The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving.
Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). Journal of Educational Psychology, 101(4), 836–852. Retrieved from: https://eric.ed.gov/?id=EJ860917
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examining95Students, grades7-8
Practice Guide
Review Details
Reviewed: January 2023
- Practice Guide (findings for Comparing multiple examples–Rittle-Johnson et al. (2009))
- Randomized Controlled Trial
- Meets WWC standards without reservations because it is a randomized controlled trial with low attrition.
This review may not reflect the full body of research evidence for this intervention.
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Findings
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
Conceptual knowledge (% correct) |
Comparing multiple examples–Rittle-Johnson et al. (2009) vs. Other intervention |
0 Days |
Used any algebra at pre-test (Compare methods vs. Sequential);
|
N/A |
N/A |
No |
-- |
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
Procedural flexibility use (% use of methods) |
Comparing multiple examples–Rittle-Johnson et al. (2009) vs. Other intervention |
0 Days |
Used any algebra at pre-test (Compare methods vs. Sequential);
|
N/A |
N/A |
No |
-- | |
|
Procedural flexibility (% correct) |
Comparing multiple examples–Rittle-Johnson et al. (2009) vs. Other intervention |
0 Days |
Used any algebra at pre-test (Compare methods vs. Sequential);
|
N/A |
N/A |
No |
-- |
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
Procedural knowledge (% correct) |
Comparing multiple examples–Rittle-Johnson et al. (2009) vs. Other intervention |
0 Days |
Used any algebra at pre-test (Compare methods vs. Sequential);
|
N/A |
N/A |
No |
-- |
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Sample Characteristics
Characteristics of study sample as reported by study author.
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Female: 57%
Male: 43% -
Urban
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Massachusetts
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Race Asian 9% Black 9% Other or unknown 9% White 73% -
Ethnicity Hispanic 9% Not Hispanic or Latino 91%
Study Details
Setting
11 classrooms in a low-performing urban middle school in Massachusetts.
Study sample
Out of 239 students in the overall intervention, 136 (56.9%) were female. 73% of students were white, and 9% each were African-American, Hispanic, and Asian.
Intervention Group
The intervention took place over three days. All students received a whole-class lesson with students attempting a problem and the instructor then solving. All participants then received packets containing 24 worked examples (algebra problems with the solution method displayed). Half the problems illustrated a conventional solution method and half illustrated a short cut. There were three types of problems. Student were assigned to pairs and pairs began working on the packets; students described their solution method and discussed accompanied questions. In the compare methods condition, a worked example was presented and solved two different ways (conventional and shortcut) on the same page--facilitating comparisons. An additional difference between conditions occurred at the end of the daily session when all students were given four practice problems, asked to solve the problems on their own, compare with their partner, and have the answers checked by an adult. In the compare methods condition only, students were presented with two problems and asked to solve each of the problems using both of the two different solution methods.
Comparison Group
In Sequential condition each worked example was presented on a different page. At the end of session, students were presented with four problems and allowed to choose their solution method.
Support for implementation
Members of the project team visited classes during the intervention and helped students to implement steps of problem solving but did not assist students in choosing solution methods or steps.
Practice Guide
Review Details
Reviewed: January 2023
- Practice Guide (findings for Comparing multiple examples–Rittle-Johnson et al. (2009))
- Randomized Controlled Trial
- Meets WWC standards without reservations because it is a randomized controlled trial with low attrition.
This review may not reflect the full body of research evidence for this intervention.
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Findings
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
Conceptual knowledge (% correct) |
Comparing multiple examples–Rittle-Johnson et al. (2009) vs. Other intervention |
0 Days |
Use no algebra at pre-test (Compare methods vs. Sequential);
|
N/A |
N/A |
No |
-- |
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
Procedural flexibility use (% use of methods) |
Comparing multiple examples–Rittle-Johnson et al. (2009) vs. Other intervention |
0 Days |
Use no algebra at pre-test (Compare methods vs. Sequential);
|
N/A |
N/A |
No |
-- | |
|
Procedural flexibility (% correct) |
Comparing multiple examples–Rittle-Johnson et al. (2009) vs. Other intervention |
0 Days |
Use no algebra at pre-test (Compare methods vs. Sequential);
|
N/A |
N/A |
No |
-- |
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
Procedural knowledge (% correct) |
Comparing multiple examples–Rittle-Johnson et al. (2009) vs. Other intervention |
0 Days |
Use no algebra at pre-test (Compare methods vs. Sequential);
|
N/A |
N/A |
No |
-- |
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Sample Characteristics
Characteristics of study sample as reported by study author.
-
Female: 57%
Male: 43% -
Urban
-
- B
- A
- C
- D
- E
- F
- G
- I
- H
- J
- K
- L
- P
- M
- N
- O
- Q
- R
- S
- V
- U
- T
- W
- X
- Z
- Y
- a
- h
- i
- b
- d
- e
- f
- c
- g
- j
- k
- l
- m
- n
- o
- p
- q
- r
- s
- t
- u
- v
- x
- w
- y
Massachusetts
-
Race Asian 9% Black 9% Other or unknown 9% White 73% -
Ethnicity Hispanic 9% Not Hispanic or Latino 91%
Study Details
Setting
11 classrooms in a low-performing urban middle school in Massachusetts.
Study sample
Out of 239 students in the overall intervention, 136 (56.9%) were female. 73% of students were white, and 9% each were African-American, Hispanic, and Asian.
Intervention Group
The intervention took place over three days. All students received a whole-class lesson with students attempting a problem and the instructor then solving. All participants then received packets containing 24 worked examples (algebra problems with the solution method displayed). Half the problems illustrated a conventional solution method and half illustrated a short cut. There were three types of problems. Student were assigned to pairs and pairs began working on the packets; students described their solution method and discussed accompanied questions. In the compare methods condition, a worked example was presented and solved two different ways (conventional and shortcut) on the same page--facilitating comparisons. An additional difference between conditions occurred at the end of the daily session when all students were given four practice problems, asked to solve the problems on their own, compare with their partner, and have the answers checked by an adult. In the compare methods condition only, students were presented with two problems and asked to solve each of the problems using both of the two different solution methods.
Comparison Group
In Sequential condition each worked example was presented on a different page. At the end of session, students were presented with four problems and allowed to choose their solution method.
Support for implementation
Members of the project team visited classes during the intervention and helped students to implement steps of problem solving but did not assist students in choosing solution methods or steps.
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students
Review Details
Reviewed: April 2015
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students Practice Guide- Randomized Controlled Trial
- Meets WWC standards without reservations
This review may not reflect the full body of research evidence for this intervention.
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Findings
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Sample Characteristics
Characteristics of study sample as reported by study author.
-
Female: 57%
Male: 43% -
Urban
-
Race Asian 9% Black 9% White 72% -
Ethnicity Hispanic 9% Not Hispanic or Latino 91%
Improving Mathematical Problem Solving in Grades 4 Through 8
Review Details
Reviewed: May 2012
- Randomized Controlled Trial
- Meets WWC standards without reservations
This review may not reflect the full body of research evidence for this intervention.
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Findings
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Sample Characteristics
Characteristics of study sample as reported by study author.
-
Female: 57%
Male: 43% -
Urban
-
Race Asian 9% Black 9% White 72% -
Ethnicity Hispanic 9% Not Hispanic or Latino 91%
An indicator of the effect of the intervention, the improvement index can be interpreted as the expected change in percentile rank for an average comparison group student if that student had received the intervention.
For more, please see the WWC Glossary entry for improvement index.
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