Literature Index

We present initial data from a collaboration between researchers in the UK and in Israel. We aimed to explore how young students (11-14 years of age) expressed uncertainty in partiallydetermined situations, where a signal might account for some, or even a substantial amount of, variation but additionally there is a need to account for noise in the system. The two teams collaborated to develop a task that drew on previous experience with Active Graphing and EDA. As well as collecting data through an experiment, the young students used the modelling functionality in TinkerPlots2 to create models (or ‘machines’) that generated similar data to that in the experiment. In the presentation, we describe the various ways in which the young students accounted for and expressed uncertainty verbally and through actions in TinkerPlots2. 

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.

Current reforms in mathematics education place increasing emphasis on statistics and data analysis in the school curriculum. The statistics education community has pushed for school instruction in statistics to go beyond measures of center, and to emphasize variation in data. Little is known about the way that teachers "see variation". The study reported here was conducted with 22 prospective secondary math and science teachers enrolled in a preservice teacher education course at a large university in the U.S. which emphasized assessment, equity, inquiry, and analysis of testing data. Interviews conducted at the beginning and end of the course asked the teachers to make comparisons of data distributions in a context that many U.S. teachers are increasingly faced with: results from their students' performance on high-stakes state exams. The results of these interviews revealed that although the prospective teachers in the study did not rely on traditional statistical terminology and measures as much as anticipated, the words they did use illustrate that through more informal descriptions of distributions, they were able to express rich views of variation and distribution. This paper details these descriptions, categorizing them into three major areas: traditional notions, clumps & chunks (distribution subsets), and notions of spread. The benefits of informal language in statistics is outlined.