<p> A learning center in the southeastern part of the United States used the Singapore mathematics curriculum (SMC) to support student learning of a wide range of mathematics skills. However, a study had yet to be conducted to gain an understanding about the administration and implementation of the program. This case study was conceptually based on constructivist pedagogical theory, where learning is constructed between the teacher and students. The research questions explored how the learning center staff administered and implemented the SMC. Data for this study were collected through multiple in-depth interviews and observations of 2 educators at the learning center. These data were analyzed through typological and inductive analyses in order to discover the underlying meaning of the data. The typologies for this study were bar modeling, textbooks, workbooks, teacher edition, activities, and games. The findings that were derived from these analyses focused on 10 themes, which became the basis of a professional development training project. These themes focused on bar modeling, manipulatives, and stages of learning: concrete, pictorial, and abstract, place value, number bonds, visualization, mastery, and games. The project will support positive social change by increasing educators' insight into how to administer and implement the SMC in order to improve student mathematics achievement.</p>

Although more students are taking courses in statistics before leaving high school, the research base on teaching and learning statistics at the high school level has not accumulated as rapidly (Garfield & Chance, 2000). Very little is known about how secondary school students learn statistics, how the misconceptions they bring to the subject impede their learning, and what should be taught or assessed (Watson & Callingham, 2003). Studies that have investigated these issues tend to focus on the K-5, undergraduate, and graduate levels of education (Groth, 2003). Therefore, more research is needed at the secondary level (Garfield & Chance, 2000). The purpose of this qualitative investigation is to examine how secondary school students' approaches to learning relate to how they assign meaning to statistics. Phenomenography (Marton & Booth, 1997) is the theoretical orientation that frames the study, and it examines the role human experience plays in learning, by reporting variations in the ways participants experience a phenomenon (Dall'Alba & Hasselgreen, 1996). The research questions for the study were: 1) What are the different ways high school students define statistics? 2) What are the different ways high school students learn statistics? 3) What are the different ways students experience learning statistics? The nine participants in the study were high school graduates who completed a course in Statistics or Advanced Placement Statistics while enrolled in high school in a suburban area in the southeast. Data sources were semi-structured interviews and journaling. Using phenomenographic methodology, students' descriptions of the experience of learning were analyzed and coded. An outcome space of the collective experiences was constructed. A hierarchical relationship between students' approach to learning and their learning strategies was found. Also, a hierarchical relationship between students' approaches to learning and the meaning they assigned to statistics was found.

<p> Due to recent waivers and current expectations of teacher performance, schools have been tasked to close their student achievement gaps in mathematics by 2014. Yet students still have not performed well in mathematics, which may be a direct link to teachers' instructional practices. Identifying a coaching model to improve student achievement and teachers' instructional practices is important to district leaders, school administrators, and teachers. The purpose of this study was to evaluate how a coaching practice with teachers affected student achievement in elementary mathematics. The theoretical foundation of this study was the coaching model, first used by Joyce and Showers, which theorized that teachers who participated in this type of professional development would improve their instructional practices in the classroom, and subsequently, student achievement. A quasi experimental design was employed to test the theory that teachers who were coached would improve student achievement in elementary mathematics. A total of 185 test scores from students were analyzed using an independent measures <i>t</i> test and a repeated measures <i> t</i> test. Findings suggested that the achievement scores of students whose teachers were coached were statistically higher on both state and local assessments. Fourth grade students showed improvement on both the local and state assessments, while 5^th and 6^th grade students demonstrated significant differences on the local assessments only, but not on the state assessments. This research contributes to positive social change by providing educators with a coaching model that demonstrates how teacher coaching can increase student achievement in elementary mathematics, Grades 4 through 6.</p>

<p> In this study, I examined the relation between various construct relevant and irrelevant variables and a math problem solving assessment. I used independent performance measures representing the variables of mathematics content knowledge, general ability, and reading fluency. Non-performance variables included gender, socioeconomic status, language proficiency and special education qualification. Using a sequential regression and commonality analysis, I determined the amount of variance explained by each performance measure on the Oregon state math assessment in third grade. All variables were independently predictive of math problem solving scores, and used together, they explained 58% score variance. The math content knowledge measure explained the most variance uniquely (12%), and the measures of math content and general ability explained the most variance commonly (16%). In the second analysis, I investigated whether additional variance was explained once student demographic characteristics were controlled and how this affected the unique variance explained by each independent performance measure. By controlling for demographics, the model explained slightly more than 1% additional variance in math scores. The unique variance explained by each independent measure decreased slightly.</p><p> This study highlighted the influence of various construct relevant and irrelevant variables on math problem solving scores, including the extent to which a language-free measure of general ability might help to inform likely outcomes. The use of variance partitioning expanded understanding of the unique and common underlying constructs that affect math problem solving assessment. Finally, this study provided more information regarding the influence demographic information has on outcomes related to state math assessments.</p>

<p> Too often, low socioeconomic school districts are associated with low performing students. The NCLB Act of 2001 dictates closure of the achievement gap by year 2014. Twenty-first century education must include instructional practices that use technology to enhance student learning. The non-experimental quantitative causal-comparative research study examined archival data from a Northwestern Arizona school district which included two dependent variables&mdash;the spring AIMS assessment and the spring ATI assessment. The statistical analysis used descriptive statistics to determine the effect of SRS on student academic achievement in mathematics. The data derived from 7th and 8th grade students to examine the ratio of the students&rsquo; scores in the highest category named Above, that included students&rsquo; scores which performed in the higher performance scale ranges on both assessments comparing the ratio of students&rsquo; scores in the Below category, that included students&rsquo; scores which performed in the lowest performance ranges on both assessments. Since the school district did not purchase the SRS technology until the 2010-2011 school year, the archival data from 2010 spring tests when students did not utilize SRS in the classroom was compared to the archival data from 2011 spring tests when students utilized SRS in the classroom environment. The data was compared horizontally from one year to the other: 7th grade to 7th grade and 8th grade to 8th grade on each test. In addition, the data was compared vertically from one year to the other: 7th grade to 8th grade on each test. The results of the research study can be used and replicated to help close the achievement gap.</p>

<p> A purpose of this study was to explore the inter-relations among eighth grade mathematics student achievements in the content domains of <i>Number, Algebra, Geometry, and Data &amp; Chance</i> and the cognitive domains of <i>Knowing, Applying, and Reasoning,</i> in the context of the Trends in International Mathematics and Science Study (TIMSS), 2007. A second purpose was to find the associations between student achievements in the cognitive domains with student-related, teacher-related, school-related, and home-related variables. The variables were selected mainly on the basis of Carroll's model of school learning. Further, the math achievement of the students of the United States in each of the domains was compared with <i> Bulgaria, Chinese Taipei, Republic of Korea, Singapore,</i> and <i> Thailand.</i> After analysis, interpretations were made on the findings of the relationships among student achievements in each of the content and cognitive domains and also on the associations between variables and math achievement in the four content domains. Further, comparative performance of the U.S. with each of the five selected countries in each of the seven domains was analyzed. For finding the relationships among student performance scores across all the countries in eighth grade mathematics in different domains, Pearson's product moment coefficient of correlation was used as the measure. For finding the associations of the scores with the variables, multiple regression method was employed. Finally, for comparing student performances of the U.S. with other states, independent samples <i>t</i>-test was used. </p><p> The findings of this study indicated that student performance in all the content and cognitive domains were highly correlated. The second finding was that the variable <i>'School Resources'</i> was significantly related to student performance in each of the content domains, whereas <i> 'Overall Home Involvement'</i> had moderately significant relation with student achievement in <i>Number</i> and <i>Data &amp; Chance. </i> The findings revealed no significant relation between the other variables considered and student achievement in the four content domains. The third finding showed that <i>Chinese Taipei, Republic of Korea,</i> and <i>Singapore</i> outperformed the U.S. in all the domains, whereas the U.S. performed better than <i>Bulgaria</i> and <i>Thailand </i> in each of the domains. These results provide some clues for improving classroom instruction and streamlining administrative priorities in order to improve student performance in the United States. Furthermore, the results indicate paths for further research in order to augment the educational practice not only in the U.S., but in all countries, for securing better student achievement in mathematics.</p>

<p> The purpose of this Executive Position Paper project was to develop resources for improving Individual Educational Program (IEP) mathematics learning goals for conceptual understanding of fractions for middle school special education students. The investigation surveyed how IEP mathematics learning goals are currently determined and proposed a new approach. It demonstrated how the approach would work through a pilot project in which two tools were developed: (1) a list of learning goals for goal writers to use as a reference when writing mathematics learning goals for middle school special needs students and (2) an assessment linked to the goals that would determine whether or not a student has achieved the goals. A description is given of the process that combines knowledge from research literature and information from instructional practice and that continually refines the products.</p><p> For this pilot project the learning goals were focused on order and equivalence of fractions. The goals were identified through a review of educational literature and examination of several sources related to practice for teaching fractions. Assessment items were then developed for the goals. Four experts reviewed the learning goals and assessments for content and clarity and the assessments for validity. Based on their feedback, edits were made to both the learning goals and the assessment items. Four middle school teachers field tested the assessment with their students. Analysis of student work confirmed that the assessment revealed detailed information on individual students' strengths and weaknesses in conceptual understanding of order and equivalence of fractions and that appropriate learning goals could be selected as a result of the assessment. </p><p> Final recommendations include expanding the project to additional math content and other grades and developing instructional lessons and resources linked to the learning goals that teachers could use to help students achieve the learning goals. Additionally, it is recommended that a system of continual improvement be incorporated into the process of further development.</p>

The use of technology has become increasingly popular in mathematics education. Instructors have implemented technology into classroom lessons, as well as various applications outside of the classroom. This thesis outlines technology developed for use in a first-year calculus classroom and investigates the relationship between the use of weekly formative online Maple T.A. quizzes and student performance on the final exam. The data analysis of the online quizzes focuses on two years of a five-year study. Linear regression techniques are employed to investigate the relationship between final exam grades and both how a student interacts with and performs on the online quizzes. A set of interactive class notes and a library of computer demonstrations designed to be used in and out of a calculus classroom are presented. The demonstrations are coded in Maple and designed to give geometric understanding to challenging calculus concepts.

The purpose of this study was to examine factors supporting college mathematics success. First, effect of a brief high school orientation to mathematical technologies used for college placement testing was examined. Secondly, the voice of participants in this orientation was heard. Finally, bootstrapped orientation data were presented to teachers and instructors of introductory statistics courses as a scaffold to their technological pedagogical content knowledge (TPCK) as these teachers and instructors strive to actively engage students to achieve college mathematics success. Many entering college students are placed into developmental mathematics classes based on scores from college placement assessments that allow extremely limited use of calculating technology and have various time constraints. Students in a rural central Texas 3A high school that were enrolled in Algebra II course were given pre- and post- tests in Arithmetic and Algebra. Each 20-minute test contained 15 mathematical content questions and one qualitative question. The post-test was given approximately a week after the pre-test. During the week, students were provided time to explore review material using only pencil and paper for the arithmetic review, and a four-function calculator on the algebra review questions. Effects of the orientation were analyzed using mean scores, confidence intervals, effect size, and GLM for whole-group and sub-groups. A paired samples t-test was calculated. These effects were discussed. A case study involving participants of the orientation was conducted. Twelve participants were interviewed after each had entered college. Five themes emerged from these interviews: (1) Knowledge of College Mathematics, (2) Technology and Mathematics, (3) Mathematics Tests/Assessments, (4) Teaching and Learning Mathematics, and (5) Mathematical Experiences, Hopes and Dreams. Each theme is discussed. Using Microsoft Excel, bootstrapping is presented to instructors of first year introductory statistics courses in support of student success as instructors’ technological pedagogical content knowledge is developed. A course project demonstrating and developing application of computational technology by bootstrapping confidence intervals at the 95 % level using Microsoft Excel is presented. Data from the orientation were further analyzed in the bootstrapping project. Confidence intervals were empirically calculated from bootstrapped resamples of the mean. The number of resamples used was 250 at each of three levels: Over-sampling, at-sampling, and under-sampling. Graphs of bootstrapped confidence intervals, using the Rule of Eye 4, showed statistically significant differences between pre-test and post-test scores for all pairs of data sets.

This qualitative case study describes how two teachers translate communication messages from curriculum statements into classroom practice. These illuminative cases illustrate the perspectives and practices of two teachers who support the spirit of the Ontario Mathematics Curriculum by working to implement communication in the Foundations of Mathematics (MFM1P), Grade 9, Applied course (Ontario Ministry of Education, 2005). Data for this study were collected from individual interviews with teachers, classroom observations, and document analysis. Grade 9 Applied mathematics teachers across Ontario indicate on surveys that they support communication in the mathematics classroom (Education Quality and Accountability Office, 2007; Suurtamm & Graves, in press). Despite evidence of support for this aspect of the curriculum, findings from this study point to a need for finer analysis of teachers’ perspectives and practices when it comes to communication in mathematics. The cases presented in this thesis illustrate different images, or meanings, associated with communication in mathematics. Furthermore, even in unique cases where the gap between curriculum developers and teachers images is minimal, the idealized vision of communication may not be realized in classroom practice since teachers may face challenges in implementation. The teachers report that despite additional challenges involved with implementing communication in Grade 9 Applied mathematics, teaching in this context can be a rewarding experience. To minimize the gap between images of communication that are translated from curriculum statements into classroom practice, findings from this study indicate that curriculum developers must find ways to help teachers understand the rationale behind curriculum initiatives. Future research might explore ways to help familiarize teachers with the theory and research underlying communication in mathematics. Research might also examine the impact that these initiatives have on teachers’ perspectives and practices. / Thesis (Master, Education) -- Queen's University, 2008-08-27 16:18:13.815