The purpose of this article is: 1) to consider the value of statistics in the secondary school curriculum; 2) to present evidence assessing the current levels of preparation in statistics with which students enter college; and 3) to determine, through statistical analysis, factors that may be associated with the secondary school preparation level of students in statistics.
I am not an expert in the theory of decision making, rather I am concerned with mathematics education and teacher training. Within the frame of this task one of my special interests is teaching statistics. Statistics - to use a definition of W. A. Wallis and H. W. Roberts - is a body of methods for making decisions in the face of uncertainty., and that is the subject of our conference.
The question of what to expect of data collected can be posed to beginners in an introductory probability course.
A family of notorious teasers in probability is discussed. All ask for the probability that the objects of a certain pair both have some property when information exists that at least one of them does. These problems should be solved using conditional probabilities, but cause difficulties in characterizing the conditioning event appropriately. In particular, they highlight the importance of determining the way information is being obtained. A probability space for modeling verbal problems should allow for the representation of the given outcome and the statistical experiment which yielded it. The paper gives some psychological reasons for the tricky nature of these problems, and some practical tips for handling them.
In the present paper we first suggest a threefold classification of dependence relationships between pairs of events, then point out some misconceptions concerning these relationships, and, lastly, speculate as to the reasons that it is not customarily employed.
The NCTM "Curriculum and Evaluation Standards for School Mathematics" (1989) reflect the current movement to introduce probability and statistics in the precollege curriculum. These standards include topics and principles for instruction in probability and statistics which are included in the Quantitative Literacy Project (QLP) curriculum materials. This paper presents results of a survey which explored the success of the QLP materials in terms of student reactions to instruction in probability and statistics.
The purpose of the present paper is, first, to show how the binomial and the hypergeometric distributions could be lent a comparable form. The suggested presentation exhibits the similarity in the structure of the two distributions in accordance with the similarity in the verbal definitions of the random variables. Likewise, the minor dissimilarity in the two formulas reflects the difference in the respective verbal definitions. Next, the law of addition of expectations will be applied in order to compute the expectations of the above two distributions. The two expectations will be shown to be equal and the computation rendered simple. Finally, the power of the addition technique will be illustrated by computing the expectation for the number of runs in a binary random sequence. In an extended application, the expectation of the number of alternations in a random binary two-dimensional table will be computed, bypassing the complex problem of the distribution of that random variable.
A model of informal reasoning under conditions of uncertainty, the outcome approach, was developed to account for the non-normative responses of a subset of the 16 undergraduates who were interviewed. For individuals who reason according to the outcome approach, the goal in questions of uncertainty is to predict the outcome of an individual trial. Their predictions take the form of yes/no decisions of whether an outcome will occur on a particular trial. These predictions are then evaluated as having been either "right" or "wrong". Additionally, their predictions are often based on a deterministic model of the situation. In follow-up interviews using a different set of problems, responses of outcome-oriented subjects were predicted. In one problem, subjects' responses were at variance both with normative interpretations of probability and with the "representativeness heuristic". While the outcome approach is inconsistent with formal theories of probability, its components are logically consistent and reasonable in the context of everyday decision-making.
The validity of the Statistics Attitude Survey (SAS) was further examined in the present study. Students were assessed on a number of pretest and posttest cognitive and non-cognitive variables, including the SAS. SAS scores were found to be significantly related to such cognitive variables as basic mathematics skills, statistics preknowledge, and course grades. Non-cognitive factors with which SAS was significantly correlated were sex, the degree to which students indicated that they had wanted to take the course and that they were glad they had taken the course, number of previous mathematics courses completed, the status of a course being required or elective, calculator attitudes, and course and instructor evaluations. In addition, SAS scores showed a significant positive change from the beginning to the end of the course.
Over the years I've strongly supported the federal government's role in gathering and circulating educational data because we can't make intelligent decisions without knowing how public education is doing. But getting adequate funding for data collection and research hasn't been easy. The Congress has been suspicious that this Administration, in particular, was more interested in cooking the facts to fit its ideology than in doing objective research, especially on the subject of education spending. This article shows proof that such suspicions are justified.