# Research

• ### Selection and use of propositional knowledge in statistical problem solving

Central in this study is the question why subjects who possess the necessary factual or propositional knowledge needed to solve a particular statistical problem often fail to find the solution to that problem. Ten undergraduate psychology students were trained so as to possess all the relevant knowledge needed to solve five multiple choice problems on descriptive regression analysis. They were asked to think aloud while attempting to solve the problems. Analysis of the think-aloud protocols showed that a failure to select the relevant information in the text, together with a failure to retrieve relevant propositional knowledge from memory and the inability to reason coherently combined to produce incorrect responses. Factual knowledge was less likely to be successfully retrieved when it was acquired only recently or when it concerned relationships of a highly abstract nature.

• ### Junior high school students construction of global views of data and data representations

The purpose of this paper is to describe and analyze the first steps of a pair of 7th-grade students working through an especially designed curriculum on Exploratory Data Analysis (EDA) in a technological environment. The verbal abilities of these students allowed us to follow, at a very fine level of detail, the ways in which they begin to make sense of data, data representations, and the "culture" of data handling and analysis. We describe in detail the process of learning skills, procedures and concepts, as well as the process of adopting and exercising the habits and points of view which are common among experts. We concentrate on the issue of the development of a global view of data and its representations on the basis of students' previous knowledge and different kinds of local observations. In the light of the analysis, we propose a description of what it may mean to learn EDA, and draw educational and curricular implications.

• ### Understanding the nature of errors in probability problem-solving

This study provides an investigation of relationships among different types of errors occurring during probability problem-solving. Fifty non-mathematically sophisticated graduate student subjects enrolled in an introductory probability and statistics course were asked to solve a set of probability problems, and their attempts at solution were analyzed for presence and type of errors. The errors contained within these solutions were categorized according to a coding scheme which identifies 110 specific kinds of errors in four categories: text comprehension errors, conceptual errors, procedural errors, and arithmetic/computation errors. Relationships among types of errors included in each category were investigated using hierarchical clustering via additive trees. Implications of these relationships for the teaching and learning of probability problem-solving are discussed.

• ### Minitab and pizza: A workshop experiment

Laboratory, workshop, and cooperative learning approaches are some pedagogical methods that raise student interest and involvement in their course work. The present article describes an experiment in applying such methods to teaching a general statistics course to non-mathematics majors, and its statistical assessment. A voluntary, one-hour weekly lab was offered to the general statistics course students. It was developed using computers, e-mail, and Minitab, in conjunction with learning groups, and with the utilization of a Lab Assistant. The results of such experience was then assessed through several instruments, including a student survey that collected their reactions, comments, and suggestions for improvements. Then, a preliminary statistical analysis of some of the course data collected, comparing grade results of students who attended the workshop with those who did not, is presented. Finally, some general conclusions regarding this workshop's effectiveness, its recruitment and retention efforts and directions for future work, are also discussed.

• ### A statistical assessment of an experiment to compare traditional vs. laboratory approach in teaching introductory computer programming

During the Spring of 1995 a statistical experiment to assess the effects of two methods of teaching introduction to Computer programming concepts was developed. The experiment implemented two teaching approaches: traditional lecture vs. laboratory (tehcnology). Several performance measures were defined and then collected throughout the course, to assess student learning. Among them are: results from common tests, quizzes, and homework/projects. In this article we assess the effects of these two teaching approaches on students' learning, retention, and success rates. We analyze statistically the data collected, testing several hypotheses based on our teaching experience. Finally, we give several conclusions drawn on the analyses results.

• ### Building the meaning of statistical association through data analysis activities

In this research forum we present results from a research project concerning students' understanding of statitical association and its evolution after teaching experiments using computers. This research has been carried out at the Universities of Granada and Jaen over the years 1991-98. We have identified different incorrect preconceptions and strategies to assess statistical association and performed two different teaching experiments designed to overcome these difficulties and to identify the critical points, which arise in attempting to do this.

• ### A sweet way to teach students about the sampling distribution of the mean

In this article, we describe a hands-on, in-class demonstration using M &amp; M's candy to illustrate the concept of the sampling distribution of the mean. With the class serving as the population, each student receives a small package of M &amp; M's. The instructor draws samples from the population and constructs an actual sampling distribution. Students in two statistics courses received either the M &amp; M demonstration or a comparable demonstration using a textbook example. They took a quiz on their knowledge and rated their attitudes toward the demonstration. Results indicated that students who participated in the M &amp; M demonstration answered more questions correctly on the quiz, believed they had learned more, enjoyed class more, and had fewer negative feelings toward the demonstration than those who received the textbook example demonstration.

• ### Making sense of the total of two dice

Many studies have shown that the strategies used in making judgments of chance are subject to systematic bias. Concerning chance and randomness, little is known about the relationship between the external structuring resources, made available for example in a pedagogic environment, and the construction of new internal resources. In this study I used a novel approach in which young children articulated their meanings for chance through their attempts to "mend" possibly broken computer-based stochastic gadgets. I describe the interplay between informal intuitions and computer-based resources as the children constructed new internal resources for making sense of the total of 2 spinners and 2 dice.

• ### Towards an electronic independent learning environment for statistics in higher eduction

This study focuses on the feasibility of implementing independent learning in a traditional university and the feasibility of providing this independent learning by means of an electronic interactive learning environment. Three experimental variables were designed: learning environment, delivery, and support. This created five different learning conditions to which subjects were assigned at random.

• ### Development of understanding of sampling for statistical literacy

The development of understanding sampling is explored through responses to four items in a longitudinal survey administered to over 3000 students from Grades 3 to 11. Responses are described with reference to a three-tiered framework for statistical literacy, including defining terminology, applying concepts in context, and questioning claims made without proper justification. Within each tier increasing complexity is observed as students respond with single, multiple, and integrated ideas to four different tasks. Implications for mathematics educators of the development of sampling concepts across the years of schooling are discussed.