Background theory

Our approach is based on constructing and sharing models. A crucial element of knowledge required by most, if not all, people, is precisely this appreciation of underlying models. A version of mathematics that emphasizes structures has the potential to help students understand the computational systems that are increasingly critical in today’s society, because computer systems are mathematical models – computer software is built out of variables and relationships. WebLabs starts from the assumption that constructing and sharing models is a powerful way to learn.

Mathematical and scientific ideas

WebLabs consists of five main topics: Infinity, Sequences, Collisions, Lunar Lander, and Models, Systems and Randomness.

In Infinity, students explore the cardinality of infinite sets, and explore the relationships between different infinite sets.
Sequences activities are centred around constructing and analysing number sequences, with a special focus on the Fibonacci sequence and explorations of sequences that converge and diverge.
Students build models of objects colliding in 1-dimension in the Collisions topic, iteratively testing against reality and refining their models to cover more cases of collision.
In Lunar Lander, students control the motion of virtual objects, record data and plot the resulting position-time and velocity-time graphs, investigating acceleration and the relationships between different representations of motion.
The Models, Systems and Randomness topic is focused on building computational models that represent and explore various real-world phenomena, including investigation of the concept of randomness, how it can be understood and used.

Constructing

The theoretical framework for WebLabs, is based on constructionism, the theory developed in the early 1990s by the mathematician and educator, Seymour Papert. The idea runs parallel to the idea of constructivism, which argues that learners build knowledge structures in their minds, irrespective of the circumstances of learning. It adds a new, and crucial idea: that the creation of these mental structures happens especially smoothly in situations where learners are building things - on the floor, on the desk, or on the computer - with appropriately designed tools, for a public or semi-public audience. Building externalises thinking and makes it available for reflection and debugging. When building on the computer, we conceptualise the building blocks as computer programs that can be put together in different ways, modified at different levels according to the requirements of the learners’ evolving models.

Sharing

The learning of mathematics and science, as much as music, story writing or poetry, benefits from discussion, collaboration, and competition. Teachers know how helpful collaboration can be for learning: but collaboration without appropriate tools makes it difficult to share what is important – not just snapshots of what is 'seen', but the structure of the models that underpin them. When learners exchange models they have something tangible on which they all can focus their attention: Let's discuss how this works. Are these two models the same? What makes your model better than mine? Can my model be used to explain what you have found? WebLabs has built tools – WebReports – so learners can engage in these sorts of discussions and share their model-based reasoning.

Learning

WebLabs is about promoting learning through design. It comprises a series of design experiments, each with specific learning goals, and all contributing to the general development of theoretical frameworks for learning. In other words, we see design as a way to support learning, and at the same time, to understand better how learning is shaped by the system we are building. Our approach is iterative – the WebLabs tools were built over a three-year period in which each innovation was tested and evaluated in real situations with students and teachers: each evaluation fed into the next phase of construction. So in each phase of our project, we learned alongside the learners.