Deep thinking

Mathematical ideas are rarely taught in one lesson. Some teachers and researchers say that a student needs to meet an idea 100 times for it to be understood well.

Of course, this does not mean 100 repetitive exercises. In fact, it means quite the opposite: that students need to meet the one idea in many different ways and contexts.

It takes time to engage with an idea deeply. Students need to:

• connect a new idea with what they already know
• think and talk about it
• be challenged to apply and extend it
• recall it for use in various contexts.