This study examines the development of learning designs based on Realistic Mathematics Education (RME) on the probability topic at the eighth-grade junior high school level. Probability abounds in everyday life, and the RME approach is believed to develop students' mathematical communication skills. This learning design development used the Plomp…

According to our approach to mathematics education, the optimal aim of the teaching of mathematics is to assist students in achieving efficient mathematical work. But, what does efficient exactly mean in that case? And how can teachers reach this objective? The model of Mathematical Working Spaces with its three dimensions--semiotic, instrumental,…

In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): If the n events E[subscript 1],…

A hypothetical framework to characterize statistical knowledge for teaching (SKT) is described. Empirical grounding for the framework is provided by artifacts from an undergraduate course for prospective teachers that concentrated on the development of SKT. The theoretical notion of "key developmental understanding" (KDU) is used to identify…

Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus…

Variability in strategy selection is an important characteristic of learning new skills such as mathematical skills. Strategies gradually come and go during this development. In 1996, Siegler described this phenomenon as ''overlapping waves.'' In the current microgenetic study, we attempted to model these overlapping waves statistically. In…

The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…

Behavioral, psychophysiological, and neuropsychological studies have revealed large developmental differences in various learning paradigms where learning from positive and negative feedback is essential. The differences are possibly due to the use of distinct strategies that may be related to spatial working memory and attentional control. In…

Estimating the difficulty level of math word problems is an important task for many educational applications. Identification of relevant and irrelevant sentences in math word problems is an important step for calculating the difficulty levels of such problems. This paper addresses a novel application of text categorization to identify two types of…

This study examined what kinds of groups can be identified according to students' task-values across four subject domains (languages, math and science, social sciences, practical subjects) and the related gender differences using a person-centered approach. Latent class analysis was applied to classify 638 students (mean age = 15) into four…

Based on a synthesis of the literature and observations of young children over 2 years, a framework for assessing probabilistic thinking was formulated, refined, and validated. For each of four major constructs incorporated into this framework--sample space, probability of an event, probability comparisons, and conditional probability--four…

Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…

Explored are the distributions of residual components in two model systems. A system of components with exponentially distributed lifetimes and the two-dimensional "leaf model" in which objects fall on a plane with positions independent and normally distributed are discussed. Included are the definition, application, computations, and theorem. (KR)

Presents an analysis of the question in the title which involves a discussion of fractions, number theory, and probability through modeling, exploring, and other mathematical connections. (MKR)

This guide provides activities based on 13 Mathnet cases that are part of the television program Square One TV. Mathnet is a detective serial which ends each program. Each Mathnet activity consists of a case summary, two short activities, and one longer step-by-step activity, with a reproducible student activity page. Topics include geometry,…