Presents placement test results showing a lack of understanding of basic math concepts among entering college students. Explains the application of the learning cycle model in teaching abstract mathematical concepts and offers examples of the model's use. (DMM)

Based on the premise that meaningful learning in mathematics occurs when children link their understandings with the symbols and procedures they are taught, three places are identified where children can link symbols and their referents, procedural rules and conceptual knowledge, and answers to problems with other knowledge about what is…

Discussed is the method of substitution of variables within the framework of precalculus level extremum problems, both maximum and minimum. Many examples with graphical representations are provided. (JJK)

Outlines two mathematics teaching strategies: the exploration/discovery approach to mathematical concepts, and the use of pair group problem-solving. These require teachers to shift from the traditional role of lecture/demonstrator to a role demanding new skills in planning and facilitating student work. Includes 10 references. (MD)

Discusses the rationale and a method for the instructional use of graphing calculators as an intermediary step between the intuitive notion of the concept of a limit and its formal epsilon-delta definition. (JJK)

Investigated was the learning of the mathematical uses of "more,""fewer," and "less" at a very early stage in the development of ideas. (CW)

Presented is a method which may be used to help students start their own original investigations and create their own conjectures about fundamental mathematics concepts. An example of this method is provided. (CW)

Presented is an exploration of a number of ways these quantities can be demonstrated and some interconnections between them. Discussed are triangular numbers, sums of squares, sums of cubes, table squares, and counting rectangles. (CW)

Two ideas for teaching mathematical Concepts are presented: "Writing Study Cards for Understanding"; and "A Conceptual Approach to Solving Equations." Examples of the applications of these methods are discussed. (CW)

Discussed are solutions to the problem "What is the expected number of rolls for the total first to exceed 6?" Several algebraic solutions are presented. A computer program which may be used to simulate this problem is included. (CW)

Discussed are several common aspects of teaching functions and statistics including graphing relations, exploring relations, transforming relations, and modeling situations. Examples of each are provided. (CW)

This article explains how this method is done, examines some reasons for including it as a topic in mathematics curricula, and uses modular arithmetic to explore its mathematical basis and its generalizability to computations in bases other than 10. (CW)

Described is a strategy that shows students how one mathematical concept can be connected to another. The emphasis is on both process and product and can lead to creating a learning environment where students do mathematics as mathematicians do. (KR)

Presents a classroom activity in which students calculate the amount and types of trash thrown out by their class at school to investigate how much trash is generated, where it goes, and speculate about alternatives. Students need to be familiar with the concepts of weight, volume, and numbers. (MCO)

Following a short introduction on the rationale and purpose for using algorithmic structures in the teaching of algebra, two topics from elementary algebra are presented in relation to control structures from computer programing, specifically: the multiplication of polynomials defined in terms of nested loops, and the distributive property…