Measurement of Time
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Here is a word of explanation before we address the measurement of time. We have no doubt about the reader's ability to tell time. This topic, as treated in this text, is not about learning to tell time. However, in order to teach children to tell time, the reader needs to understand some of the difficulties that children have with time-telling and with learning to tell time. In this particular case, pedagogical content knowledge means learning and understanding why children have difficulty learning to tell time. This is a surprisingly difficult topic for children.
Learning to tell time on a clock with hands and a face (an analog clock) has always been surprisingly challenging for children. Although this topic has traditionally been a part of the first grade curriculum, many children, even children who learn mathematics easily, have had difficulties learning to tell time on analog clocks. With the introduction of digital clocks many years ago, children have found it to be even more difficult to learn to tell time on analog clocks. Why are analog clocks difficult for children, and why does the presence of digital clocks make this even more difficult? First we will examine the digital clock question, and then we will explore the question about children's difficulty with analog clocks.
For children, the presence of digital clocks and the readouts from digital clocks are realities of their lives from the time they are born. Children see digital clock readouts even before they are able to recognize what numbers are. They are able to observe that the adults in their lives place quite a bit of importance on these instruments, but they don't know why. As children come to understand the importance of schedules and the importance of time, they also develop an awareness of numbers. As preschoolers they learn to recognize the basic digits, and they learn their names. However, there are some unusual features about the numbers they see on digital clocks. First of all, there are always three or four digits showing. There are never more than four digits. Second, if children pay attention to the digital readouts, they will notice something very unusual. The counting that those readouts report is unlike any other counting that the children see and hear. The number that comes after 59 is 00. The numbers on the right change, but the number on the left rarely does. When the number on the left does change, it only goes as high as 12. Then it turns into a 1. There is also an unusual symbol in place (the : ), although most children will not notice this at first. Children can observe all of these unusual features of digital clock readouts, and rarely do adults explain any of it to them. Children may develop the ability to read the number off the readout, but its meaning is not necessarily clear to them. Sometimes when they see or hear a number like "eight thirty-five" it is in the morning, and sometimes they see or hear this number at night. And yet, they observe that adults seem to do things in response to the numbers. It is all very confusing and appears to children to be random and unorganized.
Elementary Mathematics: Pedagogical Content Knowledge, by James E. Schwartz, is designed to sharpen pre-service and in-service teachers' mathematics pedagogical content knowledge. The five "powerful ideas" (composition, decomposition, relationships, representation, and context) provide an organizing framework and highlight the interconnections between mathematics topics. In addition, the text thoroughly integrates discussion of the five NCTM process strands.
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