This study was designed to analyze if preferences for certain statistical representations existed for a group of pre-service secondary mathematics teachers. Twenty-three surveys were distributed to two classes of pre-service teachers enrolled in a mathematic education course and 18 competed surveys were returned. Questions on the survey focused on five major statistical ideas: (1) typical value for a data set, (2) standard deviation, (3) spread/distribution of a data set, (4) recognition/effect of outliers, and (5) comparing two or more data sets. Students were asked to indicate the representation that they found most helpful in answering these questions. Students chose from box plots, dot plots, histograms, and data tables. The conclusions drawn from this study involved the use of two types of statistical analyses combined with observed trends within the data. A goodness of fit test determined that within each of the main ideas, representational preferences existed. Confidence intervals were used in combination with observed preferences to determine if and where individual representational preferences existed. The results indicated that these pre-service teachers typically focused on median as typical value for a data set, felt that any of the graphs could be used to determine distribution, lacked a complete understanding of standard deviation, and that their initial focus on individual points when recognizing outliers developed into a more global view of the data as they reasoned about the outliersâ effects. Discussions and implications from this survey along with recommendations for future research are included.

The purpose of this study was to investigate students? understanding of proof and proof writing using a new three-column method. The new three-column method consists of the traditional ?statements? and ?reasons? columns but also contains a ?picture? column in which students must draw a picture that corresponds to the ?statement.? It is believed that this third column will act as a blue print providing students with a visual representation of how the proof is constructed. By examining this blueprint students will understand which steps are needed to complete the proof as well as the proper order of those steps. Thus, students develop a deeper understanding of the proof writing process. The study was conducted in a suburban school in central North Carolina and involved two standard geometry classes. The study lasted for a week and a half and was instituted during a chapter involving different triangle congruencies (i.e. SAS, SSS, etc). The three-column proof was taught to a 3rd period class containing 31 students. Their test and quiz scores were compared to a 2nd period class containing 23 students. After examining the average quiz and average test scores for the chapter it was shown that the 3rd period class did not out score the 2nd period class. Thus, the use of a three-column picture proof is as effective as the traditional approach. An important question pursuant to this outcome is whether there are other teaching/learning benefits from using picture proofs. For example, interviews with the cooperating teacher indicated that the three-column proof was very helpful for several students and also provided good teacher feedback as to students? understanding of theorems and postulates used in proof writing.

The purpose of this research was to investigate how the order of mathematical instruction with respect to using a context affects studentsâ performance in the classroom and their attitudes towards learning. The study examined two high school Algebra I classes and was implemented over three days. On Day 1 of the study, the experimental group received the implementation of learning in a contextual setting while the control group learned in a noncontextual setting. In the noncontextual setting, students learned about one and two step equations where a lecture style lesson was implemented. On Day 2 of the study, each of the two groups received the type of instruction the other group received on Day 1. The experimental group received the traditional approach method where the control group learned the mathematics in a contextual setting. The study determined that there is a difference in studentsâ academic performance when they learn in a contextual setting first and then learn the math in a traditional based approach as opposed to learning in a traditional setting first and then learn in a contextual setting. Studentsâ attitudes toward learning in a contextual setting without regards to order were more positive. Finally, the order of instruction with respect to using a context affects lower ranked studentsâ levels of performance in the classroom more than middle or higher ranked students, but not significantly more.

The purpose of this literature review is two fold. The first is to examine the types of geometric proof and their purpose within the classroom setting and secondly to examine the factors that influence students? understanding of proofs and their proof construction. The research focuses on three main types of proof 1) Proof for the development of proficiency, 2) proof for understanding, and 3) proof for exploration. In addition to these proof types the research focuses on three components that influence students? development and understanding of proof: 1) the role of technology in students? mastery of proof, 2) the role of curricula and teachers in students? mastery of proof, and 3) the role of the student in their own mastery of proof. Through an investigation into the types of proof and the beliefs and misconceptions of individuals who teacher, learn and write proofs, the author attempts to highlight the reasons for teaching geometric proof and the responsibilities of both teachers and students in the developing understanding in and through geometric proof.

The purposes of this study were to investigate preservice mathematics teachersâ orientations, content knowledge, and pedagogical content knowledge of probability; the relationships among these three aspects; and the usefulness of tasks with respect to examining these aspects of knowledge. The design of the study was a multi-case study of five secondary mathematics education preservice teachers with a focus on their knowledge as well as tasks that were used in this study. Data from individual interviews and test items were collected and analyzed under a conceptual framework based on the work of Hill, Ball, and Schilling (2008); Kvatinsky and Even (2002); and Garuti, Orlandoni, and Ricci (2008). The researcher found that the preservice teachers held multiple orientations towards probability yet tended to be mostly objective (mathematical and statistical) with little evidence of subjective orientations. Relationships existed between the preservice teachersâ orientations and their content knowledge, as well as their pedagogical content knowledge. These relationships were found more in tasks where they were required to make a claim about a probability within some sort of real-world context. The researcher also found that tasks involving pedagogical situations tended to be more effective at eliciting knowledge than tasks involving only questions.

<p>ALLAIN, ASHLEY. Development of an Instrument to Measure Proportional Reasoning Among Fast-Track Middle School Students. (Under the direction of North Carolina State University Graduate Faculty). The purpose of the study was to develop a reliable and valid instrument for measuring proportional reasoning among fast-track middle school girls in Wake County, North Carolina. The study sample consisted of 70 girls who attended the summer 2000 Girls on Track program at Meredith College located in Raleigh, North Carolina. The grade level for each of the participants ranged from 6th grade through 8th grade for the 2000-2001 school year. The instrument used in this study is the Proportional Reasoning Assessment Instrument. This instrument was developed by the researcher and is based upon problems discussed in relevant literature. The test items chosen include missing value, comparison, mixture, associated sets, part-part-whole, graphing and scale problems. The instrument is comprised of 10 open-ended items of varying difficulty levels. Data were analyzed using Statistical Package for the Social Sciences Version 10.0 (SPSS) and EXCEL. A four-point grading rubric was used to score each test item. Two measure of internal consistency were calculated to determine reliability: Chrombach?s coefficient alpha and inter-rater reliability. A panel of experts examined the test instrument for the qualities of relevance, balance, and specificity to establish content validity. Criterion validity was established through determining the correlation between students? scores on the Proportional Reasoning Assessment Instrument and the students? scores on the North Carolina End-of-Grade exam. A detailed item analysis was performed including item difficulty, item discrimination, item means, item variances, and inter-item correlations.Results from the study reveal the Proportional Reasoning Assessment Instrument is a reliable and valid test instrument for measuring proportional reasoning among fast-track middle school girls. In addition, the instrument revealed common misconceptions among the students in the sample. The overall coefficient alpha is and inter-rater agreement was 96%. The average difficulty is and the average discrimination is . Each test item contributed to the central purpose of the instrument due to the absence of negative discrimination indices.<P>

Thesis (Ph. D.)--Open University. BLDSC no. DX94611.

Thesis (Ph. D.)--Columbia University, 1942. / Bibliography: p. 219-230.

Thesis (Ph. D.)--Columbia University, 1942. / Bibliography: p. 219-230.

Thesis--Gothenburg. / Summary in English. Includes bibliographical references (p. 136-142).