Explores first-year students' understanding of fundamental calculus concepts using written tests and interviews. Analysis of the written and verbal responses to the test items revealed significant misconceptions on which students' mathematical activities were based. Describes some of those misconceptions and errors relating to students'…

Describes a test using 155 third-year undergraduates in 15 different institutions to examine the extent to which certain core first-year material is retained and understood. Includes an analysis of the answers given by students to each question as well as some of their comments. Students' misconceptions indicate that foundations laid in the first…

Discusses how students fail to recognize the underlying equivalence when the same set of points is represented by a graph or an equation or a table. Presents activities in which more than one form of representations of the same information are included. (ASK)

Describes an episode involving conditional statements and the notion of logical equivalence that occurred in a 10th-grade college-preparatory geometry class. Illustrates some of the confusion that can arise in connection with this topic, for both students and teachers. (ASK)

Investigated are three misconceptions of probability and the differential effect of two activity-based instructional units. Response categories (law of averages, law of small numbers, and availability) are identified. Treatment differences (evaluation or no evaluation) appear to influence subjects' interpretations of the information. (YP)

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:…

Results of the most recent administration of the National Assessment of Educational Progress (NAEP) suggest that the majority of secondary students believe in the independence of random events. In the study reported here, a high percentage of high school and college students answered similar problems correctly. However, about half of the students…

The concept of function is the single most important mathematical concept studied from kindergarten to graduate school and is critical throughout the full range of education. Thus, the goals of this book are to contribute to research in learning the concept of function and to provide a resource for mathematics teachers that could help them in…

Summarizes some student misconceptions concerning the concept of equality. Provides several ways to modify present instruction. Describes a way to model the relational view of equals using balances. (YP)

Discusses the teaching of vectors and the inadequate and inappropriate examples given in many textbooks. Suggests using the motion of a sailboat or the motion of a car moving on the Earth's surface as possible examples. Details a proper vector teaching example. (MVL)

Typically, the mathematical properties concerning the golden ratio are stated correctly, but much of what is presented with respect to the golden ratio in art, architecture, literature, and aesthetics is false or seriously misleading. Discussed here are some of the most commonly repeated misconceptions promulgated, particularly within mathematics…

It is difficult for students to unlearn misconceptions that have been unknowingly reinforced by teachers. The examples "multiplication makes bigger,""pi equals 22/7," and the use of counter examples to demonstrate the numerical property of closure are discussed as potential areas where misconceptions are fostered. (MDH)

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)

The Van Hiele theory asserts that there exist five hierarchical levels of geometric thinking that a successful learner passes through. The purpose of the study described in this paper was to investigate the geometric understanding and misconceptions in students in the fourth through eighth grades who have been identified as gifted. The students…