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Online repositories of educational resources have been developed gradually, usually by people who are passionate about their subjects. Some of them have built vibrant, collaborative communities of users. These online libraries and the communities they gather can support active learning and help inform our assessment tasks.

How can we develop passion in our students for a discipline? How can we come up with assessment tasks that help them master new skills?

This challenge feels especially overwhelming for instructors in the context of online education, when they are under pressure to develop reams of original content to support their online teaching. But online education can also be part of the solution to this problem. Indeed, excellent online repositories of problems, knowledge and analysis have been developing for decades.

They can inform our assessment by breaking the weekly cycle of lecture-tutorial-solution. They provide questions on which students can work at their own pace. The pleasure of taking on a challenge or problem and coming up with an original solution makes a much more durable impression than a tutorial, whose solution can predictably be drawn from a syllabus.

A case study: Project Euler

As a lecturer in applied mathematics, I often suggest Project Euler to students as a rich source of problems to tackle. Many students quickly find themselves working on challenging questions for pleasure. The website is an interactive repository of mathematical and programming problems, created by Colin Hughes in 2001. The name is a tribute to Leonhard Euler (1707-1783), who performed precise numerical calculations two centuries before computers became available. New problems are posted weekly online. Users can browse problems and register for free. So far, more than 1 million users have solved at least one problem.

Each problem comes with a definition, an example and a question whose answer is a unique integer number. For example: “If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000.”

After uploading an answer, the user receives instantaneous feedback, right or wrong.

Problems are designed to allow for a solution in less than one minute on a typical desktop computer, with efficient implementation. Users may suggest problems satisfying this one-minute rule. After submitting a correct answer, the user can access a forum where implementations are discussed.

Experiment, formalise, reflect

Do not to simply point students to online resources as a supplement, but provide structure and guidance as they learn.

I teach and supervise students who report some programming experience but worry about not being up to speed. I direct them to Project Euler and establish a training routine for them:

• Pick a problem of interest, experiment with pen and paper on simple cases.

• Give yourself a day to formalise the problem and to write some code, until it produces numerical results.

• If the answer is correct, move on to the next problem, otherwise let us try and debug your code.

Students often find the problems too gripping to simply ask for help in debugging. They prefer addressing the challenges by themselves and to discuss a working solution.

The practice of researching self-contained problems helps students develop an inductive approach to learning. Instructor-led teaching can then be used more efficiently to optimise solutions discovered by students.

Tap into online communities

When teaching undergraduates, we can benefit from the enthusiasm of communities online by proposing group work based on online resources. Working in groups, students pick a problem on a website, work independently for a week, and report on their progress.

Group work can be assessed based on either a written report or oral presentation, in which students not only share their results but reflect on bugs and explain why some implementations may induce crashes.

Such tasks develop heuristic perspective on the learning journey. Experimenting on a problem allows students to gain mastery of concepts that can then be used to solve harder problems.

An online repository for every discipline

Programming has become an essential tool in all quantitative disciplines. Computer science has developed as an independent subject, but every scientific department must provide hands-on training to students.

The Project Euler model is a strong source of inspiration for the development of free online courses. It has been successfully transposed to other disciplines such as bioinformatics, which now has problem-solving platforms such as .

More competitive versions are aimed at students and professionals, such as Google Code Jam in programming and Kaggle in data science. This particular model cannot be transposed to all disciplines; instantaneous automatic feedback can only be provided online if the questions are quantitative enough.

However, every discipline can benefit from online repositories of challenging assignments, analysis and resources. These resources are crowd-sourced and have been developed, refined and improved over time by passionate communities of users. As educators, we should make the most of them.

Pascal Grange, programme director of the BSc applied mathematics at .