This week students worked on telling time to the half hour. I taught students about telling time to the half hour by showing them the clock and reviewing times to the hour. We worked with half hours on the large demonstration clock, on small clocks that students had, and in writing on the whiteboard. Most students appeared to understand the concept of telling time to the half hour. Students worked in their math journals and were supposed to write the time such as "half-past 4 o'clock" under the clock that showed 4:30. The particular student work that I examined was of one boy. Below the clock that showed 2:30, he wrote "half-past 6". He wrote similar answers for other problems.
This student currently understands that the time on the clock does not show a time to the hour. He understands that when the minute hand points at 12, the clock shows whichever hour the hour hand is pointing to. He understands that this particular clock problem does not show 6 o'clock. The gap in his understanding is that he does not understand how to read the clock hands to find out that the time is half-past 2. He may think that when the minute hand points to 6, that the time is showing half-past 6. Another gap in his thinking is that he did not take into account the hour hand at all. He does not yet understand that the minute hand that used to always be pointing to the 12 is now pointing to the 6. This may be a confusing concept for him since we have only worked with times to the hour up to this point.
A way to advance his thinking would be to have him compare two clocks that show different times using the same hour. He could compare a clock that shows 2:30 with one that shows 2:00. This would help him to notice the placement of the minute hand. A further way to advance his thinking would be to have him compare two clocks that do not have the same hour and have him state the times. These two times could be 4:00 and 9:30. This may help him to see more examples of times and how to read the times. One question I may ask him if I had the opportunity would be to explain his thinking behind writing "half-past 6" on his journal page. I want to know which hands he is looking at while he is reading the time. One future math task that he would benefit from is hearing a time said to him and showing the time on his own clock. This would help him to maneuver the clock hands in a way that helped him remember where each hand belongs.
Good analysis! I would encourage you to think about how this student's thinking fits in with the thinking of the rest of the class. Do other students have similar misconceptions? What might a productive class discussion around this understanding or concept look like?
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