Provides tips and guidelines for teaching students how to speak the universal language of mathematics. Recommends the unlearning of faulty vocabulary, adopting workable strategies to teach math language, and teaching appropriate names of operations, shapes, and angles. Emphasizes need for mastering math vocabulary to be able to communicate in…

The common goal of the empirical studies discussed in this analysis was to assist children in developing a meaningful understanding of the rational number construct, founded on durable fraction concepts. Some research has focused on partitioning; some on ratio and proportion. Contains 59 references. (Author/MKR)

Probability terms were scaled by 3 methods as a result of a survey of undergraduate students (n=194): rank order, percentage estimate, and successive interval. Discusses implications for the selection and placement of probability terms on rating scales in the development of assessment instruments. (JPS)

Attempts to describe a notion parallel to number sense, called symbol sense, incorporating the following components: making friends with symbols, reading through symbols, engineering symbolic expressions, equivalent expressions for non-equivalent meanings, choice of symbols, flexible manipulation skills, symbols in retrospect, and symbols in…

Explains the importance of students learning algebra, and provides examples of how it can benefit them in typical life encounters. The article reveals how algebra quantifies relationships between quantities, basic algebraic structures, and its importance in the deductive process. Several algebra problems that illustrate these points are presented.…

Discusses using counting books in the classroom, using them in language arts and reading, making counting books, and sharing and evaluating the books. (SR)

Describes a convincing and practical hands-on way to illustrate to students one part per million. (ZWH)

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…

Examines some aspects of mathematical cognition at the highest level of formal functioning. Illustrates how the structure of a mathematician's output and its cognitive complexity can be characterized by the Structure of the Observed Learning Outcome (SOLO) taxonomy. Contains 28 references. (Author/ASK)

Argues that a major difficulty in learning how to do mathematical modeling is in the first independent run through the modeling cycle. Reviews a case study (N=12) on mathematical modeling and presents the conclusions in three sections: (1) the choice of task; (2) the presentation of the task; and (3) tutor intervention and support. (ASK)

Defines ethnomathematics as the investigation of mathematical knowledge in small-scale, indigenous cultures. Puts ethnomathematics as one of five distinctive subfields within a general anthropology of mathematics, and describes interactions between cultural and epistemological features that have created these divisions. Reviews political and…

Describes several studies that challenge conventional wisdom regarding the teaching and learning of nonstandard and standard unit, rulers, and measurement sense. Discusses the educational implications of their results. (Author/CCM)

Prospective secondary teachers can explore mathematics at their own level by using the law of cosines to establish connections between topics that are usually taught separately such as cosine of the difference of two angles, Cauchy's inequality, determinants, sine of the difference of two angles, triangle inequality, and inner product of two…

Assessed the effectiveness of instruction in promoting sixth-grade students' conceptual understanding of the concept of averages using a leveling model and an open-ended problem-solving approach. Found that students were more capable of using the leveling approach and applying formal averaging algorithm to solve problems than using the open-ended…

Focuses on the study of the sum of two integer squares, neither of which is zero square. Develops some new interesting and nonstandard ideas that can be put to use in number theory class, mathematics club meetings, or popular lectures. (ASK)