In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range…

Science instructors have long known that the use of discrepant events with unexpected outcomes is a powerful method of activating thinking. A discrepant "teaching" event is similar to a discrepant science event in that it vividly portrays what is often an abstract construct or concept and has an unexpected outcome. The unexpected outcome creates…

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'…

Research indicates that students have great difficulty solving certain algebra word problems. These solutions, moreover, appear to be due to some situational factors characteristic of algebra problems, e.g., presentation and response format. This study investigates students' preconceptions, post facto alternative concepts based on key features of…

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…

Proposes a taxonomy of three levels in increasing order of mathematical demand in order to understand a set of mathematical skills of some importance to beginning undergraduates in engineering and mathematics. Suggests that the constructed instrument is robust and the taxonomy used is effective. (Contains 22 references.) (Author/ASK)

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

Surveys of 295 undergraduate students in college algebra and precalculus about their perceptions of mathematics found that agreement with some mathematical myths can be reduced with more mathematical preparation of students. Suggests strategies to overcome these myths. (13 references) (MKR)

Addresses the use of mathematics when studying the physics of electromagnetism. Focuses on common electromagnetic concepts and their associated mathematical representation and arithmetical tools. Concludes that most students do not understand the significant aspects of physical situations and have difficulty using relationships and models specific…

This study observed and documented the changes of college students' notion of mathematics functions in a virtual environment that integrated a synchronous and asynchronous Computer Mediated Communication system. Four Arizona State University undergraduates were teamed into pairs and solved function problems in the virtual classroom over a one…

Summarizes the history of the mathematical idea of function and presents questionnaire data from (n=117) mathematics teachers. Results showed that teachers had a tendency to think only in terms of continuous functions, yet had little skill in constructing continuous functions. They scarcely considered discontinuous functions. (14 references) (MKR)

An algebra test administered to (n=18) first-year college students found a disregard for negative numbers, ineffective use of counterexamples, misapplication of rules, and a lack of a good grasp of relevant mathematical terminology. (12 references) (MKR)

Raises a number of questions about knowledge generation from mathematics education and the nature of pedagogical information in the field. Considers two main activities within the realm of mathematics education: (1) pursuing investigations to improve instruction and (2) redefining the boundaries of mathematics as a subject. (DDR)

Argues that intuitive and computational knowledge can be combined by focusing more explicitly on referential and quantitative meanings in division of fractions problems. Recommends teaching mathematics as problem solving, communication, reasoning, and connections to help students overcome misunderstandings and connect their intuitive knowledge…

Discusses an activity-based, exploratory-centered model of instruction based on the Piagetian theory of developmental learning that bridges the gap between the expected and actual levels of student reasoning. Applies the method to learning the mathematical concepts of circumference, area and volume, and division by zero. (22 references) (MDH)