Working out online: Mathematics, learning analytics and Inner loop learning.

Working out online: Mathematics, learning analytics and Inner loop learning.

When I was in the classroom, I used to tell students that if two students had exactly the same answers to a GCSE paper, some right, some wrong, then the one who showed their working out would get the better marks.

I used to ban correction fluid, not because they would sniff it, but because the working out and mistakes were important to me as a teacher trying to help them understand some aspect of mathematics.

So I have always been wary of online offerings that rely on multiple choice, on simple correct/incorrect analyses and on inputting the correct answer only. Offerings that completely miss the working out, the different ways students reach an answer, the reasoning as to WHY they reached an answer.

Providing good learning analytics is hard work. So generally, we only do easy learning analytics. “Student x took 10 minutes and scored 65% on subject test y”. “Student y moved to level 3 after 10 questions”

Bill Jerome, in a recent blog post “If you like learning, could I recommend analytics?” , said:

“Getting learning analytics wrong on the learning dimension is a recipe for disaster, (it) must be done carefully and with understanding. Without a semantic ability to understand what is happening, we won’t even know if we’re doing harm to our students by using algorithms to optimise for things we don’t understand”.

But how can we do things differently and what should, could, we do to get this understanding?

And to avoid doing harm to our students?

Michael Feldstein in his ‘Taxonomy of Adaptive Analytics Strategies’ draws on the work of Kurt Vanlehn’s best practices in learning design of describing outer loop and inner loop learning.

  • Outer loop learning is that indicated above. Did the learner get the correct answer?
  • Inner loop learning examines the steps a learner is taking to solve a problem and at appropriate moments, intervenes to provide feedback directly relevant to some mistake the learner is making.

So to create an online offering where inner loop learning takes place, and in which all that learning is fed back to the teacher… that sounds good to me.

Students get hints when they need help, and be able to progress. They have to show their working out, and indicate their reasoning when solving a problem.

Teachers will be able to see all that feedback and all the working out for every student in the class.

They will be able to analyse by student – where did a student need help, even if the question was eventually right. Or analyse by question – which questions did more of the class have a problem with? What part of what question did they have a problem with?

All with the aim of aiding teachers to help students, and to help students understand more.

Now as noted above, this has not been possible in the past, but a company in Australia, Mathspace, is about to launch in the UK. In our opinion, it does Inner Loop learning and provides help to the students and details to the teacher, in real time, that have never before been possible.

Take a look at for a sample,

download the free ipad app (android and Windows 8 coming soon) to use the incredible ‘myscript’ handwriting capability,

get in contact with by email – tstirrup at – if you would like a classroom trial

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