This report succinctly summarises the essence of cognitive load theory. CLT is, in my opinion, the most important idea for teachers to understand. It has wide-ranging implications for mathematics teaching.

The second page of this paper has an excellent paragraph summary of CLT.

Perhaps one of the most rigorous and credible educational research projects ever conducted. The authors go to extraordinary lengths to ensure the validity of their results and demonstrate convincingly that interleaved maths practice significantly boosts results.

Interleaved practice involves regularly revisiting topics in mathematics, as opposed to sticking with a single topic without interruption (known as blocked practice).

Conceptual Understanding

Relational Understanding vs Instrumental Understanding

Richard Skemp (1976) discussed the difference between relational and instrumental understanding. This is a debate I’ve had with myself and other teachers many times.

Do we just teach students how or do we painstakingly teach the why as well?

More recently, Foster (2014) discussed this debate further.

I will leave you to read these amazing articles yourself, and I’d welcome your comments at the bottom of this page.

Further discussion can be found on our conceptual understand page.