The Effects of Strategic Counting Instruction, with and without Deliberate Practice, on Number Combination Skill among Students with Mathematics Difficulties [Word problem instruction (with or without strategic counting practice) vs. control]
Fuchs, Lynn S.; Powell, Sarah R.; Seethaler, Pamela M.; Cirino, Paul T.; Fletcher, Jack M.; Fuchs, Douglas; Hamlett, Carol L. (2010). Learning and Individual Differences, v20 n2 p89-100. Retrieved from: https://eric.ed.gov/?id=EJ872585
-
examining150Students, grade3
Practice Guide
Review Details
Reviewed: February 2020
- Practice Guide (findings for Targeted Math Intervention)
- 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 |
|
|---|---|---|---|---|---|---|---|---|---|
|
Find X (Fuchs & Seethaler 2008) dichotomous |
Targeted Math Intervention vs. Business as usual |
0 Days |
Aggregated sample;
|
90.75 |
58.00 |
No |
-- | ||
| Show Supplemental Findings | |||||||||
|
Find X (Fuchs & Seethaler 2008) dichotomous |
Targeted Math Intervention vs. Business as usual |
0 Days |
T1 (with deliberate practice) vs. Control;
|
95.43 |
58.00 |
-- |
-- | ||
|
Find X (Fuchs & Seethaler 2008) dichotomous |
Targeted Math Intervention vs. Business as usual |
0 Days |
T2 (without deliberate practice) vs. Control;
|
87.56 |
58.00 |
-- |
-- | ||
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|
|---|---|---|---|---|---|---|---|---|---|
|
Four subtests of the Grade 3 Math Battery (Fuchs, Powell, & Hamlett, 2003) |
Targeted Math Intervention vs. Business as usual |
0 Days |
Aggregated sample;
|
0.28 |
-0.34 |
Yes |
|
|
|
|
Double-digit Addition & Subtraction (Fuchs, Hamlett, & Powell 2003) |
Targeted Math Intervention vs. Business as usual |
0 Days |
Aggregated sample;
|
0.16 |
-0.33 |
Yes |
|
|
|
| Show Supplemental Findings | |||||||||
|
Four subtests of the Grade 3 Math Battery (Fuchs, Powell, & Hamlett, 2003) |
Targeted Math Intervention vs. Business as usual |
0 Days |
T1 (deliberate practice) vs. Control;
|
0.39 |
-0.34 |
Yes |
|
||
|
Double-digit Addition & Subtraction (Fuchs, Hamlett, & Powell 2003) |
Targeted Math Intervention vs. Business as usual |
0 Days |
T1 (with deliberate practice) vs. control;
|
0.26 |
-0.33 |
Yes |
|
||
|
Four subtests of the Grade 3 Math Battery (Fuchs, Powell, & Hamlett, 2003) |
Targeted Math Intervention vs. Business as usual |
0 Days |
T2 (without deliberate practice) vs. Control;
|
0.15 |
-0.34 |
Yes |
|
||
|
Double-digit Addition & Subtraction (Fuchs, Hamlett, & Powell 2003) |
Targeted Math Intervention vs. Business as usual |
0 Days |
T2 (without deliberate practice) vs. Control;
|
0.06 |
-0.33 |
No |
-- | ||
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|
|---|---|---|---|---|---|---|---|---|---|
|
Vanderbilt Story Problems Grade 3 |
Targeted Math Intervention vs. Business as usual |
0 Days |
Aggregated sample;
|
0.16 |
-0.41 |
Yes |
|
|
|
|
Vanderbilt Story Problems Grade 2 |
Targeted Math Intervention vs. Business as usual |
0 Days |
Aggregated sample;
|
0.20 |
-0.35 |
Yes |
|
|
|
|
KeyMath-Revised Problem Solving |
Targeted Math Intervention vs. Business as usual |
0 Days |
Aggregated sample;
|
0.03 |
-0.32 |
Yes |
|
|
|
| Show Supplemental Findings | |||||||||
|
Vanderbilt Story Problems Grade 3 |
Targeted Math Intervention vs. Business as usual |
0 Days |
T2 (without deliberate practice) vs. Control;
|
0.28 |
-0.41 |
Yes |
|
||
|
Vanderbilt Story Problems Grade 2 |
Targeted Math Intervention vs. Business as usual |
0 Days |
T2 (without deliberate practice) vs. Control;
|
0.30 |
-0.35 |
Yes |
|
||
|
KeyMath-Revised Problem Solving |
Targeted Math Intervention vs. Business as usual |
0 Days |
T2 (without deliberate practice) vs. Control;
|
0.23 |
-0.32 |
Yes |
|
||
|
Vanderbilt Story Problems Grade 3 |
Targeted Math Intervention vs. Business as usual |
0 Days |
T1 (with deliberate practice) vs. Control;
|
0.04 |
-0.41 |
Yes |
|
||
|
Vanderbilt Story Problems Grade 2 |
Targeted Math Intervention vs. Business as usual |
0 Days |
T1 (with deliberate practice) vs. control;
|
0.11 |
-0.35 |
Yes |
|
||
|
KeyMath-Revised Problem Solving |
Targeted Math Intervention vs. Business as usual |
0 Days |
T1 (with deliberate practice) vs. control;
|
0.02 |
-0.32 |
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.
-
19% English language learners -
Female: 43%
Male: 57% -
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
Tennessee, Texas
-
Race Black 56% Other or unknown 33% White 11% -
Ethnicity Hispanic 30% Not Hispanic or Latino 70%
Study Details
Setting
The study took place in two urban school districts (Houston and Nashville). Students were from 13 schools in Nashville and 18 schools in Houston (p. 5).
Study sample
The strategic counting with deliberate practice group included 39% female students. 73% of students in this group were receiving subsidized lunches and 43% were receiving special education services. For 18%, English was the student's second language. The racial and ethnic breakdown for this group was as follows: 59% African American, 8% Caucasian, 31% Hispanic, and 2% other. 31% of the students in this group had been retained in grade. The strategic counting without deliberate practice group included 43% female students. 71% of students in this group were receiving subsidized lunches and 45% were receiving special education services. For 16%, English was the student's second language. The racial and ethnic breakdown for this group was as follows: 63% African American, 14% Caucasian, 20% Hispanic, and 2% other. 35% of the students in this group had been retained in grade. The control group included 48% female students. 82% of students in this group were receiving subsidized lunches and 18% were receiving special education services. For 24%, English was the student's second language. The racial and ethnic breakdown for this group was as follows: 46% African American, 10% Caucasian, 36% Hispanic, and 8% other. 32% of the students in this group had been retained in grade (p. 22). All students in the study were experiencing math difficulty. This was determined based on the students' scores on two screening measures. All students scored below the 26th percentile on the Arithmetic subtest of the Wide Range Achievement Test-3 and below the 36th percentile on the Iowa Test of Basic Skills: Problem Solving and Data Interpretation (p. 5, 10). Students were also screened for reading difficulties using the reading subtest of the Wide Range Achievement Test-3. Students who scored below the 26th percentile on this assessment were classified as having reading difficulties. In the final analytic sample (including the control group), 27% of students met criteria for math difficulties alone and 73% met criteria for both math and reading difficulties (p. 6, 10).
Intervention Group
The study examined two variations of instruction in number combinations that was embedded in a word problem tutoring intervention, called Pirate Math: strategic counting instruction with deliberate practice and strategic counting instruction without deliberate practice. The study design also included a control group. The intervention consisted of one-on-one tutoring and was supplemental to the core mathematics. Tutoring lasted 16 weeks and included 48 sessions divided across 4 units. Each session was 20-30 minutes in duration. The tutoring conditions (T1 and T2) looked at embedding number combination instruction within validated word problem intervention. T1 included schema-based instruction on word problems where students were taught to distinguish between problems types with additive and subtractive structures (combine, compare, change). The embedded strategic counting practice included explicit teaching of counting up to solve addition and subtraction basic facts. Flash cards to build fluency were included and students were asked to correct any incorrect answers provided by using the taught strategy. T2 included schema-based instruction on word problems where students were taught to distinguish between problems types with additive and subtractive structures (combine, compare, change). Strategic counting practice was NOT included; however, students were taught at the start of tutoring on one occasion a strategy for counting up to solve addition and subtraction basic facts. To account for time spent in T1 on flash card practice, T2 also included flash cards to build fluency on number identification 0-9999.
Comparison Group
The comparison condition was business as usual instruction. This varied somewhat across the two sites (Houston and Nashville). However, in both sites, business as usual instruction involved very little instruction in number combinations. Students did receive instruction in word problems, including the three problem types taught in the intervention condition. Instruction also included more complex word problem types. The business as usual instruction did not include efforts to broaden students’ schemas about word problems. In Nashville, Houghton Mifflin Math was the curriculum that was used. Instruction in word problems focused on explicit steps that students should take to solve problems. In Houston, schools were provided with some latitude about which curriculum to use so long as it aligned with the district’s Horizontal Alignment Planning Guide, which emphasized “communication, justification, and reasoning; proper use of manipulatives; multiple models and representations; and problem-solving strategies” (p. 6-7).
Support for implementation
Tutors were provided a script for each tutoring session. Tutors studied the scripts prior to tutoring sessions so that they could conduct the tutoring sessions without having to read directly from the script (p. 7).
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.
An outcome is the knowledge, skills, and attitudes that are attained as a result of an activity. An outcome measures is an instrument, device, or method that provides data on the outcome.
A finding that is included in the effectiveness rating. Excluded findings may include subgroups and subscales.
The sample on which the analysis was conducted.
The group to which the intervention group is compared, which may include a different intervention, business as usual, or no services.
The timing of the post-intervention outcome measure.
The number of students included in the analysis.
The mean score of students in the intervention group.
The mean score of students in the comparison group.
The WWC considers a finding to be statistically significant if the likelihood that the finding is due to chance alone, rather than a real difference, is less than five percent.
The WWC reviews studies for WWC products, Department of Education grant competitions, and IES performance measures.
The name and version of the document used to guide the review of the study.
The version of the WWC design standards used to guide the review of the study.
The result of the WWC assessment of the study. The rating is based on the strength of evidence of the effectiveness of the intervention. Studies are given a rating of Meets WWC Design Standards without Reservations, Meets WWC Design Standards with Reservations, or >Does Not Meet WWC Design Standards.
A related publication that was reviewed alongside the main study of interest.
Study findings for this report.
Based on the direction, magnitude, and statistical significance of the findings within a domain, the WWC characterizes the findings from a study as one of the following: statistically significant positive effects, substantively important positive effects, indeterminate effects, substantively important negative effects, and statistically significant negative effects. For more, please see the WWC Handbook.
The WWC may review studies for multiple purposes, including different reports and re-reviews using updated standards. Each WWC review of this study is listed in the dropdown. Details on any review may be accessed by making a selection from the drop down list.
Tier 1 Strong indicates strong evidence of effectiveness,
Tier 2 Moderate indicates moderate evidence of effectiveness, and
Tier 3 Promising indicates promising evidence of effectiveness,
as defined in the
non-regulatory guidance for ESSA
and the regulations for ED discretionary grants (EDGAR Part 77).