A core aspect of statistical thinking involves engaging in and thinking about the process of statistical investigation, which can be experienced through experiments or simulations. This study examines how middle school teachers' use of probability experiments and simulations can support students in the process of statistical investigations.
This report focuses on a research project that combines three aspects of a curriculum concerning teachers' planning, teachers' classroom practice, and their students' statistical knowledge. The theoretical framework and methodology will be sketched. Next, the planning and classroom practice of four statistics teachers will be outlined. Finally, the report documents the knowledge and beliefs concerning statistics of five of each of the teacher's students.
This report compares the teacher knowledge of two early career primary school teachers (drawn from a study of four teachers) as it was needed in the classroom during the teaching of statistics through investigations. The study involved video recording a sequence of four or five lessons and audio recoding post-lesson stimulated recall interviews with the teachers. These interviews were based on the teacher viewing selected episodes from the lesson videos. The results showed marked differences in the teacher knowledge of the two teachers, as analysed against a framework developed from the mathematics teacher knowledge domain and the statistical thinking domain. The conclusions and implications drawn from the results are discussed in relation to both initial teacher education and professional development for teachers.
This paper presents results from a case study that explored elementary school teachers' understanding of essential topics in statistics. Teachers' understanding of the mean and median is presented in light of the suggestions by the GAISE document at Level A. It is important to consider where inservice teachers' understanding currently lies as we explore issues related to improving the sophistication of teaching and learning statistics in elementary schools.
In this study we analyze the conceptions of future secondary school mathematics teachers on the teaching of statistics and their influence in classifying the problems in which graphical statistics play a role. For this purpose we present a case study of four students taking the course 'Introduction to the Teaching of Mathematics', who responded to different data collection instruments and were interviewed afterwards.
The responses to four multiple-choice questions taken from delMas, Garfield and Ooms (2005) by 190 future Spanish teachers and 345 American college students are compared and then complemented with a qualitative analysis of the justifications given by a subsample of 44 Spanish teachers. Some conclusions for the training of teachers are presented.
This paper provides an analysis of the evolution of the statistical understandings related to exploratory data analysis of a cohort of middle-school mathematics teachers. The analysis is grounded in a design experiment in the context of teacher development where the teachers' understandings of statistical data analysis, in particular, distribution were the mathematical endpoint. Activities from an instructional sequence designed to support ways to reason statistically about data were the basis of the engagement. Analyses of the episodes in this paper document the teachers' learning that occurred.
Examination of the statistical literature shows that consensus on definition, terminology, and interpretation of some hypothesis testing concepts is elusive. This makes hypothesis testing a difficult topic to teach and learn. This paper reports on the results of a study of novice students' conceptual knowledge of four hypothesis testing concepts through talking aloud and interview methods. While some students seemed to have a reasonable understanding of some concepts, many students seemed to have more limited understanding. The study explores students' faulty conceptual knowledge.
Concept maps are powerful tools for representing understanding of a concept. After designing a teaching sequence for the statistics content of a senior secondary mathematics syllabus, pre-service teachers were asked to prepare a concept map to demonstrate their understanding of the connection between the different concepts that had been included in the sequence. The concept maps prepared by the pre-service teachers were analysed in relation to what connections were made and the quality of the connecting statements. Results showed that these pre-service teachers had very different perceptions of the connections between the basic statistical concepts. Drawing the concept maps assisted the pre-service teachers to consider the concepts at a meta-level. How the concepts maps might be used as a tool for aiding the planning of learning sequences is worthy of investigation.
As part of the assessment after an introductory statistics course, students had to do a small project and submit a written report describing their methods, results and conclusions. We supported the report writing and the project work by several means. Among others, we developed an "exemplary project report" they were introduced to. This project report was written in two columns. In the first column the report about a question concerning a data set is with our best knowledge, in the accompanying second column, we reflect on the choices and options to be made in the respective stages of the report. The aim is to stimulate meta-cognitive activity and to help the students seeing the general in the particular of the exemplary report. We got several dozens of project reports and analyzed them carefully. We developed a grading scheme with several dimensions, including the quality of introductory and concluding sections, the quality of method choice and the quality of analysis and conclusions. We did not only pay attention to statistical quality but also to questions of style of writing such as whether the project question is introduced in a motivating manner and whether clear and convincing conclusions are presented to the reader with good communicative means including adequate graphs. The grading scheme was used to provide feed-back to the students. On the other hand we used this scheme for a systematic analysis of the available project reports. Weaknesses and strengths, most difficult areas for our students were identified and we were able to reflect on the adequacy and the shortcomings of our guiding "exemplary report" and our grading scheme. I will present those findings of our study that seem to be generalizable with regard to the question of assessing students' knowledge by means of projects and of report writing.