Bibliography: pages 74-83. / In sum, the theoretical framework proposed here for adult numeracy, and developed from a discourse of mathematics education, has as its task the elaboration of the social implications of principles in adult education and the pedagogic outcomes of three sets of numeracy materials.

Bibliography: pages 177-183. / The dissertation is concerned with the production of a systematic analysis of HSRC research reports into mathematics education in South Africa between 1970 and 1980. Drawing on the theoretical language of Dowling (1995), the analysis focuses on the (re)production of voice and message in the reports. This entails an analysis of positioning strategies that il1ark out voices in the texts and distributing strategies that distribute message across voices. Voices include bureaucratic, academic, teacher and learner voices and knowledge and practices that constitute message distributed to voices relate to mathematical knowledge, pedagogic knowledge and curriculum innovation practices. Positioning and distributing textual strategies with respect to learner and teacher sub-voices are related to the (re)production of theories of instruction that constitute models of acquirers, transmitters and pedagogic contexts and define pedagogic competence in particular ways. The (re)production of theories of instruction in turn are related to the reproduction of social relations in the broader society. It is hoped that the analysis illustrates the generality of Dowling's language for analysing texts. The substantive focus of the study is the analysis of the reports and the language developed in the analysis is used to make some suggestive comments about current mathematics curriculum development in South Africa. It is hoped, in particular, that the focus in this study on discourses in mathematics education in South Africa in the 1970s will contribute to the documenting of the history of mathematics curriculum development in South Africa.

This action research study examined the effects of professional development on teaching for conceptual understanding in Algebra I. “Conceptual knowledge refers to knowledge of the underlying structure of mathematics - the relationships and interconnections of ideas that explain and give meaning to mathematical procedures” (Eisenhart et al., 1993). Conceptual knowledge is “explicit or implicit understanding of the principles that govern a domain and of the interrelations between pieces of knowledge in a domain” (Rittle-Johnson & Wagner, 1999). The study took place in a large metropolitan school district. The participants for the study were two Algebra I instructors with varying pedagogical experiences. Participant #1 is a novice teacher with seven months of classroom experience at the start of this study. The participant holds an undergraduate degree in mathematics and a professional mathematics teaching license. Participant #2 is a tenured teacher with five years of classroom experience at the start of this study. The participant does not hold an undergraduate degree in mathematics and is licensed in special education, not mathematics. The study was formulated in response to the growing difficulty in recruiting qualified mathematics teachers, and the increasing number of mathematics teachers with limited studies in mathematics. Concept-based instruction techniques were presented to participants through a series of six professional development workshops, the first three of which followed classroom observations, and the second three after a second round of observations. The study was qualitative in nature and the collected data were used to develop responses to two research questions. After classroom observations, a concept-based instruction checklist and scoring criteria was used to note evidence of concept-based instruction, as well as any changes to instructional strategies following professional development workshops. Student artifacts were also examined to note evidence of conceptual understanding. Study participants engaged in a semi-structured interview where they were asked to describe changes, if any, to their instructional practices as a result of participating in professional development on teaching for conceptual understanding. The research findings suggested that effective professional development positively affects pedagogical practices in mathematics. After participating in a series of professional development workshops, the researcher observed shifts in participant pedagogical practices that included emphasis on using appropriate math language and encouraging explanations and justifications through questioning as tools for fostering conceptual understanding. Responses to semi-structured interviews suggest that teachers most value professional development that leads to positive impacts on student performance. An analysis of student artifacts demonstrated growth in student written responses and problem-solving approaches. Participant #1 stated: “Participating in this research has allowed me to wonder about the misconceptions and problems within my classroom; I am able to go over student coursework and come up with a solution to better help students with common errors.”

College readiness is a challenge for numerous college-bound students in the United States. A recent high school graduate or returning to school student has to contend with collegiate curricula, unfamiliar faculty, and new peers at a foreign institution. Therefore, acclimating to the new environment and new routine of college is necessary for a student’s success. A natural question that begins to arise is whether or not this experience is different for various subjects and disciplines. Mathematics is among one of the main disciplines in which college readiness is a main concern. Further complicating the situation, a true definition of college readiness is yet to be agreed upon. This qualitative study investigates the perceptions of math college readiness (MCR) of ten participants at a small parochial school. A purposeful sample of three types of individuals participated in the study. In particular, it documents teachers’, administrators’, and alumni’s experiences and how these experiences connect to their definitions of MCR. The primary data collection method was semi structured interviews and observations. Three main ideas emerged from the data relating to the definition of MCR: (1) content, (2) student behavior, and (3) school culture. Specifically, the cumulative characteristic of mathematics requires that gaps in knowledge need to be addressed as early as possible to ensure mastery. Student’s behavior allows for the material to be absorbed more efficiently. School culture plays a role in how this environment is formed in which students become learners and citizens in their community. Investigating how MCR is perceived can shed light on how we will better address the needs of a body of students in mathematics remediation. By examining the learning of mathematics we are offered an opportunity to explore the issues to better understand a remedy. This study provides recommendations for other practitioners in mathematics education.

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The intent of this concurrent mixed method study was to examine teacher perceptions and student applications of cognitive reading comprehension strategy use as applied to the reading and interpretation of a mathematics word problem. Teachers’ perceptions of the relevance and application of cognitive reading comprehension strategies to mathematics contexts were investigated through survey methods. Additionally, students’ cognitive strategy use was explored by eliciting verbalization of cognition using think aloud protocol and clinical interview probes with purposively selected first through sixth-grade students. An experimental component of this study involved the random assignment of teachers to a professional development book study focused on either a) instructional methods supportive of integrated cognitive strategy instruction in reading and mathematics (treatment group) or b) a review of cognitive strategy instruction in reading (control group). The results of this study indicate that the elementary student participants did not recognize the cognitive comprehension strategies that they were using during the initial reading of the mathematical text as relevant to mathematics based text, which is why initial patterns of strategy use were not sustained or renegotiated, but were instead replaced or extinguished without replacement upon identification of the text as mathematical. This may be due to a lack of: 1) domain-general instruction, 2) varied text examples in their schooling, and/or 3) conditional knowledge instruction for strategy use, effects that may be caused by the students’ teachers’ own domain-specific perceptions of cognitive strategy use at the elementary level. The teachers in the treatment group demonstrated greater awareness of the relevance of cognitive reading comprehension strategies for mathematics text than the control group; however, there was no evidence that this new awareness impacted their instruction in this study. Implications for iv professional development, integrated cognitive strategy instruction, and contributions to existing literature are discussed.

Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for students’ poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with certain types of problems almost never presented (Braithwaite et al., 2017). As a result, students often err when they attempt to solve those rare types of problems (Siegler & Pyke, 2013). Two experiments, a pilot study (n = 40 students in grades 5 through 7) and a larger study (n = 127 students in grades 6 and 7), were conducted. These experiments utilized a pretest-intervention-posttest design to empirically test the benefits of providing either a complement of the typical textbook distribution of problems (hyperbalanced practice) or an equal distribution of problems (balanced practice) compared to the benefits of providing a practice set that followed the typical distribution found in math textbooks. A MANCOVA and follow-up ANCOVAs revealed significant differences between students in the textbook condition and students in the balanced and hyperbalanced conditions.For items involving adding fractions with unequal denominators, students who received typical textbook practice showed greater improvement and made fewer strategy errors than students who received hyperbalanced practice. For items involving multiplying two fractions with equal denominators, the opposite was true. Students who received hyperbalanced practice showed greater improvement and made fewer strategy errors than students who received typical textbook practice on items involving multiplying two fractions with equal denominators. Finally, students who received fully balanced practice showed greater improvement and made fewer strategy errors than students who received typical textbook practice on problems involving multiplying one whole number and one fraction. This last finding was of particular interest since none of the practice conditions included practice with that item type. The results of this study demonstrate that even a brief intervention in which students received extra practice with rare item types could improve performance. It also showed that gains in one type of item often resulted in decrements in others, which must be considered when making recommendations to textbook publishers and educators. In sum, this dissertation seeks to make a scholarly contribution to the field by discussing the role that textbooks play in student performance and by analyzing the benefits of supplementing typical textbook instruction with differently balanced fraction arithmetic practice.