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.

<p>This study investigated real life situations which learners in South Korea grade 8-10 learners would prefer to be used in school mathematics. This thesis is based on the ROSMEII (Relevance&nbsp / of School Mathematics Education) questionnaires and interviews, which was used to examine the preferred mathematical learning contexts for South Korean grade 8-10 learners. The study&nbsp / investigates the affective factors that pupils perceive to be of possible relevance for the learning and teaching of mathematic / and is aimed at providing data that might form part of a basis for a&nbsp / local theory of the mathematics curriculum. The standardized ROSMEII survey questionnaire of 23closeended items that relate to some aspects of mathematics on a 4-point Likert-type scale&nbsp / was administered to Korean grade 8-10 learners at the end of compulsory schooling, and mainly 14 to 16 year old cohorts. The data for this study were collected from a sample of 1839 learners drawn from 26 South Korean schools in the year 2009. Interviews were conducted to gauge the pupils&lsquo / preference of the ROSMEII questionnaire contexts and used to validate learners&lsquo / responses. In&nbsp / analyzing their responses, it became clear that, on the average, views expressed were common to all groups of pupils in South Korea (whether male or female, or from the metropolitan, city, or countryside). The clusters of the most preferred mathematical learning contexts are linked to youth culture, which learners are usually and easily engaged with in one way or another. These&nbsp / clusters include the sports, leisure and recreation cluster / planning a journey/popular youth culture cluster the technology cluster / the making of computer games, storing music and videos on&nbsp / CD&lsquo / s and Ipods. The lowest preferred mathematical learning contexts are: an agricultural cluster which focuses on agricultural matters and traditional games (yut). In conclusion, this study&nbsp / suggests that teachers should use contexts that increase learners&lsquo / interest in classroom activities. Therefore mathematics curricula and textbooks which are appropriate to this context must be&nbsp / provided in order to provide more efficient mathematics education. It is imperative that the Korean school system must develop a particular program for nurturing learners&lsquo / mathematical power.&nbsp / Furthermore, mathematics education policy makers must reconsider whether the current education system is appropriate, and also listen to learners&lsquo / preferences when designing appropriate&nbsp / mathematics curriculum and textbooks.</p>

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.

Thesis (M. Ed.)--Kutztown State College. / Source: Masters Abstracts International, Volume: 45-06, page: 2787. Typescript. Includes bibliographical references (leaves 33-35).

University-based initial teacher education aims at instilling in teacher candidates the idea of the interconnectedness of content, pedagogical and educational research knowledge by allowing meaningful interaction between teacher candidates and teacher educators. The theory-practice divide is presented in the literature as barrier to achieving this goal. This mixed methods research study re-conceptualizes the theory-practice divide from a problem into an opportunity. Secondary school teacher candidates can use contradictions and tensions, surrounding the theory-practice divide, for synthesizing diverse perspectives on content, pedagogical and educational research knowledge. They can integrate this perspective in their practice teaching. The study examined secondary school teacher candidates’ perspectives on the interaction of their content, pedagogical and educational research knowledge in practice teaching as well as factors contributing to these perspectives. The study found that participants’ different perspectives on their research pedagogical and content knowledge (RPACK) were associated with the different levels of their reform-mindedness in mathematics education as measured by a survey. The low, medium and high reform minded participants placed as the first priority pedagogical knowledge, content knowledge and educational research knowledge, respectively.

University-based initial teacher education aims at instilling in teacher candidates the idea of the interconnectedness of content, pedagogical and educational research knowledge by allowing meaningful interaction between teacher candidates and teacher educators. The theory-practice divide is presented in the literature as barrier to achieving this goal. This mixed methods research study re-conceptualizes the theory-practice divide from a problem into an opportunity. Secondary school teacher candidates can use contradictions and tensions, surrounding the theory-practice divide, for synthesizing diverse perspectives on content, pedagogical and educational research knowledge. They can integrate this perspective in their practice teaching. The study examined secondary school teacher candidates’ perspectives on the interaction of their content, pedagogical and educational research knowledge in practice teaching as well as factors contributing to these perspectives. The study found that participants’ different perspectives on their research pedagogical and content knowledge (RPACK) were associated with the different levels of their reform-mindedness in mathematics education as measured by a survey. The low, medium and high reform minded participants placed as the first priority pedagogical knowledge, content knowledge and educational research knowledge, respectively.

<p>This study investigated real life situations which learners in South Korea grade 8-10 learners would prefer to be used in school mathematics. This thesis is based on the ROSMEII (Relevance&nbsp / of School Mathematics Education) questionnaires and interviews, which was used to examine the preferred mathematical learning contexts for South Korean grade 8-10 learners. The study&nbsp / investigates the affective factors that pupils perceive to be of possible relevance for the learning and teaching of mathematic / and is aimed at providing data that might form part of a basis for a&nbsp / local theory of the mathematics curriculum. The standardized ROSMEII survey questionnaire of 23closeended items that relate to some aspects of mathematics on a 4-point Likert-type scale&nbsp / was administered to Korean grade 8-10 learners at the end of compulsory schooling, and mainly 14 to 16 year old cohorts. The data for this study were collected from a sample of 1839 learners drawn from 26 South Korean schools in the year 2009. Interviews were conducted to gauge the pupils&lsquo / preference of the ROSMEII questionnaire contexts and used to validate learners&lsquo / responses. In&nbsp / analyzing their responses, it became clear that, on the average, views expressed were common to all groups of pupils in South Korea (whether male or female, or from the metropolitan, city, or countryside). The clusters of the most preferred mathematical learning contexts are linked to youth culture, which learners are usually and easily engaged with in one way or another. These&nbsp / clusters include the sports, leisure and recreation cluster / planning a journey/popular youth culture cluster the technology cluster / the making of computer games, storing music and videos on&nbsp / CD&lsquo / s and Ipods. The lowest preferred mathematical learning contexts are: an agricultural cluster which focuses on agricultural matters and traditional games (yut). In conclusion, this study&nbsp / suggests that teachers should use contexts that increase learners&lsquo / interest in classroom activities. Therefore mathematics curricula and textbooks which are appropriate to this context must be&nbsp / provided in order to provide more efficient mathematics education. It is imperative that the Korean school system must develop a particular program for nurturing learners&lsquo / mathematical power.&nbsp / Furthermore, mathematics education policy makers must reconsider whether the current education system is appropriate, and also listen to learners&lsquo / preferences when designing appropriate&nbsp / mathematics curriculum and textbooks.</p>

Philosophiae Doctor - PhD / This study investigated real life situations which learners in South Korea grade 8-10 learners would prefer to be used in school mathematics.This thesis is based on the ROSMEII (Relevance of School Mathematics ducation) questionnaires and interviews, which was used to examine the preferred mathematical learning contexts for South Korean grade 8-10 learners. The study investigates the affective factors that pupils perceive to be of possible relevance for the learning and teaching of mathematic; and is aimed at providing data that might form part of a basis for a local theory of the mathematics curriculum. The standardized ROSMEII survey questionnaire of 23closeended items that relate to some aspects of mathematics on a 4-point Likert-type scale was administered to Korean grade 8-10 learners at the end of compulsory schooling, and mainly 14 to 16 year old cohorts. The data for this study were collected from a sample of 1839 learners drawn from 26 South Korean schools in the year 2009. Interviews were conducted to gauge the pupils‘ preference of the ROSMEII questionnaire contexts and used to validate learners‘ responses. In analyzing their responses, it became clear that, on the average, views expressed were common to all groups of pupils in South Korea (whether male or female, or from the metropolitan, city, or countryside). The clusters of the most preferred mathematical learning contexts are linked to youth culture, which learners are usually and easily engaged with in one way or another. These clusters include the sports, leisure and recreation cluster; planning a journey/popular youth culture cluster the technology cluster; the making of computer games, storing music and videos on CD‘s and Ipods. The lowest preferred mathematical learning contexts are: an agricultural cluster which focuses on agricultural matters and traditional games (yut). In conclusion, this study suggests that teachers should use contexts that increase learners‘ interest in classroom activities. Therefore mathematics curricula and textbooks which are appropriate to this context must be provided in order to provide more efficient mathematics education. It is imperative that the Korean school system must develop a particular program for nurturing learners‘ mathematical power. Furthermore, mathematics education policy makers must reconsider whether the current education system is appropriate, and also listen to learners‘ preferences when designing appropriate mathematics curriculum and textbooks.