The 0Maths blog

Relative answering times

The purpose of this graph is to help teachers see (through a glass, darkly) the mental arithmetic techniques a student may be using. For example:

• A red circle means an answer took more than 6 seconds which indicates that the result probably did not come from long term memory. They need more practice.
• A green circle means an answer took less than 6 seconds which indicates it likely came from long term memory.
• If times are smaller when closer to the 5 or 10 lines, the student is using an appropriate strategy to calculate each answer.
• Consistently bigger than average circles along the 9 lines (and about the same size as one another, even 2×9 and 5×9) mean a student is sticking to the 9 times table finger trick instead of trusting their memory.
• Times not roughly symmetrical about x=y mean a student is not using commutativity.
• Times increasing proportionately to the numbers in the question mean answers are likely coming from counting on.

Use with caution: any inferences are only as reliable as the data they are based on. Many other factors can influence answering times (distractions, energy levels, etc). Data would be more reliable if it's all gathered at the same time, as opposed to doing a different table every day.