BIG BANG THEORY: Mathemagenic - A journey into the emergence of learning

by Ruth Hill PhD

Hi! I’m an immersive learning design and strategy consultant. I help clients and educators bring learning to life with virtual reality experiences.

I first became a learning designer in 1994 and have since created learning solutions for the Government, Ministry of Defence and various FTSE 500 companies. In 2020, I turned my focus to VR for learning and worked with Bodyswaps to establish their design methodology and build and mentor a team of highly skilled immersive learning designers.

The soft skills training I designed and scripted for Bodyswaps continues to help tens of thousands of FE and HE students across the UK, Europe, US and Canada to build job interview, communication, teamwork, problem solving, negotiation and leadership skills.

This article is about how my journey began, my lifelong fascination with how people learn and what we, as learning designers, must do to empower the learning process.

Ed tech has evolved in so many ways since I first became a learning designer. Recent trends like AI, VR, AR (and so on) may be changing the learning landscape, but whatever the tech, one thing never changes. Great learning design begins and ends with the learner!

My fascination with the processes by which people think and learn began in my late teens whenmuch to my father’s disappointment - I enrolled myself on an A level psychology course.

I was supposed to be studying for a career in medicine, but it wasn’t for me. With Chemistry and Biology already on my timetable, I couldn’t face another ‘hard’ science. Instead, I chose psychology hoping for a little light relief, and discovered a lifelong passion.

Through my studies, I learned about the mental processes involved in making sense of the world: attention, perception, cognition, schema development, retention, recall, and so on. Upon graduation, I naturally fell into a career in learning design. But it wasn’t everything I’d hoped for. The primary focus of learning design, it seemed, was the content:

• What information should the learner garner from the training?

• What level of complexity should it be pitched at?

• How might the information be chunked to make it easier to understand?

Granted, these are all important considerations. But this was content design, surely? Where was the learning part of the job title?

Since learning is a natural part of the human experience, it is often assumed that, provided the information is palatable enough, the learner’s brain will do the rest. But in my early career, I quickly discovered that preparation of the content often involved simplifying information down to isolated facts and then testing to see how much of it had sunk in. This was rote learning at best. What I wanted to do was to elevate the learning experience to something transformational!

Giving birth to learning!

It wasn’t until I started my PhD research that I first encountered the word ‘mathemagenic’ - a term coined by Ernie Rothkopf in 1970 that is derived from the Greek root mathemain - that which is learned - and gignesthai (or genesis) - to be born. Simply put, mathemagenic activities are behaviours that give birth to learning.

Rothkopf, it turned out, was way ahead of me. He was interestednot in the information that was being provided by the teacher - but in how the actions of the students influenced their achievement of the instructional objectives. As he put it: “You can lead a horse to water, but the only water that gets into his stomach is what he drinks.”

So, while the presentation of the content is important, learning will only be achieved if the student processes the content effectively. When I discovered Rothkopf’s work, I immediately dedicated my research to investigating how learning technologies can be designed to facilitate learners in the application of mathemagenic activities (M-Acts) that promote and enhance their learning experience.

Rothkopf was particularly interested in the beneficial effects of adjunct questions on attention and recall. Over twenty years later, Diana Laurillard expanded upon this, proposing a ‘conversational framework’ comprised of 12 mathemagenic activities that could be applied to teaching and learning in any discipline.

Broadly speaking, Laurillard’s M-Acts fall into three categories of behaviour - all of which are required for effective learning to occur:

• Conceptual description

• Action and personal experience

• Reflection (linking concepts to experience)

Some learners naturally engage in these behaviours on their own. Some do so only for subject areas that they feel a natural affinity for.

And sometimes, learners need help to promote M-Acts in one or more categories of behaviour for a complete learning experience. This is where the learning design can help.

To reflect this, Laurillard broke the three categories of behaviour down into smaller actions that represent learning as a dialogue between teacher (or technology) and student, with the teacher’s actions designed to encourage and structure beneficial mental processes within the learner.

While some activities have a positive effect on learning outcomes (mathemagenic), others can have a negative one (anathemagenic) - and actually interfere with learning. For example, asking questions before presenting new information to activate prior knowledge is mathemagenic, while attuning tasks to ‘learning styles’ can be anathemagenic.

To determine which activities are helpful and which are not, Rothkopf suggests that every action should have a clear purpose that connects with the objective of the lesson - something I always emphasise when supporting learning designers today.

Fifty years ago, Rothkopf’s theory of mathemagenic activities was one of the first to emphasise the impact of the learner’s actions over the content of the curriculum or the performance of the teacher. The term has fallen out of favour in recent years, but the findings of Rothkopf and Laurillard’s research is invaluable because it helps teachers and learning designers to foster learner engagement - not only with the content - but also with appropriate mental processes to promote learning.

References:

Rothkopf, E. Z. (1970). The concept of mathemagenic activities.

Review of Educational Research, 40, 325–336.

Laurillard, D. (1993) Rethinking university teaching: A framework for the effective use of educational technology (Routledge: London)