This article describes "Build It!--The Rectangle Game" task that uses the context of a game to develop mathematical generalizations based on strategy. The underlying mathematics in this game-based task is for students to discover factors and prime and composite numbers through 100. The playful use of "The Rectangle Game"…

This article endeavours to define how the application of incorrect or wrong solutions to mathematical equations or problems can be used to help stimulate students to perform a critical analysis of the mathematics being applied or the context of the equations used. The context of the application is discussed together with the specific learning…

Middle-grades teachers and students can have different perspectives on the value of discussing students' mathematical mistakes, despite various classroom evidence that such discussions can help foster strong conceptual understanding. Some teachers consider student mistakes to be an opportunity to correct errors in individual student thinking.…

The purpose of this guide is to provide brief explanations of practices that can be implemented when working with students in need of intensive intervention in mathematics. Special education instructors, math interventionists, and others working with students who struggle with mathematics may find this guide helpful. Specific topics covered…

This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

After learning to categorize a set of alien-like stimuli in the context of a story, a group of 5-year-old children and adults judged pairs of stimuli from different categories to be less similar than did groups not learning the category distinction. In a same-different task, the learning group made more errors on pairs of non-identical stimuli…

This paper analyzes "confused history" on the part of students and where that confusion might originate. The study is based on a modified form of content analysis of articles by R. Lederer. The articles offer a compilation of student errors in history and geography. Two major categories of errors are recognized: (1) Type I, represented by errors…

Advances the idea that performance errors should contribute positively to the process of learning. Argues that errors do not occur randomly and that instructional theory should not condemn errors, but seek them. (PK)

Discusses the value of studying errors made by students in the process of learning science. Addresses 20 research questions dealing with student learning errors. Attempts to characterize errors made by students and clarify some terms used in error research. (TW)