This research is based on the Middle School Mathematics Project (MSMP) funded by the Interagency Educational Research Initiative (IERI) through a grant to the American Association for the Advancement of Science (AAAS). Both teachers’ video lessons and students’ pre-and-post test scores were used to investigate the effects of teachers’ types, quality, and quantity of questioning students’ knowledge of algebra concepts and skills in variables, change, equality, and equations in middle school students in seventh and eighth grades. The study further explored the relationship between types of questioning, quality of questioning, and quantity of questioning. Later, teachers’ intention of asking two types of questions, probing and guiding, and teachers’ questioning acquisition methods were studied through face-to-face teacher interviews. This dissertation used a mixed approach utilizing both quantitative and qualitative methods. The data were collected from 33 teachers in two different states, Texas and Delaware, who participated in the IERI project either during the 2002-2003, the 2003- 2004, or the 2004-2005 school years. A total of 103 videotapes were obtained consisting of one to five lessons for each teacher. The teachers used one of four different textbooks: MathThematics (Billstein, et al., 1999), Connected Mathematics (Lappan, et al., 1998), Mathematics: Applications and Connections Glencoe Algebra (Collins, et al., 1998), or Mathematics in Context (MiC) (Romberg, et al., 1998). The results showed that teachers’ quality of probing questions affected students’ achievements when other variables--teachers’ teaching experience, textbook, and teachers’ math preparation--were controlled. It was also found that AAAS’ two highest rated two textbooks, CMP and MiC, affected students’ understanding. Moreover, teachers’ math preparation predicted student performance. Furthermore, quality and quantity of guiding questions and probing questions were significantly correlated with each other (p < 0.01). For the qualitative part, it was found that teachers’ were asking what they intended to ask. In other words, they were aware of the role of questioning they were using. Also, there were several methods that seemed to be more used when acquiring questioning skills- -watching and observing teachers, being in the field or from student-teacher experience, and workshops.

This dissertation explores the use of history of mathematics in middle school mathematics. A rationale for the importance of the incorporation of historical dimensions (HD) of mathematics is provided through a review of the literature. The literature covers pedagogical, philosophical, psychological, and social issues and provides arguments for the use of history. The central argument is that history can help reveal significant aspects regarding the origins and evolutions of ideas that provide contexts for understanding the mathematical ideas. History can be used as a means to reflect on significant aspects—errors, contractions, challenges, breakthroughs, and changes—of mathematical developments. Noting recent NCTM (2000) calls for school math to include so-called process standards, I contend that incorporating the history of mathematics can be considered as part of this standard. This study examines how HD is addressed in a contemporary mathematics curriculum. Specifically, the study examines the Connected Mathematics Project (CMP) as a case. This curriculum has some historical references which triggered further exploration on how seriously the historical aspects are incorporated. The analysis and discussion focus on four CMP units and interviews with three curriculum experts, eight teachers, and 11 middle school students. The analysis of textbooks and interviews with the experts explore the nature and purpose of historical references in the curriculum. The interviews with teachers and students focus on their perspectives on the importance of HD in learning mathematics. This study examines specifically historical incorporations of the concepts of fractions, negative numbers, the Pythagorean Theorem, and irrational numbers. The analysis reveals that CMP exhibits some level of historical awareness, but the incorporation of HD was not systematically or seriously considered in the development of the curriculum. The interviews suggest that the teachers did not seriously use the limited historical aspects available in the textbooks. The experts’ and teachers’ interviews suggest skepticism about the relevance of HD for middle school mathematics. The teachers’ accounts indicate that students are most interested in topics that are related to their experience and to future applications. The students’ accounts do not fully support the teachers’ assessment of students’ interest in history. I contend that incorporating HD can complement instruction in ways that relate to students’ experiences and to applications besides adding an inquiry dimension to instruction. / text

This study offers a new approach to raising mathematics achievement through the synthesis of Multiple Intelligences theory and Self-Efficacy theory. It proposes that the opportunity to learn through intellectual strengths will raise mathematics achievement both directly from students' increased understanding and indirectly through raising students' self-efficacy for mathematics. A mathematics learning program was developed for year eight students in a rural secondary school based on tasks resonating with their intellectual strengths. Both quantitative and qualitative indicators were used to compare the effects of the Multiple Intelligences learning program with the standard delivery of the mathematics curriculum to year eight students over their first term of study. After nine weeks participation in the Multiple Intelligences learning program, students demonstrated improved engagement and more positive attitudes in mathematics classes relative to their peers receiving standard instruction. The expected gains in mathematics achievement and self-efficacy were not demonstrated within the one-term span of the study. Assessment of the fidelity of implementation of the principles of Multiple Intelligences theory was confirmed through assessment of the classroom learning environment. Analysis of the reasons for the lack of differentiation revealed limitations in the traditional measures used for assessing the mathematics learning outcomes gained within the Multiple Intelligences program. / The loss of available year eight classroom instruction time from institutional assessment requirements and school policy decisions were found to be higher for the class receiving the Multiple Intelligences program than for the comparison class, and this is a significant confounding variable. It is concluded that significant changes to school organisational structures and assessment procedures are required before the cognitive and affective advantages of Multiple Intelligences learning may be realised optimally in the mathematics classroom.

In this study, problem solving provided deeper meaning and understanding through the implementation of a structured problem solving strategy with the teaching of rational numbers. This action-research study was designed as a quasi-experimental model with a control closely matched to an experimental group using similar demographics and number of economically disadvantaged students. In comparison to the control group, the experimental group received their instruction in rational numbers with the addition of a structured problem solving strategy, and a pre/posttest on problem solving with proportionality between similar geometric figures, converting fractions to percents, proportionality with a given ratio, expression of a ratio, and appropriate application of ratios. The study indicates that a structured problem solving strategy can improve the mathematical accuracy, approach and the explanation of rational numbers that are focused on rates, ratio, proportion, and percents. Results showed a statistically significant difference in the performance of these two groups. Effect sizes and 95% confidence intervals (CIs) were reported to support the findings. When examining subgroups, the study showed the structured problem solving stratey not only improved students' ability to understand and use rational numbers but also improved students' problem solving skills and their attitude towards problem solving. The experimental group showed the most improvement in the approach to solving problems with rational numbers indicating deeper understanding of rates, ratios, proportions and percents.

The purpose of this study was to learn about the underlying factors that might help to explain differences in performance and engagement among middle school girls in mathematics. The study employed a qualitative approach to observe and listen directly to the voices of middle school girls and their parents and math teacher as they reflected on their experiences and thoughts about the girls‟ performance in and long-term goals related to mathematics. My goal was to hear what forces were working in and around the girls that might lead them to engagement or disengagement with mathematics. Through the use of journals, interviews, and classroom observations, I collected data on six adolescent girls attending a middle school in a small New England city. The data collected were viewed through several lenses including the triads created by parent-student-teacher and the triads of “high-performing” and “low-performing” girls. Six themes emerged: factoring in the algebra class; finding seats; relating to the teacher; social networking and engagement; untangling performance and engagement; and structuring class. These themes helped to explain some of the differences between the girls‟ performance in and engagement with mathematics. In addition, they suggested that the concept of engagement was contextual and somewhat elusive. The study raised questions about where engagement was taking place (in school or out, in math or another class), whether it was a solitary endeavor or a social creation, and the complex relationship between engagement and performance. Further longitudinal work with girls and young women as they progress through school will be important to the understanding of how, why and when girls engage or disengage from the study of mathematics.

As mathematical modeling gains popularity in K-12 classrooms, it is important to define what this entails for both students and teachers. The following study reviews various definitions of mathematical modeling and how these definitions are relevant for middle grades (5-9) teachers. Following a professional development workshop on mathematical modeling, four middle school teachers expressed their views about teaching mathematics through modeling tasks. This study documents the teachers' perceptions of what it means to model with mathematics, which tasks are most appropriate for their students, and why this is important in each of their classrooms. Although the teachers varied in their views depending on the context and circumstances surrounding each modeling task, they agreed that mathematical modeling helps students build critical thinking skills and provides an opportunity to align mathematics concepts with engaging, realistic phenomena.

Response to Intervention (RTI) has primarily been used as an early intervention in the elementary grades to improve the reading of all students; however, in recent years, mathematics has been added to the program and this addition has not been systematically evaluated. Guided by Deno's problem-solving model, the purpose of this qualitative case study was to gain insight on how middle school mathematics teachers use the problem-solving process to design interventions for struggling students and to understand the strategies they used to implement the plan. The research questions addressed how the problem-solving method is used when creating and implementing interventions, as well as the impact of the intervention on student achievement. The first phase of data collection was a focus group interview with 6 middle school RTI teachers. A convenience sample of participants described how the problem-solving method was used in planning the RTI process. The focus group interview was recorded, transcribed, and coded to find common themes among the responses. Data regarding the RTI implementation, as well as associated instructional strategies, benefits, and challenges were discussed. The second phase of data collection came from mean mathematics state test data from a cohort group of middle school students in 2012, 2013, and 2014. Scores were compared to determine if there was an increase in the percentage of students who scored at levels 3-4, as well as a decrease in the level 1 and 2 scores. Inconsistent data on the state test did not support the findings of the focus group. Social change can be achieved through this RTI mathematics study by providing teachers with instructional strategies that cultivate the growth of academic confidence and achievement of all students in the general education classroom.

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The purpose of this embedded quasi-experimental mixed methods research was to use solving simple linear equations as the lens for looking at the effectiveness of concrete and virtual manipulatives as compared to a control group using learning methods without manipulatives. Further, the researcher wanted to investigate unique benefits and drawbacks associated with each manipulative. Qualitative research methods such as observation, teacher interviews, and student focus group interviews were employed. Quantitative data analysis techniques were used to analyze pretest and posttest data of middle school students (n=76). ANCOVA, analysis of covariance, uncovered statistically significant differences in favor of the control group. Differences in posttest scores, triangulated with qualitative data, suggested that concrete and virtual manipulatives require more classroom time because of administrative issues and because of time needed to learn how to operate the manipulative in addition to necessary time to learn mathematics content. Teachers must allow students enough time to develop conceptual understanding linking the manipulatives to the mathematics represented. Additionally, a discussion of unique benefits and drawbacks of each manipulative sheds light on the use of manipulatives in middle school mathematics.

As the need for educational reform is increasingly recognized, so too is the need for effective professional development (Guskey, 2000). Historically the evaluation of professional development experiences has been limited to exit surveys, noticeably failing to examine the long-term impact of the effort. This study assessed the impact on the classroom learning environment of a yearlong, job-embedded professional development opportunity for middle-school mathematics teachers. The application of learning environment instruments to the evaluation of professional development is a unique feature of this study. The research employed the Questionnaire on Teacher Interactions (QTI) and a modified version of the What Is Happening In this Class? (WillIC) survey with over 1000 middle-school mathematics students in 57 classrooms in the state of Washington. Both instruments were administered at the beginning and end of the school year. Teacher interviews were conducted with a sample of participants in order to further illuminate the impact of the professional development. Data from the study were examined for changes in the learning environment and to cross-validate the QTI and WIHIC with this specific population. Results indicate that the QTI and WIHIC are valid and reliable with the middle-school population is this study. Statistical analyses of learning environment data indicate that any pretest-posttest changes that were observed are mostly likely too small to be of educational significance. This study contributes to a better general understanding of the impact of this professional development, and its findings could be utilized in the preparation of future professional development opportunities.