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# Measuring the Measurement PowerPoint PPT Presentation

Measuring the Measurement. An Analysis of Spatial Measurement in Elementary & Middle School Curricula Lorraine Males, Jack Smith, & the STEM Project team. Session Overview. Introductions Brief presentation of STEM results for length, K–3 (Jack) Questions about the presentation

Measuring the Measurement

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## Measuring the Measurement

An Analysis of Spatial Measurement in Elementary & Middle School Curricula

Lorraine Males, Jack Smith, & the STEM Project team

### Session Overview

• Introductions

• Brief presentation of STEM results for length, K–3 (Jack)

### Introducing yourself

• Your name, school, & community

• Your teaching assignment for 2008-09

• Do you teach measurement of length, area, and/or volume?

### Thought Question #1

Are you happy with it?

### Thought Question #2

Do you consider teaching measurement a challenge?

Why (or why not)?

### Thought Question #3

Have there been times when teaching measurement has gone really well?

If so, what made it work out well

### Thought Question #4

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

### 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?

### 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

### 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

### Which Curricula?

• Elementary

• Everyday Mathematics (Standards-based)

• Saxon Mathematics (different from both)

• Middle School

• Connected Mathematics Project

• Glencoe’s Mathematics, Concepts & Applications

• Saxon Mathematics

### 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)

### 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

### 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)

### 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.

### 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

### 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

### Frequencies of Unit Iteration

• Not many total instances

• Half (n = 9) are partial statements

• Disappointing drop off in Grade 2

### 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)