What I see is not quite the way it really is: students’ emergent reasoning about sampling variability

With the rapid, ongoing expansions in the world of data, we need to devise ways of getting more students much further, much faster. One of the choke points affecting both accessibility to a broad spectrum of students and faster progress is classical statistical inference based on normal theory. In this paper, bootstrap-based confidence intervals and randomisation tests conveyed through dynamic visualisation are developed as a means of reducing cognitive demands and increasing the speed with which application areas can be opened up. We also discuss conceptual pathways and the design of software developed to enable this approach.

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“…For results of some of the early pedagogical research, see Budgett et al. (), Parsonage et al () and Pfannkuch et al ().…”

Section: Discussionmentioning

confidence: 99%

Accessible Conceptions of Statistical Inference: Pulling Ourselves Up by the Bootstraps

Wild

Pfannkuch

Regan

et al. 2015

Int Statistical Rev

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“…It is about how the students understand data in an informal way and how they draw conclusions about a larger group than the dataset at hand [46]. Four articles in our review use IIR as a theoretical framework for explaining how students reason in statistics [45][46][47][48]. IIR is therefore one of theoretical frameworks in this review that is referred to most often.…”

Section: Informal Inferential Reasoningmentioning

confidence: 99%

Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review

Hjelte

Nilsson

2020

Education Sciences

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Mathematical reasoning is gaining increasing significance in mathematics education. It has become part of school curricula and the numbers of empirical studies are growing. Researchers investigate mathematical reasoning, yet, what is being under investigation is diverse—which goes along with a diversity of understandings of the term reasoning. The aim of this article is to provide an overview on kinds of mathematical reasoning that are addressed in mathematics education research. We conducted a systematic review focusing on the question: What kinds of reasoning are addressed in empirical research in mathematics education? We pursued this question by searching for articles in the database Web of Science with the term reason* in the title. Based on this search, we used a systematic approach to inductively find kinds of reasoning addressed in empirical research in mathematics education. We found three domain-general kinds of reasoning (e.g., creative reasoning) as well as six domain-specific kinds of reasoning (e.g., algebraic reasoning). The article gives an overview on these different kinds of reasoning both in a domain-general and domain-specific perspective, which may be of value for both research and practice (e.g., school teaching).

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“…For example Abrahamson (2012) investigated the thinking processes of primary students when analyzing the sample space of random generators that were not common for the students. Pfannkuch et al (2015) investigated emergent reasoning about sampling variability in 11-year-old students in a learning experiment. Schnell and Prediger (2012) described the process of gaining an appropriate concept of probabilities as a strategy to estimate frequencies in short series and long series of random experiments.…”

Section: Students' Thinking Processesmentioning

confidence: 99%

Empirical Research in Statistics Education

Eichler

Zapata‐Cardona

2016

ICME-13 Topical Surveys

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What I see is not quite the way it really is: students’ emergent reasoning about sampling variability

Cited by 28 publications

References 13 publications

Accessible Conceptions of Statistical Inference: Pulling Ourselves Up by the Bootstraps

Accessible Conceptions of Statistical Inference: Pulling Ourselves Up by the Bootstraps

Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review

Empirical Research in Statistics Education

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