Active Learning and Natural Language in Netmath

Netmath at the University of Illinois is a program with a difference.

It isn't that it's online (though it is).

It isn't that it flips the classroom (though it does.)

It's that at its core is a philosophy that really doing real maths is an active process that is best engaged in through constructing knowledge by doing, discussing, explaining and applying mathematics in unfamiliar situations.
"What is important is students' ability to construct knowledge - so that in the future they can reconstruct it more quickly and apply it in different situations - not rote learn solutions to predictable problems." Bruce Carpenter, Associate Director of Netmath at University of Illinois.
Professor Bruce Carpenter, Associate Director of Netmath at University of Illin

This is definitely not didactic learning - gone are the lectures, the solutions and and textbooks.

This is immersive learning; learning maths by playing with concepts and ideas in a supported online space.

Learners may find this challenging at first - as it goes against a model of learning that is often repeated in maths classrooms across the world:

- introduce a problem
- demonstrate how to solve it
- student tries
- practice
- repeat

This traditional didactic model risks totally removing opportunities for learners to figure things out for themselves. It's quite possible to get through a traditional maths education without every having discovered anything for yourself, indeed you can score very highly on exams by simply selecting and applying appropriate algorithms correctly.

But if you learn maths in this way - what happens when you are faced with a problem you haven't seen before?

Netmath attempts to move learners away from this model of learning.

It focuses learners back on the things that we say we value; communication, cooperation, analysis and problem solving skills. It focuses on helping students with what is perhaps (to paraphrase Dylan Wiliam) the only important 21st Century Skill; the ability to deal with situations for which you have not specifically been trained.

The Netmath program additionally builds into its learning and assessment structure an explicit focus on literacy.

Solving already solved problems is essentially trivial. The answer is not terribly important.

Learners instead must be able to explain how and why they attempted problems in particular ways and learn to write and describe their strategies in a way that makes their thought processes transparent.

Bruce Carpenter, Associate Director of Netmath talks here about the Pedagogy of Netmath:

I have just conducted an interview with Bruce and hope to be able to share the video soon - exploring the philosophy and pedagogy of Netmath and the power and wider implications of learning mathematics in a non-didactic way.



  1. Sounds great Mark. The discussion on 21st C skills has been ramping up again here in Oz because a recent report on employment skills has been released.
    In the mean time Westpac have released a free online Maths resource which looks to be totally didactic.

    1. PS this is a story on the employment skills report

  2. Indeed! - "We expect people to be spending double the amount of time on critical thinking, problem solving, using maths, science and technology and written and verbal skills," - virtually the ACARA General Capabilities... or 4 Cs..
    Had some very interesting conversations with the Netmath mentors - their focus was much more on how do you set up a problem to be solved - and how do you communicate your thinking to others - not what is the final answer - that's what machines are good at. Humans need to be good at defining the parameters of the problem, finding ways to set up the solution - and recognising where machines can do things better that we don't need to.


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