Reflection: Developing a Conceptual Understanding The Decimal Slide - Section 4: Exploration


When I started asking my students to explain their thinking I realized I didn't always understand their response. The language they use is not always the same as the language I use and is usually not mathematically precise. At first I felt really nervous about this and was afraid of not knowing what they would say or knowing how to respond if what they said didn't make sense to me. Sometimes I would have to go back after class and look at the video again, sometimes with a colleague, before I could "hear the math" in their words. I noticed that the more I practiced listening to them the more I started understanding what they meant. When I didn't I found that asking a specific set of question helped me dig deeper:

"what do you mean by that?"

"can you show me what you mean?"

"when you say _____, what do you mean?"

Even admitting that I didn't understand the explanation was fine as long as I stuck around and tried. They felt that I was taking an interest in their thinking and that their ideas had value. They also often felt that they were teaching me something about the math, which they often were. The best part is being able to use their insight to help others gain deeper understanding. 

I asked one of my students "how do we know where the decimal point goes when we find 10%?" and I didn't understand her response at first. But when I probed a little further I realized she was talking about the decimal slide in a way that would really help the other students understand that it is NOT the decimal moving, but the numbers. I had never heard a student come up with the idea that the digit reduces by a magnitude of ten and therefore shifts in place value before and had never imagined what the idea might sound like in "kid-speak", so I didn't recognize it at first. 


  Developing a Conceptual Understanding: Listening to students
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The Decimal Slide

Unit 8: Exploring Rational Numbers
Lesson 16 of 20

Objective: SWBAT mentally calculate 10% of any number.

Big Idea: Students connect to prior knowledge of place value and fraction sense to help understand the "decimal slide".

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Math, Fractions, Number Sense and Operations, Decimals, Place Value, percent, proportional relationships, prior knowledge, Mental Math, ratios, equivalence, box diagra, rational numbers
  54 minutes
different representations
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