exploring spatial measurement through a...
TRANSCRIPT
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Exploring Spatial Measurement through a
Conceptual Lense Lorraine Males, Funda Gonulates, Shannon
Sweeny, & Nic Gilbertson
Strengthening Tomorrow’s Education in Measurement (STEM) Project
Michigan State University
©STEM @ MSU 2011 – Math in Action, Grand Valley State University
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Introductions Lorraine – 4th yr doctoral student, working on the STEM
project all 4 years, formerly taught middle school/high school mathematics for 8 years
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Funda –
Shannon –
Nic –
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Agenda
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• Introductions
• Reflection on Measurement
• Introduction to the STEM Project
• Data from the STEM project
• National Data
• Working with some tasks
• Sharing/Summarizing
• Evaluation
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Measurement Take some time to think about and share
your answer with a partner to the following:
4
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?
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The STEM Project • Initial situation
– Problem was recognized; no explanation – So no idea about where to invest in a “solution”
• STEM I: Examine the curricular contribution (elementary curricula) – Two years (Fall 2007- Fall 2009) – Do current US elementary mathematics provide
sufficient “opportunity to learn” (OTL) spatial measurement
• STEM II: Put what we have learned to work
– Three years (August 2009 – July 2012) – PD is one project component
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STEM – Three Curricula
The three carefully chosen curricula are:
Scott Foresman-Addison Wesley Mathematics
UCSMP’s Everyday Mathematics
Saxon Math
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STEM methods
Step 1: Find the spatial measurement content
– Should be easy: look at measurement lessons & units
– More complicated
– Err on the inclusive side (don’t ignore opportunities)
– Two independent coders
Step 2: Code the resulting spatial measurement content
– All pages with L, or A, or V content
– List of measurement knowledge in small bits
– Code each bit of text on all pages with measurement content
– Two independent coders
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STEM – Our Analysis
In our analysis we are looking at every lesson, problem, and activity of teach curricula for two important aspects:
Knowledge elements - Spatial measurement knowledge (conceptual, procedural, conventional)
Textual elements - The ways in which this knowledge is expressed (statements, demonstrations, worked examples, questions, problems, games)
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Some Results (LENGTH)
• All three curricula are heavily Procedural (more than 75% of all codes, all curricula, Grades K–3)
• Common procedures
– Direct Comparison
– Visual & Indirect Comparison
– Measure with Rulers
– Draw segments
– Find perimeter
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More Results (LENGTH)
• Conceptual knowledge is addressed, but with gaps
Element Frequency
Definition of length Uncommon; hard to do
Greater <=> Longer Very common
Unit-measure compensation Pretty common
Unit Iteration Uncommon; gaps & overlaps
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Some Results (AREA)
• Even more procedural, across curricula and grades (K–4); 88% or more of all codes
• Common procedural sequence – Focus on Visual Comparison (which 2-D shape is
larger/bigger?) in primary grades – Next, covering shapes with same units and counting
them – Finally, computational procedures, beginning with
rectangles • Area is defined as a quantity in Grade 2 (all curricula) • Weaker attention to Unit Iteration for area than length
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Some Preliminary Results (VOLUME)
• Hard work (problems of conceptual clarity & duration)
• Capacity (property of containers, continuous quantity) is interleafed with volume (filling and counting, discrete quantity)
• Introduced in K, present throughout elementary grades, slow development
• Primary focus (K & 1): Capacity
• Gradual shift from Capacity to Volume across the grades
• Thus far, only Grades K–3; will code Grade 4 in early 2011
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Major Lessons
• Conceptual foundations of measurement are weakly developed
• Weak attention to Unit Iteration (length & area)
• Conjecture: The sheer extent of visual content on the page (esp. for EM & SFAW) may make it hard for teachers to find and focus on the conceptual content
• Implication: Teachers will need to enrich the curriculum as written
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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, large national sample]
Response % Responding
2.5 inches (correct) 20
10.5 inches 14
3.5 inches 23
Other 42
Omitted 2
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Lessons from Toothpick
• We are not doing so well nationally
• Too many kids don’t understand length measurement, rulers, or both
• Some errors are sensible; some remain mysterious
• Not obvious what we are doing wrong
• => Not obvious what we should change
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Some Measurement Tasks
• Crazy Rulers (Length) – original STEM task
• Crazy Cakes (Area) – Investigations, grade 4?/DMI
• Finding the Volume (Volume) – Everyday Mathematics, grade 4?
Your task:
• Pick one of these tasks
• Complete the task
• With your group members answer the following question: What would a student need to understand about measurement in order to successfully complete this task? [Record on your poster paper]
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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]
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