Everyone knows that teachers do not have unlimited time, a log of experience, or a deep understanding of all the mathematics they teach. To solve this problem, teachers often use textbooks, and the accompanying teacher's resource books, as sources of activities and advice about how to help students learn mathematics. The activity that prompted…

New capabilities in "TinkerPlots 2.0" supported the conceptual development of fifth- and sixth-grade students as they pursued several weeks of instruction that emphasized data modeling. The instruction highlighted links between data analysis, chance, and modeling in the context of describing and explaining the distributions of measures that result…

This paper focuses on the different ways in which students in lower secondary school (14-16 year olds) experience compound random events, presented to them in the form of combined junctions. A carefully designed ICT environment was developed enabling the students to interact with different representations of such structures. Data for the analysis…

According to traditional Chinese culture, families will care for their elderly. Therefore, it appears to be uncommon for elderly Chinese to live alone. This study examines the correlates for single elderly Chinese immigrants in Canada to live alone. Using a probability sample of single elderly Chinese immigrants (N = 660) in seven urban centers,…

Background: Truancy is a serious concern that affects most school districts in the United States; however, we do not have accurate estimates of the prevalence of truancy due to inconsistent tracking and reporting practices of schools. As a result, our best current estimates of the national state of truancy may be from self-reported data. In this…

An observational study of reading instruction was conducted in general education, resource, and self-contained classrooms, grades 1-4, in public schools. Participants included students who were deaf or hard of hearing and their reading teachers. Results indicated that time engaged in reading and/or academically responding varied significantly by…

Background: Depression is prevalent among children and adolescents and often goes untreated with adverse effects on academic success and healthy development. Depression screening can facilitate early identification and timely referral to prevention and treatment programs. Conducting school-based emotional health screening, however, raises the…

Recent developments in cognitive psychology suggest models for knowledge and learning that often fall outside the realm of standard test theory. This paper concerns probability-based inference in terms of such models. The essential idea is to define a space of "student models"--simplified characterizations of students' knowledge, skill,…

When measures are taken on the same individual over time, it is difficult to determine whether observed differences are the result of changes in the person or changes in other facets of the measurement situation (e.g. interpretation of items or use of rating scale). This paper describes a method for disentangling changes in persons from changes in…

The normal curve has long been important in statistics. Most interval variables yield normal or quasi-normal distributions when data are collected from large samples, and the normal "Z" distribution is also used as a test statistic (e.g., to test differences between two means when sample size is large, since "t" approaches…

Four experiments investigated college students' judgments of inter-event contingency. Subjects were asked to judge the effect of a discrete response (tapping a wire) on the occurrence of a brief outcome (a radio's buzzing). Pairings of the possible event-state combinations were presented in a summary table, an unbroken time line, or a broken time…

Using license plates to generate random number pairs, students can calculate an approximate value for pi. The author views this approach as easier to understand than Buffon's needle. (SD)

A test of attitudes toward arguments based on varied levels of probability. (CH)

Bayesian network models offer a large degree of flexibility for modeling dependence among observables (item outcome variables) from the same task that may be dependent. This paper explores four design patterns for modeling locally dependent observations from the same task: (1) No context--Ignore dependence among observables; (2) Compensatory…

Children at many levels enjoy using spinners to explore probabilities and practice predicting, tabulating and graphing outcomes, and observing results. Directions for making spinners, descriptions of several activities, and sample worksheets are provided. (SD)