During my 4th field experience, I had my students conduct an investigation of whether or not they could use a broken ruler to measure. Students used their knowledge to determine that measurement starts at a zero point, the starting point is flexible, and that units can be iterated. When sharing their ideas, students were asked to justify their thinking using mathematical language. They worked individually before sharing their ideas in a whole class discussion.
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During the discussion of Task A, measuring the smaller chocolate bar, the students expressed that the numbers on the ruler needed to be changed from 3, 4, 5 to 0, 1, 2 in order to measure since measurement starts at 0. The following conversation happened after this:
Me: "So now that we've changed the numbers on the ruler, what do we do?"
Student: "We measure the chocolate bar." Me: "We measure the chocolate bar. How are we going to do that?" Student: "You put the ruler to the chocolate bar." Me: "Like this?" Student: "No, the other way." Me: "Like this?" Student: "No, not that way." Me: "Do you want to come up and show me?" - Student comes up and shows how she measured the chocolate bar - Me: "Okay, so what are you doing?" Student: "Well I put the chocolate bar against the 1, and then I can measure how long it is. And it's 1 cm." |
By having the student come up, she was able to justify her thinking using mathematical language. This oral justification allowed for the other students to visually see as well as understand what her idea was in order to measure the chocolate bar with the broken ruler.
In the discussion surrounding Task B, in which the students were to decide if they could measure the longer chocolate bar with the broken ruler, a student came up to the board in order to use the cardboard ruler and chocolate bar to demonstrate his idea. In this, the students ideas were verbalized through me:
Me: So he lined it up... and then he moved it. Does everyone agree with what ____ did?
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By explaining to the class what the student did, I failed to provide him with the opportunity to explain his thinking. Next time, I will ask the student to "tell the class exactly what you are doing in order to measure the chocolate bar." I could also ask another student to revoice what the student just said in their own words.
This student initially did not understand the flexibility of the starting point, but understood that measurement starts at a zero point.
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This student understands that measurement starts at a zero point, as well as the flexibility of the starting point.
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Many students initially struggled with measuring the chocolate bar that is longer than the ruler in Task B. However, in order to differentiate, I provided rulers for some students and asked them to measure their desk with it. They were all successful in doing so, even though the desk was longer than their ruler. This provided students with a visual, concrete example of how to measure that is longer than their measuring tool. They were then able to apply this knowledge, along with the ideas discussed in Task A, to the problem.