The author discusses the use of calculators in calculus classes and difficulties caused by roundoff errors. References for advanced follow-up topics are given. (Author/MK)

Structuring the algebra course to provide a link between a student's existing knowledge and the new topic being presented is discussed. Developing relationships among topics is suggested through examples describing a mathematical problem and effective teaching approaches. Stress is placed on teachers reflecting on mistakes pupils are likely to…

Examines a variety of mistakes found in published materials and practiced by classroom teachers. Provides examples of mistakes in reading time, place value, price notation, geometry, and language. (YP)

Students come to the classroom with theories that they have actively constructed from their everyday experiences. However, some of these theories are incomplete half-truths. Although such misconceptions interfere with new learning, students are often emotionally and intellectually attached to them. Some common mathematical misconceptions involve:…

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…

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)

Ten crucial mathematical concepts with which errors are made are listed, with methods used to teach them to high school students. The concepts concern order, place values, inverse operations, multiplication and division, remainders, identity elements, fractions, conversions, decimal points, and percentages. (MNS)

A classroom exercise to help college students of economics conceptualize, create, and learn from graphs is described. The technique is illustrated with an exercise concerning the concept of supply and demand in consumer markets. Classroom time required for the activity is small, and students become adept at manipulating models without anxiety.…

Presents an activity applicable at the beginning of the year to review necessary algebra concepts that are often misunderstood by students. Presents a true/false worksheet made up of examples illustrating common algebra and trigonometry errors made by students. (MDH)

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)