Wallace Feurzeig

Programming-Languages as a Conceptual Framework for Teaching Mathematics

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively to reduce formal barriers. This education can also be used to enable pupils to access an accurate understanding of some key mathematical concepts. In the field of heuristic knowledge for technical problem solving, experience of programming is no less valuable: it lends itself to promote a discussion of relations between formal procedures and the comprehension of intuitive problem solving and provides examples for the development of heuristic precepts (formulating a plan, subdividing the complexities, etc.). The knowledge gained in programming can also be used for the discussion of concepts and problems of classical mathematics. Finally, it can also facilitate the expansion of mathematical culture to topics in biological and physical sciences, linguistics, etc. The authors describe a programming language called ‘Logo’ adapted to objectify an enduring framework of mathematical experimentation.

Programming-languages as a conceptual framework for teaching mathematics

This is a report of research and teaching d~r~cted toward the development of a new mathematics curriculum in which presentation depends fundamentally on the use of computers and programming. The work was centered mainly on a mathematics teaching experiment with seventh grade children utilizing a programming language, LOGO, specifically designed for the teaching of mathematics. We also conducted an investigation of the use of LOGO in teaching much younger children-a group of second and third graders. After a brief exposition of the LOGO language, the two teaching activities are described in some detail, including many examples of the classroom and laboratory materials used. The report begins with a discussion of the reasons why the learning and teaching of mathematics are so difficult, and states the underlying issues that have dictated the kind of approach undertaken here. Following the descriptive material on the teaching experiments is a discussion of the results including some evaluations of the years work and of the project. A detailed description of the LOGO programming language and system is appended. taught the group of second and third grade children. We did not begin the teaching with a large body of previously developed classroom materials. These had to be created concurrently with the teaching as the INTERFACE v4, #2 APRIL 1970

Toward a Culture of Creativity: A Personal Perspective on Logo's Early Years and Ongoing Potential.

This paper describes the creation and early uses of Logo. It includes a brief summary of more recent work on Logo-derived languages and learning applications. It closes with a lament on the unrealized potential of student programming languages as empowering tools for knowledge construction and learning.

Special Issue of Interactive Learning Environments on Modeling and Simulation in Science Education

Special Issue of Interactive Learning Environments on Modeling and Simulation in Science Education Wallace Feurzeig To cite this article: Wallace Feurzeig (1994) Special Issue of Interactive Learning Environments on Modeling and Simulation in Science Education, Interactive Learning Environments, 4:3, 193-194, DOI: 10.1080/1049482940040301 To link to this article: http://dx.doi.org/10.1080/1049482940040301

Two-Parameter Universes. Part 2. Picture a Quadratic Polynomial...

This column will publish short (from just a few lines to a couple of pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain teasers involving the use of computers or computational theory. Snapshots are subject to peer review. This issue’s snapshot is the second part in a two part series of snapshots. In the first part the authors led us on a journey to alternative mathematical universes, showing us a map between two alternative representations of the universe of rectangles. In this follow-up snapshot, they use the same approach to explore the universe of quadratic polynomials. By using the MultiMap software to explore the map between the root and coefficient planar representations of quadratics, they make the quadratic equation visually alive. Along the way, we see students studying quadratics through a refreshingly lively exploration of visual representations of solvable vs unsolvable quadratic equations.

Introduction: Special Issue of Interactive Learning Environments on Fractals and Maps

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.

Programmer Job Training for the Disadvantaged

We are developing programmer job training programs for economically disadvantaged adults. Our trainees are chronically unemployed low-income people lacking marketable skills. Most have finished high school; only a few have had any college. We have carefully screened, tested, and interviewed applicants to find suitably qualified trainees. Despite their diverse problems, our trainees have generally demonstrated the intelligence, competence, motivation, and temperament required to do professional programming work. The training is designed to give them the knowledge, skills, and effective job experience required for placement in entry-level business programming jobs.