Learning to reason from samples: commentary from the perspectives of task design and the emergence of “big data”

Ainley, Janet; Gould, Robert; Pratt, Dave

doi:10.1007/s10649-015-9592-4

Cited by 9 publications

(6 citation statements)

References 7 publications

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“…Since learners have at best only partial information about how and why such datasets were created, it is more difficult to reason about the measures and sampling methods used, what might be sources of error or uncertainty, and what inferences can be made (Ainley, Gould, & Pratt, 2015). This paper reports on an emerging line of research that builds on work in data modelling (Hancock et al, 1992;Lehrer, Kim, & Schauble, 2007), exploratory data analysis (Ben-Zvi, 2006;Cobb & McClain, 2004), and data storytelling (Pfannkuch, Regan, Wild, & Horton, 2010) to study students' data repurposing.…”

Section: Introductionmentioning

confidence: 99%

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Middle school students’ reasoning about data and context through storytelling with repurposed local data

Wilkerson

Laina

2018

ZDM Mathematics Education

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Publicly-available datasets, though useful for education, are often constructed for purposes that are quite different from students' own. To investigate and model phenomena, then, students must learn how to repurpose the data. This paper reports on an emerging line of research that builds on work in data modeling, exploratory data analysis, and storytelling to examine and support students' data repurposing. We ask: What opportunities emerge for students to reason about the relationship between data, context, and uncertainty when they repurpose public data to explore questions about their local communities? And, How can these opportunities be supported in classroom instruction and activity design? In two exploratory studies, students were asked to pose questions about their communities, use publicly-available data to explore those questions, and create visual displays and written stories about their findings. Across both enactments, opportunities for reasoning emerged especially when students worked to reconcile (1) their own knowledge and experiences of the context from which data were collected with details of the data provided; and (2) their different emerging stories about the data with one another. We review how these opportunities unfolded within each enactment at the level of group and classroom, with attention to facilitator support.

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Section: Introductionmentioning

confidence: 99%

“…Students in Stories of Our City recalculated, rescaled, or merged/supplemented data for these same reasons. These differences highlight some of the unique considerations that come from repurposing, rather than constructing, data (Ainley et al, 2015).…”

mentioning

confidence: 99%

Middle school students’ reasoning about data and context through storytelling with repurposed local data

Wilkerson

Laina

2018

ZDM Mathematics Education

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“…The second is a sampling task, such as repeatedly drawing small samples to estimate the proportion of sweets of a particular color within a bowl. Here the statistical idea of sampling is being used in a realistic way, to answer a specific question, but the task itself is not a meaningful challenge (Ainley, Gould, & Pratt, 2015). If you really wanted to know the numbers of sweets of different colors it would be quicker and more reliable to empty the bowl and count them.…”

Section: Use Real or Realistic And Motivating Data Setsmentioning

confidence: 99%

Design of Statistics Learning Environments

Ben‐Zvi

Gravemeijer

Ainley

2017

Springer International Handbooks of Education

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The goal of this article is to draw attention to the need to think about learning environments and their design as a way of considering how sustainable change in the learning and teaching of statistics can be supported. The goal is not to advocate one particular approach to the design of learning environments, but rather to raise awareness of the need to consider this lens in statistics education. We first present the rationale for the importance of a focus on learning environments for statistics education. We consider six design considerations for statistics learning environments. Finally, we discuss implications and emerging directions and goals for further implementation and research.

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“…Technological possibilities have enabled the development of alternative informal approaches for university and pre-university students to understand sampling distributions (Chance et al, 2004;van Dijke-Droogers et al, 2019;Silvestre et al, 2022). Regarding formal educational level students, research has been carried out on the development of their reasoning about sampling concepts (Ainley et al, 2015;Saldanha & Thompson, 2002, 2007, but it is still necessary to understand at a finer grain level the conceptions that students are forming in their effort to assimilate the concept of sampling distribution in a process of teaching activities.…”

Section: Introductionmentioning

confidence: 99%

Development of high school students’ conceptions of sampling distribution in the context of learning significance tests with technology

Sánchez,

García-Ríos,

Sepúlveda

2024

Educ Stud Math

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Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students’ conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools contribute to forming these conceptions, guided by an emerging theory that describes this process. A workshop for high school students was organized, involving 36 participants working in pairs across four sessions, each with access to a computer. These sessions involved problem-solving activities, with the teacher introducing key concepts in the initial three sessions. The analysis, employing grounded theory, aimed to characterize the nature of students’ conceptions of sampling distribution as evident in their responses. The findings reveal a transition from empirical to informal conceptions of sampling distribution among students, facilitated by computational mediation. This transition is marked by an abstraction process that includes mathematization, processing, uncertainty/randomness, and conditional reasoning. The study underscores the role of digital simulations in teaching statistical concepts, facilitating students’ conceptual shift critical for grasping statistical inference.

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Learning to reason from samples: commentary from the perspectives of task design and the emergence of “big data”

Cited by 9 publications

References 7 publications

Middle school students’ reasoning about data and context through storytelling with repurposed local data

Middle school students’ reasoning about data and context through storytelling with repurposed local data

Design of Statistics Learning Environments

Development of high school students’ conceptions of sampling distribution in the context of learning significance tests with technology

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