Fishbone Diagrams Boost High Schoolers’ Algebra Word-Problem Scores

Algebraic word problems have long been one of the most stubborn stumbling blocks in secondary school mathematics. Students must translate a paragraph of everyday language into symbols, identify which quantities matter, build an equation, and then carry out the arithmetic correctly. A new study from Ghana suggests that a visual tool borrowed from industrial quality management, the fishbone diagram, may offer a surprisingly effective remedy. Researchers at Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development in Kumasi found that senior high school students taught with the Fishbone Diagram Strategy significantly outperformed peers taught by conventional methods, and that the students themselves rated the approach highly.

The fishbone diagram, also known as the Ishikawa or cause-and-effect diagram, was originally developed as a quality management instrument for tracing the root causes of industrial problems. Its educational adaptation turns the diagram into a scaffold for analysis: a central spine leads to the problem to be solved, while major branches capture the key components of a solution. In the Ghanaian study, the head of the diagram held the algebraic word problem itself, and six branches represented the given information, the unknown variable, the mathematical relationships among quantities, equation formulation, solution procedures, and verification of the final answer. Sub-branches allowed students to record specific details, breaking complex problems into manageable parts before any computation began.

The research team, led by Charles Asare together with Innocent Akpage, Daniel Aboagye and Isaac Davor, recruited 128 Senior High School 3 students studying Elective Mathematics. Because the school’s timetable did not permit random assignment of individuals, the researchers used a quasi-experimental pre-test-post-test non-equivalent control group design with two intact classes of 64 students each. One class received instruction built around the Fishbone Diagram Strategy, while the other was taught the same content through conventional methods: teacher explanations, worked examples, question-and-answer sessions, and individual practice. Both groups covered identical material over six weeks, attending three 60-minute sessions per week, with the same teacher delivering instruction to both classes.

Achievement was measured with a researcher-developed Algebraic Word Problems Achievement Test consisting of five structured-response problems, each scored out of two marks for a maximum of ten. Two parallel forms of the test were created, differing only in numerical values and contextual scenarios, to minimize recall effects between the pre-test and post-test. The instrument was reviewed by three experts in mathematics education and educational measurement, and pilot testing at a comparable school yielded a Cronbach’s alpha of 0.81, indicating acceptable internal consistency. A ten-item perception questionnaire, rated on a five-point Likert scale and piloted with 15 students outside the main study, captured the experimental group’s views of the strategy; its internal consistency coefficient was 0.846.

The descriptive results were striking. At pre-test, the two groups were nearly indistinguishable: the experimental group averaged 2.45 points out of ten, and the control group averaged 2.37. After six weeks, the experimental group’s mean had climbed to 5.62 points, equivalent to 56.2 percent of the maximum score, while the control group reached only 3.36 points, or 33.6 percent. The average individual gain was 3.17 points in the fishbone group compared with 0.98 points under conventional instruction, a difference of roughly 2.19 points. Gains ranged from minus two to nine points in the experimental group and from minus three to four in the control group, showing that while average improvement was much larger with the diagram strategy, not every student benefited equally.

Statistical testing reinforced the descriptive picture. A Mann-Whitney U test confirmed that pre-test scores did not differ significantly between the groups, with a negligible effect size of r = .037, ruling out an obvious baseline advantage. Within the experimental group, the Wilcoxon Signed-Rank Test showed a significant improvement with a large effect size of r = .78, as 52 of 64 students scored higher after the intervention, seven scored lower, and five were unchanged. The control group also improved significantly, with a moderate-to-large effect of r = .49, but its gains were far smaller. On the post-test, the Mann-Whitney U comparison produced a significant difference favoring the experimental group, with an effect size of r = .49.

The centerpiece of the analysis was an analysis of covariance, which controlled for pre-test achievement when comparing post-test scores. After adjustment, the difference between instructional groups remained highly significant, F(1, 125) = 44.673, p < .001, with a partial eta squared of .263, a substantial effect. The adjusted post-test mean was 5.63 for the experimental group against 3.35 for the control group, an adjusted difference of 2.28 points. Because the achievement scores violated assumptions of normality and equal error variances, the researchers also ran an ANCOVA on ranked scores as a sensitivity analysis. That analysis produced the same substantive conclusion, F(1, 125) = 40.486, p < .001, partial eta squared of .245, suggesting the finding was not an artifact of the score distributions.

Students’ perceptions aligned with the achievement data. The overall mean perception score was 3.90 on the five-point scale, falling in the Agree category. The strongest endorsements went to two statements: that the strategy encouraged active participation in algebra lessons, with a mean of 4.38, and that it helped students understand word problems more clearly, with a mean of 4.36, both reaching the Strongly Agree band. Students also agreed that the diagram helped them organize mathematical ideas logically, identify relevant information and solution steps, boost their confidence, and solve problems more effectively. The lowest-rated item, with a mean of 3.53, concerned whether the strategy made lessons more engaging and enjoyable; it was still positive, but opinions varied more widely. Students also expressed a desire for teachers to keep using the approach in future lessons.

The theoretical grounding of the study helps explain why the strategy worked. Constructivist learning theory holds that learners actively build knowledge by organizing new information rather than passively receiving it, and the fishbone diagram operationalizes this by requiring students to decompose problems, distinguish relevant from irrelevant details, and construct mathematical representations before solving. The approach also maps neatly onto Polya’s classic four stages of problem solving: understanding the problem, devising a plan, carrying out the plan, and looking back. From a Vygotskian perspective, the small-group discussions and teacher guidance that accompanied diagram construction served as social scaffolding, allowing students to articulate reasoning, compare interpretations, and move from assisted analysis toward independent problem solving.

The authors are careful about the limits of their evidence. Because only two intact classes from a single school were studied, with one class per condition, class-level characteristics such as classroom climate and peer dynamics cannot be separated from the instructional treatment, so the findings indicate an association rather than definitive causation. The same teacher taught both groups and knew which condition each class received, creating possible expectancy effects. The pre- and post-test forms were not empirically equated, no quantitative content-validity index was established, and the six-week intervention covered only linear-equation word problems. The researchers call for replication across multiple schools, topics, and regions, with stronger controls for teacher effects, randomized assignment of classes where feasible, and longitudinal follow-up to test whether the gains persist.

Even with those caveats, the implications are practical. The authors suggest that mathematics teachers integrate the fishbone diagram into algebra instruction, that curriculum developers consider piloting diagram-based activities in textbooks, and that teacher education programs introduce pre-service and in-service teachers to visual problem-solving frameworks. If the results hold up more broadly, a diagram invented for factory floor troubleshooting may become a low-cost, scalable tool for one of the most persistent difficulties in mathematics classrooms worldwide.

Subject of Research: Effect of the Fishbone Diagram Strategy on senior high school students' achievement and perceptions in algebraic word-problem instruction

Article Title: Fishbone diagram strategy in algebraic word-problem instruction: senior high school students’ achievement and perceptions

Article References: Asare, C., Akpage, I., Aboagye, D., & Davor, I. (2026). Fishbone diagram strategy in algebraic word-problem instruction: senior high school students’ achievement and perceptions. Frontiers in Education, 11, Article 1922256. https://doi.org/10.3389/feduc.2026.1922256

Image Credits: AI Generated

DOI: 10.3389/feduc.2026.1922256

Keywords: fishbone diagram, algebraic word problems, mathematics education, quasi-experimental study, Ghana, senior high school, learner-centered instruction, ANCOVA, problem solving, Ishikawa diagram, student perceptions, instructional strategy