The Prooftoys mission and vision

The mission

The Prooftoys project aims to demonstrate how a simplified system of deductive reasoning can support effective and natural use of proof in learning mathematics, starting with basic algebra and extending to much more.

In a broader sense, Prooftoys aims to promote the understanding, appreciation, and practice of mathematical proof.

The vision

The practical successes of mathematics and its contributions to all of the sciences are main reasons for the high regard mathematics has had at least since the times of the ancient Greeks. Because mathematical reasoning is at the core of mathematical thinking, it is key to every branch of mathematics.

It turns out that the kind of reasoning gently introduced in any basic algebra course enables the deduction needed for solving many typical math problems in the sequence of topics from algebra and leading up to calculus, and more. Modest though conceptually significant extensions enable the system to work with much more advanced mathematics.

The Prooftoys effort is based on the idea that with modern technology, learning to use precise reasoning quite soon after basic algebra has the potential to help students do mathematics more easily and go beyond where they otherwise could otherwise go.

Implementation

The proof builder tool implements the logic with a user-friendly interface design to help users succeed without having to learn the details of the logic up front. The user focuses on a step or part of a step, and the tool offers next steps specifically relevant to the focused part.

The content on this website demonstrates the approach, starting with basic pre-college mathematics and showing how the reasoning extends naturally to working with more advanced concepts such quantifiers, functions, and collections.

You might be wondering

Please take a look at the Questions and Answers page if any of this raises questions in your mind. Or feel free to contact the author. Email is good, and GitHub is fine, too.