The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenge of teaching early math to children ages 3 to 6. The guide provides practical, clear information on critical topics related to teaching early math and is based on the best available evidence as judged by the authors. The guide…

Having returned to teaching the basics of pricing fixed-income securities after several years, the author recalls the difficulty students have in understanding the total return provided by fixed-income securities that are purchased at either a discount or premium from face value. This teaching note attempts to clarify the concept by suggesting…

Learning Curves has its roots in economics and behavioral psychology. Learning Curves theory has several business applications and is widely used in the industry. As faculty of Operations Management courses, we cover this topic in some depth in the classroom. In this paper, we present some of our teaching methods and material that have helped us…

Most high school students are at an age when they are learning to drive. They often want to offer input when their parents decide on what vehicle to purchase, so the activity described in this article should have direct personal interest for them. It allows students to use technology and mathematics to determine the environmental impacts of…

Gathering high school completer and dropout data and maintaining annual records provides longitudinal information on students which allows a district to observe its unique patterns of school dropouts. That information may assist schools to target prevention and intervention programs and policies that focus on local circumstances and address the…

The purpose of the study was to examine differences in early numerical competencies, as well as subtraction skill, as a function of children's mathematics difficulty (MD) status: computational difficulty (CD), word problem-solving difficulty (PD), concurrent difficulty (CDPD), or neither difficulty (i.e., typically developing; TYP). Based on…

The combined seventh-grade and eighth-grade class began each day with a mathematical reasoning question as a warm-up activity. One day's question was: Is the product of two odd numbers always an odd number? The students took sides on the issue, and the exercise ended in frustration. Reflecting on the frustration caused by this warm-up activity,…

As is the case for any statistical model, a multidimensional latent growth model comes with certain requirements with respect to the data collection design. In order to measure growth, repeated measurements of the same set of individuals are required. Furthermore, the data collection design should be specified such that no individual is given the…

The purpose of this study was to examine how selected linguistic components (including consistency of relational terms and extraneous information) impact performance at each stage of mathematical word problem solving (comprehension, equation construction, and computation accuracy) among students with different levels of computation achievement. …

This paper estimates the marginal returns to college for individuals induced to enroll in college by different marginal policy changes. The recent instrumental variables literature seeks to estimate this parameter, but in general it does so only under strong assumptions that are tested and found wanting. We show how to utilize economic theory and…

In recent months a number of states, such as Tennessee, have considered tying teacher evaluations and tenure to student achievement as part of their Race to the Top plans. This research brief evaluates how well early-career performance signals teacher effectiveness after tenure. The brief presents selected findings from a larger study using North…

Apprentice and trainee data are reported by the State and Territory Training Authorities to NCVER (National Centre for Vocational Education Research) on a quarterly basis, starting at the September quarter of 1994. The set of data submitted that quarter is referred to as the National Apprentice and Trainee Collection 1. The sets of data submitted…

Clustering is one of the most common data mining tasks, used frequently for data organization and analysis in various application domains. Traditional machine learning approaches to clustering are fully automated and unsupervised where class labels are unknown a priori. In real application domains, however, some "weak" form of side…

Two people take turns selecting from an even number of items. Their relative preferences over the items can be described as a permutation, then tools from algebraic combinatorics can be used to answer various questions. We describe each person's optimal selection strategies including how each could make use of knowing the other's preferences. We…

The focus of this presidential address is on the contemporary treatment of reliability and validity in educational assessment. Highlights on reliability are provided under the classical true-score model using tools from latent trait modeling to clarify important assumptions and procedures for reliability estimation. In addition to reliability,…