This article describes a subset of results from a larger study (Rubel, 2002) that explored middle school and high school students' probabilistic reasoning abilities across a variety of probabilistic contexts and constructs. Students in grades 5, 7, 9, and 11 at an urban, private school for boys (n = 173) completed a Probability Inventory, comprising adapted tasks from the research literature, which required students to provide answers as well as justifications of their responses. Supplemental clinical interviews were conducted with 33 students to provide further detail about their reasoning. This article focuses specifically on the probabilistic constructs of compound events and independence in the context of coin tossing. Analyses ofjustifications of correct and incorrect answers are provided, offering insight into students' strategies, reasoning, and underlying cognitive models. A belief framework is supported by the results of this study. Potential implications for research and instruction are also discussed.
Laurie H. Rubel
Expand the focus on diversity and equity to discuss the importance of gender and sexual identity for mathematics education.
Laurie H. Rubel
Consider the following problem: Compare the probabilities of the following two events: (1) 7 tails out of 10 tosses of a fair coin and (2) 700 tails out of 1000 tosses of a fair coin. Which of the events is more likely, or are they equally likely? (adapted from Fischbein and Schnarch 1997, p. 99)
Laurie H. Rubel
NCTM's Communication Principle states that instructional programs at all grade levels should enable students to “organize and consolidate their mathematical thinking through communication; communicate their mathematical thinking coherently and clearly to peers, teachers, and others; [and] analyze and evaluate the mathematical thinking and strategies of others” (NCTM 2000, p. 60). He then shares two limitations of SmartView and follows with instructions on using scripts, emulator states, and the keystroke history features and on taking screen shots. A thirty-day trial CD of TI-SmartView 2.0 can be requested by calling 1-800-TI-CARES. Learn more about SmartView by visiting education.ti.com/educationportal/sites/US/productDetail/us_smartview.html.
Laurie H. Rubel
Readers are likely to be familiar with the infamous Monty Hall problem, played on the Let's Make a Deal game show and later addressed in the “Ask Marilyn” column in a 1990 issue of Parade.
Betina A. Zolkower and Laurie H. Rubel
A vignette from a middle school classroom discusses how “low threshold, high ceiling” number puzzles will intrigue and interest students and teachers.
Laurie H. Rubel, Haiwen Chu and Lauren Shookhoff
Maps at four levels of scale—global, national, regional, and local—provide a context for mathematical investigations that help teachers learn about their students.
Laurie H. Rubel and Betina A. Zolkower
The National Council of Teachers of Mathematics (2000) recommends that students at all grade levels be provided with instructional programs that enable them to “create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; and use representations to model and interpret physical, social, and mathematical phenomena” (p. 67). This article describes a particular classroom activity used to highlight the significance of mathematical representations.
Laurie H. Rubel and Anders J. Stachelek
In this article, we share our experiences in mathematics teacher education around professional development for teachers with a focus on student participation as an opportunity to learn. We describe a process through which teacher educators can support teachers in increasing and improving classroom participation opportunities for their students. We present Lesson Activity Bars and Difference in Participation Proportion, complementary tools that quantify and represent student participation in the mathematics classroom. We demonstrate the effectiveness of these tools in supporting teacher growth in the context of a professional growth project for teachers in urban secondary schools. In general, the teachers in this project increased the amounts of active participation they made available to their students. The cases of two teachers are analyzed in detail, using Clarke and Hollingsworth's (2002) Interconnected Model of Professional Growth, to add depth and nuance to our understanding of processes of teacher growth around increasing student participation opportunities in the mathematics classroom.
Laurie H. Rubel, Michael Driskill and Lawrence M. Lesser
Redistricting can provide a real-world application for use in a wide range of mathematics classrooms.