Improving Children’s Understanding of Units of Measure: A Training Study

Susan C. Levine & Kristin R. Ratliff

University of Chicago

Measurement• Measurement skills lag behind

all other mathematics topics (National Center for Education Statistics, 1996)

• Particularly difficult:– Items not aligned with the start of a ruler

Study 1: Continuous (ruler) vs. Discrete (coins)

1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

inches

1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

inches

1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

inches

1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

inches

Aligned ruler Misaligned ruler

Aligned coins Misaligned coins

Results for the kindergarteners

Study 1 (K) : Ruler

0

20

40

60

80

100

High SES Low SES

SES

Mean

Perce

nt Co

rrect

aligned

misalinged

Study 1 (K): Coins

0

20

40

60

80

100

High SES Low SES

SES

Mean

Perc

ent C

orrec

t

coins ruler

High Low High Low

aligned

mis-aligned

SES SES

Results for the 2nd graders

Study 1 (2-G) : Ruler

0

20

40

60

80

100

High SES Low SES

SES

Mean

Perce

nt Co

rrect

aligned

misalinged

Study 1 (2-G): Coins

0

20

40

60

80

100

High SES Low SES

SES

Mean

Perc

ent C

orrec

t

coins ruler

High Low High LowSES SES

aligned

mis-aligned

Study 2A: No Numbers

Aligned ruler Misaligned ruler

Aligned circles Misaligned circles

Results

coinsStudy 2A: Coins

0

20

40

60

80

100

Kindergarteners 2nd graders

Mean

Perce

nt Co

rrect

aligned

misalinged

circles

HighK G-2

Study 2A: Ruler

0

20

40

60

80

100

Kindergarteners 2nd graders

Mean

Perce

nt Co

rrect

aligned

misalinged

ruler

aligned

mis-aligned

HighK G-2

Study 2B: Numbers

1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

inches

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

inches

1 2 3 4 5 6 7 8

Misaligned rulerAligned ruler

Aligned circles Misaligned circles

Results

Study 2B: Coins

0

20

40

60

80

100

Kindergarteners 2nd graders

Mean

Perce

nt Co

rrect

aligned

misalinged

circles

HighG-2 KHigh LowK G-2

Study 2B: Ruler

0

20

40

60

80

100

Kindergarteners 2nd graders

Mean

Perce

nt Co

rrect

aligned

misalinged

aligned

mis-aligned

rulerruler

HighG-2HighK G-2

• Development of Training Study– Engage spatial thinking during task– Use the ruler as a spatial tool

• Children improve on measuring misaligned items following training

• Learning is maintained after a 1 week delay

0

10

20

30

40

50

60

70

80

Control Training

Pre-test

Post-test

• Training effectively corrects the counting strategy but not the read-off strategy

• Both groups understood inverse relations and correctly used units of different sizes

Geographic Learning• Using Maps

• Units of Distance– Using scale as

measurement– Taking into account

differences in scale requires concept of units