Seneca talks about not jumping from book to book or from idea to idea constantly. Rather we should be sticking with something to embed the learning before look at something else. This applies to teaching too. We often jump from topic to topic and students only get a shallow understanding, what we need to be doing is going deeper into concepts, integrating the new knowledge into other aspects of the curriculum before moving on.
This isnt a new idea, as I mentioned, Seneca was advocating this thousand of years ago. More recently the likes of Benjamin Bloom, Thomas Guskey, Mark McCourt etc advocate mastery learning. Teaching from where students currently are and deepening their knowledge in a topic before moving to something else. Mastery has been a buzzword for a number of years but the idea of embedding knowledge is centuries old.
I know that I am guilty of 'covering' a topic so students have seen it and making sure I am getting through the curriculum. The more I read though the more I am thinking that if we deepen learning early on, taking our time, we can potentially speed up later topics because we won't need to reteach key foundational knowledge, we can just look to build on it. As an example, if we use multiple representations and variation to reveal the underlying concept of negative numbers, when students come to factorise quadratic equations that involve negatives, we can be certain that they are fluent in finding factors of -15 and can comfortably add or subtract negatives to get other terms of the equation. Obviously there are certain topics that are relied on more heavily in later mathematics, like negative numbers and fractions, that I believe we need to truly invest time in with students before even looking at more difficult concepts that combine lots of these ideas.
The tasks we ask students to do can make a massive difference to how deep they cover the content. NCETM push variation to help reveal the underlying structure of a concept. The image belows shows how if we just have students answer random questions without a link or reason then they are just following a procedure. This is where often later in students Mathematical career, we have to reteach this procedure. The second set of questions allows the deeper understanding of subtraction being a difference of two numbers. As a teacher we need to encourage the discussion about these questions so students can realise the key ideas. Making sure they can spot this gives learners a greater chance of learning the concept and then be able to transfer it to multiple scenarios.
From a selfish viewpoint I have fully embraced CPD through lockdown but have been guilty of jumping from webinar to webinar or book to book without really embedding the learning. I think the amount of CPD available online is fantastic but feel that as teachers we may find ourselves shallowly covering an idea without really embedding the knowledge into our own teaching. I am going to go back over some key books and webinars and relearn the key concepts, fully investing in them so that rather than briefly learning them they are embedded into my systems and practices to help improve myself.