Thesis / Dissertation

  • This study investigated the relationship between students' learning styles and their choice of grade weightings for and performance on three classroom assessment instruments. The student learning styles were measured using McCarthy's Learning Type Measure. Students chose weightings for a take home examination, a research project, and an in-class examination. The sample for the study consisted of 44 students in two sections of an elementary statistics course at an urban community college. Using analysis of variance of the weighting and performance data when organized by student learning type, the investigator found no significant relationship between learning types and the grade weightings and no significant relationship between learning types and performance on the assessment instruments. There was a significant positive correlation between the score for Type 2 learners and the performance on the in-class examination and also a significant positive correlation between the score for Type 4 learners and the weight assigned for the project. Both of these correlations validate the characteristics of these learning types as they are conceptualized by McCarthy, Kolb, and others. Type 4 learners are generally risk takers and learn by perceiving through concrete experience and processing through active experimentation. Type 2 learners generally perceive information through reflective observation data, the investigator conducted clinical interviews to ascertain differences between students' rationales for their grade weightings and how student learning styles may have affected students' performances on the various assessment instruments.

  • Notre probl&eacute;matique se situe dans le cadre de la lecture et l'interpr&eacute;tation des repr&eacute;sentations graphiques des donn&eacute;es statistiques (RGDS), enseign&eacute;es au niveau secondaire. Pour mieux la fonder, nous avons proc&eacute;d&eacute; &agrave; l'&eacute;tude de l'&eacute;volution des programmes de statistique du niveau coll&eacute;gial et secondaire, &agrave; l'analyse descriptive des orientations p&eacute;dagogiques associ&eacute;es &agrave; ces programmes et &agrave; celle des manuels scolaires correspondants. Comme nous avons proc&eacute;d&eacute; &agrave; l'analyse des r&eacute;sultats d'un questionnaire que nous avons adress&eacute;, dans ce but, &agrave; des enseignants de math&eacute;matiques du secondaire. Notre revue de litt&eacute;rature a permis de pr&eacute;ciser le sens de la terminologie utilis&eacute;e, d'&eacute;laborer un mod&egrave;le de compr&eacute;hension des RGDS, utile pour l'analyser de nos graphiques et de d&eacute;gager les diff&eacute;rentes fonctions des RGDS &agrave; partir d'une &eacute;tude de l'&eacute;volution historique de ce type de graphiques. Ces &eacute;l&eacute;ments ensemble, ont men&eacute; aux deux objectifs suivants: 1. Identifier le statut que les enseignants du secondaire associent aux RGDS, et les r&eacute;actions qu'ils manifestent &agrave; l'&eacute;gard de leur interpr&eacute;tation. 2. Identifier les difficult&eacute;s de lecture et d'interpr&eacute;tation des RGDS, chez les &eacute;l&egrave;ves du secondaire, ainsi que les aspects de compr&eacute;hension auxquels ces difficult&eacute;s sont associ&eacute;es Pour atteindre le premier objectif, nous avons adress&eacute; un questionnaire &agrave; 221 enseignants de math&eacute;matiques du secondaire. Nous avons aussi eu des entretiens avec certains entre eux. Pour atteindre le deuxi&egrave;me objectif, nous avons &eacute;labor&eacute; un questionnaire ayant quatre versions, deux pour l'histogramme , une pour le diagramme en b&acirc;tons et une pour le diagramme circulaire. Chacune de ces versions a &eacute;t&eacute; administr&eacute;e &agrave; un nombre d'&eacute;l&egrave;ves, variant entre 130 et 150, de la premi&egrave;re sciences exp&eacute;rimentales. Les r&eacute;sultats concernant les enseignants, ont mis en &eacute;vidences diff&eacute;rentes conceptions erron&eacute;es concernant l'objet de la statistique, les fonctions des RGDS, la d&eacute;finition de leur lecture et de leur interpr&eacute;tation. Pour les deux premi&egrave;res unit&eacute;s, les conceptions dominantes ont un aspect, soit descriptif, soit formel et calculatoire. Alors que pour les deux derni&egrave;res, nous avons souvent constat&eacute; une confusion entre la lecture et l'interpr&eacute;tation des RGDS. Les r&eacute;sultats concernant les &eacute;l&egrave;ves ont mis en &eacute;vidences diff&eacute;rents modes de lecture et d'interpr&eacute;tation des RGDS. Parmi ces derniers ''le mode discret'', ''le mode ordinal'', ''le mode fonctionnel'', ''le mode direct'' et le ''mode fonctionnel''. Ces modes de lecture et d'interpr&eacute;tation des RGDS, engendrent des difficult&eacute;s associ&eacute;es aux diff&eacute;rents aspects de compr&eacute;hension de ces derni&egrave;res. Les aspects concern&eacute;s sont l'aspect structurel, l'aspect s&eacute;miotique, l'aspect descriptif et l'aspect fonctionnel. Les autres difficult&eacute;s sont li&eacute;es au r&ocirc;les de destructeur visuel, que peut jouer le graphique. Nous avons aussi pu constater que chacune des RGDS trait&eacute;es est caract&eacute;ris&eacute;e par un type particulier de difficult&eacute;s ou par la dominance d'un aspect particulier de compr&eacute;hension. Ainsi pour l'histogramme et le diagramme en b&acirc;tons, ce sont surtout les difficult&eacute;s engendr&eacute;es par le mode "ordinal", li&eacute;es aux aspects structurel et descriptif, qui dominent. Alors que le diagramme circulaire est caract&eacute;ris&eacute; surtout par les difficult&eacute;s engendr&eacute;es par son r&ocirc;le<br>destructeur, d&ucirc; &agrave; la domination de ses aspects iconique et spatial et &agrave; leur interference avec les constituants du contexte de la situation.

  • The purpose of this study was to investigate the effectiveness of computer manipulatives compared to concrete manipulatives in teaching selected elementary probability topics. With the growing availability of computers in the classroom and the advancements in technological capabilities, computer manipulatives have the potential to have the same benefits of concrete manipulatives. It has been well documented that when used properly, concrete manipulatives benefit student's mathematical learning. Despite this fact, few teachers use concrete manipulatives because of classroom management issues. Several studies have shown that computer manipulatives are more manageable compared to their concrete counterparts and that computer manipulatives can facilitate students' mental operations better with the movements on screen. Thirteen fourth-grade students and two teachers were participants in the study. The students were separated into two groups of comparable ability. All students were to complete two activities which addressed nine probability-related target objectives. The first activity involved number cubes while the second involved spinners. When performing the number cube activity, half the students completed the activity using concrete cubes, the other half using computer cubes. To complete the second activity involving spinners, students who had used the computer number cubes for the first activity now used concrete spinners, and students who had used concrete number cubes for the first activity now used computer spinners. Students and teachers filled out a questionnaire and were interviewed at the completion of the study. Several comparisons showed that students using concrete manipulatives did just as well as those using computer manipulatives. Two out of four comparisons showed that students using concrete manipulatives scored better than those using computer manipulatives. Students and teachers reported that they enjoyed using computer manipulatives, and found them easy to use. Eight out of thirteen students saw no difference between the manipulatives with respect to their contribution to their learning, while about four out of thirteen students believed that concrete manipulatives were better for learning. Teachers did not change their belief that computer manipulatives are one of many tools that could be used to teach concepts however they reported that computer manipulatives will not replace concrete manipulatives.

  • This study examined the role of attitudes toward statistics, mathematics anxiety, mathematics attitude, mathematics background, demographic variables, and performance for students in an undergraduate introductory statistics course. The study participants were 155 students enrolled in five classes of introductory statistics at a four year college in metropolitan Atlanta. Using a self-selected ID to assure anonymity, the students completed the Survey of Attitudes Toward Statistics (SATS) at the beginning and end of the term. The SATS provides scale scores for Affect, Cognitive Competence, Value, and Difficulty. They also completed a mathematics attitude and anxiety measure, a demographic questionnaire, and a mathematics history. Students revealed their ID's after completion of the study. This allowed performance data from the course and prerequisite mathematics information to be linked with other student data. Students participating in this study had fairly positive attitudes concerning their Cognitive Competence and the Value of statistics at the beginning of the course. Their feeling of Affect was almost neutral and they expected the course to be somewhat difficult. Statistics attitudes were slightly less positive at the end of course. There were no statistically significant differences in attitudes between first time enrollees and those who were repeating the course or between students who did and did not complete the course. Pre-course SATS attitudes were generally not related to gender or age of the students nor to the years of high school mathematics or number of college mathematics courses. All of the SATS subscales were correlated with student grades in the prerequisite course. Pre-course Affect and Cognitive Competence scales were highly correlated to mathematics attitude, math self-concept and statistics self-confidence and moderately correlated with mathematics anxiety. Path analysis was used to develop a conceptual model for statistics attitude and performance in the course using mathematics attitude, mathematics anxiety, and prequisite grade as the exogeneous variables. In the path model, performance in the course was not influenced by either the pretest or posttest SATS. Performance during the statistics course did affect the posttest SATS scores.

  • The purpose of this study was to investigate the conceptions secondary school students have when dealing with stochastic questions and the heuristics these students use to solve stochastic questions. The second purpose of this study was to determine if there were any effects of gender, grade level, mathematical placement, reading ability and prior stochastic experience on the students' stochastic achievement. The students' stochastic achievement was based on the percentage correct on a multiple-choice stochastic test and the students' conceptions and the heuristics they used were based on the answers students gave on a stochastic reasoning test. The analysis sample for the study consisted of 392 secondary school mathematics students in the Toms River, New Jersey, school district who took the multiple-choice stochastic test. Eighteen of the 392 students volunteered to take the reasoning test, where six students were from each group of students who scored in the top third, middle third and bottom third of the multiple-choice test. Statistical methods were used to test if there were any effects of the variables mentioned earlier on students' stochastic achievement, and whether there was a difference in the proportion of correctly answered questions on the multiple-choice test between probability and statistics questions. The results indicated that, at the 0.05 significance level, reading ability, grade level (Grade 9), the interaction between gender and mathematical placement (track 3), and the interaction between reading ability and stochastic experience had a significant effect on students' stochastic achievement. In addition, there was a significant difference in the proportion of correct answers between probability and statistics questions. Another question that was investigated in this study was if secondary school students use heuristics to solve stochastic questions. This question was qualitatively researched. From the results of the reasoning test, it was concluded that secondary school students use the following heuristics to solve stochastic problems: Belief Strategy, Equiprobable Bias, Bigger is Better, Prior Experience and Normative Reasoning. Belief strategy was used more often than the other heuristics. Also, it was determined that students do not always use the same heuristics to solve similar types of problems.

  • The major assumption underlying this research is that all knowledge and understanding about statistics is constructed. Given that students construct their own knowledge, teaching must be designed to support knowledge construction. In this context, the global purpose addressed in this research is: "How do accomplished statistics educators support knowledge construction in their introductory statistics courses?" This global purpose is studied by attending to two more manageable questions: 1) What instructional strategies are being used in and around the statistics classroom?, and 2) What are the results of an analysis of these instructional strategies when the analysis is grounded in a constructivist perspective? "The Quest for the Constructivist Statistics Classroom" is a qualitative research study that investigated the teaching of four accomplished statistics educators (Paul Velleman at Cornell University, David Moore at Purdue University, Gudmund Iversen at Swarthmore College, and Beth Chance at California Polytechnic State University). Data collection methods included e-mail questionnaires, on-site interviews, and classroom observations of the participants. Instructional strategies employed by the participants were grouped into categories: strategies for how students come to know statistics; strategies involving technology; and, strategies for assessing student learning. For the purpose of data analysis, the following definition of constructivism was used: Constructivism is a theory of learning that allows students to develop and construct their own understanding of the material based upon their own knowledge and beliefs and experiences in concert with new knowledge presented in the classroom. During the analysis, it was decided that the instructional strategies being used in the participants' classrooms did not dichotomously support or not support constructivism, but rather supported constructivism to varying degrees. Some findings of the study included: 1) all four participants supported student construction of knowledge to some degree; 2) each of the participants employed multiple instructional strategies to involve the students in the learning process; and, 3) class size impacted the ability of the instructors to employ instructional strategies that were more supportive of knowledge construction. In addition, a series of questions intended to inspire further thought and research emerged from the study.

  • This study investigated the following three questions: What are the Chinese students main misconceptions of probability? What is the developmental structure of students' understanding of probability? Can an activity-based short-term teaching programme improve ordinary grade 8 students' understanding of probability? The first two questions were answered in the main study. The sample was 567 Chinese students from three grades (6, 8 and 12) and two school streams (ordinary and advanced). After one year, six activity-based lessons which focused on empirical probability were given to two grade 8 classes in an ordinary school. The approaches were parallel except that one class had the opportunity to see computer simulations of a long series of experiments, while the other class was given the data in written form. All the students were tested and interviewed both prior to and after the teaching intervention. Fourteen groups of misconceptions were observed in this study. The outcome approach, chance cannot be measured mathematically, compound approach and equiprobability were the main misconceptions for each grade and each stream of students. The context and data used in an item were found to play a role in eliciting some misconceptions. Using the SOLO taxonomy, it was found that, generally, there was no improvement in developmental level at grades 6 and 8, the two grades without any formal probability training. Grade 12 students have a better understanding than the younger students. The results of the teaching show that a short intervention can help students overcome some of their misconceptions. Students in the two classes improved substantially in their answers and reasoning but no statistically significant difference was found between the classes.

  • This study documented the learning of a research team as it engaged in the process of instructional design. An 11-week classroom teaching experiment conducted in a seventh-grade classroom and the planning year prior to the teaching experiment were the sites for the research team's instructional design investigation. The goal of the teaching experiment was to support students' development of statistical understandings related to data analysis through the design of an instructional sequence. Two computer-based data analysis tools were integral aspects of the instructional sequence and served as primary means of supporting the students' learning. This dissertation clarified the instructional design decisions made by the research team and described how those decisions created learning opportunities. These decisions emerged as the research team continually tested and revised its conjectures about how to support students' mathematical development as it designed the instructional sequence. To this end, this dissertation focused on critical issues that guided the research team in its initial attempts at instructional design. These critical issues were tracked from the planning year throughout the classroom teaching experiment in order to understand what the research team learned about (a) the mathematics involved in teaching and learning statistics and (b) how to support students' development of ways to reason statistically while engaging in data analysis.

  • The purpose of the study was to identify the important aspects of statistical knowledge needed for teaching at the middle school level and to assess prospective teachers' conceptions and misconceptions of statistics related to teaching data analysis. An analytic study of the current literature, including state and national standards, was conducted to identify the important aspects of statistical knowledge for teaching. A written assessment instrument was developed and administered to a sample of 42 prospective middle school teachers. The purpose of the instrument was to gather data in order to describe teachers' conceptions for teaching data analysis and statistics. A subset of the sample (n = 7) was interviewed to provide deeper insight into their conceptions and to assure reliability of the instrument.<br><br>Results show that state and national standards differ greatly on their expectations of what students and teachers should know about data analysis and statistics. The variation is also large for the emphasis or importance given to the content. The average emphasis of all the documents reviewed is given to the selection and proper use of graphical representations of data, and measures of center and spread. Important aspects of knowledge applied to teaching are proper selection and use of teaching strategies and inferring students' understanding from their work and discourse.<br><br>Prospective teachers that participated in this study performed better at the level of pure statistical knowledge than at the level of application of this knowledge to teaching. In particular, they showed abilities on reading, interpreting, and constructing graphical representations, and computing measures of center and spread. Difficulties were shown in judging students' comments and identifying students' mistakes.

  • Recent research has been aimed at finding out how precollege students think about variation, but very little research has been done with the prospective teachers of those students. Absent from the literature is an examination of the conceptions of variation held by elementary preservice teachers (EPSTs). This study addresses how EPSTs think about variation in the three contexts of sampling, data and graphs, and probability situations.<br><br>A qualitative study was undertaken with thirty students in an elementary teachers' mathematics course. The course included three classroom interventions comprised of activities promoting an exploration of variation in each of the three contexts. Written surveys were completed by all students both before and after the class interventions, and six students participated in pre and post interviews.<br><br>Collective results from the survey data, interview data, and class observations were used to describe components of an evolving framework useful for examining EPSTs' conceptions of variation. The three main aspects of the framework address how EPSTs reason in expecting, displaying, and interpreting variation. Each of the three aspects is further defined by different dimensions, which in turn have their own constituent themes. The depth in describing the evolving framework is a main contribution of this research.<br><br>Particular tasks created or modified for this research proved useful in examining EPSTs' conceptions of variation. One kind of task asked students to evaluate supposed results of experiments and decide if the results were genuine or not. Another kind of task provided specific arguments to which subjects could react. A third kind of task involved a comparison of data sets that were displayed using different types of graphs.<br><br>The framework was used to compare the thinking of the six interviewees from before to after the class interventions. Changes included richer conceptions of expectations of variation, more versatile understanding about displays of variation, and better interpretations of variation. The most notable changes were the overall depth in maturity of responses and an increased sophistication in communication during the post interview. Evidence suggests that the class interventions, and the survey and interview tasks, stimulated changes in the way students thought about variation.