Conceptual Development in Area Measurement

1
Conceptual Development in Area Measurement

• Funda Gonulates, Lorraine Males, Nic Gilbertson
• Strengthening Tomorrows Education in Measurement
  (STEM) Project
• Michigan State University

MCTM Conference 2010 Dakota High School
2
Welcome

• Wed like to take some time for everyone to
  introduce themselves
• Name
• Position
• Grade level
• District/School

3
Area

• Take some time to think about and share your
  answer to the following

• What is area?
• What issues or difficulties do you think students
  might have with area measurement?

4
Pentagon Task

• Find the area
• Draw a second pentagon with the same area

5
Pentagon Task

• With a partner,
• Share your solutions
• What might students have difficulties with in
  solving this problem?
• What would students need to know in order to
  solve this problem?

6
Pentagon Task NAEP results

• Scoring Rubric
• Incorrect (both parts a b incorrect)
• Partial (either a or b correct)
• Correct (both a b correct)
• Omitted
• Off Task

7
Pentagon Task NAEP results

• Scoring Rubric
• Incorrect (both parts a b incorrect)48
• Partial (either a or b correct)47
• Correct (both a b correct)2
• Omitted2
• Off Task(rounded to 0)

8
Pentagon Task NAEP results

• Grade 8 2005
• Scoring Rubric
• Incorrect (both parts a b incorrect)48
• Partial (either a or b correct)47
• Correct (both a b correct)2
• Omitted2
• Off Task(rounded to 0)

9
STEM Who, Where, and When
Strengthening Tomorrows Education in Measurement

• Who
• PI Dr. Jack Smith
• Research Assistants Dan Clark, Kuo-Liang Chang,
  Leslie Dietiker, Hanna Figueras, Nic Gilbertson,
  Funda Gonulates, Pat Greeley, Jia He, Kosze Lee,
  Lorraine Males, Aaron Mosier, Matt Pahl, Gulcin
  Tan Sisman, Shannon Sweeny, Alexandria Theakston
• When
• 2007 present
• Where
• Michigan State University
• Work beginning in various districts throughout
  Michigan including Eastern UP, Grand Rapids,
  Jackson, Kalamazoo, Oakland

10
STEM What

• What
• Research
• analyzing the capacity of three written
  elementary curricula to support robust learning
  of spatial measurement (length, area, volume)
• Professional Development
• worked with pre-service teachers during their
  year-long internship on measurement lesson study
• working with facilitators throughout Michigan
  who are in turn working with teachers in their
  areas

11
STEM Three Curricula

• The three carefully chosen curricula are
• Scott Foresman-Addison Wesley Mathematics
• UCSMPs Everyday Mathematics
• Saxon Math

12
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)

13
STEM Area Core Principles

• Area as a measurable quantity
• Conservation under partitioning.
•  Conservation under motion 
• Identical Units
• Unit iteration 
• Transitivity
• Spatial structure of rectangular arrays
• Multiplicative composition from lengths

14
STEM Area AnalysisFlow of Area Topics
Analysis of area content in all curricula K-4
(Gonulates Mosier, 2010)
15
Area Lesson Analysis SFAW Grade 3, P.468A
16
Area Lesson Analysis SFAW Grade 3, P.468
17
(No Transcript)
18
(No Transcript)
19
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 starting this fall you can
  go to http//www.msu.edu/stemproj
• If you have any questions please e-mail us at
  stemproj_at_msu.edu