activities to support conceptual understanding of spatial measurement lorraine males, shannon...
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Activities to Support Conceptual Understanding of Spatial Measurement
Lorraine Males, Shannon Sweeny, Nic Gilbertson, Funda Gönülateş
©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN
Strengthening Tomorrow’s Education in Measurement (STEM) Project
Agenda
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• Introductions• Reflecting on Measurement• A Look at Some National Data• Measurement Tasks• Discussion
©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN
IntroductionsLorraine – 4th yr doctoral student, working on the STEM project all 4
years, taught secondary methods, currently supervising interns, taught middle/high school mathematics for 8 years
Shannon – 4th yr doctoral student, taught elementary & middle school for 8 years (2 years as a math specialist), taught elementary math methods & currently supervise elementary interns @ MSU
Nic – 2nd year doctoral student, 2nd year on STEM project, taught middle school & high school math for 6 years, currently teaching elementary methods courses at MSU,
Funda – 3th yr doctoral student, working on the STEM project all 3 years, formerly taught middle school mathematics for 4 years
3©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN
Reflecting on MeasurementTake some time to think about and share your answer with a partner to the following:
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What are the key ideas you want your students to know about measurement?
What do you find challenging about teaching length, area and/or volume?
©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN
The Toothpick (Broken Ruler) Problem
“What is the length of the toothpick?”
[NAEP, Grade 4, 2003, Open response]
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Toothpick Performance Data[Grade 4, 2003, open response]
Response % Responding
2 ½ inches (correct)
10 ½ inches
3 ½ inches
Other
Omitted
6
20
14
23
42
2
©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN
Toothpick Performance Data
Response % Responding
2 ½ inches (correct)
58
10 ½ inches 13
3 ½ inches 20
8 ½ inches 7
7
Response % Responding
2 ½ inches (correct)
20
10 ½ inches 14
3 ½ inches 23
Other 42
Omitted 2
[Grade 8, 2003, multiple choice][Grade 4, 2003, open response]
©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN
Toothpick Results Over Time
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Percent Correct
Assessment Year 4th Grade 8th Grade
1996 24 64
2000 25 64
2003 20* 58*
* Statistically lower than 1996 and 2000.
NAEP results across three assessments
©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN
Measurement Tasks
Skim the tasks and choose as many as you can to focus on
Do the task and discuss with people near you
We are always looking for good tasks and so we will also be passing out some reflection cards which we
will collect to get your opinions of the tasks.
9©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN
Measurement TasksLength
Strange Rulers[original STEM task]
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VolumePacking a Truck
[Saxon, gr. 5/4]
Area Crazy Cakes
[Investigations, gr. 4]
Participant Thoughts on the Tasks• What key ideas about measurement might these
tasks help to elicit?
• How might these tasks address some of the challenges to the teaching and learning of measurement?
• What features of these tasks do you find productive or helpful in teaching / learning measurement?
11©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN
Why these Tasks?• Present non-conventional problems• Provide good avenues for discussions about
measurement• Provide problems in which there are multiple
solution paths• Highlight key conceptual ideas
- Units- Additivity
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Why these Tasks?
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Strange Rulers
(Length)
Crazy Cakes(Area)
Packing a Truck
(Volume)
Ruler construction
Measuring with ruler
Partitioning
Composing & Decomposing
Fractions
Equal area does not imply congruence
Meaning of volume
Finding volume w/
non-cube units
Connects to divisibility
UnitsAdditivity
Thank you!We want to thank the National Science
Foundation for funding this work
We want to thank you for coming!Please take a few minute to fill out our evaluation.
For more information :http://www.msu.edu/~stemproj
If you have any questions please e-mail us at: [email protected]
14©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN