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.

Addition

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.

Subtraction

Again left to right and gives a better feel in terms of number awareness, the students are constantly reinforcing place value.

Multiplication

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.

Division

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.

Memory

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.

Hi Barry

Thank you for your blog – which I read with great interest. I was particularly interested in the memory section – how would you measure the outcome of changing your practice?

LA

I have taught the same set of students( 9 out of 9 ) in S1 for 3 years in a row and the assessments will remain constant.

So I hope to measure improvement in these assessment along combined with students views through a survey.

So keeping content, teacher , set , assessment, year group stable with a change in curriculum sequencing and I would want to see an increased level of achievement through regular assessments and increased student motivation for maths with pupil surveys.

Hi Barry

Thanks for your reply – would you consider one to one interviews? They may yield a certain type of data.

LA

Yeah definitely, people views with quantitative data and observations . To gather data from different streams . I was thinking surveys but one to one interviews , could be good if I have clear enough plan what information I’m after.

Oh and thanks for reading , if you can think of any ways I could make it more robust that would be great.

Thanks

Barry

Hi Barry,

As someone who professes to struggle with numeracy- I found your new approach very interesting.

A question I would have is whether you think when examining the impact, there is potential for one intervention to mask the other? for example how would you distinguish if the impact was due to the new numeracy strategy or memory strategy?

Yeah, that is true. With s1 I was going to try both but with my other classes just the memory part. If it has an impact with all classes then that shows some effect but that still leaves the problems that if the s1 improve it will be hard to know which. I suppose I could look at their overall performance in terms of the memory techniques and their performance on these specific techniques and create a model that accounts for the weighted effect but may be easier said than done once I have looked at the figures.

I found this really interesting, the first way is how I learned math and looking at the second way I actually find it more confusing. (old dog new tricks and all that)! I am in a faculty with Maths so looking forward to finding out how you get on sharing it with my colleagues!

Thanks , yeah I know what you mean . These classes have tried the other ways and failed , so maybe give them different insight but I’m not sure I would change for everyone.

When my daughter has homework I explain it the second way (subtracting), which is strange because it is not how I would do it! Hope it benefits the pupils and a different method is all they were needing!

This is a really interesting idea, looking forward to seeing how it progresses.

I think this has the potential to be really powerful for those students that the more traditional methods haven’t worked for.

I agree that it might be tricky to identify which intervention is having impact where you are trying both with a class. The pupil interviews could shed some light on this though. I have found that a focus group of around three works well for a cross section of the class and it is good if the interviewer has an understanding of what you are trying to impact on in the class so that they can promote discussion and offer supplementary questions to support gathering that info for you.