Conference Paper

  • This paper argues that the two models of curriculum development currently used to interpret Australian mathematics education history--the Colonial Echo model and the Muddling Through model--are both deficient, and proposes a more complex model--the Broad Spectrum Ecological model. This considers the physical, social and intellectual forces operating within a specific environment. One small aspect of mathematics education history, the introduction of probability teaching into Australian schools, is used to illustrate the superiority of this model.

  • This paper addressed the broad issue of relating research findings with pedagogical practices by analysing the responses to questions set in an undergraduate statistics examination using Eisner's connoisseurship and crticism approach, supported by general pedagagical and psychological principles. Comparisons are made between responses to the same course given in two different countries to assess similarities, differences, and weaknesses in order to indicate possible ways in which future courses might be modified to improve student learning.

  • 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.

  • 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.

  • We shall describe episodes of middle school students working on Exploratory Data<br>Analysis (EDA) developed within an innovative curriculum. We outline the program and<br>its rationale, analyze the design of the tasks, present extracts from students' activities and speculate about their learning processes. Finally, from our observations, we propose a new construct -- learning arena, which is suggested as a curriculum design principle, which may also facilitate research.

  • 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 &amp; 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.

  • Statistical literacy is a complex developmental construct requiring both mathematical skills and contextual understanding. The development of statistical literacy is an important objective of classrooms where the curriculum is approached through considering problems that require the active engagement of learners with relevant social material. Such approaches are often advocated for the middle years of schooling. Little attention has been paid, however, to the effects of these approaches on male and female students. This paper reports on a study that considers Differential Item Functioning (DIF) with respect to gender of questions on a statistical literacy scale derived from archived data. Multi-faceted Rasch models were applied to polytomous data to determine the interactions between gender and item. Three criteria were applied to the results: statistical significance, replicability and substantive explanation of DIF. The results suggested that although there was no overall difference in the average performance of male and female students, items requiring numerical responses or calculations were less difficult for male students and, conversely, items demanding written explanations were less difficult for female students. The implications of these findings for both assessment and teaching are discussed.

  • The authors (teachers-researcher) carried out an exploratory study in which they designed , on the basis of a didactic analysis similar to the one proposed by Vallecillos (1996), three problems of hypothesis tests. Our purpose was to analyze the effects of graphic calculators use in the application and understanding of the concepts of p-value and significance level in the solving of these problems. The study was done with students of a statistics course for Social Sciences at the university level.<br>We studied, on the basis of the problem solving activities done by the students, their errors and difficulties concerning the concepts of significance lebel and p-value. We thought that the graphic calculator use was going to promote the use of the graphic and numeric representations. However, we found that the graphic calculator was used only in order to represent the p-value numeric representation. Even though each student "seems to understand" the concepts of p-value or significance level because he or she can resolve a problem, we find that little changes in data, (i.e., change in test laterality), generate new errors.<br>This result and other similar ones suggest the need to reflect about the phenomena that put into play the concepts in question, the kind of diactical activities that are designed and used in order to work with these concepts, and the conceptions and obstacles which are behind the errors made by the students.

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