The Effects of Using Diagramming as a Representational Technique on High School Students' Achievement in Solving Math Word Problems

Date of Award


Document Type


Degree Name

Doctor of Education (EdD)


College of Science and Mathematics


Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Kenneth C. Wolff

Committee Member

Alina Reznitskaya

Committee Member

Mika Munakata


Methods and procedures for successfully solving math word problems have been, and continue to be a mystery to many U.S. high school students. Previous studies suggest that the contextual and mathematical understanding of a word problem, along with the development of schemas and their related external representations, positively contribute to students' accomplishments when solving word problems. Some studies have examined the effects of diagramming on students' abilities to solve word problems that only involved basic arithmetic operations. Other studies have investigated how instructional models that used technology influenced students' problem solving achievements. Still other studies have used schema-based instruction involving students with learning disabilities. No study has evaluated regular high school students' achievements in solving standard math word problems using a diagramming technique without technological aid.

This study evaluated students' achievement in solving math word problems using a diagramming technique. Using a quasi-experimental experimental pretest-posttest research design, quantitative data were collected from 172 grade 11 Hispanic English language learners (ELLS) and African American learners whose first language is English (EFLLs) in 18 classes at an inner city high school in Northern New Jersey. There were 88 control and 84 experimental students. The pretest and posttest of each participating student and samples of the experimental students' class assignments provided the qualitative data for the study.

The data from this study exhibited that the diagramming method of solving math word problems significantly improved student achievement in the experimental group (p<.01) compared to the control group. The study demonstrated that urban, high school, ELLs benefited from instruction that placed emphasis on the mathematical vocabulary and symbols used in word problems and that both ELLs and EFLLs improved their problem solving success through careful attention to the creation and labeling of diagrams to represent the mathematics involved in standard word problems. Although Learnertype (ELL, EFLL), Classtype (Bilingual and Mixed), and Gender (Female, Male) were not significant indicators of student achievement, there was significant interaction between Treatment and Classtype at the level of the Bilingual students ( p<.01) and between Treatment and Learnertype at the level of the ELLs (p<.01).


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