# E-Proof/TPD Module-1

## Learning Goals

• Learn the background of the e-proof-system and the basic functions of the e-proof system.
• Learn to install the authoring support for the e-proof environment.
• Learn the basic functions of the authoring support system.
• Learn to decompose an easy proof into proof fragments.
• Learn to implement the developed proof into the e-proof system as proof puzzle.
• Learn to save the proof in the desirable format.

## The E-Proof System

### Background

Reasoning skills form the basis for the proving of mathematical statements and relations themed in higher school grades in different contexts. It is important that students acquire or expand their reasoning skills as part of their teacher training in order to provide age appropriate reasoning skills to their pupils.
The project "QED" (Quality of E-Proofs in Didactics) is an inter-university cooperation project, which deals with electronic mathematical proofs in teaching. The goal of QED is the development of an Open Source (OS) e-proof system that supports not only learners in understanding of proof structures, but also teachers in the evaluation of proving tasks. For this purpose, a first prototype for a diagnostic based exercise environment for automatically supported proving was developed on the basis of the mathematical evaluation system OS IMathAS (a web-based mathematics assessment tool for automatic or semi-automatic review of mathematical homework).[1]

#### E-Proof

In the e-proof system, interpolation proofs can be depicted. We classify the considered prototype for an e-proof environment just in between understanding of a given proof of a certain theorem (e. g. in a textbook) and the creation of an own proof for the same given theorem on a blank piece of paper. An e-proof has e. g. some kinds of options where the students can select fragments of a proof or order them. Therefore, an e-proof is not as flexible as a proof on a blank piece of paper.

#### Developments

The initial architecture of an e-proof system was compiled from existing OS software, that is IMathAS, and refined by considering several requirements. A first collection of contents and functionalities of an open browser-based e-proof system was thus compiled. Based on this, a pilot prototype was developed and improved through the consideration of students' experiences with the system, among others within electronic examinations.[2]
The first pilot prototype was developed to a beta-version implemented with HTML and Javascript, to allow offline use.

### Basic Functions

Following the link, you can test the e-Proof environment in the students' view.

The environment is implemented with HTML and Javascript only. So there is no need to install iMathAS for a first checkout. Currently, a theorem which requires a comparatively easy proof is implemented:

Precondition: Let ${\displaystyle a,b\in \mathbb {R} .}$

Proof the following Conclusion: ${\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}.}$
First, read the theorem and try to create a proof for the theorem on your own. If you could not create a proof for the theorem, try to read a few given proofsteps and justifications to get an idea of one possible proof and try to write your version down with paper & pencil. Enter your final proof into the system to check for correctness.
It is possible to get feedback and assessment for all proof steps. The sequence of proof steps provided by the student is checked against a teacher solution.