This thesis investigates the teaching of statistical literacy in the first two years of secondary school mathematics. The teachers involved in the research aim to make changes to classroom practice in the teaching and learning of statistics and statistical literacy in response to changes in the New Zealand curriculum. An action research methodology is adopted by the research. A group of three teachers and the author undertake an action research cycle of planning, observing, acting and reflecting in three different Year 9 and 10 mathematics classrooms. The research documents the designing and implementing of strategies by a group of teachers in a mathematics department for integrating statistical literacy into teaching programmes. The research adopts framework for improving practice that utilise models for statistical literacy and thinking and principles for teaching with a language learning or literacy focus. Data is collected through discussions with teachers, observations of lessons and interviews with teachers and students. Themes emerge from the data. They include the significance of teacher and student concepts of statistics and statistical literacy, the importance of language and literacy in the statistics classroom, the adoption of teaching principles to facilitate statistical literacy and the challenge of adopting a critical literacy stance in the statistics classroom. The study highlights the importance of literacy and language skills in statistical literacy. The research concludes that the important changes needed for developing statistical literacy are about classroom methodology rather than content knowledge and shows that adoption of language learning principles into the teaching programme may achieve this.

Students at university encounter quantitative information in tables and graphs or through prose in textbooks, journals, electronic sources and in lectures. The degree to which students are able to engage with this kind of information and draw their own conclusions, influences the extent to which they need to rely on the interpretation of others. In particular, students who are studying in non-mathematical disciplines often fail to engage seriously with such material for a number of reasons. These may include a lack of confidence in their ability to do mathematics, a lack of mathematical skills required to understand the data, or a lack of an awareness of the importance of being able to read and interpret the data for themselves. In this thesis, the successful choice and use of skills to interpret quantitative information is referred to as numeracy. The level of numeracy exhibited by a student can vary depending on the social or cultural context, his/her confidence to engage with the quantitative information, the sophistication of the mathematics required, and his/her ability to evaluate the findings. The first part of the thesis is devoted to the conceptualisation of numeracy and its relationship to mathematics. The empirical study that follows this is focused on an aspect of numeracy of importance to university students: the reading and interpreting of tables of data in a range of non-mathematical contexts. The students who participated in this study were enrolled in degree programs in the social sciences. The study was designed to measure the effectiveness of a one-hour intervention workshop aimed at improving the levels of the students’ numeracy. The short length of the intervention was dictated by practical and organisational constraints. This workshop involved reading and interpreting a table of data using strategies based on the SOLO taxonomy (Biggs & Collis, 1982). The SOLO taxonomy was developed mainly as a means of classifying the quality of responses across both arts and science disciplines. The categorisation uses five levels: prestructural, unistructural, multistructural, relational and extended abstract. It can be used as a diagnostic tool at all levels of education as it can be seen as a spiral learning structure repeating itself with increasing levels of abstraction. It can also be used as a teaching tool in feedback to students. A measuring instrument, also based on the SOLO taxonomy, was designed to gauge the levels of the students’ responses to these tasks. Each response was allocated a level that was subsequently coded as a number from zero to seven. Because the responses were in distinct ordered categories, it was possible to analyse the scores using the Rasch Model (Rasch 1960/80) for polytomous responses, placing both the difficulty of the tasks and the ability of the students on an equal interval scale. The Rasch Model was also used to evaluate the measuring instrument itself. Some adjustments were made to the instrument in the light of this analysis. It was found that it is possible to construct an instrument to distinguish between levels of students’ written responses for each of the chosen table interpretation tasks. The workshop was evaluated through a comparison of the levels achieved by individual students before and after the workshop. T-tests for dependent samples indicated a significant improvement (p < 0.01) in student performance.

Thesis (Ph. D.)--Illinois State University, 2007. / Title from title page screen, viewed on April 8, 2008. Dissertation Committee: Edward S. Mooney (chair), Cynthia W. Langrall, Sherry L. Meier, Norma C. Presmeg. Includes bibliographical references (leaves 112-121) and abstract. Also available in print.

Following international trends, statistics is a relatively new addition to the South African mathematics curriculum at school level and its implementation was fraught with problems. Since 2001 teaching statistics in the Further Education and Training Phase (Grades 10 to 12) has been optional due to lack of professional development of teachers. From 2014 teaching statistics will be compulsory. This study is therefore timely as it provides information about different discourses in discussions of an ill-structured problem in a data-rich context, as well as in discussions of the meaning of the statistical mean. A qualitative case study of informal statistical reasoning was conducted with a group of students that attended an introductory course in descriptive statistics as part of an honours degree in mathematics education at the University of the Witwatersrand. The researcher was the course lecturer. Transcripts of the discussions in four video recorded sessions at the start of the semester long course form the bulk of the data. The discussions in the first three sessions of the course were aimed at structuring the data-context, or grasping the system dynamics of the data-context, as is required at the start of a cycle of statistical investigation. The discussion in the fourth session was about the syntactical meaning of the mean algorithm. It provides guidelines for meaningful disobjectification of the well-known mean algorithm. This study provides insight into informal statistical reasoning that is currently described as idiosyncratic or verbal according to statistical reasoning models. Discourse analysis based on Sfard’s (2008) theory of Commognition was used to investigate and describe discursive patterns that constrain shifting from colloquial to informal statistical discourse. The main finding is that colloquial discourse that is aimed at decision making in a data-context is incommensurable with statistical discourse, since comparison of data in the two discourses are drawn on incommensurable scales – a qualitative evaluation scale and a quantitative descriptive scale. The problem of comparison on a qualitative scale also emerged in the discourse on the syntactical meaning of the mean algorithm, where average as a qualitative judgement conflicted with the mean as a quantitative measurement. Implications for teaching and teacher education are that the development of statistical discourse may be dependent on alienation from data-contexts and the abstraction of measurements as abstract numerical units. Word uses that confound measurements as properties of objects and measurements as abstract units are discussed. Attention to word use is vital in order to discern evaluation narratives as deed routines from exploration narratives and routines.

The aim of the study is to investigate pre-service middle school mathematics teachers&rsquo / critical thinking processes through statistical and probabilistic knowledge in the context of popular media texts. The study was conducted with a qualitative case study method. Participants of the study consisted of four senior pre-service middle school mathematics teachers enrolled in a public university. Data were collected through in-depth interviews with the participants. Analysis of the data was conducted on the basis of two dimentions / critical thinking skills, and statistical and probabilistic knowledge. The results of the study indicated that pre-service middle school mathematics teachers reflected different critical thinking skills and made use of different statistical and probabilistic knowledge in different contexts. They mostly reflected interpretation skill on the basis of their statistical and probabilistic knowledge. Moreover, to what extent they made use of critical thinking skills was differentiated on the basis of their statistical and probabilistic knowledge. They reflected complicated critical thinking process dealing with conditional probability statements. They had difficulty with probabilistic statements underlying conditional probability especially in this process.

The aim of the study is to investigate pre-service middle school mathematics teachers&rsquo / critical thinking processes through statistical and probabilistic knowledge in the context of popular media texts. The study was conducted with a qualitative case study method. Participants of the study consisted of four senior pre-service middle school mathematics teachers enrolled in a public university. Data were collected through in-depth interviews with the participants. Analysis of the data was conducted on the basis of two dimentions / critical thinking skills, and statistical and probabilistic knowledge. The results of the study indicated that pre-service middle school mathematics teachers reflected different critical thinking skills and made use of different statistical and probabilistic knowledge in different contexts. They mostly reflected interpretation skill on the basis of their statistical and probabilistic knowledge. Moreover, to what extent they made use of critical thinking skills was differentiated on the basis of their statistical and probabilistic knowledge. They reflected complicated critical thinking process dealing with conditional probability statements. They had difficulty with probabilistic statements underlying conditional probability especially in this process.

The purpose of this study was to investigate the statistical literacy of 8th grade students and their attitudes towards statistics. Moreover, the relationship between their statistical literacy and attitudes towards statistics was examined. The study was conducted in Yenimahalle district of Ankara in the Spring semester of 2011-2012 academic year. The sample of this study was obtained through cluster random sampling. Nine schools were randomly selected for the study. A total of 1074 eighth grade students in these schools participated. The scales used in the data collection were Statistical Literacy Test (SLT) adapted from Probability Attitudes Scale previously developed for Turkish students (Bulut, 1994) and Attitude towards Statistics Questionnaire (ATSQ) developed by the researcher based on Watson&rsquo / s (1997) three tier framework. The analysis of the mean scores of statistical literacy in terms of content domains revealed that although sample, graphs, and chance contents had closer mean scores to each other which was around moderate value / average, inference, and variation content domains had lower mean scores. A one-way within subjects ANOVA indicated that there were significant differences between Tier 1, Tier 2 and Tier 3 aspects of statistical literacy. The pairwise comparisons indicated that students performed lowest in third tier of statistical literacy where students were required to evaluate inappropriate statistical claims. Although, students performed slightly higher in the first tier where they showed their ability in understanding statistical terminology / their performance was the highest in the second tier which was interpreting statistical claims in context. Eighth grade students&rsquo / attitudes towards statistics were positive with a mean score of 3.52 in five point scale. The correlation analysis indicated that there were positive and significant relationship between students&rsquo / attitudes towards statistics and statistical literacy scores.

The problem of the research is systematic approach and accessibility of the content of developing statistical skills for primary school pupils. The content of developing elements of statistical skills and probability theory integrates pupils’ mathematical skills, knowledge of the content of other subjects, general skills of cognition and their personal experience, therefore it is a general problem of primary education; A system of items intended for teaching elements of statistics and probability theory is valid and accessible for pupils provided it covers: - technical skills of statistics (an ability to read and represent data); - skills of mathematical operations (to calculate the mean, classify data, round off numbers, grasp elements of probability theory, determine percentage of a number); - cognitive skills of the level accessible to pupils (ability to word a problem, define a hypothesis, compile data to verify the hypothesis, analyse and interpret data, draw conclusions). The premises for successful development of primary school pupils’ statistical skills are as follows: - development of primary school teachers’ statistical skills in the framework of their academic and continued education; - establishment of the content of developing statistical skills corresponding to international standards in the general curricula of the primary school; - provision of teaching statistics and probability theory elements based in the skills acquired in the primary school in the... [to full text]

The problem of the research is systematic approach and accessibility of the content of developing statistical skills for primary school pupils. The content of developing elements of statistical skills and probability theory integrates pupils’ mathematical skills, knowledge of the content of other subjects, general skills of cognition and their personal experience, therefore it is a general problem of primary education; A system of items intended for teaching elements of statistics and probability theory is valid and accessible for pupils provided it covers: - technical skills of statistics (an ability to read and represent data); - skills of mathematical operations (to calculate the mean, classify data, round off numbers, grasp elements of probability theory, determine percentage of a number); - cognitive skills of the level accessible to pupils (ability to word a problem, define a hypothesis, compile data to verify the hypothesis, analyse and interpret data, draw conclusions). The premises for successful development of primary school pupils’ statistical skills are as follows: - development of primary school teachers’ statistical skills in the framework of their academic and continued education; - establishment of the content of developing statistical skills corresponding to international standards in the general curricula of the primary school; - provision of teaching statistics and probability theory elements based in the skills acquired in the primary school in the... [to full text]

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