As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.

In this article, the authors describe their experiences with planning, implementing, and revising a lesson for which the goal is for students to consider the mathematical and pragmatic issues that are related to a task of maximizing the area for a fixed perimeter. The authors also wanted students to engage in the Standards for Mathematical…

Tarsia Formulator is a software package that enables management teachers to create innovative and engaging learning materials that test understanding. Available freely on the Internet via Hermitech Laboratory, it is widely used in the United Kingdom in the school sector. The author has used Tarsia in management classes and has received very…

Basic courses on logic are common in most computer science curricula. Students often have difficulties in handling formalisms and getting familiar with them. Educational software helps to motivate and improve the teaching-learning processes. Therefore, incorporating these kinds of tools becomes important, because they contribute to gaining…

Mathematical induction is one of the major proof techniques taught to mathematics students in the first years of their undergraduate degrees. In addition to its importance to mathematics, induction is also required for computer science and related disciplines. However, even if the concepts of a proof by induction are taught and understood, many…

This article describes the system ProofWeb developed for teaching logic to undergraduate computer science students. The system is based on the higher order proof assistant Coq, and is made available to the students through an interactive web interface. Part of this system is a large database of logic problems. This database will also hold the…

There are many arguments that reflect on inductive versus deductive methods in mathematics. Claims are often made that teaching from the general to the specific does make understanding better for learners or vice versa. I discuss an intervention conducted with Grade 10 (15-year-old) learners in a small suburb in South Africa. I reflect on the…

In many mathematical problems, students can feel that the universality of a conjecture or a formula is validated by their experiment and experience. In contrast, students generally do not feel that deductive explanations strengthen their conviction that a conjecture or a formula is true. In order to cope up with students' conviction based only on…

Visual logic puzzles provide a fertile environment for teaching multiple topics in discrete mathematics. Many puzzles can be solved by the repeated application of a small, finite set of strategies. Explicitly reasoning from a strategy to a new puzzle state illustrates theorems, proofs, and logic principles. These provide valuable, concrete…

Investigates using the microcomputer to develop a sentence parser to simulate intelligent conversation used in artificial intelligence applications. Compares the ability of LOGO and BASIC for this use. Lists and critiques several LOGO and BASIC parser programs. (MVL)

This paper reports the introduction of electronic handsets, like those used on the television show Who Wants To Be A Millionaire? into the teaching of philosophical logic. Logic lectures can provide quite a formidable challenge for many students, occasionally to the point of making them ill. Our rationale for introducing handsets was threefold:…

This article describes the experiences gained from a seminar in the teaching of mathematical reasoning and problem solving designed to prepare in-service high school mathematics teachers to teach genuine mathematical activity in a computer-based environment. Presented with a set of unfamiliar tasks and activities, the participants were encouraged…

Describes use of the little-known Shuttle Puzzle in computer programming to elucidate the process of analyzing a problem and synthesizing observations into an algorithm that can be used to generate a programming solution. The process used to solve the problem reflects one that an expert uses. The method could be adapted for small-group cooperative…

This document provides an introduction to the relationship between the current knowledge of focused and creative thinking and artificial intelligence. A model for stages of focused and creative thinking gives: problem encounter/setting, preparation, concentration/incubation, clarification/generation and evaluation/judgment. While a computer can…

Compares BASIC and LOGO systems in developing artificial intelligence systems. Provides listings of programs used for translating and sentence making. Describes methodology and compares the BASIC and LOGO programs. (MVL)