'Maths Wars' : Which camp are you in?

(Views my own)

(The image above shows just some of the headlines of articles that have appeared in the news in the last 3 months)

Introduction

The most recent call for review into the Australian curriculum* has unexpectedly thrown coal on the flames of the supposed ‘maths wars’. For the unenlightened on this subject, there is currently an ‘edu-dispute’ about whether children best learn mathematics explicitly or through being allowed to discover concepts for themselves, guided by a teacher.

Background

If you have a background in education, this will likely evoke memories of the so called ‘reading wars’ which have continued for decades: pinning phonics (a ‘bottoms up’ approach’) against whole language (a ‘top down’ approach). In fact, there are many parallels- one is the building blocks, the other the application. In mathematics this is the traditional, explicit teaching of rote facts and memorisation of formulas juxtaposed with the more student driven constructivist, inquiry style learning.

Prior to the 1980s, students were typically taught mathematics explicitly, with a strong emphasis on memorisation and practice to the point that knowledge and skills ­became automatic – think times tables. This method of mathematics education is still prevalent, particularly in schools and systems which rely heavily on facts, speed and textbooks.

National Curriculum

As it stands, there are currently 3 "Aims of the Mathematics National Curriculum" (ACARA, 2021):

• are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as active citizens

• develop an increasingly sophisticated understanding of mathematical concepts and fluency with processes, and are able to pose and solve problems and reason in number and algebra, measurement and geometry, and statistics and probability

• recognise connections between the areas of mathematics and other disciplines and appreciate mathematics as an accessible and enjoyable discipline to study.

I have taken the liberty of underlining skills which I believe are difficult to cultivate without some inquiry-style levels of teaching in a given ‘mathematics week’.

My thoughts

In a newspaper article last year exploring the 'reading wars', Sarah Mitchell, NSW Minister for Education and Early Childhood Learning (2020) found that “phonics must be explicitly taught within a literacy program that also develops language and reading habits”. Hard to disagree with. Moreso, I would argue this could equally apply to our mathematics classroom: that basic facts should be explicitly taught within a mathematics program that also develops mathematical understanding and problem solving. Mitchell went on to say “that phonics and authentic literature experiences are not mutually exclusive". The same could be said for the two sides of these 'maths wars'.

Having been a student in a system which in hindsight I believe had an over-reliance on explicit teaching, I left school with a few key thoughts about mathematics:

1) If you were fast at mathematics, you were good at it.

2) Mathematics is something you do on your own.

3) Mathematics is complex, but if you follow the formula you’ll get the answer (to what question I never really knew!)

I’ve since found out that I couldn’t have been more wrong about mathematics, and as a result, I am often found to be helping students (and teachers!) overcome similar misconceptions.

All of this is not to say that I think explicit teaching doesn’t have its’ place. In fact, I would opine it should be towards half the time spent in our mathematics week (which to current guidance is approximately 6 hours total per week). It’s hard to direct your thinking to applications if you don’t have a basic foundational understanding of the content. Clearly though, inquiry-style learning does have a role to play in helping our students develop a love for, and an application of, mathematics (We at least owe ourselves a chance to successfully answer the fabled question "but when will I ever use this!?")

High-quality resources backed by research that I have seen help students develop their understanding of the problem solving and reasoning strands of the curriculum include#:

• 3 Acts (Meyer, 2011): "Storytelling gives us a framework for certain mathematical tasks that is both prescriptive enough to be useful and flexible enough to be usable. Many stories divide into three acts, each of which maps neatly onto these mathematical tasks."

• Mathematical story telling courtesy Natural Maths (2013): “Introduce the problem as a narrative, kids connect best to learning when they feel part of it and when they can see the relevance. Become a story teller” and Tierney Kennedy (2019).

• Open-Ended Questions (Sullivan & Lilburn, 2019): practical advice on how teachers can create their own open-ended and problem-solving questions, and use them effectively in the classroom.

I’ll give one caveat, and that is to cede the floor to the image below which details Dr Kevin Larkin’s (2016) mathematics manipulatives mapped against Bruner’s (1960) stages of development. Whether we are explicitly teaching concepts, or using inquiry-style learning aimed towards mastery of abstract concepts, we need to ensure children have had sufficient time and experience working with concrete materials as shown below.

Conclusion

So: explicit or inquiry? Which camp are you in, or are you somewhere in the middle? What does your 'maths week' look like? You can find mine here: https://mathsclassrenos.wixsite.com/index/post/renovate-your-maths-week

* a reasonable, easy-to-read summary of some key proposed changes can be found here: https://theconversation.com/the-proposed-new-maths-curriculum-doesnt-dumb-down-content-it-actually-demands-more-of-students-162088

# full links to all of these are in the biography

Biography

• ACARA. (2021). Retrieved 3 July 2021, from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/aims/

• Baker, A. (2013). Natural Maths. Retrieved 3 July 2021, from https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwiw68SC88XxAhXKT30KHf3QDhwQFjADegQIDBAD&url=http%3A%2F%2Fwesttorrenspartnership.edublogs.org%2Ffiles%2F2014%2F03%2FAnn-Baker-PD-Notes-2013-2h11ybj.doc&usg=AOvVaw3IZf0SJE7WyBXdfRSJUnm8

• Bruner, J. (1960). The Process of Education. Cambridge, MA: The President and Fellows of Harvard College

• Kennedy, T (2019). Back to Front Maths. Retrieved 3 July 2021, from https://www.backtofrontmaths.com.au/daily-teaching-help/tips-and-tricks-for-problem-based-teaching

• Larkin, K. (2016). Mathematics education and manipulatives: which, when, how?. APMC, 21(1), pp.12- 17.

• Meyer, D. (2011). The Three Acts Of A Mathematical Story. Retrieved 3 July 2021, from https://blog.mrmeyer.com/2011/the-three-acts-of-a-mathematical-story/

• Mitchell, S. (2021). Retrieved 3 July 2021, from https://www.smh.com.au/national/nsw/the-reading-wars-are-over-and-phonics-has-won-20201127-p56ioj.html

• Sullivan, P., & Lilburn, P. (2019). Open Ended Maths Activities Revised Edition. Melbourne: Oxford University Press Australia.

• Urban, R. (2021. Retrieved 3 July 2021, from https://www.theaustralian.com.au/inquirer/maths-wars-the-great-divide/news-story/74a078640e0b30687871f0f900deba55