at a young age does not to underestimate the frequent higher levels of mathematical content that the Chinese regularly use (Wang et al., 2017). They found by adult staged higher education, the Chinese are much more likely to be encouraged at abstract problems which involve deeper learning because of their over exposure throughout. They found the English curriculum to have children more at the process stage of situation solving at a much shallower level instead of the Shanghai mathematical structures.
The common practice in the UK is to answer questions in which the background mathematical structure is invariant but the numbers and images vary (Al-Murani et al., 2018). The process of repeating the same format but changing a small digit has been common practice in the classrooms in teaching in England until the roll out of the Chinese based approaches. In this study three teachers who studied the Chinese models then recorded their lessons and analysed performances with the new style. One teacher showed multiplication as repeated addition, arrays, context with centre metres, pictures with practical examples such as eggs as well as word based challenges. All these helping to show the children the different variety in which contexts could appear. The teacher in the study found some misconceptions within the variety of formats while some were able to use the word commutative to express the organisation of the arrays. All these were credited for supporting a deeper understanding of multiplication.
Representations and Structure
Representations are used to help expose the mathematical structure being taught.
Figure 3 representation of number for problem solving (Jerrim & Vignoles, 2016).
They found a greater emphasis on bar models in Asian mathematic problem solving. The questions 42 – 2 is classified as linear but by seeing the questions in representations it helps to show that subtraction is less than the total as well as 40 + 2 being the inverse.
Maths fluency in England is often mistaken for purely memorising as many facts as possible (Boaler, 2015). The 2014 curriculum looks to give students the impression that unless they know many facts then they cannot succeed in maths. This unproductive way was highlighted when MP Byers mistakenly recalled the incorrect fact to a multiplication question that he was asked. Instead Boaler believes more understanding of number sense in in a variety of ways will increase competence. She worked with American academics and found they too have poor number sense, taught from a young age. Instead she believes that students should show multiplication facts in a variety of ways so that they never forget the answer but understand the process of finding it out.
Figure 4 Number fluency (Boaler, 2015).
The essence of progress is shown with breaking concepts into small key components (Al-Murani et., 2018). Lessons are based on introducing the learning on a simpler concept and many small gradual steps so that all the students understand the levels and the process behind the deeper challenges later in the lesson. This level runs through all the areas of learning, as shown in the NCETM figure above. The mastery roll out involved not setting children into ability groups but the correct coherence during a lesson can help scaffold the lesson for all children to have the prospect of achieving.
2.5 How the literature has helped me to refine my research aims and research question
The literature has helped me to understand that the government’s mastery maths initiative is not as linear as I expected by reading the English perspectives prior. There are a range of complex issues which can affect the outcome. Social factors of the sample students selected for the tests which then are magnified to represent much larger regions. The variation of national teaching and delivery of maths causes complexities in understanding the singular format of test questions which some nations have claimed disadvantages them. Finally, the issue of countries cherry picking their favourite parts of other education systems; like England replicating Shanghai and Singapore’s primary education maths format, without assessing the huge variations in the early years teaching prior the subsequent knock on effect.
Primarily, for this study I will be evaluating:
• Whether the introduction of mastery maths at a primary school in the West Midlands in England increases attainment and understanding of maths.
As subsidiary results I will also aim to evaluate:
• Whether mastery maths is more popular with the children who took part in the new teaching style.
Chapter 3 –Proposed Research Methodology and Research Design
3.1 Research Paradigm (336 words)
Paradigms are a concept in which scientists make sense of their world and realities. Developed by Kuhn in 1962, they are ever changing as our society and science evolve (Kelly et al., 2018). Kuhn’s ideas that philosophy and sociology of science are eternally intertwined has led to numerous recognised research models. It is important to be able to locate the research paradigm within which the research sits. I am taking a pragmatic approach to this piece of research (Kelly et al., 2018). This is because a professional issue primarily drives the research. However, I also have a personal interest with mostly quantitative research.
In terms of epistemological position, this research is largely interpretive. This emic approach to relativist ontology is valued as it takes on the culture of the community to help construct knowledge at various levels that can only be achieved because of researcher participation (Packer & Goicechea, 2000). I have chosen an inductive approach for my professional development I do not believe realist, quantitative data alone will be beneficial to bring depth in context for my work place. However, by this study being a mixed methods interpretivist research, my research will accept that individuals construct their own reality so multiple interpretations of the world will really exist (Wignall, 1998). This allows qualitative data taken from the school policy, children’s views and interviews from the teacher to be combined with quantitative attainment data from children’s maths. This will triangulate the data, add more validity, and enhance the findings (Robson, 2011).
Unfortunately, there are limitations with any research method. When an individual researches an organisation that they participate in then it is more difficult to obtain accurate data, especially where there are politically sensitive issues, as this creates natural resistance of individuals taking part (Walker & Dewar, 2001). Whilst the data will have limited replicable generalisations across large-scale UK schools, by using accurate child attainment data and feedback from a head teacher anonymous child questionnaire then reasonable steps will be taken to reduce the effects mentioned by Walker & Dewar. This will need to be of though when analysing the teacher interview.
3.2 Research Question
In order to answer my research question and subsidiary questions I have set out my intended research plan in figure 5.
Research question Subsidiary questions Data sources Research methods
Does the ‘mastery in mathematics’ government funded initiative improve subject understanding in a rural village primary school in England?
1) Has school attainment data improved since the roll out of the initiative • Attainment data from over the last 2 years. • Data analysis (quantitative)
2) What do participating teachers view of the new teaching initiative? • Interview with year 5/6 teacher. (Teacher K)
• Mixed methods approach (qualitative)
3) Do children feel a benefit to the new teaching and their understanding of maths? • School council students: focus group.
• Secondary data analysis
Figure 5 A breakdown of the research questions
3.3 Data source
Included are three different data sources, which are in the table above.
To answer one of the subsidiary questions using semi-structured, in-depth qualitative interview helps uncover participant’s opinions and helps emphasis their areas of particular value (Marshall & Rossman 2006). This should help my study achieve more depth in understanding of the teachers’ perception and experience when answering my main research question.
A non-statistical analysis will include a face-to-face interview with the year 5/6 teacher (Teacher K), asking her views on the mastery approach, which areas she has found worked well and her thoughts on the children’s responses and progress. Teacher K was selected to interview as the other teacher using the new mastery approach in her teaching. She was pre warned that her responses will remain confidential within the study as part of her consent form, as a way of building more honesty in her responses (Yow, 2005). Along with that, good eye contact and being reminded that she could withdraw at any point if she changes her mind (Robson, 2011).
By using a semi-structured interview instead of a questionnaire, I aim to gain her views, perceptions and explaining of how the children reacted at various stages (Yow, 2005). A fully structured interview will not allow her the freedom to respond with depth in the way in which I want her to talk freely about her views. A closed interview can potentially lead to a bias with me guiding her answers (Alweis et al., 2015), that is unnecessary with only one participant to interview. Her views alone will not form the form the evaluation of the study, but it will help contextualise the attainment data.
Whilst I am using a qualitative study for my personal examination into a small sample view on mastery in maths, I acknowledge there are drawbacks to this method. My results will never comparable to make large generalisations because of the use of qualitative research (Marshall & Rossman, 2006). Interviews are also time consuming and quality of the research relies on a firm relationship between interviewer and participant or they answers can remain closed and lack the depth required for high-level examination (Marshall & Rossman, 2006). I believe my level of relationship with Teacher K is strong enough for her to share personal information on the subjects in the interview (appendix 1).
After initially open to the idea of ‘phenomenological interviewing’ for multiple interviews and focusing on various stages of past and present experience, I decided against it due to limited research time on the course specifications (Bowden & Galindo-Gonzalez, 2015).
In order to answer question 3 in my research plan, I intend to use a survey in the form of a questionnaire, as a way of conducting research. This secondary source data will be using a questionnaire that the head teacher has authorised for the school council, regarding their feedback about mastery maths [need to source secondary data].
Questionnaires are widely used in research data gathering, and even when taken as a secondary source they can still help to form views and conclusions when taken in the correct context.