Document Type



Doctor of Education (EdD)


Curriculum and Instruction

First Advisor's Name

Maria L. Fernandez

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Eric Dwyer

Second Advisor's Committee Title

committee member

Third Advisor's Name

Benjamin Baez

Third Advisor's Committee Title

committee member

Fourth Advisor's Name

Mido Chang

Fourth Advisor's Committee Title

committee member


mathematics, problem solving, elementary education, metacognitive behaviors, writing in mathematics, third graders, ELLs, quasi-experimental design, one-way repeated measures ANOVA

Date of Defense



The gap that exists between English language learners and English speaking students’ achievement in mathematics continues to grow. Moreover, students are now required to show evidence of their mathematics knowledge through writing in standardized assessments and class assignments.

The purpose of this study was to analyze students’ writing in mathematics and the metacognitive behaviors they portrayed through their writing as they solved mathematics problems. The instruments included a pretest, two biweekly tests, and a posttest. The writing instruction encompassed students learning to solve problems by using Polya’s four phases of problem solving which was completed in 12 sessions over a period of 6 weeks. Garofalo and Lester’s framework which renamed Polya’s phases into orientation, organization, execution, and verification, was used to look at the metacognitive behaviors students used. The participants included 67 students enrolled in four third grade classes, who were English language learners and English speakers.

This research followed a quasi-experimental design, with a treatment group and a control group. A one-way repeated ANOVA was used to analyze the data. The findings showed no significant difference between the mathematics achievement scores of treatment and control. However, growth trends in achievement scores revealed that the treatment group scores were increasing faster than the control group scores across the four tests during the 6-week study. Moreover, significant differences were found between the treatment and the control groups when the problem solving with metacognitive behaviors scores were analyzed. Descriptive statistics showed the frequency of occurrence of each of the problem solving phases increased steadily across the four tests for the students in the treatment group. During the posttest, 100% of treatment group students wrote about metacognitive behaviors they used during the orientation and organization phases, 91.4% wrote about their metacognition for executing the solution, and 80% wrote about the verification process they followed.

These findings are useful to education professionals who are interested in creating programs for teaching mathematics at the elementary level that include effective problem solving practices. This evidence-based method may be adopted in school districts with large populations of ELLs in order to assist these students when solving problems in mathematics.




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