of number to space, we might as well save our breath. I've heard educators say, "Problem solving and thinking may be fine, but certain things, such as math facts and multiplication tables, must be memorized." Unfortunately, some teachers and parents take this to mean only one thing: drill and practice through the use of worksheets, flash cards, and other rote activities. These people seem to have a "no pain, no gain" mentality about learning math facts. The very name "math facts" implies that these "facts" are simply external data to be memorized through practice rather than relationships to be constructed by a thinking individual. In workshops on creating supportive math environments, I ask teachers to think back to how they felt as children when they were asked to complete worksheets. Occasionally, someone will say that he or she liked doing worksheets. At first, that response shocked me, for I have no such fond memories of the dreary task. But, I suppose, if you were among the students who could get the answers and if you got a bang out of gold stars and teacher praise, you might remember them more fondly than I. There is a profound dilemma inherent in the drill-and-practice mentality of teaching early math relationships. Since children have to know these relationships in order to do the worksheets, what possible purpose do the worksheets serve? If you already know your "math facts," you surely don't need them. If you don't know them, the worksheet does nothing to teach them; it simply reminds you that you are a failure in math. Children do benefit by committing to memory what have come to be known as "math facts." However, passively learning them by rote is not only unpleasant, it may also be counterproductive. When memorizing prevents children from actively thinking about and figuring out number solutions for themselves, there is little, if any, mental growth. …