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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
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