I have been looking into both aspects of my inquiry focus for some time so much so this latest blog is a month late ( sorry BigBrother maybe BigSister), it’s been busy.
In one sense my exploration was fruitless, after much toiling in the field to find the effectiveness of different approaches to teaching standard computations my harvest returned barren and villagers are in for a famine. Many of the different approaches I have been trying, come from 2 different sources, Professor Arthur Benjamin who has written a series of books https://www.amazon.co.uk/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401/ref=sr_1_1?keywords=arthur+benjamin&qid=1573195097&sr=8-1
and Professor James D.Tanton
In these books and video lectures, they offer a series of alternative teaching methodologies, making arguments from the theory of multiple representation and links with mental calculations but I have yet to find the paper with a comparative study.
Jo Morgon is soon to publish a book on the use of different approaches (https://www.amazon.co.uk/dp/1912906600/?coliid=I2C8H7H393BK8Q&colid=13VVNRXI8UQ9Y&psc=1&ref_=lv_ov_lig_dp_it
I will read this with great interest.
Memory and Spacing
In my other area of interest changing the balance of lessons to review, the harvest was bountiful.
” Our data, to stress the point, suggests that three complete sets of complete information interpreted and integrated into working memory, are the minimum needed for the construction of a new belief or concept”
Graham Nuthall , 2007
In my experience, the word minimum is vital in this sentence. With students with the poorest prior attainment needing more in the region 5 or 6 exposures spaced over time.
Direct Instruction the most successful program in Project follow through follows this 20% new to 80% review allocation.
” In this structure, lessons are shaped around multiple skills or topics rather than around a single skill or topic and each of these skills/topics is attended to for a short segment of time (five to ten minutes) and revisited over several days until these discrete skills/topics are mastered”
Explicit and Direct Instruction, Adam Boxer, 2019.
I’m looking forward to further exploring my practice in these areas, they are potential benefits in both but also areas where I can see problems arising.