This paper explores some observed confusions held by pre-service teachers about concepts of probability and statistics. The writer uses information about confusion and misconceptions held by pre-service teachers gained by examination of teaching assignments written by her tertiary students. It considers some other research in this field and makes some suggestions about what steps may be taken to provide pre-service teachers with a better understanding of stochastics.
In task-based interviews 48 Kindergarten to Year 6 children were asked to choose between two jars containing different mixes of read and yellow toy bears, with the aim of giving themselves a better chance at drawing out a read bear. The children applied a variety of strategies, ranging from idiosyncratic reasons to proportional reasoning. These strategies are examined in relation to the ratio pairs presented in each jar and are compared to other strategies reported in the literature.
Throughout introductory tertiary statistics subjects, students are introduced to a multitude of statistical concepts and procedures. One such term, significance, has been given considerable emphasis in the statistical literature with respect ot the topic of hypothesis testing. However, systematic research regarding this concept is very limited. This paper investigates students' coneptual and procedural knowledge of this concept through the use of concept maps and standard hypothesis tests. Eighteen students completing a first course in university -level statistics were interviewed twice during a 14-week semester.
A most basic and long standing conern of philosophers, psychologists, and educators is the probblem of knowledge elicitiation and represntation. How do we assess and represent an individual's knoledge? Philosophers, when asking these questions, have usually expressed an interest in general or world knowledge. Pschologists and educators, on the other hand, have often been more internerestedin the problem of assessing and representing a person's knowledge of some particular topic or area. It is this problem , as it arises in the assessment of classroom types of knoledge, that is the concern of the present chapter. Knowledge assessmetn and representation, as carried out in the classroom, appears as a relatively straghtforward matter. Knowledge is assessed by simply asking factual questions and is represented by presenting the indicidual's relatice standing in terms of a percentile. We begin with a critique of this conventional approach to assessing and representing classroom knowledge.
In this report we present the results of an international research study on the training of researchers in mathematics education. The study was carried out by some members of The International Study Group on Theory of Mathematics Education.<br><br>The research consisted of developing a questionnaire which was mailed to numerous institutions all over the world, and the anlaysis of the answers which were received.<br><br>The main objective of the study was to collect international data about the training of researchers in mathematics education and to establish an information network about graduate programs in the field.<br><br>A total of about 150 questionnaires were sent out and 78 answers received. Fifteen of these answers came from universities that wish to participate in the network but which do not at present have a program.
In this report we present the results of an international research study on the training of researchers in mathematics education. The study was carried out by some members of The International Study Group on Theory of Mathematics Education.<br><br>The research consisted of developing a questionnaire which was mailed to numerous institutions all over the world, and the anlaysis of the answers which were received.<br><br>The main objective of the study was to collect international data about the training of researchers in mathematics education and to establish an information network about graduate programs in the field.<br><br>A total of about 150 questionnaires were sent out and 78 answers received. Fifteen of these answers came from universities that wish to participate in the network but which do not at present have a program.
In spite of the apparent simpicity of averages, many researchers have described difficulties in its understanding by students at different educational levels. In this work we present an assessment of these difficulties for future primary teachers, with the aim of adquately guiding the taching of this topic.<br><br>The analysis of the answers shows that these future teachers have difficulties in understanding the following points: Dealing with zero and atypical values when computing averages, relative position of mean, median and mode in asymmetrical distributions, choosing an adequate mesure of central value and using averages to compare distributions.<br><br>We conclude that the traditional approach to studying averages in context-free data collections, does not allow pupils to fully understand the meaning of the concept, what must include the following: a) relationships of averages with other central position values, b) representativeness of mean in symmetrical distributions; b) the mean as expected value in random sampling processes; c) the mean as fair quantitiy to distribute for obtaining uniform distributions in finite populations.
The statistics reform will only be successful if those teaching statistics understand and react to the changing direction of the discipline. To this end, the Mathematical Association of America, in conjunction with the National Science Foundation, administered a series of development workshops for mathematicians teaching introductory statistics courses at the post secondary level. The purpose of these STATS Workshops (Statististical Thinking with Activie Teaching Strategies) is to help mathematics faculty who have no formal teaching in statistics gain the training and knowledge needed to be successful.<br><br>The particpant observer recorded the day-to-day activities and surveyed the attainment of workshop objectives. The participant observer interviewed attendees to bring additional depth to the traditional evaluation and to enhance the clarity of experiences and opinions of the participants.
This experiment contrasts learning by solving problems with learning by studying examples, while attempting to control for the elaborations that accompany each solution step. Subjects were given different instructional materials for a set of probability problems. They were either provided with or asked to generate solutions, and they were either provided with or asked to create their own explanations for the solutions. Subjects were then tested on a set of related problems. Subjects in all four conditions exhibited good performance on the near transfer test problems. On the far transfer problems, however, subjects in two cells exhibited stronger performance: those solving and elaborating on their own and those receiving both solutions and elaborations from the experimenter. There also was an indication of a generation effect in the far transfer case, benefiting subjects who generated their own solutions. In addition, subjects' self-explanations on a particular concept were predictive of good performance on the corresponding subtask of the test problems.
Traditional Israeli junior high school statistics usually emphasizes computation and neglects the development of a broader integrated view of statistical problem solving. Students are required to memorize isolated facts and procedures. Statistical concepts rarely originate from real problems, the learning environment is rigid, and, in general, there is just one correct answer to each problem. Even when the problems are real, the activities tend to be "unreal" and relatively superficial. The only view of statistics students can get from such a curriculum is of a collection of isolated, meaningless techniques, which is relatively irrelevant, dull, and routine. Many teachers ignore the compulsory statistics unit. The teachers maintain that there is no time, or that there is pressure to include "more important" mathematic topics, as well as lack of interest and knowledge. We have developed a statistics curriculum (Ben-Zvi & Friedlander, 1997) in an attempt to respond to the need for more meaningful learning of statistics and have incorporated the use of available technology to assist in this endeavor.