### Abstract

We report on a sequence of two classroom teaching experiments that investigated high school students' understandings as they explored connections among the ideas comprising the inner logic of statistical inference-ideas involving a core image of sampling as a repeatable process, and the organization of its outcomes into a distribution of sample statistics as a basis for making inferences. Students' responses to post-instruction test questions indicate that despite understanding various individual components of inference-a sample, a population, and a distribution of a sample statistic-their abilities to coordinate and compose these into a coherent and well-connected scheme of ideas were usually tenuous. We argue that the coordination and composition required to assemble these component ideas into a coherent scheme is a major source of difficulty in developing a deep understanding of inference.

Original language | English (US) |
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Pages (from-to) | 1-30 |

Number of pages | 30 |

Journal | Journal of Mathematical Behavior |

Volume | 35 |

DOIs | |

State | Published - Sep 2014 |

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### Keywords

- Margin of error
- Sampling distribution
- Statistical inference
- Stochastic event

### ASJC Scopus subject areas

- Education
- Applied Psychology
- Applied Mathematics