I started with the goal of investigating will alternative approaches to the 4 operations lead to better learning and the results are in; its a “Definitely maybe”.

From the experiential perspective, I think the new methods created greater motivation for learners who hadn’t experienced success with the standard methods ( a fresh start). The quantitative data would suggest no harm done with the possibility of a positive effect. I will use these new methods as an intervention strategy in the future with similar learners.

I have discussed these new methods with the department and we are in agreement that the traditional methods have slightly more flexibility but these methods are a good alternative. It’s definitely time to talk about methods.

At the start of my enquiry, I wanted to investigate the introduction of new teaching methods of the four operations, their impact on fluency and understanding for the lowest attaining s1 class.

Many of these new techniques were inspired by a series of visual teaching strategies from Professor Arthur T Benjamin and Dr James Tanton.

I introduced each of the new strategies at first using a physical resource ( Dienes blocks),  atomising each of the components, before bringing the information together in the formal method.

The student’s reaction to these methods at first was a greater engagement than in previous years (subjective judgement), a novelty effect but an important one when trying to reteach something the students have failed to learn on many previous occasions.

For each of the four operations, I gave students an opening and closing test ( with delay), re-teaching any areas highlighted as insecure. This resulted in improved performance in each of these tests for students. I will monitor next year for the fade-out effect of this teaching. Performance or learning?

A key goal was to make sure the students in the intervention group made more progress in the departmental model that any other class. The results are positive in this area with students in the intervention group making the most progress, a feat not realised in previous years. This would suggest the new method at least did not have a negative effect.

Throughout the process, I shared with the students the vision of what we wanted to achieve by the end of the year and I’m disappointed that we were unable to conclude our journey. The lack of the final parental and students survey is a big miss in the data due to the Covid-19 outbreak, this is an area I will rectify when schools return.

I have shared some of the new teaching strategies with colleagues in the department, the general view was scepticism, this is understandable. The current methods have been commonplace in Scottish Education for 30 years. My colleagues are justified in stating this is evidence for the effectiveness of current methods but I feel this has created a lack of reflection or understanding of alternative methods that may be superior for some young people.

I have been thinking for years why a significant number of students (approximately 20 students,14% of our cohort ) enter high school without basic level 1 Cfe skills.

These students can’t number bond within 100, some can’t do it within 10. They are highly inaccurate in terms of any written algorithm. This is in the context of high performing catchment, about 50% of our cohort gain National 5 in s4(much higher than the national average).

I have worked with a similar group for the last 3 years and have made steady improvements, using physical resources, lots of spacing, interweaving and re-teaching on areas of weakness. It was in this vein I wanted to trial new methods for the algorithmic version of the four operations linking with mental agility and manipulatives.

The National progression framework highlights the importance of strong foundations of place value and mental addition before progressing to algorithmic methods( I agree). I disagree with the frameworks late addition of negative numbers. Students should meet this as soon they begin subtraction i.e 5+-3 should come before   5-3, others share this belive such as director of La Salle Education     Mark McCourt. I spent a significant amount of time teaching addition and subtraction of negatives before the new algorithms.

There has been very little research into which methods promote best understanding and fluency. The Lindy effect would suggest a type of cumulative professional evidence for the current methods.

Jo Morgon published a very timely book “a compendium of mathematical methods“, this gave me a much greater understanding of current and alternate techniques for teaching the four operations but Jo draws no conclusions as to which methods are superior.

Most of the students have made positive progress this year and greater progress than their peers from the in house models. This shows the new methods have at least not had a negative effect on learning but I do worry about transitions to other classes if this was not a consistent departmental method.