Compared with What? The Effects of Different Comparisons on Conceptual Knowledge and Procedural Flexibility for Equation Solving
Rittle-Johnson, Bethany; Star, Jon R. (2009). Journal of Educational Psychology, v101 n3 p529-544. Retrieved from: https://eric.ed.gov/?id=EJ861179
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examining106Students, grades7-8
Practice Guide
Review Details
Reviewed: June 2019
- Practice Guide (findings for Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students)
- 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) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
0 Days |
"Types" vs "equivalent" comparison, where the intervention group saw two different types of equations solved with the same method.;
|
52.41 |
47.93 |
No |
-- | ||
| Show Supplemental Findings | |||||||||
|
Conceptual knowledge (% correct) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
2 Weeks |
"Types" vs "equivalent" comparison, where the intervention group saw two different types of equations solved with the same method. ;
|
55.22 |
54.33 |
No |
-- | ||
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|
|---|---|---|---|---|---|---|---|---|---|
|
Procedural flexibility use (% use of methods) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
0 Days |
"Types" vs "equivalent" comparison, where the intervention group saw two different types of equations solved with the same method.;
|
55.74 |
33.33 |
No |
-- | ||
|
Procedural flexibility (% correct) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
0 Days |
"Types" vs "equivalent" comparison, where the intervention group saw two different types of equations solved with the same method.;
|
59.40 |
53.37 |
No |
-- | ||
| Show Supplemental Findings | |||||||||
|
Procedural flexibility use (% use of methods) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
2 Weeks |
"Types" vs "equivalent" comparison, where the intervention group saw two different types of equations solved with the same method. ;
|
60.28 |
39.33 |
No |
-- | ||
|
Procedural flexibility (% correct) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
2 Weeks |
"Types" vs "equivalent" comparison, where the intervention group saw two different types of equations solved with the same method. ;
|
65.43 |
57.19 |
No |
-- | ||
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|
|---|---|---|---|---|---|---|---|---|---|
|
Procedural knowledge (% correct) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
0 Days |
"Types" vs "equivalent" comparison, where the intervention group saw two different types of equations solved with the same method.;
|
52.85 |
55.85 |
No |
-- | ||
| Show Supplemental Findings | |||||||||
|
Procedural knowledge (% correct) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
2 Weeks |
"Types" vs "equivalent" comparison, where the intervention group saw two different types of equations solved with the same method. ;
|
61.96 |
66.03 |
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: 50%
Male: 50% -
Rural, Suburban, Urban
-
Race Asian 5% Black 5% Other or unknown 1% White 89% -
Ethnicity Hispanic 1% Not Hispanic or Latino 99%
Study Details
Setting
Participating students came from three schools (in three different settings--one was a rural public school, one was a suburban public school, and one was an urban private school).
Study sample
There were 81 girls and 81 boys participating. The participating students were predominately Caucasian (5% were African American, 5% were Indian/Asian and 1% were Hispanic). 14% of participants received free or reduced price lunch. The mean age of participants was 13.1 years old.
Intervention Group
During the intervention, students studied the worked-example pairs with a partner and answered explanation prompts designed to guide attention to the example features targeted in each condition. Students also solved practice problems and received minilectures during the intervention." (p. 533) Students were also given homework assignments at the end of each class period." Materials. "Packets of worked examples were created for each condition. On each page of the packet, a pair of worked examples was presented side by side…. The packets were as similar as possible. They all contained four instances of each of the three equation types for a total of 12 worked examples. Half the worked examples illustrated the conventional solution method and half illustrated the composite-variable shortcut method. The primary difference between the packets was how the worked examples were paired. In the methods packets, each worked-example pair contained the same equation, solved using the conventional and shortcut method. … In the problem types packets, each worked-example pair contained two different types of equations, each solved with the same method. For example, a combine composite equation and a divide composite equation were shown together, each solved using the shortcut method …. In the equivalent packets, each worked-example pair contained two instances of the same problem type solved with the same solution method. Across all packets, each solution step was labeled using one of four step labels (distribute, combine, add–subtract on both, multiply– divide on both). … "Each pair of worked examples was presented along with two questions prompting students to compare and contrast the targeted dimensions for a given condition. … questions in the methods condition focused on comparing the solution steps, including their feasibility and efficiency; those in both the problem types and equivalent conditions focused on comparing both the problem features and the particular solution steps. Each packet also included one guided practice problem, on which students were asked to use a particular shortcut method to solve a new equation, and four independent practice problems, on which students could choose their solution methods. In the methods condition, students were asked to solve two practice problems each in two different ways, whereas four different equations were presented in the packets for the other conditions. … "Three brief homework assignments were developed, primarily using problems in the students’ regular textbooks. The homework assignments had six problems each and were review problems similar to those solved in class. They were the same across all conditions." (p. 533-534)
Comparison Group
As stated in the intervention description cell, there were three groups compared: (1) comparing similar problems solved using the same method, (2) comparing different problem types solved with the same solution method, and (3) comparing different solution methods to the same problem. Students received packets of practice problems to work with. This analysis compares group (2) to group (1).
Practice Guide
Review Details
Reviewed: June 2019
- Practice Guide (findings for Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students)
- 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) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
0 Days |
"Methods" vs "equivalent" comparison, where the intervention group saw the same set of questions solved in with two different methods.;
|
58.27 |
47.93 |
No |
-- | ||
| Show Supplemental Findings | |||||||||
|
Conceptual knowledge (% correct) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
2 Weeks |
"Methods" vs "equivalent" comparison, where the intervention group saw the same set of questions solved in with two different methods.;
|
63.58 |
54.33 |
No |
-- | ||
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|
|---|---|---|---|---|---|---|---|---|---|
|
Procedural flexibility (% correct) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
0 Days |
"Methods" vs "equivalent" comparison, where the intervention group saw the same set of questions solved in with two different methods.;
|
63.06 |
53.37 |
Yes |
|
|
|
|
Procedural flexibility use (% use of methods) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
0 Days |
"Methods" vs "equivalent" comparison, where the intervention group saw the same set of questions solved in with two different methods.;
|
48.36 |
33.33 |
No |
-- | ||
| Show Supplemental Findings | |||||||||
|
Procedural flexibility (% correct) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
2 Weeks |
"Methods" vs "equivalent" comparison, where the intervention group saw the same set of questions solved in with two different methods.;
|
70.65 |
57.19 |
Yes |
|
||
|
Procedural flexibility use (% use of methods) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
2 Weeks |
"Methods" vs "equivalent" comparison, where the intervention group saw the same set of questions solved in with two different methods.;
|
61.03 |
39.33 |
Yes |
|
||
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|
|---|---|---|---|---|---|---|---|---|---|
|
Procedural knowledge (% correct) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
0 Days |
"Methods" vs "equivalent" comparison, where the intervention group saw the same set of questions solved in with two different methods.;
|
53.78 |
55.85 |
No |
-- | ||
| Show Supplemental Findings | |||||||||
|
Procedural knowledge (% correct) |
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students vs. Other intervention |
2 Weeks |
"Methods" vs "equivalent" comparison, where the intervention group saw the same set of questions solved in with two different methods.;
|
67.29 |
66.03 |
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: 50%
Male: 50% -
Rural, Suburban, Urban
-
Race Asian 5% Black 5% Other or unknown 1% White 89% -
Ethnicity Hispanic 1% Not Hispanic or Latino 99%
Study Details
Setting
Participating students came from three schools (in three different settings--one was a rural public school, one was a suburban public school, and one was an urban private school).
Study sample
There were 81 girls and 81 boys participating. The participating students were predominately Caucasian (5% were African American, 5% were Indian/Asian and 1% were Hispanic). 14% of participants received free or reduced price lunch. The mean age of participants was 13.1 years old.
Intervention Group
During the intervention, students studied the worked-example pairs with a partner and answered explanation prompts designed to guide attention to the example features targeted in each condition. Students also solved practice problems and received minilectures during the intervention." (p. 533) Students were also given homework assignments at the end of each class period." Materials. "Packets of worked examples were created for each condition. On each page of the packet, a pair of worked examples was presented side by side…. The packets were as similar as possible. They all contained four instances of each of the three equation types for a total of 12 worked examples. Half the worked examples illustrated the conventional solution method and half illustrated the composite-variable shortcut method. The primary difference between the packets was how the worked examples were paired. In the methods packets, each worked-example pair contained the same equation, solved using the conventional and shortcut method. … In the problem types packets, each worked-example pair contained two different types of equations, each solved with the same method. For example, a combine composite equation and a divide composite equation were shown together, each solved using the shortcut method …. In the equivalent packets, each worked-example pair contained two instances of the same problem type solved with the same solution method. Across all packets, each solution step was labeled using one of four step labels (distribute, combine, add–subtract on both, multiply– divide on both). … "Each pair of worked examples was presented along with two questions prompting students to compare and contrast the targeted dimensions for a given condition. … questions in the methods condition focused on comparing the solution steps, including their feasibility and efficiency; those in both the problem types and equivalent conditions focused on comparing both the problem features and the particular solution steps. Each packet also included one guided practice problem, on which students were asked to use a particular shortcut method to solve a new equation, and four independent practice problems, on which students could choose their solution methods. In the methods condition, students were asked to solve two practice problems each in two different ways, whereas four different equations were presented in the packets for the other conditions. … "Three brief homework assignments were developed, primarily using problems in the students’ regular textbooks. The homework assignments had six problems each and were review problems similar to those solved in class. They were the same across all conditions." (p. 533-534)
Comparison Group
As stated in the intervention description cell, there were three groups compared: (1) comparing similar problems solved using the same method, (2) comparing different problem types solved with the same solution method, and (3) comparing different solution methods to the same problem. Students received packets of practice problems to work with. This analysis compares group (3) to group (1).
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: 50%
Male: 50% -
Rural, Suburban, Urban
-
Race Asian 5% Black 5% White 89% -
Ethnicity Hispanic 1% Not Hispanic or Latino 99%
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: 50%
Male: 50% -
Rural, Suburban, Urban
-
Race Asian 5% Black 5% White 89% -
Ethnicity Hispanic 1% Not Hispanic or Latino 99%
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