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, K–3 (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 text’s 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 Tomorrow’s 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 don’t 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 • 20–25% 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-Wesley’s Mathematics (publisher-developed) • Saxon Mathematics (different from both) • Middle School • Connected Mathematics Project • Glencoe’s 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??? • We’ll 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@msu.edu (Lorraine); jsmith@msu.edu (Jack)