Research

  • This study explores school students' understanding of variation within a probabilistic setting involving spinners. Sixty-six students in Grades 3 to 9 answered survey questions involving a single 50/50 spinner and then were interviewed using a protocol involving compound events with different types of spinners (50/50 and 25/75). Of interest in interviews were students' initial responses and changes in response and reasoning that occurred after experimentation with the spinners. Because there was the possibility of variation occurring in the experiments that could be considered contrary to expectation, responses following experimentation were analysed based on their appropriateness in terms of the observed experimental outcome. Data were used to determine a developmental progression among the students in the study and data from survey responses were considered in relation to the interview data. Differences were found between primary and secondary students. The outcomes of the study lead to suggestions for the classroom and for future research in relation to expectation and variation in probabilistic settings.

  • A developmental model involving four response levels is proposed concerning how students arrange pictures to represent data in a pictograph, how they interpret these pictographs, and how they make predictions based on these pictographs. The model is exemplified by responses from three related interview-based studies. In Study 1, examples of each response level are provided from 48 preparatory- to tenth-grade students. Students from higher grades were more likely to respond at higher levels. In Study 2, 22 students were interviewed longitudinally after a three-year interval; many improved in response level over time, although a few responded at lower levels. In Study 3, 20 third-grade students were interviewed and then prompted with conflicting responses of other students on video; many improved their initial responses to higher levels after exposure to the conflicting prompts. Associations among levels of representing, interpreting, and predicting were explored. Educational implications are discussed concerning reasonable expectations of students and suggestions to develop these skills in students at different grades.

  • The development of the understanding of average was explored through interviews with 94 students from Grades 3 to 9, follow-up interviews with 22 of these students after 3 years, and follow-up interviews with 21 others after 4 years. Six levels of response were observed based on a hierarchical model of cognitive functioning. The first four levels described the development of the concept of average from colloquial ideas into procedural or conceptual descriptions to derive a central measure of a data set. The highest two levels represented transferring this understanding to one or more applications in problem-solving tasks to reverse the averaging process and to evaluate a weighted mean. Usage of ideas associated with the three standard measures of central tendency and with representation are documented, as are strategies for problem solving. Implications for mathematics educators are discussed.

  • Statistical education and general Mathematical education has changed in Argentina in the last decade. The same has happened in many other countries in the world because the need for students to have a satisfactory Statistical training is an important preoccupation in today's information society. Any citizen, not only scientists and technologists, needs to understand the information available. Although changes already exist in the secondary school Mathematics curriculum, the results are not visible in the university classroom where the students' knowledge of statistics or probability are almost none. This paper describes the results of a survey about the previous knowledge of Probability and Statistics in university students before a first and formal statistical course is carried out. The experience was made among students in the geographic area in Argentina namely Litoral area. We try to identify the reasons why teachers tend to teach descriptive Statistics only, a few elements of Probability and nothing of data analysis.

  • The primary purpose of the study was to determine the extent to which the public examination test items in statistics reflect the syllabus aims and assessment objectives. In addition to this, the nature of responses of a group of final year secondary school students, to selected non-routine and routine items in statistics was also studied. The aims of the syllabus and assessment objectives as well as the suggested methodologies place emphasis on problem solving skills, discovery learning and application of learned concepts in real life situation where as examination items do not reflect these objectives. Students' responses to non-routine tasks too confirm their inability to handle anything that is not routine. Currently, certification is based on one shot examination, where items are routine in nature, which implies that teaching is geared towards preparing the students for the public examination. Certification, instead of depending on just one external examination, should move towards incorporating continuous assessment component thereby providing the opportunity to use projects and open - ended tasks as part of teaching and learning.

  • We report an experiment which involves teaching statistics at compulsory school in Italy (145 primary school teachers and 2130 pupils, 6-10 years old, living in six Italian regions from north to south, giving a total of 132 primary classes were involved) where we evaluate the different efficiency of two different methods of teaching: by Objectives or by Concepts. In this experiment the fact that both these approaches anticipated working with real data reflecting a phenomenon of daily life is of importance. For testing this hypothesis we used multidimensional permutation tests by non parametric combination of dependent tests. Overall the results show that the method by Objectives is better than the method by Concepts.

  • The teaching of probability is currently being reinforced in many countries, as it is visible from new curricular documents such as the NCTM Standards (2000), where the acquisition of a precise language in connection to chance and probability is considered to be a main learning goal. On the other hand, textbooks are an important resource for teachers who can find in these books ideas and activities to facilitate students' learning. In recent Spanish curricular documents (M.E.C., 1992) the teaching of probability is introduced at earlier ages with a teaching methodology based on simulation and experimentation. A main concern is children's progressive acquisition of a precise language in connection to chance and probability. This curriculum is not an exception, since we find similar concerns in curricular documents from other countries, such as the United Kingdom or the United States. On the other hand, when children are first taught probability, they have frequently used terms and expressions to refer to randomness, sometimes with a meaning different to what is usual in the mathematics classroom. All these reasons suggest the interest to carry out an empirical study to determine the specific language that about chance and probability is presented in the textbooks.

  • This paper highlights the statistical thinking of teachers in analyzing their own students' high-stakes test data. The research here emphasizes the impact that an immersion model for teachers-doing statistics as statisticians-can provide in raising statistical content knowledge, engendering a mindset of inquiry, developing facility with technology, and enriching understanding of student outcome data. Four constructs - measurable conjectures, tolerance for variability, context, and inference & conclusions - provide the basis of a taxonomy to describe teachers' statistical thinking about comparing two groups in the context of an accountability system.

  • This study investigated whether elementary education majors in the teacher education program at Montana State University (MSU) acquire and retain knowledge of statistical data analysis concepts and skills consistent with expectations specified in the NCTM "Principles and Standards for School Mathematics" (2000). The following statistical topics were covered: Finding, describing and interpreting mean, median and mode; interpreting the spread of a set of data; understanding the meaning of the shape and features of a graph; comparing centers, spreads, and graphical representations of related data sets; and using scatter plots and lines of best fit.

  • This paper will report on the outcomes for international students from two different cohorts, undertaking equivalent courses. The two streams are differentiated by their course entry standards. The entry level for one stream is an academic ENTER score of 68 and an IELTS language score of 5.5 and for the other an academic ENTER score of 80 with an IELTS language score of 6.0 was needed. Each of these two cohorts' is taught in a different manner. The two cohorts of students have been tracked over a period of years and their educational outcomes compared. The tracking indicates that the student cohort with the lower entry level has achieved similar outcomes to that with the higher entry level. Can it be concluded that the similarity in outcomes can be attributed to teaching methodology?

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