The emergence of empirical approaches to L2 pronunciation research and teaching is a powerful "fourth wave" in the history of the field. Authored by two leading proponents of evidence-based instruction, this volume surveys both foundational and cutting-edge empirical work and pinpoints its ramifications for pedagogy. The authors begin by…

Algebra word problems were analyzed in terms of the information integration tasks that are required to solve the problems. These tasks were classified into three levels: value assignment, value derivation, and equation construction. Novices (35 first year algebra students) and experts (13 analytic geometry students) were compared on the proportion…

On the Australian Mathematics Competition, boys responded correctly to more questions than did girls, but this difference came largely from a handful of questions. Responses to questions where sex differences occurred are 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…

How computers have affected diagnosis in mathematics is discussed. A distinction is made between errors and mistakes, followed by consideration of computers as a diagnostic tool. The development of algorithms to diagnose errors and of models of student performance is described. (MNS)

Analysis of errors children make is modeled both with and without computers. Patterns of thinking are traced for a fifth grader, with the discussion focused on getting clues for remedial instruction by analyzing the dialog. (MNS)

The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical approach to errors as springboards could be…

The contributions of acceptance of misconceptions about mathematics, mathematical self-concept, and arithmetic skills to mathematics anxiety and to statistics course performance were studied in 92 adult students aged 18 to 57 with a median age of 27, (16 males and 76 females). Results showed that acceptance of misconceptions and mathematical…

A collection of student distortions, represented by student-invented variations of theorems, are presented. They were drawn from examination papers of 17-year-old students in Israel. (MNS)

Seeks to assist instructors in recognizing two basic errors that can occur in processing student evaluation data on instructional development efforts; offers a research framework for future investigations of the error tendencies and related issues; and suggests ways in which instructors can confront and manage error tendencies in practice. (MBR)

Recall of multiplication number facts is a major educational objective in elementary grades, yet some children never acquire total mastery. A microcomputer multiplication number facts training program was developed which incorporated programmed instructional features including feedback, positive reinforcement, vanishing, branching and pairing.…

An overall schema of interpretation for programming instructors is given, so that the misconceptions students develop in programming can be determined more readily. Types of language-independent and -dependent bugs, how they can be identified, and how to help students overcome them are addressed. (MNS)

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

Seventh-grade students were tested to uncover arithmetic errors. Answers and intermediate steps were analyzed and models to represent students' behavior were developed. Certain errors were common across students. Others were tied to the format of the test item. Some superficial understandings of mathematical concepts were exposed. (Author/DC)

Maintains that having students estimate the size and width of a class waste paper can (placed on a desk) is a simple and effective way of illustrating perceptual distortion. Tests show that people will consistently overestimate the height of the can, allowing for a useful discussion on sensory distortion. (MJP)