Table of Contents Page
Chapter 1 – Introduction
1.1 Rational and Background _____
1.2 My Role in Education _____
1.3 Dissertation Structure _____
Chapter 2 – Literature Review
2.1 PISA Aims and Limitations _____
2.2 PISA League Tables _____
2.3 Examining the Data _____
2.4 UK response to PISA _____
2.5 Literature Review Guide my Research _____
Chapter 3 –Proposed Research Methodology and Research Design
3.1 Research Paradigm _____
3.2 Research question _____
Is teaching Mastery Maths effective?
Chapter 1 Introduction: (650 words)
1.1 Background and Rationale
In 2014 the United Kingdom (UK) hosted a total of 93″,419 Chinese students. This was also a sharp increase from the 2002 figure of 36″,026 (Cebolla-Boado et al., 2018). The amount is only a small percentage of the huge total population but still a sizeable number, mostly at the age aged 16 years and over. Yet in the same year, English primary schools had just rolled out their new curriculum with a focus on a Singapore based ‘mastery approach’ in mathematics. This news maths approach was an attempt to close the gap with them in international league tables at a young age, so that they will be better equipped with problem solving skills by the time they reach 16 years old and over (Brunskill, 2016). These apparent contrasting actions reduce the clarity on which education system worldwide is the most effective and how easily it is to compare across cultures and subjects.
The mastery roll out in the UK caused early confusion amongst teachers. Two years after the roll out, 20 teachers all had different explanations of what it meant to them (Brunskill, 2016). He found that teachers had their own ideas and thoughts about what it meant to them, which was mirrored well with the department of education (DfE) making an extra £41 million available to speed up the roll out of this approach to the 8″,000 primary schools. This deeper learning approach is being rolled out by Education Minister Gibb by allocating the money to the National Centre for Excellence in the Teaching of Mathematics (NCETM) and their 35 school led centres to change the cannot do maths culture (Gov.uk, 2016). The change in teaching strategy was influenced from international league tables which show the UK to be lagging behind Singapore and Shanghai (in China) (Brunskill, 2016). He also stated that only a whole cultural change in maths would bring it into the 21st century were reasons given by Gibb to bring in such a large scale approach.
1.2 My Role in Education
This study will seek to analyse the new approach in a school in central England during its’ first year of implementation to analyse the effectiveness. As a current maths leader within a primary school setting, it is important to extend and improve upon subject and pedagogical knowledge. Training, studying and teaching for five years in the same county can lead to a small range in ideas, so the aims of this study will be to broaden teaching styles and deepen maths subject knowledge. This case study will also aim to provide solutions into how effective mastery maths is in a primary school setting. This then directly to affect my own practice and those teachers whom I guide as a subject leader.
1.3 Dissertation Structure
The literature review will examine background research and government policy into maths teaching worldwide. As well as this theory analysis, comparisons will be examined between countries and variation in practical teaching methods.
The methodology section will be a case study of KS2 primary school children teaching mastery maths. This will include children’s attainment data from my class of year 3 and 4 [20 children in 3/4] as well as year 5 and 6 [26 children in 5/6] in the second class using mastery maths. Also examined will be attainment data from last year without mastery maths, and this academic year, to be compared and scrutinised for variations and potential improvements. Finally the case study will also include an interview with year 5/6 teacher and student voice feedback from children learning with the new style of pedagogy.
A detailed analysis was chosen to directly help benefit my future practice in leading maths at the school. For those purposes, qualitative research has been selected to gain maximum scrutiny as possible, instead of comparing with a range of schools which may have many other alternating factors which affect their outcomes (Santiago-Delefosse et al., 2016).
Chapter 2: Literature Review (3360 words)
2.1 PISA aims and limitations
Since the year 2000 the most recognised basis for comparing students across countries has been the run by academics from the (French founded) Organisation for Economic Co-operation and Development (OECD) (Prados De La Escosura, 2016; Borsuk, 2015). The OECD have been conducting international comparisons of education every three years since by comparing self-run tests across 80 countries by a Program for International Student Assessment (PISA acronym). These tests have an ever growing importance of results in an ever expanding list of countries (Sellar & Lingard, 2014). The stringent PISA tests are designed for 15 year olds and compare student performance to international benchmarks on knowledge, skills and competencies (OECD, 2018a). Tests lasting two hours with questions that aim to access critical thinking and problem solving instead of a specific skill which is deemed of high value in a particular country (Borsuk, 2015). This is then followed up with a 30 minutes of student questionnaire to help understand layers of information behind the outcomes (OECD, 2018a). The range in their data; from test scores, socio economic data and participant questionnaires, means different countries can take real personalised and detailed account of their education systems which will be analysed separately later in the literature review (Borsuk, 2015; Stellar & Lingard, 2014).
Carvalho, (2012) sought to understand key aims behind PISA. He found that they are part of a long term movement for institutionalising a knowledge – policy relationship by individual countries. He believes, due to their impartial principles, PISA have become highly accredited. Their key principles are based on regular systematic assessments which have directly lead to improvements in national education systems (Stellar & Lingard, 2014; Carvalho, 2012). PISA also work to understand, and internationally compare, students’ performance in relation to socio economic background, government policy choice and learning structures. They have been accredited with helping raise the attainment and quality of those education systems that which to raise their performance as a result of such data (Stellar & Lingard, 2014).
Limitations with PISA
However, before analysing league tables, and reactions to domestic policies, it is important to put into perspective the potential fragility when making whole scale assumptions based off PISA testing (Yariv & Lefstein, 2014). The OECD are trying to compare different educational systems but there are difficulties which can blur these conclusions from being so replicable. Chinese immigrants score higher than Australian students in attainment even when they are using the same educational system (Yariv & Lefstein, 2014). In finding this contrasting information, they ironically used PISA’s own data taken from 15 year olds in Australia. They instead believed that cultural and historical factors such as family upbringing were as apparently evident as the policies and educational structures. They found that Asian families place a high value on education with 60% of (the former Chinese colony) Shanghai students attending out of school maths tutoring. When comparing Shanghai student PISA attainment scores with the group that migrated to Australia, the Chinese and Shanghai scores were more aligned that the native Australians. These findings taken by independent academics, are generally ignored by nation’s policy makers who to focus on changes that can be made to educational structures (Brunskill, 2016).
Alexander is another academic who disapproves of the simplicity into criticising educational structures when comparing nations (Alexander, 2012). He refers back to many drastic structural changes in primary education that span nearly 100 years. By focusing on the PISA era of international league tables more thorough analysis can be made. The application of the New Labour standardised textbook strategies for all children to use, reducing classroom differentiation and confusion, did not raise international league table positions. The change of governance in England led to a reducing of essential subjects in the national curriculum. This policy change was more difficult to fathom because it was an attempt to replicate what ‘high performing jurisdictions do’ without any reference to what essential subjects are (Alexander, 2012).
The impartial primary education professor is Chairman of the Cambridge Primary Review Trust, which is England’s biggest enquiry into primary education for over forty years (Alexander & Doddington, 2010). The review published 31 interim reports into a full range of primary school issues, resulting in Alexander becoming a credible source of debate on education in England. He does acknowledge the improvements in PISA from previous organisations attempts to compare across nations. It is rather their disproportionate influence they exert on policy makers (Alexander, 2012). He emphasises profoundly that they are down playing the complex interplay of culture variation to help massage policy makers urge for a quick fix to raise economic performance (Alexander, 2012).
2.2 PISA league tables
Their latest worldwide results in 2015 show the countries given average scores for each of the three subjects. Obviously this report will focus on the maths league table for purposes of supporting the research question. The methodology of the 2015 test was replicated in all 72 countries, except in 57 who used laptops, and the remaining nations completed the same test with paper and pencil (OECD, 2015, page 178).
Countries were then given scores based off their results, which were then comparable in positions. The top 30 countries or economies are shown in figure 1 below. The mean score across all the different countries and economies was 490 (OECD, 2015, page 179). Therefore this is the number I have chosen to stop on, with it showing the UK I did not see personal value for this study in continuing.
China could potentially cause confusion with multiple positions on the list. Due to its billion people population has been broken into smaller divisions for PISA rankings with primary education being regulated at these provisional – level administrations (OECD, 2016). Hong Kong and Macao are independent special administrative regions and positioned separately while the four municipalities and provinces that took part are a collective position of 6th and account for less than a quarter of China’s whole population (OECD, 2016).
Position Country / Economies Mean Score
1 Singapore 564
2 Hong Kong (China) 548
3 Macao (China) 544
4 Taipei (China) 542
5 Japan 532
6 Bejing – Shanghai – Jiangsu – Guangdong (China) 531
7 Korea 524
8 Switzerland 521
9 Estonia 520
10 Canada 516
11 Netherlands 512
12 Denmark 511
13 Finland 511
14 Slovenia 510
15 Belgium 507
16 Germany 506
17 Poland 504
18 Ireland 504
19 Norway 502
20 Austria 497
21 New Zealand 495
22 Vietnam 495
23 Russia 494
24 Sweden 494
25 Australia 494
26 France 493
27 United Kingdom 492
28 Czech Republic 492
29 Portugal 492
30 Italy 490
Figure 1 Maths League Table, (OECD, 2015, page 179)
2.3 Examining the data
I did find it of value to examine further the two missing countries from the world economies top eight from this list (Caliendo et al., 2017). This is noticeable because the Organisation for Economic Co-operation and Development was originally founded on the basis of helping stimulate economic progress (OECD, 2018a) and therefore these two missing countries are unfair to completely exclude from the records. Caliendo et al., examined internal and external distortions linked to economic within each country and separate rankings were created for each. The same countries were amongst the world leading the economies regardless of factors changed in measuring, with minor change in ordering. Firstly the USA scored a below mean average 470 and finished 40th place, which brings to question the economic importance and value of the PISA testing. Secondly India did not participate in the study after two regions attempted the 2010 study and finished below 70th.
US response to the results
When examining case studies into which countries use results to help guide and reform their education systems it is not always lower performers who use the data to strive to improve. Euope’s top performer Switzerland have introduced reforms into social equity as a result of PISA outcomes whereas the USA consistently records below the OECD average and pays very little political and public attention to the results (Bieber & Martens, 2011). They found with no national curriculum or national standards at a federal level, the US has a schooling variations from decentralised state to state run education. By no generalisation can it be claimed that the USA don’t care about the PISA tests and in fact many individual academics and school leaders do use the results at a school comparison level (Borsuk, 2015). This particular Wisconsin school applied and found initially found it difficult to get selection for the 2012 PISA test sample schools without reason. Which itself could cause into question how accurate it is to replicate generalisations of a nation as large as the USA off a small sample of chosen schools.
With India being the second country in the world with a billion inhabitants, two states of Himachal Pradesh and Tamil Nadu participated in 2009 PISA testing representative of the whole nation (Areepattamannil, 2014). With around 70 million students in these education systems, 80% of the tested participants were performing below PISA expected level, which resulted in India scoring positions in the 70s across the various subjects. Examining the tests and states he found clear rote learning and not a competency based approach which is put forward by PISA The study even examined differences found between one parent and two parent families and found it varied the outcome of children’s attainment. Possible explanations were that one parent families had children spending long hours with grandparents who were pushed and encouraged education to a higher priority than working parents. This adding more layers and complexities to an already complex generalisation of international league tables. India’s low attaining position in the league table lead to it subsequently withdrawing from PISA and the ministry of education cited that the test had socio – cultural disconnect between the questions and the Indian students (Indian Express, 2018). The Express continues further by explaining the Indian Education Board have agreed to re-enter for 2021 testing without the agreements on adapting the tests that they were seeking. One interesting note to be taken from this is the changing of state that will enter the next testing. Chandigarh will be the only testing state for the nation in 2021 (Indian Express, 2018). The city only holds one million population (a tiny fraction of the billion overall) and is currently one of the top states or union territories in the country (Indian Express, 2018; Census India, 2011).
Variations within cultures
Both huge disparities in children receiving education and being able to self-select which student’s take the tests are important factors to bring when looking at the internal UK governance and reactions to the PISA testing. It is also important not to assume that these disparities in standards only happen in such populous countries. It has been found by PISA’s very own data collection that the difference in students’ scores can vary from as much as 502 to 437 when comparing the north – south divide in Italy, a country smaller than the UK (Bulle, 2011). She examined data taken from multiple countries across the world and was very damning of a ‘reductionist comparative logic’ by western countries who take simplified data to define a whole system for themselves. Her detailed analytical criticism mostly focused on France and their obsession with the statistics, but her generalisation claims were quoted at the western countries in general. Thus, including the UK and its new primary curriculum changes in a time of international PISA enthusiasm.
Prior to these PISA lead changes research into the delivery of teaching had shown wide variety across cultures and very little variety into teaching within cultures (Stigler & Hiebert, 2009). They came to similar views as Gibb by videotaping lessons across United States (USA), Germany and Japan they found teaching in the western culture is limited and focused on repeated practice of narrow procedural skills. While teaching in eastern culture spends much more time focusing on solving challenging problems and discussing how mathematical concepts help support this. Importantly for the UK it really emphasized how little variation there is in one culture and how vast it is across cultures. Stigler & Hiebert managed to fully video record lessons with transcripts with locals help in each country. These were brilliant to compare like for like countries, but unfortunately it did take over 10 years from the start of recording until the publication which is a large time frame for procedural changes. This widespread view does fail to explain how some countries can have such a variety in scores though, such as found by Bulle (2011). Instead it further clouds the generalizable blanket concepts put forward by academics which refined qualitative analysis fails to support.
2.4 UK’s reaction
UK’s education authorities
Before examining how PISA tests are received in the UK it is important to note that there are four different school authorities: England, Wales, Scotland and Northern Ireland (Gov.uk, 2012). Each authority is then broken into five stages depending on the age of the student: early years, primary, secondary are the compulsory three stages across all authorities. There are variations between the authorities, three finish primary school at the age of 11 with the exception of Scotland’s which lasts until 12. Wales use teacher assessments instead of testing like the remaining three (Gov.uk, 2012). This paper focus on England Primary Schools reaction as it is most beneficial to the researcher within this study.
Early Years comparisons
With early years being the only stage prior to primary then I believed this to be worth noting pedagogical differences between England and alternative leading PISA scoring. While government in England have made no major attempts to overhaul the early year’s curriculum from foreign comparisons, they continue with the western based culture of regular learning through play experiences (Zhang & Pelletier, 2012). Eastern cultures, including China have always focused on academically oriented, teacher directed tasks. This Chinese study was examining the views of both cultures and claims that the Chinese have made progress in the last few decades as they are now introducing some child initiated study by replicating the Western style. The Chinese early childhood teachers are finding the transition difficult because they have never experienced such freedom as a practical reality themselves. This may b