This article describes a unit of instruction designed to promote algebraic thinking in second graders. Students examined second- and fourth-grade students' ages and heights on a table and graph and described the patterns that they observed in the data.

In 2 experiments with 74 high school students, subjects studied worked examples while learning how to translate English expressions into algebraic equations. Those using worked examples outperformed the control group on posttests, made fewer errors, completed work more rapidly, and required less assistance from the teacher. (SLD)

The "I CAN Learn[R] Mathematics Curriculum" is designed to help ethnically diverse, inner-city students in grades 7 through 10 achieve parity in mathematics and problem-solving skills. It uses an interactive software program to teach pre-algebra and algebra. The "I CAN Learn[R] Algebra 1" course, which was used in all of the…

The original version, Version 1.0, of this document was first published in 2005. This current version, Version 2.0, includes updates based on feedback from faculty across the state. Also a listing of the Algebra I California Content Standards organized into clusters has been added in Appendix #1. Cal-PASS is unique in that it is the only data…

Learning in educational settings most often emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other, equally important components of learning, especially improvements produced by experience in the extraction of information: "Perceptual learning." Here we describe research that combines principles of…

In the fall of 2005 the Maui Educational Consortium began a project that was funded through the Math Science Partnership program to implement the "Cognitive Tutor[R]" (CT) program, published by Carnegie Learning, in some of the Algebra 1 classes in the Maui School District and at the Maui Community College. At that time, Empirical…

This evaluation examined the implementation and effectiveness of the AVID program in middle schools throughout the Wake County Public School System (WCPSS). Survey results and school visits revealed considerable inconsistencies in implementation across schools. Specifically, selection criteria were not consistently understood and applied, all…

The purpose of this research is to compare American and Albanian students' achievement in Algebra 1 and to identify the educational practices that influence students' achievement in each country. The study compared algebraic solving abilities of 242 ninth-grade American students in Grand Forks (U.S.) and 219 students in Durres (Albania). The data…

Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting third graders' development of mathematics problem solving. In the fall, 122 third-grade students were…

Understanding student performance in Algebra I is important because this course serves as the gateway to advanced coursework in mathematics and science through the remainder of high school and into postsecondary education. In the current study, we analyzed secondary data to evaluate the relationship between selected indicators of mathematics and…

We present principles for the design of an online system to support computer algebra enabled questions for use within the teaching and learning of mathematics in higher education. The introduction of a computer algebra system (CAS) into a computer aided assessment (CAA) system affords sophisticated response processing of student provided answers.…

How did it happen that both full-time and adjunct faculty at Scottsdale Community College embrace a standards-based curriculum from beginning algebra through differential equations? Simply put, it didn't just happen. Not only did it take well over a decade, but it was also the result of a sequence of initiatives, decisions, discussions, targeted…

The purpose of this study was to demonstrate the effectiveness of web-based homework (WBH) assignments on the overall comprehension measured by the final examination in a first year college algebra course. This study included 1653 students over a three year period. Results indicate a strong correlation between achievement on the WBH assignments…

This document presents activities and information related to Fibonacci numbers, which are based upon the Golden Ratio, in areas of the arts, sciences, and mathematics. The work is organized into eight chapters: (1) "Origins and Definitions"; (2) "Fibonacci Numbers in Nature"; (3) "Fibonacci Numbers in Art and…

This study reports evaluation data from a statewide inservice project to retrain mathematics teachers to implement a new algebra curriculum required by all students for high school graduation. The new course places more emphasis on problem solving, use of graphing calculators, and real-life applications. Pretest and posttest data were collected…