Successful pedagogical applications of symbolic computation

Ravaglia, Raymond; Alper, Theodore M.; Rozenfeld, Marianna; Suppes, Patrick

doi:10.1007/978-3-7091-6461-7_5

Cited by 8 publications

(2 citation statements)

References 6 publications

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“…This project is an outgrowth of a long history of similar projects at Stanford University under the direction of Patrick Suppes (see [1,[9][10][11]). The current system is being used by students in courses in Euclidean geometry and linear algebra, and it is planned for use in courses in multivariable calculus and differential equations.…”

Section: Introductionmentioning

confidence: 99%

A Proof Environment for Teaching Mathematics

Sommer

Nuckols

2004

J Autom Reasoning

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The EPGY Theorem Proving Environment is a computer program used by students to write mathematical proofs in a selection of computer-based, proof-intensive mathematics courses at the high-school and university level. The system allows easy input of mathematical expressions, application of standard proof strategies and logical inference rules, application of mathematical rules, and verification of logical inference. Each course has its own language, database of theorems, and mathematical rules. The system uses a combination of automated reasoning and symbolic computation to verify individual proof steps. The proof environment has been used by over 170 students who have taken the EPGY high-school geometry course. In addition to providing a general overview of the system, we describe what we have learned from student use of the Theorem Proving Environment in the EPGY geometry course.

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Section: Introductionmentioning

confidence: 99%

A Proof Environment for Teaching Mathematics

Sommer

Nuckols

2004

J Autom Reasoning

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“…In addition, computer algebra systems have only a small number of very powerful operations (Simplify, Solve, …) that enable to get the answer of a task in one step but not to build traditional step-by-step solution. The latter deficiency has been overcome in rule-based learning environments [1,6] that have much more detailed rules. But they also perform the selected transformations mainly automatically.…”

Section: Introductionmentioning

confidence: 99%

Designing Next-Generation Training and Testing Environment for Expression Manipulation

Prank

Issakova

Lepp

et al. 2006

Computational Science – ICCS 2006

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Abstract. T-algebra is a project for creating an interactive learning environment for basic school algebra. Our main didactical principle has been that all the necessary decisions and calculations at each solution step should be made by the student, and the program should be able to understand the mistakes. This paper describes the design of our Action-Object-Input dialogue and different input modes as an instrument to communicate three natural attributes of the step: choice of conversion rule, operands and result.

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Formal Reasoning About Systems, Software and Hardware

Boute¹

2004

Information Technology

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Formal reasoning in the sense of "letting the symbols do the work" was Leibniz's dream, but making it possible and convenient for everyday practice irrespective of the availability of automated tools is due to the calculational approach that emerged from Computing Science. This tutorial provides an initiation in a formal calculational approach that covers not only the discrete world of software and digital hardware, but also the "continuous" world of analog systems and circuits. The formalism (Funmath) is free of the defects of traditional notation that hamper formal calculation, yet, by the unified way it captures the conventions from applied mathematics, it is readily adoptable by engineers.The fundamental part formalizes the equational calculation style found so convenient ever since the first exposure to high school algebra, followed by concepts supporting expression with variables (pointwise) and without (point-free). Calculation rules are derived for (i) proposition calculus, including a few techniques for fast "head" calculation; (ii) sets; (iii) functions, with a basic library of generic functionals that are useful throughout continuous and discrete mathematics; (iv) predicate calculus, making formal calculation with quantifiers as "routine" as with derivatives and integrals in engineering mathematics. Pointwise and point-free forms are covered. Uniform principles for designing convenient operators in diverse areas of discourse are presented. Mathematical induction is formalized in a way that avoids typical errors associated with informal use. Illustrative examples are provided throughout.The applications part shows how to use the formalism in computing science, including data type definition, systems specification, imperative and functional programming, formal semantics, deriving theories of programming, and also in continuous mathematics relevant to engineering.

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Successful pedagogical applications of symbolic computation

Cited by 8 publications

References 6 publications

A Proof Environment for Teaching Mathematics

A Proof Environment for Teaching Mathematics

Designing Next-Generation Training and Testing Environment for Expression Manipulation

Formal Reasoning About Systems, Software and Hardware

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