The student sample that I chose was from the student's
homework this week. The homework assignment had students draw a picture of an
interesting clock or watch that they see in their homes. The student drew a
clock with roman numerals on it. Each roman numeral was written correctly
around the outside of the clock. The student also drew two hands on the clock,
one shorter and one longer. I was very surprised that the student drew this
because students have not explored roman numerals at this time. A family member
could have assisted the student with finding the interesting clock, but I still
think it's a very interesting sample of work.
This reveals that the student currently understands that
other symbols can be on clocks and watches and that they are still clocks and
watches without visual numbers on them. The student also understands that there
are two hands on the clock, with one shorter and one longer. The sample reveals
that there are gaps in this students thinking. The student was not required to
locate this clock on her own, so an adult may have assisted her. She could have
simply copied down the symbols of the roman numerals without having
understanding that they represented numbers.
If I could ask this student a question about her work, I
would ask her what the symbols mean that she drew. I would see if she knew that
roman numerals corresponded with numbers. A way to advance this students
thinking would be to show her many clocks that have different numerical values
(one with only the 12, 3, 6, 9; one with no numbers but tick marks; one with
only the 12 and 6; one with roman numerals). I would have this student compare
the clocks to see what she noticed and if she thought they were all still clocks
even though they looked differently. I might advance her thinking about what
the two hands on the clock mean in a more complex way. In class, we talked
about the minute and hour hands, but we mostly explored telling time to the
hour. I would work with her to practice telling other times than just to the
hour, so that she is using the minute hand, as well. A future math task that
she might benefit from is telling time on one of these less common clocks. This
would help her to estimate time by using a clock with only 12, 3, 6, and 9.
I think your ideas for advancing the student's thinking are very good, and all lead students closer towards thinking about the "big ideas" or clocks and time telling. This case is also a good example of not necessarily knowing the full story of the student's understanding just from what they show (e.g., does the student really understand roman numerals? or what they represent in the context of clock?). This leads to a number of follow-up problems and questions that are necessary in order to fully explore what the student understands, as you detail in your analysis.
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