The topic "Recurrence relations" and its place in teaching students of Informatics is discussed in this paper. We represent many arguments about the importance, the necessity and the benefit of studying this subject by Informatics students. They are based on investigation of some fundamental books and textbooks on Discrete Mathematics,…

Early lexical acquisition is affected by biases and constraints within learners, but also by patterns and statistical regularities within a learner's environment. Much of the previous work examining the effect of statistical regularities on word learning has been directed at phonological regularities. Particularly, research has focused on the…

This study reports how the difficulty of simple worded percentage problems is affected by the problem structure and the complexity of the numbers involved. We also investigate which methods students know. Results from 677 Year 8 and 9 students are reported. Overall the results indicate that more attention needs to be given to this important topic.…

Randomized trials of educational interventions often face logistical hurdles (Cook, 2002). For example, sometimes they are prevented from reaching their full-term. This would happen if, as a condition of participation, subjects insist on receiving the treatment program within a certain timeframe. This timeframe may be shorter than the full-term…

The Center on Education Policy, an independent nonprofit organization, collected and analyzed data from state Web sites and other sources to determine how many schools in the nation and in each state did not make adequate yearly progress (AYP) under the No Child Left Behind Act (NCLB). Findings of the study include: (1) About one-third of U.S.…

Phase thermodynamics is often perceived as a difficult subject with which many students never become fully comfortable. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based…

An overview of a course on modeling and simulation offered at the Nanotechnology Engineering undergraduate program at the University of Waterloo. The motivation for having this course in the undergraduate nanotechnology curriculum, the course structure, and its learning objectives are discussed. Further, one of the computational laboratories…

We propose a simple, direct estimate of the Sun's diameter based on penumbra observation and measurement in a two-level approach, the first for middle-school pupils and making use of simple geometrical arguments, the second more appropriate to high-school students and based on a slightly more sophisticated approach. (Contains 5 figures.)

Interruptions are common in joint activities like conversations. Typically, interrupted participants suspend the activity, address the interruption, and then reinstate the activity. In conversation, people jointly commit to interact and to talk about a topic, establishing these commitments sequentially. When a commitment is suspended, face is…

In this article, we discuss the effect of removing the independence assumptions between the residuals in two-level random effect models. We first consider removing the independence between the Level 2 residuals and instead assume that the vector of all residuals at the cluster level follows a general multivariate normal distribution. We…

Models of modern test theory imply statistical independence among responses, generally referred to as "local independence." One violation of local independence occurs when the response to one item governs the response to a subsequent item. Expanding on a formulation of this kind of violation as a process in the dichotomous Rasch model,…

Existing studies of mediation models have been limited to normal-theory maximum likelihood (ML). Because real data in the social and behavioral sciences are seldom normally distributed and often contain outliers, classical methods generally lead to inefficient or biased parameter estimates. Consequently, the conclusions from a mediation analysis…

For many students, geometry is the first course in which mathematical proof takes center stage. To help ease students into writing proofs, the author tries to create lessons and activities throughout the year that challenge students to prove their own conjectures by using tools learned in previous mathematics courses. Teachers cannot get all…

In this article, we study financing in the real estate market and show how various types of mortgages can be modeled and analyzed. With only an introductory level of interest theory, finance, and calculus, we model and analyze three types of popular mortgages with real life examples that explain the background and inevitable outcome of the current…

This paper discusses a Fermi-problem exercise through which I take students in several of my college courses. Students work in teams, determining the average daily Caloric needs per person. Then they use insolation values to determine the size of a collection area needed to absorb the previously determined daily energy requirements. Adjustments to…