It is interesting to note the competing tensions in the Curriculum Refresh that speaks to an ideological arm wrestle.
This is perhaps no better emphasised than by examining the state of Mathematics achievement that has, since the advent of the Numeracy Project, been declining. In 2018, in NMSSA Mathematics, 81% of Year 4 pupils achieved ‘at’ or ‘above’ curriculum expectations while 45% of Year 8 pupils achieved ‘at’ or ‘above’.
We must ask ourselves what has caused such a significant decline in achievement.
A major problem at the heart of our decline in mathematics has been the prioritisation of strategy over knowledge, understanding over competence. The fallacy of this ideological approach is evident in data from the 2019 Trends in International Mathematics and Science Study (TIMSS):
· only 30% of New Zealand 10-year-olds could calculate 6 x 312 (2nd to last in participant country ranking, international average 64%)
· only 26% could add 385 to 5876 (last, international average 63%)
· only 16% could choose the correct answer to 27 x 43 in a multiple choice question with four options (last, international average 52%). In other words, if participants had guessed the result would likely be 25%
Instead of creating flexible problem solvers, the teaching of multiple number strategies, before students have an adequate grasp of number knowledge and decimal place value, has left New Zealand students struggling to perform even the most basic number tasks. This has caused a loss of mathematical confidence, particularly in upper primary learners who struggle with the cognitive load of thinking across multiple strategies and are left with little capacity for higher-order problem-solving.
New Zealand’s own Dr Audrey Tan has identified this problem, emphasising the disjuncture between our ideology and its impact on achievement. Our mathematics approach over the past 20 years has emphasised building understanding first (through the exploration of strategy) to establish mathematical competence. Dr Tan argues that this is back-to-front, and overlooks the importance of student confidence. We should be building competence to establish confidence first, the necessary combination/platform to enable understanding.
In the early years, confidence is built when simple procedures are practised. Mistakes provide valuable opportunities to build understanding. Once a procedure is mastered and young people have experienced success, they see themselves as mathematically minded and can build towards a wider exploration of strategy and a deeper level of understanding.
In their seminal report to the Ministry of Education in September 2021, Robin Averill, Fiona Ell, and Jane McChesney argued that the 2007 Mathematics Curriculum didn’t have enough detail for teachers to successfully plan for mathematics and statistics teaching. They claimed that what was needed was a more detailed and specific curriculum.
I agree. However, inherent in the challenge to be much clearer is to address the absence of practices that would assist young people to improve their mathematics achievement and their enjoyment of the subject.
Coming up with a novel solution to every mathematical problem is exhausting, and contributes to the maths anxiety experienced by so many. The current ideology actively encourages this approach, but in fact, many mathematical problems are made easier by applying well-practised procedures. At the simplest level, this might be using an algorithm to add, subtract, multiply or divide, but mathematical procedures become increasingly helpful as the complexity of the problems increases. Indeed, that is the power of mathematics! It is a sad travesty that little muscle memory of mathematical procedures remains in our primary teaching workforce, and that our young people have little, if any, experience of this powerful, structured learning.
The Numeracy Project inappropriately branded the standard written algorithms as divorced from an understanding of numbers such as can be demonstrated when using number properties to solve problems. The fallacy of such a view is plainly obvious! Many young people need the confidence of an algorithm to accurately figure out a problem and in doing so come to understand how our Base 10 number system works. Once gained, this knowledge can then be expanded into mental models.
The draft Mathematics and Statistics learning area statement is a good start in our build-back to improved achievement. However, while number properties are explicitly mentioned as progress outcomes, the standard written algorithms are noticeably absent. It speaks to the persistence of ideological practices that ignore the evidence of what our learners really need. It is a missed opportunity to address the inequity that our current system perpetuates, indeed exacerbates.
Ignoring, as this draft Curriculum does, acknowledging the importance of key foundational procedures is counter-intuitive to the goal of ultimately growing students with a complex understanding of numbers. This mistake is akin to the error frequently made by teachers who judge that supporting student agency, for example, requires them to give more freedom to students to ‘own’ their learning. However, the opposite is true. If a student is to be successful as an agent in their own learning, the teacher must step closer in support of that student, to scaffold the learning to ensure it has rigor and achieves important goals. The same is true of the foundational procedures necessary to enable young people to flourish in the development of complex mathematical thinking. If one aims for creativity and complexity, then the curriculum must be designed to help teachers, first, step closer to the student to scaffold them with clear and simple procedures.
In New Zealand schooling we tend to inappropriately deploy sophisticated expectations for children at younger and younger phases of their development and often in the name of growing a ‘growth mindset’ and ‘creative thinking’. While these goals are not inappropriate ends, this frequently occurs long before children are ready.
We must be careful to avoid the cognitive overload of young people who are not developmentally ready to think in abstract or complex ways.
If we fail to address this disjuncture, then we will simply be launching a new curriculum without dealing with one of the fundamental causes of our mathematics achievement decline.
My hope is that the pending development of the Common Practice Model in Mathematics & Statistics takes a common-sense approach and will emphasise the building of mathematical knowledge to grow confident mathematically-minded young people. We need to acknowledge the importance of procedure and practice in helping build competence, confidence, and understanding.
With some subtle and important tweaks to this draft Mathematics and Statistics Curriculum, we could have the basis for powerful and immediate change.
