Adding

Assessment week at school. In the moments when I wandered around the room rather than frantically marking at the front of the class, I was absolutely fascinated by the journeys the students were going on. 
For example, for this question, I watched a student for five minutes

  1. First, stare at the question and do nothing for two minutes
  2. Suddenly, without warning, start to write out the numbers from 36 to 90 (missing out a few by accident on the way)
  3. Start to count how many numbers there are
  4. Get confused, so start from the beginning, this time labelling as you go
  5. Get confused, so add 36 to 49, just in case
  6. Write 50 as your answer, because 50 is close to 49

The student was completeley focussed, attacking the problem from multiple perspectives, and persevering. 

Addition has no inverse.

Another student used trial and improvement. Built his own subtraction algorithm.  If you don’t understand that subtraction is the inverse of addition, then you learn increasingly ingenious ways of using other tools. Look closely at the sequence he chose – it reveals a lack of place value understanding too.

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