This article describes an interactive activity that involves students participating in a memory recall test. Data collected from the activity may be used to illustrate the one-sample t test or one-sample sign test.
This article describes an interactive activity that involves students participating in a memory recall test. Data collected from the activity may be used to illustrate the one-sample t test or one-sample sign test.
This article describes a lively classroom demonstration that may be used to help develop students' understanding of the concept of a distribution, and to provide a foundation for the intuitive link between distributions and hypothesis testing.
This paper describes a randomized experiment conducted in an undergraduate introductory statistics course that investigated the impact of clickers on students. Specifically, the effects of three features of clicker use on engagement and learning were explored. These features included: 1) the number of questions asked during a class period, 2) the way those questions were incorporated into the material, and 3) the grading or monitoring of clicker use. Several hierarchical linear models of both engagement and learning outcomes were fit. Based on these analyses, there was little evidence that clicker use increased students' engagement. There was some evidence, however, that clicker use improved students' learning. Increases in learning seemed to take place when the clicker questions were well incorporated into the material, particularly if the number of questions asked was low.
This theoretical paper relates recent interest in informal statistical inference (ISI) to the semantic theory termed inferentialism, a significant development in contemporary philosophy, which places inference at the heart of human knowing. This theory assists epistemological reflection on challenges in statistics education encountered when designing for the teaching or learning of ISI. We suggest that inferentialism can serve as a valuable theoretical resource for reform efforts that advocate ISI. To illustrate what it means to privilege an inferentialist approach to teaching statistics, we give examples from two sixth-grade classes (age 11) learning to draw informal statistical inferences while developing key concepts such as center, variation, distribution, and sample without losing sight of problem contexts.
Context is identified as an important factor when considering the learning of informal statistical inferential reasoning, but research in this area is very limited. This small exploratory study in one grade 10 (14 year olds) classroom seeks to learn more about the role context plays in learners' inferential reasoning, where both teacher and students are positioned as learners. Two frameworks for context are used to analyze the classroom dialogue: The data-context used in statistical enquiry and in the formation of statistical concepts and the learning-experience-contexts such as prior statistical knowledge, which can affect the learning process. The analysis tracks the learning of informal inferential reasoning before, during, and after the introduction of sampling variability concepts. Data-context was found to assist learners in finding meaning from observed patterns, but could divert their attention during the construction of concepts and when attempting to apply newly-learned theory. Learning-experience-contexts played a significant role in mediating learners' development of informal inferential reasoning. Implications for developing concepts for informal inferential reasoning and for research are discussed.
Our research addresses the role that context expertise plays when students compare data. We report findings from a study conducted in 3 countries: Australia, United States, and Thailand. In each country, six middle school students analyzed authentic data relating to selected students' areas of interest. We examined the data analysis processes and discussion among students as each country cohort worked in two groups of three, where only one group included a student with particular expertise with the data context. We found that students used context knowledge to (a) bring new insight or additional information to the task, (b) explain the data, (c) provide justification or qualification for claims, (d) identify useful data for the task at hand, and (e) state facts that may enhance the picture of the data but are irrelevant to the process of analyzing the data. Implications for practice are discussed
A core component of informal statistical inference is the recognition that judgments based on sample data are inherently uncertain. This implies that instruction aimed at developing informal inference needs to foster basic probabilistic reasoning. In this article, we analyze and critique the now-common practice of introducing students to both "theoretical" and "experimental" probability, typically with the hope that students will come to see the latter as converging on the former as the number of observations grows. On the surface of it, this approach would seem to fit well with objectives in teaching informal inference. However, our in-depth analysis of one eighth-grader's reasoning about experimental and theoretical probabilities points to various pitfalls in this approach. We offer tentative recommendations about how some of these issues might be addressed
Explanations are considered to be key aids to understanding the study of mathematics, science, and other complex disciplines. This paper discusses the role of students' explanations in making sense of data and learning to reason informally about statistical inference. We closely follow students' explanations in which they utilize their experiences and knowledge of the context, statistical tools, and ideas to support their emerging informal inferential reasoning (IIR). This case study focuses on two independent inquiry episodes of sixth-grade students (age 12) within an unstructured, inquiry-based, technology-rich learning environment that was designed to promote students' IIR. We discuss research and practical issues related to the role of explanations and context in developing students' IIR.
Recent studies have highlighted the potential importance of informal inferential reasoning (IIR) in supporting learners' general statistical reasoning. This paper presents a framework based on a retrospective analysis of design research in the context of technology-rich statistical professional learning experiences for high school mathematics teachers. The framework was developed to understand elements of the tasks - identified as statistically, contextually, and/or technologically provocative - that appeared to trigger the teachers' engagement and IIR. Characteristics that make a task provocative and how tasks may interact to impact learning are explored and connected to theories including expectation failure and epistemological obstacles.
To support 11th-grade students' informal inferential reasoning, a teaching and learning strategy was designed based on authentic practices in which professionals use correlation or linear regression. These practices included identifying suitable physical training programmes, dyke monitoring, and the calibration of measurement instruments. The question addressed in this study is: How does a teaching and learning strategy based on authentic practices support students in making statistical inferences about authentic problems with the help of correlation and linear regression? To respond to this question we used video-recordings of lessons, audio-taped interviews, classroom field notes, and student work from a teaching experiment with 12 Dutch students (aged 16-17 years). The analysis provided insights into how the teaching and learning strategies based on authentic practices supported them to draw inferences about authentic problems using correlated data. The evidence illustrates how an understanding of the authentic problem being solved, collecting their own data to become acquainted with the situation, and learning to coordinate individual and aggregate views on data sets seemed to support these students in learning to draw inferences that make sense in the context.