measuring the measurement an analysis of spatial measurement in elementary & middle school...

Measuring the MeasurementMeasuring the MeasurementAn Analysis of Spatial

Measurement in Elementary & Middle School Curricula

Lorraine Males, Jack Smith, & the STEM Project team

An Analysis of Spatial Measurement in Elementary &

Middle School Curricula

Lorraine Males, Jack Smith, & the STEM Project team

Session OverviewSession Overview

Introductions Brief presentation of STEM results

for length, K–3 (Jack) Questions about the presentation Discussion about your teaching

measurement (Lorraine)

Introductions Brief presentation of STEM results

for length, K–3 (Jack) Questions about the presentation Discussion about your teaching

measurement (Lorraine)

Introducing yourselfIntroducing 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?

Your name, school, & community Your teaching assignment for 2008-

09 Your math curriculum (textbook) Do you teach measurement of

length, area, and/or volume?

Thought Question #1Thought Question #1

How do you feel about your current text’s approach to measurement?

Are you happy with it?

How do you feel about your current text’s approach to measurement?

Are you happy with it?

Thought Question #2Thought Question #2

Do you consider teaching measurement a challenge?

Why (or why not)?

Do you consider teaching measurement a challenge?

Why (or why not)?

Thought Question #3Thought Question #3

Have there been times when teaching measurement has gone

really well?

If so, what made it work out well (in your view)?

Have there been times when teaching measurement has gone

really well?

If so, what made it work out well (in your view)?

Thought Question #4Thought Question #4

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

measurement?

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

measurement?

What is STEM?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?

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?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

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 UnderstandingJust 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”

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”

Which Curricula?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

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

Coding Measurement Knowledge

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)

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 LengthFocus 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

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 FocusA 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)

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)

EM SFAW Saxon Grade K 1 2 K 1 2 K 1 2 Conceptual 28 52 26 5 140 77 4 7 24 Procedural 173 374 281 250 689 713 124 150 304 Conventional 9 52 12 1 50 62 3 8 24

What is Missing?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.

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.)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

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 IterationExamples 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

[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 IterationFrequencies of Unit Iteration EM SFAW Saxon Total

Kindergarten 1 1 0 2 Grade 1 5 3 3 11 Grade 2 1 1 2 4 To tal 7 5 5 17

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

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

ClosingClosing

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)

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)