measuring the measurement an analysis of spatial measurement in elementary & middle school...
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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: [email protected] (Lorraine); [email protected] (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: [email protected] (Lorraine); [email protected] (Jack)