Can feedback, correct, and incorrect worked examples improve numerical magnitude estimation precision? [Grades 1-2]
Fitzsimmons, C. J., Morehead, K. T., Thompson, C. A., Buerke, M., & Dunlosky, J. (2021). The Journal of Experimental Education, 1-26. https://doi.org/10.1080/00220973.2021.1891009 .
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examining46Students, grades1-2
Single Study Review
Review Details
Reviewed: September 2022
- Single Study Review (findings for Magnitude estimation practice with feedback – Fitzsimmons et al., (2021))
- 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 |
|
|---|---|---|---|---|---|---|---|---|---|
|
Researcher-developed percent absolute error in number line estimation |
Magnitude estimation practice with feedback – Fitzsimmons et al., (2021) vs. Business as usual |
0 Days |
Full sample;
|
37.96 |
29.06 |
Yes |
|
|
|
|
Researcher-developed percent absolute error in categorization |
Magnitude estimation practice with feedback – Fitzsimmons et al., (2021) vs. Business as usual |
0 Days |
Full sample;
|
26.20 |
25.58 |
No |
-- | ||
| Show Supplemental Findings | |||||||||
|
Researcher-developed percent absolute error in number line estimation |
Magnitude estimation practice with feedback – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
39.30 |
30.48 |
Yes |
|
||
|
Researcher-developed percent absolute error in categorization |
Magnitude estimation practice with feedback – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
32.40 |
27.22 |
Yes |
|
||
|
Researcher-developed percent absolute error in number line estimation |
Magnitude estimation practice with feedback – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
19.91 |
19.36 |
No |
-- | ||
|
Researcher-developed percent absolute error in categorization |
Magnitude estimation practice with feedback – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
20.24 |
22.56 |
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: 58%
Male: 42% -
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- A
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- i
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- w
- y
Ohio
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Race Other or unknown 21% White 79% -
Ethnicity Other or unknown 100% -
Eligible for Free and Reduced Price Lunch Free or reduced price lunch (FRPL) 31% Other or unknown 69%
Study Details
Setting
The study was conducted in four elementary schools in two school districts in Ohio.
Study sample
This manuscript examines three different versions of the magnitude estimation practice intervention with elementary school students. This review focuses on one version called magnitude estimation practice with feedback. The other two versions of the intervention, and a description of their differences, can be accessed through the drop-down menu. The manuscript also describes an experiment using versions of this intervention with undergraduate students. The details of that experiment can be found on a separate study page. A total of 49 students in first and second grade were included in the study. Fifty-eight percent of students were female. The study authors do not describe the demographics of the student sample further. In the schools from which the students were recruited, 31% of students were eligible for free or reduced-price lunch and 79% were White.
Intervention Group
The intervention provides students with practice in magnitude estimation which is intended to improve students’ accuracy placing whole numbers on a number line. The intervention was provided by members of the study team and delivered to individual students. The intervention was administered in a single 30-minute session. During that 30-minute session, students first took the pretest, then iteratively practiced number line placement problems with the support of the study team member who administered the session, followed by the student taking 10 of the 30 posttest questions at a time. Students were asked to place numbers on a number line that ranged from zero to one thousand. Students moved a slider along the line to make their estimate. Students completed the study practice problems and test problems on a computer in a quiet room at their school. In the magnitude estimation practice with feedback group, the study team member asked the student to place the number on the number line, after which the study team member showed the student where the number really belonged and asked the student to explain why their placement was similar, higher, or lower than the correct placement. If the student did not respond, the study team member continued to prompt the students until they provided an answer. The student responses were recorded by the study team member.
Comparison Group
The business-as-usual comparison was to a group of students that engaged in magnitude estimation practice without guidance or feedback in a single 30-minute session. Students completed number line practice problems and test problems individually on computers. In this group, the study team members did not provide students with any prompts for explanations and students were not asked to judge the confidence of their answers. The intervention group was compared to other versions of the intervention as well: In the magnitude estimation practice with incorrect worked examples group, the study team member showed students an incorrect number line placement and then asked the student to explain why the answer was wrong. In the magnitude estimation practice with correct worked examples group, the study team member showed students a correct number line placement and then asked the student to explain why the answer was correct.
Support for implementation
The study team administered the activities in the intervention and comparison conditions. No information about training or preparation of the study team is provided.
Single Study Review
Review Details
Reviewed: September 2022
- Single Study Review (findings for Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021))
- 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 |
|
|---|---|---|---|---|---|---|---|---|---|
|
Researcher-developed percent absolute error in number line estimation |
Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021) vs. Business as usual |
0 Days |
Full sample;
|
29.14 |
29.06 |
No |
-- | ||
|
Researcher-developed percent absolute error in categorization |
Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021) vs. Business as usual |
0 Days |
Full sample;
|
24.70 |
25.58 |
No |
-- | ||
| Show Supplemental Findings | |||||||||
|
Researcher-developed percent absolute error in categorization |
Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
19.56 |
22.56 |
No |
-- | ||
|
Researcher-developed percent absolute error in categorization |
Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with feedback – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
21.19 |
24.00 |
No |
-- | ||
|
Researcher-developed percent absolute error in number line estimation |
Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
11.09 |
19.36 |
Yes |
|
||
|
Researcher-developed percent absolute error in number line estimation |
Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with feedback – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
12.02 |
20.84 |
Yes |
|
||
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: 58%
Male: 42% -
- 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
Ohio
-
Race Other or unknown 21% White 79% -
Ethnicity Other or unknown 100% -
Eligible for Free and Reduced Price Lunch Free or reduced price lunch (FRPL) 31% Other or unknown 69%
Study Details
Setting
The study was conducted in four elementary schools in two school districts in Ohio.
Study sample
This manuscript examines three different versions of the magnitude estimation practice intervention with elementary school students. This review focuses on one version called magnitude estimation practice with incorrect worked examples. The other two versions of the intervention, and a description of their differences, can be accessed through the drop-down menu. The manuscript also describes an experiment using versions of this intervention with undergraduate students. The details of that experiment can be found on a separate study page. A total of 46 students in first and second grade were included in the study. Fifty-eight percent of students were female. The study authors do not describe the demographics of the student sample further. In the schools from which the students were recruited, 31% of students were eligible for free or reduced-price lunch and 79% were White.
Intervention Group
The intervention provides students with practice in magnitude estimation which is intended to improve students’ accuracy placing whole numbers on a number line. The intervention was provided by members of the study team and delivered to individual students. The intervention was administered in a single 30-minute session. During that 30-minute session, students first took the pretest, then iteratively practiced number line placement problems with the support of the study team member who administered the session, followed by the student taking 10 of the 30 posttest questions at a time. Students were asked to place numbers on a number line that ranged from zero to one thousand. Students moved a slider along the line to make their estimate. Students completed the study practice problems and test problems on a computer in a quiet room at their school. In the magnitude estimation practice with incorrect worked examples group, the study team member showed students an incorrect number line placement and then asked the student to explain why the answer was wrong. If the student did not respond, the study team member continued to prompt the students until they provided an answer. The student responses were recorded by the study team member.
Comparison Group
The business-as-usual comparison was to a group of students that engaged in magnitude estimation practice without guidance or feedback in a single 30-minute session. Students completed number line practice problems and test problems individually on computers. In this group, the study team members did not provide students with any prompts for explanations and students were not asked to judge the confidence of their answers. The intervention group was compared to other versions of the intervention as well: In the magnitude estimation practice with correct worked examples group, the study team member showed students a correct number line placement and then asked the student to explain why the answer was correct. In the magnitude estimation practice with feedback group, the study team member asked the student to place the number on the number line, after which the study team member showed the student where the number really belonged and asked the student to explain why their placement was similar, higher, or lower than the correct placement.
Support for implementation
The study team administered the activities in the intervention and comparison conditions. No information about training or preparation of the study team is provided.
Single Study Review
Review Details
Reviewed: September 2022
- Single Study Review (findings for Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021))
- 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 |
|
|---|---|---|---|---|---|---|---|---|---|
|
Researcher-developed percent absolute error in number line estimation |
Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021) vs. Business as usual |
0 Days |
Full sample;
|
37.41 |
29.06 |
Yes |
|
|
|
|
Researcher-developed percent absolute error in categorization |
Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021) vs. Business as usual |
0 Days |
Full sample;
|
27.92 |
25.58 |
No |
-- | ||
| Show Supplemental Findings | |||||||||
|
Researcher-developed percent absolute error in number line estimation |
Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
38.75 |
30.48 |
Yes |
|
||
|
Researcher-developed percent absolute error in categorization |
Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with incorrect worked examples – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
30.22 |
27.22 |
No |
-- | ||
|
Researcher-developed percent absolute error in categorization |
Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with feedback – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
24.56 |
24.00 |
No |
-- | ||
|
Researcher-developed percent absolute error in number line estimation |
Magnitude estimation practice with correct worked examples – Fitzsimmons et al., (2021) vs. Magnitude estimation practice with feedback – Fitzsimmons et al., (2021) |
0 Days |
Full sample;
|
20.29 |
20.84 |
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: 58%
Male: 42% -
- 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
Ohio
-
Race Other or unknown 21% White 79% -
Ethnicity Other or unknown 100% -
Eligible for Free and Reduced Price Lunch Free or reduced price lunch (FRPL) 31% Other or unknown 69%
Study Details
Setting
The study was conducted in four elementary schools in two districts in Ohio.
Study sample
This manuscript examines three different versions of the magnitude estimation practice intervention with elementary school students. This review focuses on one version called magnitude estimation practice with correct worked examples. The other two versions of the intervention, and a description of their differences, can be accessed through the drop-down menu. The manuscript also describes an experiment using versions of this intervention with undergraduate students. The details of that experiment can be found on a separate study page. A total of 47 students in first and second grade were included in the study. Fifty-eight percent of students were female. The study authors do not describe the demographics of the student sample further. In the schools from which the students were recruited, 31% of students were eligible for free or reduced-price lunch and 79% were White.
Intervention Group
The intervention provides students with practice in magnitude estimation which is intended to improve students’ accuracy placing whole numbers on a number line. The intervention was provided by members of the study team and delivered to individual students. The intervention was administered in a single 30-minute session. During that 30-minute session, students first took the pretest, then iteratively practiced number line placement problems with the support of the study team member who administered the session, followed by the student taking 10 of the 30 posttest questions at a time. Students were asked to place numbers on a number line that ranged from zero to one thousand. Students moved a slider along the line to make their estimate. Students completed the study practice problems and test problems on a computer in a quiet room at their school. In the magnitude estimation practice with correct worked examples group, the study team member showed students a correct number line placement and then asked the student to explain why the answer was correct. If the student did not respond, the study team member continued to prompt the students until they provided an answer. The student responses were recorded by the study team member.
Comparison Group
The business-as-usual comparison was to a group of students that engaged in magnitude estimation practice without guidance or feedback in a single 30-minute session. Students completed number line practice problems and test problems individually on computers. In this group, the study team members did not provide students with any prompts for explanations and students were not asked to judge the confidence of their answers. The intervention group was compared to other versions of the intervention as well: In the magnitude estimation practice with incorrect worked examples group, the study team member showed students an incorrect number line placement and then asked the student to explain why the answer was wrong. In the magnitude estimation practice with feedback group, the study team member asked the student to place the number on the number line, after which the study team member showed the student where the number really belonged and asked the student to explain why their placement was similar, higher, or lower than the correct placement.
Support for implementation
The study team administered the activities in the intervention and comparison conditions. No information about training or preparation of the study team is provided.
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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