Framing the Analysis of Written Measurement CurriculaMichigan State University

Research Questions

Project Background

• What is the capacity of U.S. K – 8 written and enacted curricula to support students’ robust learning of measurement?

Rationale

What is Measurement?

Types of Measurement

Contexts

Pre-measurement -- Comparative, non-metric measurement, such as determining which of two objects is longer

Measurement Proper – The iteration of a spatial unit (and possibly subunit) to quantify the spatial attribute of an object or figure

Reasoning with or about measurement -- Reasoning with or about spatial quantities, such as determining the time it takes to travel a certain distance at a given constant rate or using the Pythagorean Theorem to find the length of the side of a triangle

We have limited our focus to SpatialMeasurement of length, area, and volume.

Beyond traditional measurement content,several other content strands involve spatialmeasurement:

• Looking at this bar graph, what food is most popular for lunch?

• Given part of a figure and the line of symmetry draw the other part

• Given a square draw lines that divide the square into fourths.

Research Team

Principal Investigator: Dr. Jack Smith, MSU

Project Team:

Gulcin Tan Sisman (METU), Kuo-Liang Chang, Leslie Dietiker, Hanna Figueras, Pat Greeley, KoSze Lee, Lorraine Males, Aaron Mosier, Matt Pahl

Types of Knowledge• Conceptual knowledge concerns the basic

principles that underlie and justify measurement procedures, systems, notations, and tools.

• Procedural knowledge concerns the processes of measuring and estimating the three spatial quantities.

• Conventional knowledge concerns the systems, notations, and tools that human have invented to carry out measurement in standardized ways.

Why focus on spatial measurement?

• Poor national performance (NAEP)

• U.S. 8th graders lag further behind other developed countries in this content area (TIMSS; National Center of Education Statistics, 1997)

• Largest gap between white students and black and Hispanic students is greatest in this content area (Lubienski, 2003)

• Important for both college-bound and work- bound students

• Research has documented errors and misconceptions in measurement, but has not given any

explanation of the difficulty and the problem cannot be addressed without an explanation

Conceptual Coding Scheme

Sample coding shown for p. 341 of SFAW Grade 1

Sta

tem

ents

Qu

esti

ons

Dem

onst

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ons

Wor

ked

Exa

mp

les

Pro

ble

ms

Gam

es

CO

NC

EP

TU

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[6

2 L

engt

h] Meaning/Definition of the Quantity of Length

Length quantifies distance along a path. 1

(A)

Unit-measure Compensation Larger units of length produce smaller measures of length; smaller units of length produce larger measures.

1 (B)

1 (C)

1

(D)

PR

OC

ED

UR

AL

[3

5 L

engt

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Measure Segment/Object/Distance with Sufficient Number of Non-Standard Units: Select an object that shorter than the segment/object/distance to be measured (the target). Place a series of those objects end to end, starting from one end of the target object, until that series is as long as the target. Count the number of smaller objects ( = X). The length of the target is X small objects.

4

(E, F)

8

(G, H, I)

Direct Comparison: To compare the lengths of two or more objects, align them next to each other and see which is “taller” or if they are the same length. Only comparative judgments are possible (e.g., taller/shorter, longer/shorter, the same).

3

(J, K)

2

(L)

CO

NV

EN

TIO

NA

L

[8 L

engt

h]

Basic Ruler/Measuring Tape Construction Rulers and measuring tapes often have a customary side and a metric side, with inch units on one side and centimeters units on the other. The zero mark, which may or may not be labeled, is located at the one end of rulers and at the “free end” of measuring tapes. Common rulers are one-foot, yardstick, and meter stick.

Saxon Math, 2007,Saxon Publishers, Course 2 (MS), p. 108 Michigan Mathematics, Scott Foresman Addison Wesley, Grade 1, p. 341Everyday Mathematics, 2007, Wright Group/McGraw Hill, Grade 1, p. 287

J

C

D

A

K

F

E

G

I

B

HL

Locate Measurement

Content

Locate Measurement

Content

Design Basic

Framework

Design Basic

Framework

Generate Knowledge Elements

Generate Knowledge Elements

Code Measurement

Content

Code Measurement

Content

Compile ResultsCompile Results

DevelopmentProcess