Lesson Study 3: Towards a Framework

Our question: How to assess collaborative problem-solving?

  • In the first lesson, we thought about assessing before and after collaborative problem-solving.
  • In the second lesson, we explored alternating more systematically between solo and collaboration, maximising the benefits of both.
  • In the third lesson, we shall develop a possible framework for assessing collaborative problem-solving.

Design Principles:

I spoke to Zek, art teacher, about how to assess problem-solving. Assessing a mathematical journey is very similar to assessing a portfolio of artwork?

  • Keep the checklist as short as possible.
  • Don’t always try to prescribe numerical values to everything, you might kill it.
  • Assess a portfolio over time, to clearly evidence improvement


First draft:

  1. 50% through traditional written exam, to measure mastery of standard content
  2. 50% through assessment of collaborative problem-solving. This is split between measuring how the student works within a group, and measuring how the student writes up problems individually, after having struggled on them within a group. Portfolio of work over time.

With pretty colours:


The lesson:

What is the biggest rectangle that can fit in a right-angled triangle?

No help given from teachers at all.

  1. Each of the three teachers observed two groups of 3 students, noting down examples of kindness, self-awareness and spark.
  2. Students write up the problem, individually
  3. Teachers give live feedback on the write-ups, assessing for self-awareness, understanding and rigour.

Examples of work:

Excellently confused struggle – keep on going Fardeen!
On the left, the write-up of the mathematician who drove the thinking in the group. On the right, the write-up of his colleague, who explained the thinking with more clarity. Great example of a person with spark, and a person with rigour.
An example of a teacher’s assessment sheet.


  • Kindness and awareness are too similar? Merge into one, and instead, assess the application of problem-solving tools? For example, W kept on saying “Okay, so how can we make this problem easier?”, deliberately stealing the key question from previous problem-solving sessions.
  • Were the students pressurised by having three teachers strolling around assessing? Is this a bad thing?
  • Should we decide what amazing problem-solving is a priori, or by watching teachers/students/PHD students attack a problem, and note down what they do well?

Next steps:

  • Observe more problem-solving, fighting the temptation to leap in and guide. Watch for generalisable techniques that excellent problem-solvers exhibit.
  • Try in other subjects, not just Maths.
  • Try in the summer exams! Utilise the opportunity that no public exams in Yr12 has given us.

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