Sticking points in maths teaching and learning – global issues, local solutions

A few days ago, a colleague kindly pointed out to me that we were over 1/5th of the way through the 21st Century. Seeing as I feel that I have been in a weird dream for the last 12 months this didn’t come as a total shock. We are properly in the 21st Century now and have been for quite some time. So, where are we at with these 21st Century skills that employers want people to have? And with more relevance, what has the construct of 21st Century skills meant for us in the mathematics classroom? Has the container ship of mathematics pedagogy become wedged in the Suez Canal of unclear intent, or are we in the middle of a revolution, transforming the way we understand the maths that people need and how people engage with number in their everyday life?

The global direction is clear. A move away from rote learning and memorisation towards problem solving, experimentation and creativity. A process, identified by the Indian National Council of Education Research and Training (NCERT) as mathematisation – that ability to think logically, to be able to formulate and handle abstractions – drawing from the Realistic Mathematics Education (RME) community incubated in the Netherlands. These ideas now percolate through curricula in India, Indonesia and the Philippines and influence the mastery approach in Singapore and through the NCETM in the UK. Elements of the approach, such as working through staged, scaffold, real world problems present maths in a different way to the ‘textbook’ approach adopted by many classroom teachers.

Friends of Equals Online, such as Professor Steve Chinn and Dr Tom Hunt, have warned against the destructive nature of didactic rote methods on learners who find it difficult to acquire mathematical knowledge. Amongst the population of learners who are particularly vulnerable to this approach are those with inefficiencies in working memory and speed of processing. The learners who often struggle to gain automaticity of maths facts and mathematical processes.

In the field of Specific Learning Difficulties, these inefficiencies are often referred to as domain general difficulties because they are common to many SpLD’s, dyslexia, dyscalculia, dyspraxia, ADHD and Autism.  Steve Mould, the science evangelist and youtuber, who is dyslexic, describes his difficulties with rote learning of times tables facts in this TED Talk (https://youtu.be/iAcvYqDKznE). As I also have dyslexia and struggle with automaticity his story resonates with me. Like Steve, I struggled to remember facts, but became flexible at calculating them. I rely on a few key facts and flexibility with numbers. I see numbers within numbers, and this helps me to be confident with calculations beyond the 12 tables that many know. The flipside is speed – or the relative lack of it – and forgetting where I started if I don’t write things down. The easy remedy, write things down and take the emphasis off speed towards efficiency – accuracy and timely completion.

An examination of curricula from around the World identifies that what have become known as 21st Century Skills have prominence in developing abilities in learners. There is some variation in what is considered to constitute these skills, but a good overview can be “the dexterity employees must have in order to remain in or enter (the) global labour market” (Hadiyanto, et al. 2021). A concise list is the ‘4 C’s’; Critical thinking; communication; collaboration; and creativity (Partnership for 21st Century Skills, 2008). The NCERT Document ‘learning Outcomes at Secondary Stage’ (2019, P10) includes:

The ultimate goal is not achieving mastery over the content as content is only the medium used to develop competency. Learners need to comprehend, compare, manipulate, and apply the knowledge for real life purposes. These competencies, acquired using various pedagogical processes, would serve as an instrument not simply developing creativity, critical thinking, communication skills, and securing grades in examinations, but the learners would also be able to contribute towards nation building by learning, thinking, and applying these skills at work.

The National Curriculum document from Indonesia states:

The process of learning mathematics in educational units should be interactive, inspirational, fun, challenging, motivate students to participate actively, and provide sufficient space for initiative, creativity, and independence according to student’s talents, interests, and physical and psychological development (Kementerian Pendidikan dan Kebudayaan, 2016, p. 6).

The Education Inspection Framework in the UK states:

In order to develop understanding, pupils connect new knowledge with existing knowledge. Pupils also need to develop fluency and unconsciously apply their knowledge as skills. This must not be reduced to, or confused with, simply memorising facts. Inspectors will be alert to unnecessary or excessive attempts to simply prompt pupils to learn glossaries or long lists of disconnected facts.

The school’s curriculum identifies opportunities when mathematical reasoning and solving problems will allow pupils to make useful connections between identified mathematical ideas or to anticipate practical problems they are likely to encounter in adult life. Pupils have sufficient understanding of, and unconscious competence in, prerequisite mathematical knowledge, concepts and procedures that are necessary to succeed in the specific tasks set.

Whilst the EIF still seems to be orientated towards fluency and memorisation (efficient recall, discriminating against those with inefficiencies in this area), it is explicit that skills in reasoning and problem solving are important and sustainable in developing knowledge and understanding.

Alongside the RME community of practice (In the UK a good place to start is the RME research group at Manchester Metropolitan University What is RME? | Realistic Maths Education), we have a number of organisations that take a more rounded approach to mathematics education focusing on reasoning and problem solving. Those of you of a certain age will recall the orange folders of the Malcolm Swan led ‘Standards Unit: Improving Learning in Mathematics’ (Improving learning in mathematics | STEM). Many of the  approaches suggested in that document have been recognised for the effect on attainment they bring by the EEF (Teaching and Learning Toolkit | Education Endowment Foundation | EEF) and by the Jeremy Hodgen led study for the Nuffield Foundation (2020). Collaborative learning on rich, tangible, real world tasks, effective feedback, allowing students to reflect and go again, heuristics that scaffold flexibility in problem solving and the use of manipulatives and pictures all fit with the approaches set out by guiding organisations throughout the World.

We should be in a good place but there are still areas of concern that I encounter when talking to people around the world. Firstly, we shouldn’t assume that rote learning and memorisation, or more precisely, “just copy what I do, and do that in the exam” doesn’t exist. In reality, with the pressures we are under (and these will only increase in the post-covid world), people are quite open about the need to “get them through”. And, unfortunately, for our learners that struggle, when faced with the pressure of time and resources and the importance that a GCSE pass holds, both for the learner and the school, “get them through” is often the approach taken. But what leads learning, competence, or a piece of paper?

I recently had a conversation with teachers in India about strategies that develop mathematisation, and how they can help learners with inefficient working memory systems. They admitted that they were aware of the move towards a curriculum that develops problem solving skills and flexibility but had just drifted back to their “do what I say” style of teaching. It is the easiest path, but it does a disservice to our learners. However, increasingly we are seeing people get results from a range of approaches. Visualisation of mathematical ideas is gaining a strong evidence base and has moved beyond a niche approach in SEN maths teaching to become a mainstream staple. Bar modelling has a group of avid fans, including myself, and heuristics such as George Polya’s four step problem solving cycle are enjoying a renewal. Vygotsky and scaffolding, Bruner and the move towards Concrete, pictorial, abstract blending, and Piagetian approaches to problem solving are back in fashion.

Perhaps the problems don’t always lie with the teacher. As Ricky Yabo (2020) identifies “ most of the time during mathematics discussion students are sleepy, inattentive and disengaged, henceforth teachers are also having challenges in making the subject more appealing and captivating”. More on the solution shortly, but we feel his pain. Previously I have written about the impact of the environment in which maths is done, and the stress this can cause, and Tom Hunt wrote about this recently as well. There is the perpetual meme of “hey, I’m rubbish at maths”, “I’ve never been good at maths”, statements that crop up in our lives, in the media, and sometimes from teachers. Yet, 45% of adults describe some level of maths anxiety. It’s OK to be bad at maths, but, boy, it makes me anxious. Memorisation and rote learning have their role to play in this, as does the “just get ‘em through” mantra.

Ricky Yabo draws attention to the power of joyful learning in mathematics. Like RME, Joyful learning is a developing movement (Joyful Learning Network – Home) with a strong focus on motivation and engagement. Again, in the UK we recognise the power of games to engage, but perhaps, struggle to justify the time in using them. Some of the best lessons I have watched have used game-playing. The other skill that I see employed to huge affect is the art of storytelling. Taking the learners on a journey, as fantastic as you like, but built around the specific objective you are focusing on. We can still be explicit and have fun, and fun engages and motivates – and sometimes wakes up the sleepy.

Around the world there are movements that are gaining traction. We have a strong resource base in the OK, and perhaps we should use these tools to re-engage actively with the 21st Century skills – Critical thinking; communication; collaboration; and creativity.

Hadiyanto, Hadiyanto; Failasofah, Failasofah; Armiwati, Armiwati; Abrar, Mukhlash; and Thabran, Yulhenli, Students’ Practices of 21st Century Skills between Conventional learning and Blended Learning, Journal of University Teaching & Learning Practice

, 18(3), 2021. Available at:https://ro.uow.edu.au/jutlp/vol18/iss3/07

Hodgen, J., Coe, R., Foster, C., Brown, M., Higgins, S., & Küchemann, D. (2020). Low attainment in mathematics: An investigation focusing on Year 9 students in England. Final Report. London: UCL Institute of Education.

Kementerian Pendidikan dan Kebudayaan. (2016). Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 22.Tahun 2016 Tentang Standar Proses Pendidikan Dasar dan Menengah [Regulation of the Minister of Education and Cultureof the Republic of Indonesia Number 22. 2016 concerning Basic and Secondary Education Process Standards]. Jakarta: Kementerian Pendidikan dan Kebudayaan.

Partnership for 21st Century Skills. (2008). 21st Century Skills. Education & Competitiveness: A Resources and Policy Guide. [Online]. Retrieved from: http://www.p21.org/storage/documents/ 21st_century_skills_education_and_competitiveness_guide.pdf. Accessed on 21th February 2017.

Yabo, R.S. (2020) The Joyful Experience In Learning Mathematics. Southeast Asia Mathematics Education Journal. Volume 10, no.1. 2020.

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