### 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) |
---|---|

Pages (from-to) | 1-30 |

Number of pages | 30 |

Journal | Journal of Mathematical Behavior |

Volume | 35 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Applied Psychology
- Education

### Cite this

**Conceptual issues in understanding the inner logic of statistical inference : Insights from two teaching experiments.** / Saldanha, Luis A.; Thompson, Patrick.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Conceptual issues in understanding the inner logic of statistical inference

T2 - Insights from two teaching experiments

AU - Saldanha, Luis A.

AU - Thompson, Patrick

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Margin of error

KW - Sampling distribution

KW - Statistical inference

KW - Stochastic event

UR - http://www.scopus.com/inward/record.url?scp=84897934477&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897934477&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2014.03.001

DO - 10.1016/j.jmathb.2014.03.001

M3 - Article

VL - 35

SP - 1

EP - 30

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

ER -