A tour through seven different perspectives on the learning of probability offered by the chapter authors of Chance Encounters is simultaneously enlightening and frustrating. It is enlightening because each perspective provides some conceptual morsels for researchers in probability to assimilate or to reject. It is frustrating because no synthesis of the perspectives, no careful distillation of the major ideas in the book, was attempted either by the editors or by any chapter author. The book can be thought of as a series of cognitive photographs from a river tour of stochastic thinking. Like real photos, some of the pictures we receive are in crystalline focus, whereas others are either underdeveloped or overdeveloped. Each reader will have to construct an overall perspective for himself or herself in order to bring the main ideas into focus.
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Review: Cognitive Snapshots of the Stochastic River
J. Michael Shaughnessy
A Letter from the NCTM President: Linking Research and Practice: The Research Agenda Project
J. Michael Shaughnessy
About the same time that this issue of JRME arrives at your doorstep or in your computer, NCTM will release the report Linking Research and Practice: The NCTM Research Agenda Report. This publication summarizes the work and recommendations from a conference of practitioners and researchers that was held in summer 2008. The conference was charged with identifying and prioritizing a set of guiding research questions that could help to focus researchers' attention on critical problems of practice. With this letter I have an opportunity to share information and recommendations from the Research Agenda Conference Report, and point to some next steps for NCTM to implement the vision shared in the Report.
Connecting Research to Teaching: Probability and Statistics
J. Michael Shaughnessy
This issue introduces a new department to the Mathematics Teacher, “Connecting Research to Teaching.” Articles will focus on mathematical and pedagogical ideas related to the NCTM's Curriculum and Evaluation Standards (1989) and the Professional Standards for Teaching Mathematics (1991). Authors will strive to present information to help teachers (1) understand students' conceptions or misconceptions of important ideas, (2) consider various approaches to teaching, and (3) offer activities that probe students' understanding. Although research offers no one correct answer to the many perplexing problems surrounding teaching and learning mathematics, the suggestions and perspectives may help teachers pursue their work with new insights. It is hoped that the department will also stimulate researchers to reflect on connecting research to the classroom. Communication and collaboration between teachers and researchers will benefit both groups and help each grow in appreciation of the other's tasks.
Then: Surprisingly Impactful Past Mathematics Education Events
J. Michael Shaughnessy
In celebration of NCTM's 100th birthday I'm very pleased to have this opportunity to share this retrospective on two early career events that had a big impact on mathematics education nationally and internationally, and turned out to be surprisingly instrumental in my own professional development.
Commentary: Mathematics Teacher Educator: The Evolution of a New Journal
J. Michael Shaughnessy
In the past decade, there has been a growing interest in the role that practitioners play as stakeholders in and coproducers of professional knowledge and of research knowledge in mathematics education (Kieran, Krainer, & Shaughnessy, in press). Although the wellspring of professional knowledge and craft wisdom of teachers has been sparsely tapped in previous decades, there are now signs from all over the world that teachers are playing an increasingly important role in research on the teaching and learning of mathematics (Bednarz, 2004; Fernandez & Yoshida, 2004; Herbel-Eisenmann & Cirillo, 2009; Huang & Bao, 2006; Jaworski et al., 2007; Makar & O'Brien, in press). A recent conference brought together practitioners, teacher educators, and researchers in mathematics education to develop a research agenda that will provide closer links between research and practice (NCTM, 2010).
Aspects of Students' Reasoning About Variation in Empirical Sampling Distributions
Jennifer Noll and J. Michael Shaughnessy
Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions.
How Faithful Is Old Faithful? Statistical Thinking: A Story of Variation and Prediction
J. Michael Shaughnessy and Maxine Pfannkuch
Statistics is a relatively new discipline. Only in the last one hundred years have common methods and common reasoning evolved that can be applied to data from many fields. In the early years, the field of statistics was influenced by the work of Ronald A. Fisher, Karl Pearson, and Jerz Neyman. They focused on developing tools and methods that primarily focused on randomization More recently, exploratory data analysis has been emphasized (Tukey 1977). As statistics continues to mature as a discipline, statistics educators are paying more attention to developing overall models of statistical thinking (Wild and Pfannkuch 1999). This shift in statistics means refocusing the emphasis in teaching from how to do statistics to how to think about statistics.
Connecting Research to Teaching: Professional Communities: Teachers Supporting Teachers
Lisa Byrd Adajian
Edited by J. Michael Shaughnessy
In the past decade, numerous projects aimed at improving the teaching and learning of mathematics have been developed. One theme that has repeatedly emerged from these and other reform efforts is the importance of a strong professional community for helping teachers implement reform. When teachers are active participants in a professional community of their peers, they gain important knowledge and psychological support. In addition, when teachers' efforts are guided by their professional community, reform is more widespread and long lasting.
Monty's Dilemma: Should You Stick or Switch?
J. Michael Shaughnessy and THOMAS DICK
Recently, a colleague in our department shared a version of this problem with us. Since then, we have had a great deal of fun with it, provoking considerable debate among students, teachers, and mathematicians alike. The problem involves introductory probability concepts, and we have found it appropriate for, and interesting to, students from middle school to college.
A Causal Analysis of Attitude toward Mathematics
Tom Haladyna, Joan Shaughnessy, and J. Michael Shaughnessy
A model was hypothesized in which teacher quality, social-psychological classroom climate, and management-organization classroom climate were assumed to affect a class's attitude toward mathematics and, to a lesser extent, its motivation. Path analyses of data from 28 fourth-grade, 34 seventh-grade, and 38 ninth-grade classes were employed to test the validity of the model. Support was moderately positive at Grade 4 and improved substantially at Grades 7 and 9.
