Students’ emergent articulations of uncertainty while making informal statistical inferences

Ben‐Zvi, Dani; Aridor, Keren; Makar, Katie; Bakker, Arthur

doi:10.1007/s11858-012-0420-3

Cited by 65 publications

(57 citation statements)

References 12 publications

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“…Ben-Zvi (2006) found that the growing samples task design combined with Bwhat-if^questions not only helped students make sense of the data at hand, but also supported their informal inferential reasoning by observing aggregate features of distributions, identifying signals out of noise, accounting for the constraints of their inferences, and providing persuasive data-based arguments (see also Gil & Ben-Zvi, 2011). The growing awareness of students to uncertainty and variation in data enabled students to gain a sense of the middle ground of Bknowing something^about the population with some level of uncertainty and helped them develop a language to talk about the grey areas of this middle ground (Ben-Zvi et al, 2012).…”

Section: Studies Involving School Studentsmentioning

confidence: 83%

“…Growing samples is an instructional heuristic mentioned by Konold and Pollatsek (2002), worked out by Bakker (2004Bakker ( , 2007 and Bakker and Frederickson (2005), and elaborated by Ben-Zvi (2006) and Ben-Zvi, Aridor, Makar and Bakker (2012). In this approach, students are gradually introduced to increasing sample sizes that are taken from the same population.…”

Section: Studies Involving School Studentsmentioning

confidence: 99%

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Learning to reason from samples

2015

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The goal of this article is to introduce the topic of learning to reason from samples, which is the focus of this special issue of Educational Studies in Mathematics on statistical reasoning. Samples are data sets, taken from some wider universe (e.g., a population or a process) using a particular procedure (e.g., random sampling) in order to be able to make generalizations about this wider universe with a particular level of confidence. Sampling is hence a key factor in making reliable statistical inferences. We first introduce the theme and the key questions this special issue addresses. Then, we provide a brief literature review on reasoning about samples and sampling. This review sets the grounds for the introduction of the five articles and the concluding reflective discussion. We close by commenting on the ways to support the development of students' statistical reasoning on samples and sampling.

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Section: Studies Involving School Studentsmentioning

confidence: 83%

Section: Studies Involving School Studentsmentioning

confidence: 99%

Learning to reason from samples

2015

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“…When the students were encouraged to express their confidence about how certain they were about their inferences, they tended to either express extreme confidence in knowing that something can be inferred from samples or express that nothing could be concluded (i.e., complete certainty vs. extreme doubt; Ben-Zvi et al, 2012). The growing samples task design provided students with opportunities to witness increasing evidence for (or against) particular conjectures, thus develop a language to talk about "grey areas of this middle ground" (p. 923).The research reported in this paper is based on the growing samples design of the investigations that support students' informal inferential reasoning when estimating population parameters from samples.…”

Section: Growing Samplesmentioning

confidence: 99%

Estimating Parameters from Samples: Shuttling between Spheres

Prodromou¹

2013

IJSP

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In order to better understand the thinking of students' learning to make informal statistical inferences, this research examined the thinking of senior secondary school students (age 17) engaged in the task of using observed data to make point estimates of a population parameter within a computer-based simulation. Following the "Growing Samples" instructional model, the point estimation activity involved sampling and estimating across three tasks with different sample sizes. This research study aimed to trace the evolution of the students' thinking, with particular attention to use of the statistical concepts in making informal inferences from sampling. The students in this study were observed to rely primarily on mathematical thinking, which, perhaps, inhibited their ability to construct meanings about the basic statistical concepts underpinning sampling when performing point estimates. At times in the process students were seen to shift between mathematical thinking, statistical thinking, and thinking about the context, but the mathematical thinking seemed to dominate their attempts to create estimates. These research findings are useful for informing the teaching of point estimation of a population parameter to school-aged students. The research findings also stress the need for teachers to rethink the relationship between statistical thinking and mathematical thinking in order to promote statistical thinking in relevant learning situations for their students.

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“…Variation is the "act, process, condition or result of changing or varying" (Farlex, 2012) and the main purpose of the sample is to represent the variation in a heterogeneous population. Understanding the sampling concept also depends on understanding other statistical concepts, including distribution, randomness, likelihood, and representativeness (Ben-Zvi, Aridor, Makar, & Bakker, 2012;Watson & Moritz, 2000b). For a more detailed understanding of sampling, an understanding of the various sampling techniques that can be used would also need to be developed (Watson, 2004).…”

Section: Understanding Sampling and Related Conceptsmentioning

confidence: 99%

“…Research into developing a better understanding, from a pedagogical perspective, of how to approach differentiating between sample and population provides useful insights into student understanding of core concepts. One such approach, Growing Samples, originally suggested by Konold and Pollatsek (2002), was formally developed by Bakker (2004), and is now widely used (see, e.g., Ben-Zvi et al, 2012;Prodromou, 2011). This approach, based on the integration of core statistical concepts including sampling and variation, was developed to help students reason about sampling in a context of variability (Bakker, 2004).…”

Section: Understanding Sampling and Related Conceptsmentioning

confidence: 99%

Informal Inferential Reasoning: Interval Estimates of Parameters

Prodromou¹

2013

IJSP

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This research examined the informal inferential reasoning of senior secondary school students (age 17) when engaged in a computer-simulated sampling activity calling for the estimation of population parameters. The students undertook a task involving interval estimation of parameters within a computer-simulated environment. The research observed the students while they made and then explained their parameter estimates in order to better understand how the students formed the interval estimates, with particular attention to different strategies they adopted in forming these estimates. Activities involved sampling and estimating across three different sample size situations followed by a reflection stage to compare the estimates. Results of the analysis of the discussion between the students and the researcher during the students' activities are presented. A number of strategies for forming an interval estimate emerged. The students experimented with choosing different strategies for forming the interval estimate when a new sample (observed values) was drawn. The research findings are useful for informing the teaching of interval estimation to school-aged students.

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Students’ emergent articulations of uncertainty while making informal statistical inferences

Cited by 65 publications

References 12 publications

Learning to reason from samples

Learning to reason from samples

Estimating Parameters from Samples: Shuttling between Spheres

Informal Inferential Reasoning: Interval Estimates of Parameters

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