How to Teach Maths

Understanding Learners' Needs

Steve Chinn

• Publisher: Routledge
• Year: 2020
• eBook ISBN: 9781000217131
• Edition: 1
• Topic: Education
• Subtopic: Education General

How to Teach Maths challenges everything you thought you knew about how maths is taught in classrooms. Award-winning author Steve Chinn casts a critical eye over many of the long-established methods and beliefs of maths teaching. Drawing from decades of classroom experience and research, he shows how mathematics teaching across the whole ability range can be radically improved by learning from the successful methods and principles used for the bottom quartile of achievers: the outliers. Chinn guides readers through re-adjusting the presentation of maths to learners, considering learners' needs first, and explains the importance of securing early learning to create a conceptual foundation for later success.

This highly accessible book uses clear diagrams and examples to support maths teachers through many critical issues, including the following:

• The context of maths education today
• Topics that cause students the most difficulty
• Effective communication in the mathematics classroom
• Addressing maths anxiety

The perfect resource for maths teachers at all levels, this book is especially useful for those wanting to teach the foundations of mathematics in a developmental way to learners of all ages and abilities. It has the potential to change the way maths is taught forever.

Chapter 1

Where we are with maths education

Obviously, I’m not going to write a book like this if I’m happy with where I think we are with maths education now and recently. I should define ‘recently’. Maybe later.

What follows in this chapter is a collection of data and evidence to support my unhappiness with where we are now. If you take that as a blunt statement, you could leave this chapter on hold and look at the rest of the book first. Then maybe come back to this chapter? Otherwise, read on.

The 2018 PISA – Programme for International Student Assessment from the Organisation for Economic Co-operation and Development (OECD) – results for maths for the UK showed a significant improvement in ranking, but we are still some way off the leading Asian countries. There are worrying statistics around those who are still struggling with maths after the age of 16, after failing the national exams for 16-year-old students.

To balance up the good news, we can look at some data from the YouGov/National Numeracy survey from 2014:

Twenty-six per cent of adults believe that ‘You cannot change your ability to do maths as some people are naturally good at maths, some are not’. The better news is that 70% disagree. Four per cent think that that adds up. Beliefs play a big role in maths. Some are worth challenging. And some are worth encouraging. The persuasion to move to positive beliefs is likely to be subliminal and based on experiences of success rather than on indoctrination.

Data on performance in maths

It’s not all bad. I like a few platitudes, so let’s go for ‘We could be better’. In this book, I am suggesting one source of ideas – the outliers – on how to help things get better. Low achievers need attention for their own sakes, but I believe that what we learn from teaching them successfully can be a way of improving our overall statistics in surveys such as those PISA results.

Since this is a book about maths, here are some numbers.

There is some data around that supports my opening paragraph. For example, the 2010 Sheffield Report’s evidence on levels of achievement in maths showed that 22% of 16- to 19-year-olds in England are functionally innumerate. This is a problem that has been in existence for at least 20 years. A 2011 report from the Conservative Party, ‘A World-class Mathematics Education for All Our Young People’, stated that ‘much greater attention needs to be paid to those students (nearly half of each cohort) who currently are deemed to “fail” mathematics at age 16’. The 2017 National Numeracy booklet ‘A New Approach to Making the UK Numerate’ stated that ‘Government statistics suggest that 17 million adults – 49% of the working-age population of England – have the numeracy level that we expect of primary school children’. This is relatively consistent data but at least it’s not worse. But, then, it’s certainly not better. Of course, ‘what we expect of primary school children’ doesn’t have much mathematical precision in the minds of many people (but see Appendix 1). Further evidence that the situation is not so good for older learners in the UK was that we were the worst-performing of the 17 OECD countries in the ‘Numeracy/Knowledge’ component of Adult Financial Literacy (2016).

According to the Nuffield Foundation UK report ‘Understanding Mathematics Anxiety’ (2019), the proportion of adults with functional maths skills equivalent to a General Certificate of Secondary Education (GCSE) grade C (the passing grade) fell from 26% in 2003 to 22% in 2011. In contrast, functional literacy skills were steadily increasing, and 57% of working-age adults gained the equivalent level. The PISA data released in 2019 suggests that maths for 15-year-old UK students is improving and pushing us up the international rankings. Of course, it may be more complicated than that but it is encouraging.

In terms of students re-taking the UK national maths examination (GCSE) for 16-year-old students, results for maths show that of the 155,000 entries in 2018–2019, 37.2% achieved a lower point score for this re-take than for the previous attempt and 36.5% made progress, according to Julia Belgutay (Times Educational Supplement, 21 October 2019). In terms of pass rates, the data is stark: ‘Fewer than a quarter of maths entries from candidates aged 17 and over across the UK resulted in a pass at grade 4 (equivalent to C) or better, with the pass rate dropping from 23.7 per cent in 2018 to just 22.3 per cent this summer, according to data from the Joint Council for Qualifications published’ on 13 November 2019. (https://webcache.googleusercontent.com/search?q=cache:FWX-ZzalL4UJ:https://www.tes.com/news/gcse-results-english-and-maths-resits-pass-rates-drop+&cd=1&hl=en&ct=clnk&gl=uk). We seem to have a cohort of learners for whom the current system is not working. I am suggesting, again, that maybe we could do even better on the PISA rankings if we could reach this cohort.

When we seek international data, the key source is PISA. It tests students at age 15. New results on their 2018 international assessments were released in December 2019. The UK’s ranking in maths had remained stable from 2006 to 2015, around the OECD average. A sample of the positions in the 2015 survey has Shanghai (1), Singapore (2), Hong Kong (4), Switzerland (9), New Zealand (16), the UK (27), Ireland (28) and the US (35).

In the 2019 results for maths, the UK was 18th, up from 27th in 2015. This represented a ‘particular improvement’, according to an analysis by the National Foundation for Educational Research. The education director of the OECD said that these were ‘positive signals’ which demonstrated ‘modest improvements’.

And since I’m with this recent PISA, I’ll include this statistic: Boys scored lower than girls in mathematics by 12 score points, which is wider than the average gender gap across OECD countries (5 score points).

The TIMSS (Trends in International Mathematics and Science Study) provides data on the mathematics and science achievement of 10-year-old students from the US compared with that of students in other countries. The 2015 results put Singapore at 1, Hong Kong at 2, Ireland at 9, England at 10 and the US at 14.

It seems to me that sometimes statistics are out there to be abused, especially by politicians. For example, in England, there is our national examination for maths for students who are 16 (and then older if they need to re-take after failing the first time). I love – although maybe that’s not the right word for such depressing content – this observation from Professor Alan Smithers, director of the Centre of Education and Employment at Buckingham University:

What is happening is that this year (2019) the exams are harder, and the Office of Qualifications and Examinations Regulation [Ofqual] has wanted to keep the grade pattern comparable with previous years, so it has had to lower the number of marks required to get a pass grade. These grades will lead to us fooling ourselves into assuming that young people are doing much better than they actually are. Ofqual are creating an illusion.

Education ministers are in a win–win situation. They make exams harder, thinking that this is enough to raise standards, so that’s a win. Then, if results are (inevitably it seems) lower, they lower the pass mark and – ‘Hey presto!’ – standards have risen. That’s a win, too. We should include a cynical component when we teach statistics.

Later, I will talk about the ‘curse of knowledge’, defined as ‘a cognitive bias that happens when an individual, communicating with other individuals, unknowingly assumes that they have the background knowledge to understand’ (taken from a 1...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Introduction
• Chapter 1: Where we are with maths education
• Chapter 2: Key identifiers of future and current maths difficulties
• Chapter 3: The core curriculum for arithmetic
• Chapter 4: The developmental nature of maths
• Chapter 5: Topics which cause the most difficulty
• Chapter 6: Learner characteristics and key skills
• Chapter 7: Metacognition
• Chapter 8: Linking facts and concepts
• Chapter 9: The role of language, vocabulary and symbols: Communication and perspectives on communication
• Chapter 10: The inconsistencies of maths and their impact on learning
• Chapter 11: How to use materials and visual images
• Chapter 12: Two visual methods
• Chapter 13: Anxiety and withdrawal
• Chapter 14: Assessment and diagnosis of mathematical difficulties
• Chapter 15: Classroom management
• Chapter 16: Bringing it all together
• Appendix 1 What an 11-year-old is expected to know
• Appendix 2 Books and resources
• Index