This paper reports three experiments with the curriculum of Sophomore Economics and Business statistics. Their purpose was to improve students' performance in the course and to offer them more useful tools for later courses and for employment Evaluations are based on my own perceptions and on anonymous written comments by students.
The research-project CUPS took place in the years 1975-1981. We intended; (1) to develop a curriculum for the last three grades 7,8,9 of the German Hauptschule which enables even a slow learner to behave adequately in simple stochastic situations, i.e. to cope with them by simple statistical and probabilistic methods; and (2) to develop strategies for planning, performing and evaluating such a curriculum.
This chapter discusses the attempts to included probability and statistics in the curriculum at the secondary level.
Productive reasoning of any kind is achieved through heuristics, and motivated by an anticipatory approach structured as intuition. This recognition has had important consequences in thinking about probability, since the intuitive substrate available in this domain is relatively inconsistent and ambiguous. A proper curriculum of probability learning should, then, take into account this primary intuitive substrate, and concern itself with improving it and with finding methods of building new intuitions which are readily compatible with it. Two main directions of research have been taken in relation to the formation of the concept of probability. The first originated by Tolman and Brunswick, concerns what has been termed probability learning. The second main line of research concerns the organisation of conceptual schemas in the domain of probability: the development of concepts such as chance, proportion, and the estimation of odds, and the development on children of the concepts and procedures of combinatorial analysis. These two directions of research are focussed on rather different problems, and the techniques they use are, consequently, different. Yet, as will be seen in the following chapters, their findings can be successfully combined in an effort to reach a unified view of this area.
The differential effect of two activity-based instructional treatments on subjects' concepts of probability was investigated.
We are beginning to identify problems that children and adults have in constructing the notion of average. In addition, we are examining the mathematical and organizational concepts that are needed to successfully solve averaging problems. Even though we are in the midst of this research, we know enough at this point to question the methods usually used to teach averaging in the 4th grade. Children no doubt can be taught to do the appropriate calculation, but our research shows that understanding of central tendency is far more complex. Given a good deal of experience in working with data sets, children do show a deeper, although by no means a complete, understanding of average. Experiences in which children are given more opportunities to connect their informal strategies with their formal mathematical knowledge seem to facilitate this deeper understanding.
There is a growing movement to introduce elements of statistics and probability into the secondary and even the elementary school curriculum, as part of basic literacy in mathematics. The literature reviewed in this paper indicates a need for collaborative, cross-disciplinary research on how students come to think correctly about probability and statistics.
We examined the motivational patterns and self-regulatory activities of 119 students in introductory statistics. Toward the end of the course subjects were given a questionnaire which assessed perceived ability, goal orientation (learning and performance), valuing of statistics (intrinsic and extrinsic), and the extent to which subjects used self-regulatory activities such as goal-setting, self-monitoring, and task-appropriate cognitive strategies. Predictions from Dweck's goal orientation theory were tested. The findings were generally consistent with the theoretical predictions; however, the predicted interaction of dominant goal orientation and perceived ability failed to emerge.
This report covers the progress of the ELASTIC project.
The goal of this paper is to report on the development of a dynamic computer-based simulation of the concept of statistical power and the misconceptions students have regarding this concept. The paper will include three sections briefly summarized below: (1) considerations in constructing a dynamic computer-based simulation for statistical instruction; (2) discerning misconceptions and addressing their remediation and (3) plans for future development.