• School Mathematics
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• v.13 no.4
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• pp.599-614
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• 2011

According to prior research studies, comparison of two data sets promote informal and formal statistical reasoning, which may mediate descriptive and inferential statistics. However, there has been relatively little attention given to the mediation of both descriptive and inferential statistics. We attempted to identify which statistical concepts or factors students used and how they applied concepts or factors to make decisions when they compared data sets. We also investigated the characteristics and changes of the view of concepts and factors. As a result, we identified that students paid attention to data value, center, spread, and sample, which are important factors of inferential statistics. Students' understanding of each factors were sometimes appropriate for inferential statistics, but sometimes not. From the results, we suggest instructional ideas for a task which can connect descriptive and inferential statistics.

• School Mathematics
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• v.19 no.3
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• pp.533-551
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• 2017

The statistical education researchers advise instructors to educate informal statistical inference and they are paying close attention to the progress of the statistical inference in general. This study was conducted by analyzing the levels and the traits of each levels of the informal statistical inference of the middle and high school students for comparing the samples of data and estimating the graph of a population. Research has shown that five levels of the informal statistical inference were identified for comparing the samples of data: responses that are distracted or misled by an irrelevant aspect, responses that focus on frequencies of individual data points and hold a local view of the sample data sets, responses that the student's view of the data is transitioning from local to global, responses that hold a global view but do not clearly integrate multiple aspects of the distribution, and responses that integrate multiple aspects of the distribution. Another five levels of the informal statistical inference were identified for estimating the graph of a population: responses that are distracted or misled by an irrelevant aspect, responses that focus only on representativeness, responses that consider both representativeness and variability and focus on one particular aspect of the distribution, responses that focus on multiple aspects of distribution but do not clearly integrate them, and responses that integrate multiple aspects of the distribution.

• Journal of the Korean School Mathematics Society
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• v.26 no.1
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• pp.21-47
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• 2023

This study examines the activity system of teaching and learning about informal statistical inference using sampling simulation, based on cultural-historical activity theory. The research explores what contradictions arise in the activity system and how the system changes as a result of these contradictions. The participants were 20 elementary school students in the 5th to 6th grades who received classes on informal statistical inference using sampling simulations. Thematic analysis was used to analyze the data. The findings show that a contradiction emerged between the rule and the object, as well as between the mediating artifact and the object. It was confirmed that visualization of empirical sampling distribution was introduced as a new artifact while resolving these contradictions. In addition, contradictions arose between the subject and the rule and between the rule and the mediating artifact. It was confirmed that an algorithm to calculate the mean of the sample means was introduced as a new rule while resolving these contradictions.