One of the greatest challenges facing students new to calculus is the ability to persevere in the face of failure. Whether the student is choosing an integration technique or a series test, calculus is often the first course in mathematics where the path to the solution is not prescribed in an algorithmic way. At Jacksonville University we…

This paper describes an approach for pre-service or in-service mathematics education that teaches sophisticated mathematics using only the tools of high school mathematics. The idea is to start with a standard problem from high school mathematics and let the solution to this problem serve as a platform for asking good mathematical questions and…

The Math Lab is a creative approach to teaching math concepts. Students are introduced to skills through several conceptual levels. Concrete level activities are followed by semiconcrete, semiabstract, and abstract levels of instruction. Examples of teaching methods for each level are offered. (DF)

Explaining new ideas to oneself can promote transfer, but how and when such self-explanation is effective is unclear. This study evaluated whether self-explanation leads to lasting improvements in transfer success and whether it is more effective in combination with direct instruction or invention. Third- through fifth-grade children (ages 8-11;…

A personal experience is described concerning problem solving that incorporates the computer to help generate multiple examples of proposed conjectures as solutions. The positive potential of technology to allow students of mathematics to experience the process of discovering mathematics through conjecture and generalization is emphasized. (MDH)

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

Described is an activity that categorizes a two-digit number as "sneaky" if the continued process of taking the difference of the squares of its digits leads to a difference of zero. Other categorizations are determined by whether the difference process ends in a one-digit number or continues in a loop of numbers. (MDH)

Presents a study to determine whether computer use in guided-discovery learning episodes would enhance the problem-solving ability of secondary school students (n=147). Results indicate interaction between low- and middle-level students' mathematical achievement and treatment groups, while high-level students performed well regardless of approach.…

Twelve middle school students, working in pairs, used a computer microworld to explore introductory geometric transformational concepts. Despite a tendency for symbolic overgeneralization, the students were able to use visual feedback from the microworld and discussions with partners to correct their own mistakes. (Author/JJK)

Challenged is the traditional model for the transmission of mathematics in the elementary school classroom. An inquiry approach to learning mathematics is proposed and supported with results of a year long research project that exposed second graders to mathematical learning experiences using this approach. (MDH)

One class of interactive, computer-based learning environments (microworlds) for the exploration of school mathematics (and science) entails the incorporation of appropriate concepts within the engaging context of self-directed discovery learning. The objective of this research was to investigate and describe in detail the constructive learning…

Described is the attempt to identify relationships between pedagogy and student behavior in a mathematical microworld. The patterns of teaching associated with LOGO-based computer activities involving ratio and proportion and the teachers role in helping students bridge the gap between LOGO- and school-mathematics practices are explored. (MDH)

Illustrates where several unexpected patterns of antiderivatives can be realized during calculus instruction via the application of integration by parts to the exploration of particular members of families of functions. (JJK)

Focusing on how expert writers in various disciplines convey complex ideas, this paper shows how the techniques used by the mathematician, Clark Kimberling, in various writings can (1) be transferred to other disciplines, (2) show learning taking place, and (3) provide models for students to re-enact learning in all subject areas. The paper…

Presents the template method developed by Galileo for calculating areas of geometric shapes constructed of uniform density and thickness. The method compares the weight of a shape of known area to the weight of a shape of unknown area. Applies this hands-on method to problems involving calculus, Pythagorean's theorem, and cycloids. (MDH)