Discusses errors made by remedial intermediate algebra students in factoring polynomials in light of student definitions of factoring. Found certain beliefs about factoring to logically imply many of the errors made. Suggests that belief-based teaching can be successful in teaching factoring. (16 references) (Author/MKR)

Illustrates, categorizes, and analyzes typical mathematical errors in algebra and trigonometry made by high school and lower division college students. (16 references) (Author/MKR)

The history of mathematics is full of rich examples that can help students to see the place of the discipline within our cultural heritage. Valuable as this can be, it also has the unfortunate side-effect of making students think that all the math has already been done and they do not get a sense that the subject is dynamic and growing.…

A set of brief reflections about different aspects of mathematical errors and their roles in education is given. The nature and variety of errors and their positive use in learning mathematics are highlighted. (MNS)

Attention is called to the apparent widespread misunderstanding of algebraic notation by secondary school students, and how this may arise from some common approaches to teaching algebra to beginners is discussed. (MNS)

Seven graduate students in a seminar on classroom computing received instruction in LOGO programming. Programming protocols were collected periodically and examined for errors and misconceptions; in-depth interviews were conducted in order to understand specific misconceptions better. As novice students transit from instruction to experience in…

The need for teachers to be proficient in diagnosing pupil difficulty in mathematics is advocated. Some facets of student behavior to be observed by the teacher are noted, including reversals, lack of retention, and lack of differentiation. All are characteristics associated with dyslexia. Problems of dyslexic pupils are noted and some general…

This article recommends a holistic approach to student problems in mathematics. Teachers need to be aware of all paradigms (e.g., developmental, behaviorist, psychoanalytic) explaining causes of problems in mathematics. Examples of misunderstandings resulting from insufficient knowledge, insufficient mathematical vocabulary, and overgeneralization…

Discusses the use of feedback from students and the analysis of students' error patterns to understand why students develop misconceptions in mathematics. Looks at learning vis-a-vis the abstract nature of mathematics and the students' cognitive development. (MDH)

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)

The objective of this paper is to explain the need for and defend the sufficiency of the child's-play method of teaching the place value notation concept to preschool and elementary school children. Discussion first illustrates error patterns of school children in the use and interpretation of place value notation, arguing that the errors reflect…

This report resulted from work with primary grade children and teachers in Kankakee, Illinois. Essays by four resource persons and two observers are included, each expressing insights and feelings in order to share ideas with resource persons for primary mathematics teaching in other schools. A main objective is to represent the ways elementary…