The Effectiveness of Mathematics Teaching in Primary Schools

Lessons from England and China

Zhenzhen Miao, David Reynolds

• Publisher: Routledge
• Year: 2017
• Print ISBN: 9781138680326
• eBook ISBN: 9781317191063
• Edition: 1
• Topic: Education
• Subtopic: Education General

The Effectiveness of Mathematics Teaching in Primary Schools: Lessons from England and China provides a unique insight into the mathematics classrooms of these two countries and arrives at a time when the world is eager to know how Chinese learners consistently excel at learning mathematics and other core subjects.

Showcasing the kinds of teaching methods that work within and across countries, this book presents a rich collection of views, including those from teachers, their native colleagues, their foreign colleagues and the researcher, regarding the quality of mathematics teaching today. Interweaving scientific results about teaching and learning evaluations with multiple perspectives of various roles in and out of the classroom, Miao and Reynolds offer insights into how and why different approaches of teaching have led to different learning outcomes in mathematics internationally. Building on rigid and robust analyses of the most up-to-date data in England and China, the book indicates that it is through changing teaching rather than changing teachers that mathematics learning can be improved, because it is what teachers do in the classroom that really makes a big difference.

Containing four decades of wisdom from the field of teaching effectiveness research, this book is essential reading for all who want to improve the quality of mathematics teaching worldwide. This book is particularly relevant for educational researchers, postgraduate students and teachers, as well as school leaders, policymakers and parents.

1 The effectiveness of mathematics teaching study

Chapter overview

• Rationale and questions
• Contexts and schools
• What’s in the book?

In this increasingly digitalised and globalised world, the quality of education in mathematics and other STEM subjects predicts the competitiveness of a country’s future workforce. International comparative studies on achievement have repeatedly identified the disparity in mathematics performance between East Asia and the West (Mullis et al., 1997; Mullis, Martin, & Foy, 2008; Mullis, Martin, Foy, & Arora, 2012; Mullis, Martin, Gonzalez, & Chrostowski, 2004; Reynolds & Farrell, 1996) and between China and England (Lapointe, Mead, & Askew, 1992; Lapointe, Mead, & Phillips, 1989; OECD, 2010, 2013).

Evidence from empirical studies has consistently proved that schools make a difference and teachers have a much larger impact upon pupils’ achievement than do schools (Hill & Rowe, 1995; Reynolds & Teddlie, 2000; Willms, 2000). It has been argued that it was necessary to get into the classroom and see what actually happened if one wanted to improve learning (Hiebert et al., 2003). This study thus set out to (1) investigate teaching factors that work across England and China and make a difference in pupils’ mathematics learning outcomes, (2) understand how different roles in and beyond classrooms view mathematics teaching across two countries and (3) interpret the interconnections between hard evaluations of teaching and learning and soft perspectives of practitioners and the researchers.

This introductory chapter reflects upon the importance of mathematics, explains the research rationale and questions of the study, puts you in the national and local contexts where the teachers and pupils in the study come from and finally offers an overview of the remaining chapters of the book.

Rationale and questions

First of all, why mathematics? As one of the most important bodies of knowledge, mathematics has developed across cultures and over millennia. It is the oldest school of human thought, alongside philosophy (Krantz, 2010). The mathematical historian, Carl Boyer, affirmed in his work, “that the beginnings of mathematics are older than the oldest civilisations is clear” (Boyer, 1968, p. 7). As far as archaeologists have discovered, the formal application of mathematics can be traced back to the era of Old Egypt and Old Babylonia around 3200 BC (Nuffield Foundation, 1994, Ch. 2). Since the era when Arabians drew together the two lines of mathematics – the East (ancient India) and the West (ancient Greece) – through translation and introduced it to Europe, mathematics has gradually become an international body of knowledge (Boyer, 1968; Hodgkin, 2005).

Throughout history, mathematics has come from humans’ observation of the world and guided human beings in tackling real-world problems, providing powerful tools to the development of all sciences. In today’s world, mathematics remains a crucial part of almost every branch of science, including physics, chemistry, biology, architecture and electronic and computer science. For its importance in the past, present and future, mathematics is regarded, in schools across the world, as a core subject that provides essential foundations for other school subjects. The importance of mathematics makes it important that children be well educated in the subject. Such an importance also results in the increase of the number of educational studies focusing on the quality or process of mathematics education over the past 50 years. The following section will explain why a new study like this is so much needed.

International comparative surveys, conducted by the International Association for the Evaluation of Educational Achievement (IEA) and the Organisation for Economic Cooperation and Development (OECD), have been regularly evaluating educational outcomes of core subjects, such as mathematics and science, cross-nationally. Although the target ages of pupils those international surveys choose to focus on are different from one another, they all include mathematics as an assessed subject. The results of international assessments draw much attention and raise questions as to how educational effectiveness differs amongst nations and cultures (Hiebert & Stigler, 2004). The number of international surveys on maths learning outcomes is much greater than that on maths teaching practices which have been mainly looked at on a within-country basis.

Empirical evidence from teacher effectiveness research (TER) consistently reveals positive correlations of certain teacher behaviours with pupil learning outcomes/gains in mathematics and other core subjects (Muijs & Reynolds, 2011). However, over the past four decades, such evidence has been limited to the national level. In this increasingly globalised world, there is a lack of international attempts to reshape educational research agendas, evaluate which teaching variables “travel” across nations and which do not, “tap the full range of variation”, generate “more complex, sensitive and multi-layered explanations” of differences in learning outcomes, and subsequently inform classroom innovations, as for the case of school effectiveness research (SER) (see Reynolds, Stringfield, Teddlie, & Creemers, 2002b, pp. 5–6).

This study, therefore, seeks to fill the research gap by collecting and analysing data across countries to find up-to-date evidence on the effectiveness of mathematics teaching (EMT) that could travel confidently across countries as mathematics itself did, does and will undoubtedly continue to do.

Applying a combination of convenience and stratified sampling strategies, the study collects data in two countries – England and China – and involves maths teachers and their pupils aged 9 to 10 (i.e. Year 5 in England and Grade 4 in China). In each country, a city from the medium-to-high level stratum was chosen, and within each city (Southampton, England and Nanjing, China), schools were sampled from the average stratum. Whilst detailed sampling techniques, procedures and rationales are illustrated in Chapter 4, the next section of this chapter draws a picture of the research contexts.

As will be reviewed in Chapter 3, the area of TER is bounded by national borders, has a strong quantitative characteristic, but lacks rich descriptions (Reynolds, Sammons, De Fraine, Townsend, & Van Damme, 2011; Reynolds et al., 2002b). To make meaningful contribution to the area of TER and to children’s education in mathematics worldwide, this study is intended to fulfil the research purposes as follows:

• To evaluate and correlate the quantity and quality of mathematics teaching with learning outcomes cross-nationally;
• To collect multiple voices on the effectiveness of mathematics teaching;
• To connect hard measurement with soft views and throw light on the improvement of mathematics teaching and learning within and across countries.

These purposes then lead to the formulation of research questions to be followed and the design of research methods in Chapter 4.

Motivated by the learning gaps of school mathematics between pupils across countries in international performance surveys, the study aims at measuring the teacher effects in two countries’ mathematics lessons on pupil learning outcomes with internationally validated instruments and collecting multiple views regarding the effectiveness of mathematics teaching. A list of methods was applied to collect and analyse data so as to answer the following questions:

RQ1	What are the correlations between various teaching approaches and learning outcomes in mathematics across two countries?
RQ1a	What is the quantity and quality of mathematics teaching in classrooms across two countries?
RQ1b	How do children perform in two standardised mathematics tests?
RQ1c	How does teaching correlate with learning across mathematics classrooms in the two countries?
RQ2	How do different roles in and beyond classrooms perceive the effectiveness of mathematics teaching in the two countries?
RQ2a	How does the researcher interpret the quality of mathematics teaching in the two countries?
RQ2b	How do individual teachers view the effectiveness of mathematics teaching in general and that of the specific lesson they delivered for observation?
RQ2c	How do groups of teachers view the effectiveness of two mathematics lessons – one from England and the other China?
RQ3	How does the rigid evaluation of teaching and learning (RQ1) connect with the diverse perceptions of different roles about the effectiveness of mathematics teaching (RQ2)?

This book is a report of the EMT project through which we seek answers for the above questions.

Contexts and schools

Now we will have a close look at the research contexts – the participating nations, cities and schools and the comparability between them.

England and China

As follows, a brief introduction is given to England and China, in terms of geography, population, culture, politics, education and economy. Comparability of the two countries is explained as well.

Geography

England is the largest of the four countries in the United Kingdom of Great Britain and Northern Ireland (the UK or Britain). The area of England is 130, 281 km² – more than a half of the total area of the UK (Office for National Statistics, 2013b). It is bordered by Scotland to the north and Wales to the west and surrounded by the Irish Sea to the northwest, the North Sea to the east, and the English Channel to the south. Divided by the 33-km English Channel from France, England is the nearest country of the UK to mainland Europe. The People’s Republic of China (generally called China) is located in East Asia, between latitudes 18° and 54°N,...

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Contents
• List of figures
• List of tables
• Acronyms and abbreviations
• 1 The effectiveness of mathematics teaching study
• 2 Growing apart: worldwide pursuit of effective maths education
• 3 Four decades of educational effectiveness research in the West
• 4 Research paradigm, design and methods
• 5 Children and their maths teachers
• 6 Evaluating and correlating maths teaching and learning
• 7 Seeing maths teaching through different eyes
• 8 Connecting the dots
• 9 Improving maths teaching cross-nationally
• References
• Index