Measuring the Measurement

1
Measuring the Measurement

• An Analysis of Spatial Measurement in Elementary
  Middle School Curricula
• Lorraine Males, Jack Smith, the STEM Project
  team

2
Session Overview

• Introductions
• Brief presentation of STEM results for length,
  K3 (Jack)
• Questions about the presentation
• Discussion about your teaching measurement
  (Lorraine)

3
Introducing yourself

• Your name, school, community
• Your teaching assignment for 2008-09
• Your math curriculum (textbook)
• Do you teach measurement of length, area, and/or
  volume?

4
Thought Question 1

• How do you feel about your current texts
  approach to measurement?
• Are you happy with it?

5
Thought Question 2

• Do you consider teaching measurement a challenge?
• Why (or why not)?

6
Thought Question 3

• Have there been times when teaching measurement
  has gone really well?
• If so, what made it work out well
• (in your view)?

7
Thought Question 4

• What do you look for as indicators that your
  students understand measurement?

8
What is STEM?

• Strengthening Tomorrows Education in Measurement
• A very careful examination of the spatial
  measurement content of 3 elementary 3 middle
  school curricula
• Do our present texts provide students with
  sufficient opportunity to learn measurement?

9
Why do this?

• Measurement is important mathematics
• Our students dont show they know /understand
  what we want them to
• Textbooks are important, for both students and
  teachers
• Deficits there would be hard to fix

10
Just a bit on Understanding

• A National Assessment (NAEP) item How long is
  the toothpick?
• Choices 2.5 inches 8 inches 10.5 inches 3.5
  inches
• 2025 of U.S. 4th graders and 60 of U.S. 8th
  graders answer correctly
• 20 of 8th graders answer 3.5 inches

11
Which Curricula?

• Elementary
• Everyday Mathematics (Standards-based)
• Scott-Foresman/Addison-Wesleys Mathematics
  (publisher-developed)
• Saxon Mathematics (different from both)
• Middle School
• Connected Mathematics Project
• Glencoes Mathematics, Concepts Applications
• Saxon Mathematics

12
Coding Measurement Knowledge

• Count all instances of three different kinds of
  knowledge
• Conceptual (basic principles)
• Procedural (measurement processes)
• Conventional (notations tools)
• Watch for how knowledge is expressed (e.g.,
  statements vs. questions)

13
Focus on Length

• Completed the analysis of Grades K-3
• This is where the foundation of length is
  presented (and learned?)
• Our focus today will be on the holes we have found

14
A Common Procedural Focus

• Procedural percentages (of all elements)
• K 82 (EM) 98 (SFAW) 95 (Saxon)
• Grade 1 78 (EM) 78 (SFAW) 91 (Saxon)
• Grade 2 88 (EM) 84 (SFAW) 86 (Saxon)

15
What is Missing?

• Unit iteration (a conceptual element)
• You have a length unit
• You move it (iterate it) along the object
• You count units (to accumulate distance)
• Our phrasing Measures of length are produced by
  iterating a length unit from one end of an
  object, segment, or distance to the other and
  then counting the number of iterations. Iterated
  units may not overlap or leave gaps.

16
What is Missing? (cont.)

• Why is Unit Iteration important?
• Not clear that students understand how rulers are
  tools that iterate units for them
• Remember the broken ruler problem

17
Examples of Unit Iteration

• See the sheet of examples
• Most examples are partial have gaps
• Key missing element motion unit sweeping
  through the object or distance

18
Frequencies of Unit Iteration

• Not many total instances
• Half (n 9) are partial statements
• Disappointing drop off in Grade 2

19
Closing

• Questions???
• Well be back next year with more results (e.g.,
  area, primary grades)
• If you are interested in this work, we would
  like to work with you
• E-mails maleslor_at_msu.edu (Lorraine)
  jsmith_at_msu.edu (Jack)