This article is the result of a comprehensive research study investigating the impact of computer-learning technology as well as the impact of a synergistic teaching approach (Keystone Method) on developmental mathematics classes at the college level. The study focused on mathematics skills of elementary and intermediate algebra students and…

This study took a broad view of generalization, exploring how classroom instruction within opportunities of implicit generalization may be related to students' abilities to generalize. From an integrated perspective of generalization and problem solving, we investigated twelve lessons of two middle level teachers based on three pattern-based…

In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…

In California, an increasing number of 8th graders have taken algebra courses since 2003. This study examines students' California Standards Test (CST) results in grades 7 through 11, aiming to reveal who took the CST for Algebra I in 8th grade and whether the increase has led to a rise in students' taking higher-level mathematics CSTs and an…

The present study tries to identify the "picture in mind" that students' have about defining, proving and modelling. We access to it through external representations of their mental representations; in particular, from the way in which these representations are expressed in written form (sentences and situations). In the study we have…

There has been increased attention to the development of assessment measures for evaluating mathematical skills in young children in order to inform instruction and intervention. However, existing tools have focused primarily on number sense with little attention to other areas of mathematical thinking such as geometry and algebra. The purpose of…

We present an analysis of several characteristics of examples in 10 college algebra textbooks used in community colleges or 4-year institutions. We analyzed the examples along four dimensions: cognitive demand, the responses expected, the use of representations, and the strategies available for verifying the correctness of the solutions. We found…

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

There is continuing interest in the identification of student and instructional factors associated with the mathematics achievement of students in Japan. The Trends in International Mathematics and Science Study (TIMSS) assessments have provided opportunities to examine factors associated with mathematics achievement. The purpose of this study was…

Mathematics and science course graduation requirement (CGR) increases in the 1980s and 1990s might have had both intended and unintended consequences. Using logistic regression with Census and American Community Survey (ACS) data (n = 2,892,444), we modeled CGR exposure on (a) high school dropout, (b) beginning college, and (c) obtaining any…

Despite extensive scholarship about the importance of teaching mathematics with multiple strategies in the elementary grades, there has been relatively little discussion of this practice in the middle and high school levels or in the context of introductory algebra. This article begins our exploration of this practice by addressing the following…

In a diverse classroom, there are students who are in need of both mathematics and English as a second language instruction. One of the challenges faced at Lake Washington Institute of Technology (LWIT) was the development of a pathway for English language learners into core academic courses at the college. In addition, English language learners…

This "Eighth Annual Report Card" tracks progress on Boston's goals for educating learners of all ages. The report lays out Boston Opportunity Agenda's current metrics, the baseline that has been established for the future, and the progress to be made over the course of the next five years. This report card contains the most up-to-date…

Data and information are critical tools of school improvement. They are the foundation for making informed education decisions for our schools, districts and the state. The 2019 edition of the Annual Condition of Education Report (COE) marks the 30th edition of the Iowa Department of Education report. Much has changed in the past 30 years since…

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills,…