Exploring My Itch

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.


Reforming Scotland : “What future for Scottish Education” – Reflection

I recently reviewed “Reforming  Scotland Future: What future for Scottish Education”.  The main suggested reforms from the author where

  1. Increased Autonomy: His conclusion was increased Automony would improve results, this, of course, is the current policy of the Uk government in relation to English schools but as Dylan Willaim points out in his book “Creating the Schools our Children Need” increased autonomy has little impact on increasing a nations educational standard. If given complete freedom some schools will perform exceptionally well ( Michaela in England being an example) and some will perform extremely poorly ( Al-Madinah school in England). The overall effect is a net-zero or negligible improvement in the overall educational attainment of a nation.
  2.  Learning from experience: This improvement strikes with a sense of irony since the introduction of the curriculum for excellence educational experience in every international metric has fallen in Scotland and in internal metrics such as SSLN. His conclusion from the piece is it’s just not been implemented correctly this strikes me as a classic case of “new true Scotsman fallacy”, what evidence would be acceptable to show CfE has been a failure? We have respected international educationalist posting articles such as
    Learning lessons from the failure of Scotland’s “Curriculum for Excellence”   https://gregashman.wordpress.com/2017/03/22/learning-lessons-from-the-failure-of-scotlands-curriculum-for-excellence/

    3. Technology is transforming education argument, this argument can be found in books of 19th-century philosophers. I have yet to read a study in which the use of technology in the classroom has significantly improved leaning.   The mere presence of a mobile phone in the classroom led to 20% reduction in attention, concentration and performance ( Thorton 2014 Social Psychology)   Schools that banned mobile phones received a 6.4% increase in their exam results going up to 14% for the previous lowest-achieving ( Beland and Murphy 2015).   “laptops use can negatively affect performance on educational assessments , even or perhaps especially – when the computer is used for its intended function of easier note-taking” (Muller and Oppenheimer, 2014).

To transform Scottish education and close the achievement gap we need to focus on the areas that have been shown to work time and time again. Teaching for long term memory, spacing, interleaving retrieval, a strong knowledge-based coherent curriculum with a focus on mastery at each step, firm and loving discipline.

We should invest in teachers and in CPD, scrap failing skills-based curriculums and invite our poorest children to share in rich knowledge-based culture, giving them opportunities and life chances currently reserved only for they’re well off piers.