Using Informal Inferential Reasoning to Develop Formal Concepts: Analyzing an Activity

Weinberg, Aaron; Wiesner, Emilie; Pfaff, Thomas J.

doi:10.1080/10691898.2010.11889494

Cited by 14 publications

(11 citation statements)

References 11 publications

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“…The above goal is in line with Weinberg et al (2010) who noted that educational researchers have been advocating the development of tools for informal inferential reasoning and who suggested that these tools should facilitate connections between the informal reasoning and the formal concepts. Our objective is similar to that of Lesser and Melgoza (2007) who are also interested in teaching ANOVA to students with a limited mathematical background (i.e.…”

Section: • Variancesupporting

confidence: 56%

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Naive Analysis of Variance

Braun

2012

Journal of Statistics Education

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The Analysis of Variance is often taught in introductory statistics courses, but it is not clear that students really understand the method. This is because the derivation of the test statistic and p-value requires a relatively sophisticated mathematical background which may not be well-remembered or understood. Thus, the essential concept behind the Analysis of Variance can be obscured. On the other hand, it is possible to provide students with a graphical technique that makes the essential concept transparent. The technique discussed in this article can be understood by students with little or no background in probability or statistics. In fact, only the ability to add, subtract, compute averages, and interpret histograms is required.

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Section: • Variancesupporting

confidence: 56%

“…This was noted by Weinberg et al (2010) in their review of several studies. The implication is that there are several points at which a breakdown in the understanding of ANOVA can occur.…”

Section: • Variancementioning

confidence: 88%

Naive Analysis of Variance

Braun

2012

Journal of Statistics Education

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“…The three main strategies outlined in the research literature are interrelated and mutually supportive. Our synthesis of the literature (in particular, Erickson, 2006;Garfield et al, 2012;Chance & Rossman, 2006;Liu & Thompson, 2005;Makar & Confrey, 2004;Weinberg, Wiesner, & Pfaff, 2010; suggests these three strategies support a particular pedagogical approach where students begin their study of statistics by experiencing the sampling process (physically or electronically) to generate empirical sampling distributions. Students then discuss unusual samples using an empirical sampling distribution as a tool for a statistical argument.…”

Section: Impact Of Research On Pedagogical Approachesmentioning

confidence: 92%

“…The third strategy suggested by researchers is that instruction should begin with an informal approach to statistical inference before introducing formal statistical inference (e.g., Chance & Rossman, 2006;Erickson, 2006;Garfield & Ben-Zvi, 2008;Garfield, delMas, & Zieffler, 2012;Rubin & Hammerman, 2006;Weinberg, Wiesner, & Pfaff, 2010;Zieffler, Garfield, delMas, & Reading, 2008). By building on informal approaches, educators can better support students' learning of statistical inference concepts because new knowledge is constructed from the learner's prior knowledge, and thus making formal procedures more accessible.…”

Section: Impact Of Research On Pedagogical Approachesmentioning

confidence: 99%

Using Guided Reinvention to Develop Teachers’ Understanding of Hypothesis Testing Concepts

Dolor

Noll

2015

SERJ

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Statistics education reform efforts emphasize the importance of informal inference in the learning of statistics. Research suggests statistics teachers experience similar difficulties understanding statistical inference concepts as students and how teacher knowledge can impact student learning. This study investigates how teachers reinvented an informal hypothesis test for categorical data through the framework of guided reinvention. We describe how notions of variability help bridge the development from informal to formal understandings of empirical sampling distributions and procedures for constructing statistics and critical values for conducting hypothesis tests. A product of this paper is a hypothetical learning trajectory that statistics educators could utilize as both a framework for research and as an instructional tool to improve the teaching of hypothesis testing. First published May 2015 at Statistics Education Research Journal Archives

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“…In response to these challenges, research has been conducted, on the one hand, on how to approach inference from an informal perspective, called informal inferential reasoning (IIR) [7][8][9][10] and, on the other hand, on the need to introduce stepwise inference; in other words, how to promote formal inferential reasoning progressively (FIR) on the basis of IIR [9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Inferential Statistical Reasoning of Math Teachers: Experiences in Virtual Contexts Generated by the COVID-19 Pandemic

Lugo-Armenta

Pino-Fan

2021

Education Sciences

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The COVID-19 pandemic generated a new scenario in education, where technological resources mediate teaching and learning processes. This paper presents the development of a virtual teacher training experience aimed at promoting inferential reasoning in practicing and prospective mathematics teachers using inference problems on the Chi-square statistic. The objective of this article is to assess the implemented or intended institutional meanings and the degree of availability and adequacy of the material and temporal resources necessary for the development of the training experience. For this purpose, we use theoretical and methodological notions introduced by the Ontosemiotic Approach to Mathematical Knowledge and Instruction (OSA), among which are the notions of practice and suitability criteria. The participants of this experience were divided into three groups; one of them was comprised of practicing teachers and the other two of prospective teachers. The intervention used different virtual modalities that enabled the development of the participants’ inferential reasoning in a similar way.

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Using Informal Inferential Reasoning to Develop Formal Concepts: Analyzing an Activity

Cited by 14 publications

References 11 publications

Naive Analysis of Variance

Naive Analysis of Variance

Using Guided Reinvention to Develop Teachers’ Understanding of Hypothesis Testing Concepts

Inferential Statistical Reasoning of Math Teachers: Experiences in Virtual Contexts Generated by the COVID-19 Pandemic

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