The development of calculus and science by being permanent, didactic, demands on one part an analytical, deductive study and on another an application of methods, rhochrematics, resources, within calculus, which allows to dialectically conform knowledge in its different phases and to test the results. For the purpose of this study, the motivation…

Presents a sequence for mathematics lessons designed to facilitate students' competency in executing mathematical processes and to apply the processes to real-life situations. The sequence involves: conceptualization of the process, knowledge of terminology, knowledge of algorithms, and ability to recognize when the process is applicable to…

Problem solving is presented as a resource for creating curriculum through reflections on intuition such as: exploring available intuitions, making explicit the intuitions used, and using intuition to generalize. (MP)

The method of finite differences is discussed with some applications. The method is described in detail, with illustrative sequences, and several problems are presented. (MNS)

Four activities with window panes are described and illustrated as they extend children's knowledge of fractional numbers. (MNS)

First year chemical engineering students are required to take a two-semester sequence in applied mathematics at the University of Pennsylvania, with the option of taking a third semester elective course. The content of the courses and the approaches used are discussed. A list of textbooks used is also provided. (JN)

Portions of the Cockcroft Report which seem confusing are discussed. The connections among problems, applications, and investigations are considered in sections on being a mathematician; open is in the mind; assumptions, rules and patterns; and learning not to be anxious. (MNS)

The theorem is seen as the foundation for large-sample statistical inferences, and is usually difficult for students to understand because one expects to take only one sample from a population. A description of how a table of random numbers readily available to students could be used is provided. (MP)

Approaches to teaching verbal problems that are interesting and useful are reviewed. Four basic difficulties in teaching problem solving are also covered. (MP)

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

The author observes that the predictor functions determined geometrically by Ranucci (EJ 090 184) can be algebraically derived, and that capable students might enjoy verifying them. Algebraic formulations and derivations are provided. (SD)

Discover the treasure of learning activities in your daily paper. This 20-cent text has resources for teaching reading, language arts, mathematics, science, social studies, art, career education, and local history. (Editor)

Graphs are viewed as extremely useful tools in communication, which enable readers to see at a glance facts that might take several paragraphs to describe adequately. An ability to read graphs critically is seen to be an important objective for any elementary curriculum, and ways to introduce them are presented. (Author/MP)

The problems many students have on the senior high school mathematics functional literacy test in Florida are discussed. Instructional exercises designed to improve students' reading comprehension of word problems are noted, and prototypes of some of the exercises viewed as more useful are provided. (MP)

A four-step sequence of desirable student cognitive behaviors is described and discussed. Teaching implications are noted. (MK)