Background: Although the generation of errors has been thought, traditionally, to impair learning, recent studies indicate that, under particular feedback conditions, the commission of errors may have a beneficial effect. Aims: This study investigates the teaching strategies that facilitate learning from errors. Materials and Methods: This 2-year…

"Low threshold, high ceiling" tasks are accessible to diverse learners; invite a wide range of approaches; and hold the potential to further challenge, strengthen, and extend everyone's mathematical reasoning. In this article, the authors present a family of Brick Pyramid problems as examples of "low threshold, high ceiling"…

One of the many roles of two year community colleges in the United States is to bridge the gap between secondary school and college for students who graduate from high school with weak mathematics skills that prevent them from enrolling in college level mathematics courses. At community colleges remedial or developmental mathematics courses review…

Mathematics teachers face the challenge of integrating calculator use in their classrooms. Calculators provide advantages for students when performing calculations and they can provide teachers with a versatile instructional tool. Students face high-stakes mathematics tests each year in middle school and must take Regents and college entrance…

It is important for teacher educators to understand new alternative certification middle and high school teachers' mathematical problem solving abilities and perceptions. Teachers in an alternative certification program in New York were enrolled in a proof-based algebra course. At the beginning and end of a semester participants were given a…

The purpose of the study is to present research focused on validating the four algebra cognitive models in Gierl, Wang, et al., using student response data collected with protocol analysis methods to evaluate the knowledge structures and processing skills used by a sample of SAT test takers.

In this important resource, Dr. Fleming (a noted expert in the field of minority retention) draws on educational evaluations she has developed in the course of her distinguished career. This book analyzes the common factors and the role institutional characteristics play in minority student retention to show what really works in increasing…

The purpose of this study was to describe elementary preservice teachers' difficulties with understanding algebraic generalizations that were set in an authentic context. Fifty-eight preservice teachers enrolled in an elementary mathematics methods course participated in the study. These students explored and practiced with authentic, hands-on…

This document outlines part one of the third year course of the newly implemented New York State Mathematics Curriculum. The three-year Sequential Mathematics sequence designed by New York State is a move in the direction of fusing the formerly separate topics found in algebra, geometry, and intermediate algebra/trigonometry, and introducing…

This document outlines part two of the third year course of the newly implemented New York State Mathematics Curriculum. The three-year Sequential Mathematics sequence designed by New York State is a move in the direction of fusing the formerly separate topics found in algebra, geometry, and intermediate algebra/trigonometry, and introducing…

A study was conducted with forty-seven preservice childhood (elementary) education teachers (42 F, 5 M) enrolled in two mathematics methods classes taught by the same instructor to determine the effect of these college students making curriculum materials appropriate for upper elementary students on the preservice teachers' knowledge of…

The National Assessment of Educational Progress (NAEP) is the only nationally representative and continuing assessment of what students in the United States know and can do in various academic subjects. The 1996 NAEP in mathematics assessed the current level of mathematical achievement as a mechanism for informing education reform. In 1996, 44…

In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment which, for the first time in the NAEP's history, made voluntary state-by-state assessments. This 1992 mathematics report marks the first attempt of the National Center for Education Statistics to shift to standards-based reporting of National…

The purpose of this revised syllabus/guide is to help teachers and administrators plan and implement Course I in the State of New York Three-Year Sequence for High School Mathematics for Regents credit. Course I builds upon the State mathematics curriculum outlined in the Department's mathematics K-6, Grade 7, and Grade 8 publications. This guide…