Visible Thinking and Maths

Last week, we had the most phenomenal Numeracy session in Year 3 and it was all because of Visible Thinking.

Visible Thinking was developed by Harvard’s Project Zero and aims to assist students to make their cognition (usually invisible) visible. Not only does Visible Thinking develop and grow students’ ability to deepen their thinking about learning and metacognition but it leads students to be more conscious of their thinking.

For more information on Visible Thinking and associated routines, go to .

Prior to the lesson, students had conducted a “National Testing”-type assessment online through Mathletics. After analysing the data and spying a few consistent misunderstandings about Stage 2 Numeracy concepts, I collated a list of questions that could be thought about more thoroughly. I then printed these questions onto A3 paper and spread them around the space.


During the lesson, each student (in triplets) was given 3 post-it-notes for each poster. They were required to write each of the following on each post-it-note in response to the numeracy problem given:

  • I see… (what do you see? a graph? a title? an algorithm?)
  • I think… (what do I think the answer will be? why?)
  • I wonder… (thinking beyond the question – ie. I wonder how many students they surveyed.)
photo 1 (1)
Which is an angle?

Students then arranged each post-it-note into each category and discussed their responses to the problem. If they had different ‘I think…’ responses, students were encouraged to discuss and justify their position.

The A3 poster was then passed to the next triplet. The new triplet discussed the previous responses and added their own.

I think the fraze [sic] (phrase) DOES NOT is important.

                                                                                                           Response from a Year 3 student.

The process continued until each triplet had responded to each numeracy problem. We then debriefed as a whole class by focusing on the problems that had the most discrepancies in responses.

If you were rolling a 6-sided dice, which outcome is impossible?
If you were rolling a 6-sided dice, which outcome is impossible?

All students agreed that although the process was tiring, it was helpful. I’m going to ensure I do it every time.

If you buy two items at $3.40 each, how much change would you get from $20?
If you buy two items at $3.40 each, how much change would you get from $20?

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