This case study described the experiences of secondary students and preservice mathematics teachers in the teaching and learning of social justice mathematics (SJM). Specifically, participants’ experiences in making connections among the mathematics curricula and the real world, perceptions about mathematics, and responses to an integrated curriculum approach were described. Students participated in SJM activities designed by preservice teacher participants: one component of a pre-existing extracurricular Social Issues Club at a high school in Southeastern Ontario. Mathematics activities, led by the researcher or one of the preservice teacher participants, were designed to complement the social justice issues that were being explored by the members of the Social Issues Club. Data were obtained through observations, questionnaires, focus group, individual interviews, written reflections, and artifacts. Results demonstrated that preservice teacher participants had unique professional and educational encounters prior to SJM that they connected to their SJM experience. Subsequent to this experience, preservice teachers suggested limited ideas about integrating curriculum into their future teaching practice beyond the content and contexts made familiar to them through SJM. With limited exposure to examples of curriculum integration identified by preservice teachers as a barrier, results suggest that preservice teachers need more opportunities to engage in mathematics curriculum integration. Students showed an expanded view of connections between mathematics and the real world through their descriptions of the various ways in which SJM had helped them to apply mathematics concepts and understand the issues they were exploring. They enjoyed SJM’s collaborative mathematics learning approach and valued the opportunity to discuss the social issues about which they were concerned. Although the preservice teachers were confident about what they thought to be topics of interest for secondary students, there was a disconnect between students’ choices of contexts for mathematics learning and the beginning teachers’ assumptions about students’ interest. This finding suggests that there is a need to support preservice teachers to understand students’ interests in mathematics learning and that students’ opinion needs to be solicited. In addition, participants’ visions about enhancing mathematics teaching and learning through collaboration and providing students with autonomy allowed suggestions for the practice of mathematics teaching. / Thesis (Master, Education) -- Queen's University, 2012-10-14 16:18:44.922

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Thesis (Ed.M.)--Boston University

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The purpose of this grounded theory study was to discover the factors that contribute to the success or failure of college algebra for students taking college algebra by distance education Internet, and then generate a theory of success or failure of the group of College Algebra Internet students at one Utah college. Qualitative data were collected and analyzed on students’ perceptions and perspectives of a College Algebra Internet course that they took during the spring or summer 2006 semesters at a bachelor’s degree-granting college in Utah. The participants were chosen from any of the six sections, and purposeful sampling was applied. Interviews played a major role in data collection. Each interview took place in person and was taped and later transcribed for analysis. The outcomes showed that one theme emerged as the catalyst for success for a College Algebra Internet student, that of self-responsibility. Four other themes found in the data helped, but were not necessary for success. Many enrolled based upon past experiences with personal environmental factors. It also helped to have a solid mathematical background, a good attitude, and a strong structural support network. However, those participants who prioritized and devoted their time to enriching their mathematical skills and staying focused on the goal had the most success in the course regardless of any other factor. By setting aside time and staying completely devoted to the course from the very beginning established, above all else, a successful outcome. Motivation to continue in this path occurred either from an outside influence or by an innate drive to be successful in the course.

There has been much attention about improving the skills and abilities of students in Science. One critical factor is the quality of teacher education programs for preparing science teachers. There has been little research and much debate about what constitutes an effective science teacher education program. Teacher beliefs are thought to be important factors which influence how science teachers teach. This is a three year longitudinal study which explores changes in twelve teachers using a mixed method design. Semi-structured interviews were used to explore the beliefs about teaching, learning, and the Nature of Science. Four cohorts of teachers represented the different critical stages of the teaching continuum. Two cohorts of teachers represented entry and exit stages of preservice education. The other two cohorts represented teachers who taught less than four years and more than four years in the classroom. Classroom observations and self-reported surveys were gathered. The major outcomes of this research include: 1) Teacher beliefs about teaching and learning shift towards being more student-centered during their preservice education; 2) Despite previous reports that most graduates revert to teacher-centered beliefs in the first years of teaching, the beliefs of Iowa preservice teacher beliefs, remained similar to their previous student-centered beliefs 3) Teacher beliefs about the Nature of Science, which were initially represented as a socially constructed entity, became less frequent as teachers progress through the teaching continuum from preservice to inservice teachers; 4) Student-centered beliefs about teaching and learning, derived from teacher interviews, are correlated with classroom observations and self-reported surveys of instructional strategies. The findings from this study shed light on understandings concerning the evolution of teacher beliefs. Factors effecting teacher beliefs include college preparatory education programs, school communities, and the individual teachers themselves. There is a need to continue explorations of how these factors are interrelated, as well as how to influence and sustain the development of reformed-based beliefs about teaching and learning in order to influence instructional practices.

The purpose of this study was to investigate the relationship between addition and subtraction as inverse operations, to determine how drill in addition facts will affect knowledge of subtraction facts; to infer, if possible, when addition is conceptualized as an operation with reversibility; and to determine at which grade levels a particular method of drill is effective. The sample was drawn from Logan, Utah , small, city school district of 3700 students. The experimental groups consisted of 12 elementary and eight secondary existing classrooms of students. The control groups consisted of 10 elementary and five secondary existing classroom groups. A total of 1007 elementary and secondary students were involved in the study. The sample included treatment and control groups from first through the ninth grades. The treatment consisted of administering drill on the addition facts, to classroom groups using the overhead projector. All students were tested three times, at the beginning of the study, after one week and after two weeks; using two tests, an Addition Facts Test, which contained the 100 basic addition facts, and a Subtraction Facts Test which contained the 100 basic subtraction facts. Four scores were considered for each test; "time'', the "number left out", the "number missed", and the "total error". Gain scores showing loss or progress from the pretest to each of the two posttests were computed for each of these four scores. All groups corrected their own test papers immediately after taking the tests . The statistical analysis included the following: Correlation coefficients were computed between addition and subtraction scores for each of the four scores mentioned. Correlation coefficients were computed between the addition and subtraction scores for each gain score. Two-way analyses of variance were computed for grade level effect and treatment effect for each of the 16 gain scores. The results included: The correlation coefficients for addition and subtraction "time" scores were positive and significant at every grade level. The correlation of the first grade, .30, was significantly lower than that of the second grade, .72. The correlations showed an increasing trend to .87 at the seventh grade, then a falling off in the eighth and ninth grades. The correlation coefficients for addition and subtraction error scores were positive and significant for the "number left out" and "total missed" scores for grades one through seven. For the two posttests, the correlation coefficients for the "time" gain scores from the first grade were negative. They were positive and significant for grades two, four, five, seven, and eight. The results for the correlation of error gain scores were mixed. Of the 16 two-way analyses of variance for gain scores, five showed significant F ratios, two were concerned with addition and three with subtraction; four analyses showed significant grade level effect, three analyses showed significant treatment effect, and two showed significant interaction. On nine scores there were large differences between fir s t and second grade grou ps . The results are consistent with what one would expect if first grade students had not formed the concept of addition as an operation with reversibility. The results are consistent with what one would expect if: at the second grade level, addition were conceptualized as an operation with reversibility for a good portion of the students, yet the r e were a good number for whom this reversibility were limited or inoperative; the concept of addition as an operation continued to develop with a more pronounced reversibility during grades three and four. It was concluded that: First grade children do not possess the requisite understanding to profit from drill of the type used in this study. Second grade students have a good start on understanding and can profit from practice experiences in addition and subtraction. Maximum gains were made in third and fourth grade gr oups with the type of drill used in the study.