After watching the lecture series ” The Power of Mathematical Visulasisatioin ” by Professor James Tanton
( side note the great course has loads of brilliant maths courses).
I have been inspired to alter the way I teach the four operations, linking with a visual model of teaching.
As with all new methods, I am working left to right. This links well to how you would use dienes blocks and mental methods. It has the added benefit of making adding in alternative bases simpler.
Again left to right and gives a better feel in terms of number awareness, the students are constantly reinforcing place value.
Links well to physical resources and links well with multiplying brackets (5x + 6)(4x+3) = 20x^2 + 39x +18. Here the students can start to spot the relationships.
I have made the choice to leave the final answer in mixed fraction form, again to link with a manipulative and further algebraic division. Later on, I will explore the link between fractions and decimals.
I hope to test these methods with my 9th set s1 class. These students have had exposure to standard methods and failed. I will hope to show that these methods will allow the students to acquire the knowledge to complete basic calculations and develop a greater conceptual understanding.
The second drive I wish to explore is the link between memory and forgetting.
In his recent book “Teaching for Mastery” Mark McCourt recommend an 80%-20% split in the review of each lesson and the teaching of novel content, this point was also made by Siegfried Engleman in his book ” Successful and Confident Students with Direct Instruction”.
Both authors make similar justifications that content has to be embedded throughout time, revisited after forgetting and moved in with a phased approach from direct teacher instruction to independent practice /behaviour. This is an idea I think has the power to improve understanding and retention for all pupils.
I will adjust the ratio of my lessons to have 80% review, 20% or so independent practice/ behaviour of material spiralled in the curriculum, guided practice through the use of mini-whiteboards of recently learned material (interleaved) 60% and then 20% novel idea teaching with a heavy focus on direct instruction. I hope this change will improve retention and far transfer.