WWC review of this study

The Effect of Explicit and Direct Generative Strategy Training and Working Memory on Word Problem-Solving Accuracy in Children at Risk for Math Difficulties [Word problem instruction - complete condition vs. control (students with mathematics difficulties only)]

Swanson, H. Lee; Moran, Amber; Lussier, Cathy; Fung, Wenson (2014). Learning Disability Quarterly, v37 n2 p111-123. Retrieved from: https://eric.ed.gov/?id=EJ1022817

  • Randomized Controlled Trial
    , grade

Reviewed: March 2020

No statistically significant positive
Meets WWC standards with reservations
Whole Numbers Word Problems/Problem Solving outcomes—Indeterminate effect found for the domain
Comparison Period Sample Intervention
Significant? Improvement

Schema Assessment Task – modified for children

Targeted Math Intervention vs. Business as usual

0 Days

Complete intervention group vs. comparison group with MD;
45 students





Comprehensive Mathematical Abilities Test and KeyMath problem-solving subtests

Targeted Math Intervention vs. Business as usual

0 Days

Complete intervention group vs. comparison group with MD;
45 students





Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.

Characteristics of study sample as reported by study author.

  • Female: 44%
    Male: 56%
  • Race
    Other or unknown
  • Ethnicity


The study took place in 12 regular classrooms in four elementary schools in two southwest school districts. Students in the intervention groups and students in the comparison group participated in small group instruction, and presumably the small-group sessions took place in classrooms.

Study sample

The authors do not provide sample characteristics by group. The entire study sample (across all 4 groups) included 46 males and 36 females. Eleven percent of the sample was Caucasian, 87% Hispanic, and 2% Asian. The sample included 54 children with Spanish as a first language, though these children were considered proficient in English based on California English Language Development Test (CELDT) scores. The authors state that no significant difference was found in terms of English language learner (ELL) status, but it’s not clear who the ELLs are in this study given that the 54 Spanish-speakers mentioned were also proficient in English. Information on the participants' sex, race, ethnicity, and language status is provided for the analytic sample only (not broken down by experimental group)

Intervention Group

For the contrast in this review, the intervention group was the complete intervention group. Students participated in 20 lessons, delivered twice per week for 10 weeks. Each lesson lasted 30 minutes. Intervention sessions were led by undergraduate and graduate student tutors, and during each lesson they followed a script as they moved through four phases. As with the other three intervention conditions in the study, the complete intervention involved the presentation of word problems taken from the classroom text (Macmillan McGraw-Hill Mathematics, 2009) and modified to include irrelevant sentences. The number of irrelevant sentences increased over time. Lessons 1 to 5 included no irrelevant sentences and lessons 16 to 20 included four irrelevant sentences. Student work was recorded in a booklet. During the warm-up phase, which lasted about 5 minutes, children solved calculation problems and puzzles. This was followed by the modeling phase, which also lasted about 5 minutes. During this phase, the tutor read a word problem out loud and asked students to identify what the problem was asking (the question), what information was needed to answer the question (the relevant propositions), and what information was included in the problem that was not necessary for answering the question (the irrelevant propositions). Then the tutor asked the students to explain what they would do to solve the problem and they solved the problem together. During the guided practice phase, the tutor read another problem out loud to the students. Students were then prompted to write the question and the relevant and irrelevant propositions in their own words in their notebooks. Children shared what they wrote with each other. Finally, the students solved the problem. Once students demonstrated that they had mastered the steps in the guided practice phase, they moved on to the independent practice phase, which lasted 15 minutes. During this time, children worked on three problems individually using the strategies they had used during guided practice.

Comparison Group

In the comparison condition, children participated in small-group instruction from the classroom teacher on the week’s normal math work. As in the intervention conditions, students in the comparison condition participated in 30-minute lessons twice a week for 10 weeks for a total of 20 lessons.

Support for implementation

Tutors participated in a four-hour training session. During the training session, tutors practiced delivering to other tutors and the project director each of the 20 scripted lessons. Additionally, the project director and project coordinator observed each tutor at three or four random times and assessed the sessions using a fidelity rubric checklist, which covered each phase of the lessons and was sensitive to intervention condition. Observations of tutors occurred during 17.5 percent of the lessons, and mean implementation fidelity was 96 percent with T1, 93.1 percent with T2, and 97.1 percent with T3 (range = 80 percent to 100 percent). Any tutor who fell below 90 percent received additional assistance, direct coaching, and immediate follow-up observations. Before a tutor could move from the guided practice phase to the independent practice phase, all children in a given intervention condition needed to demonstrate knowledge and correct usage of the strategies targeted in a given lesson.


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