• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.117-136
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• 2012

The goal of this study is to investigate a didactic transposition method of text books and high school students' understanding for the Normal Distribution. To accomplish this goal, framework descriptors were developed to analyse the didactic transposition method and interpret the students' understanding based on the Historico-Genetic process of the Normal Distribution, the meaning of the Normal Distribution as a scholarly knowledge and the results of previous studies on students' understanding for the Normal Distribution. This study presented several recommendations for instruction of the Normal Distribution according to the results of analysing the didactic transposition method and interpreting the students' understanding in terms of the developed framework.

• School Mathematics
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• v.9 no.1
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• pp.29-44
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• 2007

The aim of statistics education is to enhance statistical thinking. Variability is the key components of statistical thinking. The research has been reviewed preceding research about variability of data. Proceeding from what has been considered above, this research developed learning materials that investigated the concept of variability as it relates to Freudenthal's context by having students sort a particular context. The research is executed the case study evidently aimed at Junior High School 3rd Grade Student's Understanding of Variability. The study of variability in data can be an important start to reach a testing of statistical hypothesis; students reduce data and draw graphs by relating probability distribution to relative frequency and normal distribution. Thus, this study offers basic materials into developing both contents and methods of education need to consider with this sense of purpose held by students to achieve this goal.

• School Mathematics
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• v.12 no.3
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• pp.273-299
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• 2010

The purpose of the study is designing and implementing 'Sampling Distributions Simulation' to help students to understand concepts of sampling distributions. This computer simulation is developed to help students understand sampling distributions more easily. 'Sampling Distributions Simulation' consists of 4 sessions. 'The first session - Confidence level and confidence intervals - includes checking if the intended confidence level is actually achieved by the real relative frequency for the obtained sample confidence intervals containing population mean. This will give the students clearer idea about confidence level and confidence intervals in addition to the role of sampling distribution of the sample means among those. 'The second session - Sampling Distributions - helps understand sampling distribution of the sample means, through the simulation method to make comparison between the histogram of sampling distributions and that of the population. The third session - The Central Limit Theorem - includes calculating the means of the samples taken from a population which follows a uniform distribution or follows a Bernoulli distribution and then making the histograms of those means. This will provides comprehension of the central limit theorem, which mentions about the sampling distribution of the sample means when the sample size is very large. The forth session - the normal approximation to the binomial distribution - helps understand the normal approximation to the binomial distribution as an alternative version of central limit theorem. With the practical usage of the shareware 'Sampling Distributions Simulation', we expect students to have a new vision on the sampling distribution and to get more emphasis on it. With the sound understandings on the sampling distributions, more accurate and profound statistical inferences are expected. And the role of the sampling distribution in the inferences should be more deeply appreciated.