Transcript Levine and Ratliff

Improving Children’s Understanding of
Units of Measure: A Training Study
Classroo
m
Lab
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)
Aligned ruler
1
2
3
Misaligned ruler
4
5
6
7
8
1
3
2
4
5
6
7
inches
Aligned coins
1
2
3
8
inches
Misaligned coins
4
5
6
7
8
inches
1
2
3
4
5
6
7
8
inches
Results for the kindergarteners
Study 1 (K) : Ruler
ruler
100
Mean Percent Correct
Mean Percent Correct
Study 1coins
(K): Coins
80
60
40
20
0
High SES
High
Low SES
Low
SES
SES
100
80
60
aligned
aligned
40
misalinged
misaligned
20
0
High SES
High
Low
SES
Low
SES
SES
Results for the 2nd graders
Study
1 (2-G) : Ruler
ruler
100
Mean Percent Correct
Mean Percent Correct
Study 1 (2-G):
Coins
coins
80
60
40
20
0
High SES
High
Low SES
Low
SES
SES
100
80
60
aligned
aligned
40
misalinged
misaligned
20
0
High SES
High
Low
SES
Low
SES
SES
Study 2A: No Numbers
Aligned ruler
Misaligned ruler
Aligned circles
Misaligned circles
Results
Study coins
2A: Coins
circles
Study 2A:ruler
Ruler
100
Mean Percent Correct
Mean Percent Correct
100
80
80
60
aligned
60
aligned
aligned
mismisalinged
aligned
misalinged
40
40
20
20
0
0
Kindergarteners
KHigh
2ndG-2
graders
Kindergarteners
KHigh
2nd graders
G-2
Study 2B: Numbers
Aligned ruler
1
3
2
Misaligned ruler
4
5
6
7
8
1
3
2
4
5
6
7
inches
Misaligned circles
Aligned circles
1
2
3
4
5
8
inches
6
7
8
1
2
3
4
5
6
7
8
Results
Study
2B: Coins
circles
Studyruler
2B: Ruler
ruler
100
Mean Percent Correct
Mean Percent Correct
100
80
60
80
60
aligned
aligned
aligned
mismisalinged
aligned
misalinged
40
40
20
0
20
0
G-2
High
Kindergarteners
K
High
K
2ndG-2
graders
Low
G-2
High
Kindergarteners
K
High
2ndG-2
graders
• Development of Training Study
– Engage spatial thinking during task
– Use the ruler as a spatial tool
80
70
60
50
Pre-test
Post-test
40
30
20
10
0
Control
Training
• Children improve on measuring misaligned
items following training
• Learning is maintained after a 1 week delay
• 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