Over the past twenty years, journal writing has become more common in mathematics classes at all age levels. However, there has been very little empirical research about journal writing in college mathematics (Speer, Smith, & Horvath, 2010), particularly concerning the relationship between journal writing in college mathematics and college students' motivation towards learning mathematics. The purpose of this dissertation study is to fill that gap by implementing homework journals, which are a journal writing assignment based on Powell and Ramnauth's (1992) "multiple-entry log," in a college mathematics course and studying the relationship between homework journals and students' motivation towards learning mathematics as grounded in self-determination theory (Ryan & Deci, 2000). Self-determination theory predicts intrinsic motivation by focusing on the fundamental needs of competence, autonomy, and relatedness (Ryan & Deci, 2000). In addition, the purpose of this dissertation study is to explore and describe the relationship between homework journals and students' attitudes towards writing in mathematics. A pre-course and post-course survey was distributed to students enrolled in two sections of a college mathematics course and then analyzed using a 2Ã 2 repeated measures ANOVA with time (pre-course and post-course) and treatment (one section engaged with homework journals while the other did not) as the two factors, in order to test whether the change over time was different between the two sections. In addition, student and instructor interviews were conducted and then analyzed using a constant comparative method (Anfara, Brown, & Mangione, 2002) in order to add richness to the description of the relationship between homework journals and students' motivation towards learning mathematics as well as students' attitudes towards writing in mathematics. Based on the quantitative analysis of survey data, no differences in rate of change of competence, autonomy, relatedness, or attitudes towards writing were found. However, based on the qualitative analysis of interview data, homework journals were found to influence students' sense of competence, autonomy, and relatedness under certain conditions. In addition, students' attitudes towards writing in mathematics were strongly influenced by their likes and dislikes of homework journals and the perceived benefits of homework journals. / Ph. D.

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The purpose of this study was to investigate how writing in mathematics is treated in one 4th grade National Science Foundation (NSF)-funded mathematics textbook titled Everyday Mathematics and one publisher-generated textbook titled enVision MATH. The developed framework provided categories to support each of the research questions. The results indicate that writing is supported in both traditional and NSF developed 4th grade mathematics textbooks Results also indicated the number of exercises and writing prompts was higher in the enVision MATH textbook. However, Everyday Mathematics had a higher percentage of exercises that were coded as writing prompts. The framework domains of content strand in enVision MATH and Everyday Mathematics are similar in percentages with the exception of prompts coded in the other category. Everyday Mathematics appeared to be the only textbook analyzed to support writing across different content areas. Furthermore, the content strand of number sense had the largest percentage of writing prompts coded between both textbook series. Other findings from this study suggest that the type of vocabulary coded within the writing prompts was similar in all categories between both textbook series analyzed. Additionally, vocabulary specific to the domain of mathematics and symbols appeared to have the largest percentage in this category for both textbook series. The teacher and student editions were explored in enVision MATH and Everyday Mathematics to provide more depth to the research. An exploration of the teacher edition indicated how writing was supported for instructional purposes. The teacher editions in both textbook series had the largest percentage of support in the form of one sample response. Within the student edition category, the layout varied in the enVision MATH and Everyday Mathematics textbook series. As a result, only the language of Everyday MATH could be analyzed for patterns in the sections, sub-sections, and additional sub-sections of where the prompts were located. Although this investigation did not involve analyzing student responses to the writing prompts, the findings provide information regarding the expectations of the writer in order to construct a mathematical response. For example, the domain specific vocabulary (DSV) and symbols category was rated the highest in percentage for both textbooks indicating that students will need to have command of the language and symbols of mathematics in order to engage in meaning making written discourse. Because most of the math prompts were specific to the problem solving category, it was determined after a linguistic analysis that the affordance of the prompt is much more complex than then binary categories of content and process Additionally, in order for students to respond to these content writing prompts, many process words known as meta-language (i.e., explanation, description, why question, how question) need to be comprehended in order for composition to begin. In light of these findings, I recommend that special attention be given to the teacher and student editions regarding the implementation of writing in mathematics. The development of these materials has important implications regarding instruction and learning of mathematical concepts through writing, potentially impacting student performance on national and international assessments.

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Students' critical thinking in mathematics was a concern for grade 5 through 8 teachers at a Title 1 public school in the northeastern United States because of the students' poor performance on constructed response questions on the state's mathematics exam. In this exam, students were required to justify their answers in writing. When teachers recognize the connection between writing and critical thinking, they can devise strategies to help students develop mathematical literacy. The purpose of this qualitative case study was to explore how 5th through 8th grade mathematics teachers use the GoMath mathematics literacy program to teach the critical thinking skills students need to justify an answer in writing. The conceptual framework of critical thinking theory drove this study examining critical thinking pedagogy in general and special education mathematics classrooms. Qualitative data were collected from pre- and post-observation interviews and classroom observations from 4 purposefully selected mathematics teachers in grades 5 through 8 who taught GoMath. Thematic analysis was used to analyze the data. Teachers reported that oral communication among students before writing justifications and students' critical thinking skills were integral components in solving mathematics problems. Based on the findings, it is recommended that ongoing professional development be adopted to assist teachers in developing strategies for teaching critical thinking skills to help students justify answers in writing when solving mathematics problems. This endeavor may contribute to positive social change by providing teachers with the necessary skills and strategies to enhance students' communication and critical thinking, thus, increasing their academic performance in mathematics.

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.