1
How can I develop metacognitive and self-regulated strategies to improve
mathematical reasoning and problem solving?
Submitted in partial fulfilment of the requirements for the degree of
Bachelor of Art (Hons) in Primary Education
By
April 2020
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Acknowledgements
I would like to take this opportunity to thank all those who have contributed in any
way, shape or form to the completion of this research project.
To my dissertation supervisor Deliah thank you for your patience, support and
reassurance throughout this process.
Lastly, I would like to thank my family and friends who have kept me motivated
throughout my time at university.
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Abstract
Metacognition and self-regulation strategies can be used to improve children’s
reasoning and problem-solving capabilities. Research has shown that metacognitive
and self-regulated strategies can influence children’s attitudes and attainment. This
action research project aims to determine how metacognitive and self-regulated
strategies can be brought into the classroom effectively to improve children’s
reasoning and problem-solving abilities. My research project question was chosen
as a result of school experiences but also as a result of my own personal area of
interest. Additionally, my placement school where the research was conducted has
a focus on metacognition and the effect this can have on children’s learning.
The children were at the heart of the research that took place, with all decisions
taking into account their best interests. Throughout the research, ethical guidelines
were adhered to. Participants gave informed consent and all data was collected
anonymously, whilst being stored on a password protected computer and a locked
filing cabinet in the school. Due to the children being at the forefront of this
research study all decisions were made with the children’s best interests in mind.
During this research study, ethical guidelines were adhered to. All participants gave
their informed consent, all data was collected anonymously with data being stored
on a password protected computer and in a locked filing cabinet in the school
(GDPR, 2018).
The study investigates how metacognitive and self-regulated learning approaches
can be developed and the impact these can have on children’s reasoning and
problem-solving abilities. I conclude that further research is needed to determine
how effective metacognitive and self-regulating strategies are to children’s learning.
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Chapter One: Introduction
Pg. 7
Chapter Two: Literature Review
Pg. 8
2.1 Attitudes and beliefs towards reasoning and problem-solving
Pg. 8
2.2 Problem-solving and heuristics
Pg. 10
2.3 Metacognition and self-regulation
Pg. 13
2.4 Conclusion
Pg. 15
Chapter Three: Methods and Methodology
Pg. 16
3.1 Ethics
Pg. 16
3.2 Research Strategy
Pg. 17
3.3 Methodology
Pg. 18
3.4 Triangulation
Pg. 19
3.5 Methods
Pg. 19
3.6 Sampling
Pg. 22
Chapter Four: Results and Discussion
Pg. 23
4.1 Research Cycle
Pg. 23
4.2 Reconnaissance
Pg. 23
4.3 Attitudes and beliefs towards reasoning and problem-solving
Pg. 24
4.4 Problem-solving and heuristics
Pg. 27
4.5 Metacognition and self-regulation
Pg. 30
Chapter Five: Conclusion
Pg. 32
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List of Appendices
Appendix One- Ethics protocol
Pg. 43-45
Appendix Two- Self audit
Pg. 46
Appendix Three- Interview questions for children
Pg. 47
Appendix Four- Cycle two observation
Pg. 48
Appendix Five- heuristics poster
Pg. 49
Appendix Six- Cycle three observation
Pg. 50
Appendix Seven - Children’s reflections from cycle
Pg. 51
Appendix Eight- 4R’s poster
Pg. 52
Appendix Nine- End of research questions for children
Pg. 53
Appendix Ten - Exit Cards
Pg. 54
Appendix Eleven- Dissemination poster to staff
Pg. 55
Appendix Twelve- Child friendly dissemination poster
Pg. 56
Appendix Thirteen - Independent study proposal
Pg. 57-60
Appendix Fourteen- Children responses to interview
Appendix Fifteen- Overview of research cycles
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Pg. 61
Pg. 62-63
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List of figures
Figure 1- Table of heuristic strategies ............................................................. 11
Figure 2- Overview of Singapore Mathematics curriculum (Ministry of Education
Singapore, 2012). ........................................................................................ 12
Figure 3- Action Research Cycle ..................................................................... 17
Figure 4- Attitude graph from reconnaissance stage ......................................... 25
Figure 5- Attitudes graph from end of research ................................................ 26
Figure 6- children's reflections from cycle one ................................................. 27
Figure 7- the use of a heuristic strategy .......................................................... 30
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Chapter One: Introduction
My enquiry outlines “how metacognition and self-regulated learning can improve
children’s reasoning and problem-solving capabilities”. Reasoning and problemsolving is a big part of the curriculum, not only in England (GB. DfE, 2013) but also
Singapore, America and Australia (Australian Curriculum, Assessment and
Reporting Authority [ACARA], 2017; The Common Core Standard for Mathematics,
2010; Ministry of Education Singapore, 2012). It is an important aspect in year 6
due to the SAT’s reasoning paper. During PP4, I observed a class of year 6’s
undertaking problem-solving and reasoning questions in relation to addition and
subtraction. It was clear how much emphasis teachers were placing on problemsolving and reasoning as each week there was an allocated slot to teach these in
relation to the focus at the time. However, I believe that problem-solving and
reasoning should not be taught as stand-alone lessons, instead they should be
woven throughout lessons to ensure maximum coverage and impact. My research
school has begun to use metacognitive approaches throughout their curriculum. For
these reasons, it seemed beneficial to focus my research on this area with the hope
that I can improve children’s understanding of reasoning and problem-solving
through while incorporating the school’s policy on metacognition and self-regulated
learning (Teaching and learning policy, n.d.). From the literature (Tornare et al,
2015; Larkin and Jorgensen, 2016) and my own experiences, it is apparent that not
only do children have negative attitudes towards reasoning and problem-solving but
also mathematics as a whole. These negative emotions that children have towards
mathematics, reasoning and problem-solving can often impact on the children’s
well-being.
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Chapter Two: Literature Review:
Mathematics is a key component in every education system not just in England
(GB. DfE, 2013). Mathematics offers children the opportunity to develop skills that
will prepare children to be productive in their life and in society in the 21st century
(Ministry of Education Singapore, 2012). It was noted that “mathematical reasoning
is foundational to children’s conceptual understanding” (Bragg et al 2015, as cited
in Buchheister et al 2017 pg. 7). Thus, emphasizing reasoning and problem-solving
as a critical element of a mathematician’s instruction. Such thinking is illustrated in
government curriculum documentations including the English National Curriculum
(GB. DfE, 2013), the Australian National Curriculum (Australian Curriculum,
Assessment and Reporting Authority [ACARA], 2017), the American curriculum (The
Common Core Standards for Mathematics 2010) and the Singapore Curriculum
(Ministry of Education Singapore, 2012). The American curriculum has strands that
focus on “problem solving, reasoning and proof, communication, representations
and connections” (The Common Core Standards: Mathematics Standards, 2010 pg.
7). Mathematical reasoning refers to the ability to analyse mathematical situations
and construct logical arguments (Ministry of Education Singapore, 2012; Stein and
Burchartz, 2006). It is a skill that can be developed through the application of
mathematics in different contexts. Mathematics in the National Curriculum (GB.
DfE, 2013) has 3 aims; to ensure children become fluent in fundamentals of
mathematics, can reason mathematically following a line of enquiry (making
relationships, developing an argument and using justification and proof with
mathematical language) and be able to solve problems by applying their
mathematics to routine and non-routine problems.
2.1 Attitudes and beliefs towards reasoning and problem-solving
Neale (1969 as cited in Ma and Kishor, 1997) defined attitudes towards
mathematics as a liking or disliking for the subject, engagement or avoidance of
mathematical activities and one’s belief that they are good or bad at mathematics.
Educators need to encourage children to develop positive attitudes towards
mathematics as it is believed that children learn more effectively when they are
interested in the subject (Suydam and Weaver, 1975). Research has found a
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relationship between attitudes towards mathematics (ATM) and mathematical
achievement (MA) (Kiwanuka and Van Damme, 2016; Ma and Kishor, 1997).
However, there is no conclusive evidence as to whether or not ATM causes MA or
vice versa. Kiwanuka and Van Damme (2016) found that children who enjoyed
mathematics reported positive ATM, valued the subject more and achieved greater
MA. Kiwanuka and Van Damme (2016) recommended that educators improve
attitudes of children through programmes and varying strategies and continuously
reinforce positive attitudes in order to impact children’s MA. Elçi (2017) identified
several practices that educators can put in place in order improve children’s
attitudes. For example, work should be suitable to the children’s cognitive demand
level, no time limits on their work, mistakes are welcomed as long as the children
learn from them, be able to express their honest opinions and mathematics should
be altered to become fun.
Schoenfeld, (1985) illustrates that one’s beliefs and attitudes towards mathematics
can impact how they approach a problem, the length of time they will spend on the
problem and the amount of effort they will put into working on it. Problem solving is
very demanding and time consuming as it entails following different avenues and
using varying strategies until a solution can be reached (Schoenfeld, 1985). A
belief that children have which can be counterproductive to problem solving is the
belief that problem solving is not enjoyable. McLeod (1994 as cited in Stylianides
and Stylianides, 2014) implies this belief stems from problem solving requiring high
cognitive demands which can cause children difficulties which can result in failure.
The literature surrounding children’s attitudes and beliefs has led to the design of
interventions. These interventions were designed to have a positive impact on
children’s beliefs and attitudes. However, the majority of these interventions were
conducted over extended periods of time making it difficult to be used in certain
settings where educational programmes are already in place (Stylianides and
Stylianides, 2014). This suggests that in order for educators to have an impact on
children attitudes, these interventions need to begin at an early age (Stylianides
and Stylianides, 2014). After identifying a gap in the research Stylianides and
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Stylianides (2014) developed the ‘blond-hair problem’ which is a short 75-minute
intervention designed to have a positive impact through a short intervention. The
intervention was successful among teachers at an American University at impacting
problem-solving attitudes and beliefs (Stylianides and Stylianides, 2014).
Research conducted by Hwang et al (2017) found a relationship between children’s
confidence in mathematics and mathematical reasoning. Their study investigated
the relationship between children’s attitudes and mathematical reasoning skills in
US and Finish schools. Three contextual variables were considered during their
research: liking mathematics, valuing mathematics and confidence in mathematics
(Hwang et al, 2017). Confidence in mathematics showed the strongest relationship
out of all the variables. Through higher levels of confidence, there is a greater
chance of positive beliefs in ability which could lead to positive attitudes. Hwang et
al (2017) highlights that positive attitudes and beliefs can allow children to reason
through a problem unhindered and therefore have a higher chance of success. As
the children’s reasoning ability begins to improve over time, they can develop
conceptual understanding and mathematical ideas which can continue to develop
their confidence but also impact on their achievement. Hwang et al (2017)
acknowledge that there are limitations and implications with their research, noting
that cultural and social factors can impact on children’s attitudes and achievement.
2.2 Problem solving and heuristics
“Problem-solving is at the heart of mastering mathematics” (Drury, 2018 pg. 1).
Similarly, in Singapore, problem-solving is the focus of the mathematics curriculum.
They believe that the learning of mathematics should focus on understanding. Only
with understanding can children begin to reason mathematically and apply their
mathematics to a range of problems not limited to the classroom. The Ministry of
Education Singapore (2012) defines mathematical processes as the process skills
that are involved in children acquiring and applying what they have learnt.
According to the Singapore curriculum (2012) the process skills include reasoning,
communication and connections, applications and modelling, modelling and thinking
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skills as well as heuristics (see figure 2). They stress that all these skills are
important for mathematics but also for life beyond school.
In the history of mathematics, as well as mathematics teaching, problem-solving
has always played an important role because creative mathematical work demands
actions of problem-solving. Thus, it is not surprising that problem-solving has been
analysed from many different viewpoints and in different fields (Stein and
Burchartz, 2006). Lester (1994) provided a large number of studies on problemsolving, focuses on the heuristics process. Polya (1957) observes that heuristics are
a strategy that problem solvers can utilise to gain insight into the problem
(Schoenfeld, 1985). Polya (1957) suggests that heuristics can become a common
strategy used by children to tackle a problem where the outcome is not obvious.
However, children require guidance on how to understand and implement these
strategies.
Figure 1- Table of heuristic strategies
As seen in figure 1 the use of heuristics provides children with different strategies,
they can use to break down the problem in front of them. It provides them with
different avenues they can take to come up with a solution, whether it is through
creating their own representation or solving part of the problem so that it is more
manageable. The idea of heuristics links closely to the National Curriculum in
England and its idea that problems can be solved by breaking down the problem
into a series of simpler steps and persevering in seeking solutions (GB. DfE, 2013).
The Singapore curriculum (2012) has always referred to the mathematics
framework. Although it was introduced in 1990, it is still relevant to mathematical
education to date. The framework focuses on using mathematics to solve problems
and offer guidance on how teachers can facilitate the teaching, learning and
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assessment of mathematics in varying areas. Thinking skills and heuristics are
essential for mathematical problem-solving (Ministry of Education Singapore,
2012).
Figure 2- Overview of Singapore Mathematics curriculum (Ministry of
Education Singapore, 2012).
Teachers can facilitate and model the use of heuristics to the children, ultimately it
is down to the children to make use of the heuristic strategies where necessary.
Schoenfeld (1985) conducted research which highlighted the fact children were not
creating representations or using heuristics to aid in the problem-solving process
due to a lack of confidence and their beliefs that they are unable to use new
strategies (Weber et al, 2010).
Swanson (2016) views word problems in mathematics as a medium in which
children can learn to select and apply a range of strategies. Word problems are a
type of problem-solving question that children struggle with because the question
and answer are not obvious. Word problems are used in mathematics in several
countries (GB. DfE, 2013; Ministry of Education Singapore, 2012). However,
research conducted in the United States highlighted that children showed
substantial weaknesses in solving word problems in comparison to other
industrialised countries (OECD, 2012; National Mathematics Advisory Panel, 2008).
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As a result of this research, children need to understand the cognitive mechanisms
and process that are needed when solving word problems.
2.3 Metacognition and self-regulation
“Children who understand how they learn and who can take responsibility for their
own learning, have a higher chance of achieving” (Teaching and learning policy,
n.d. pg. 15). This concept is in line with Flavell’s (1976; 1981) definition of
metacognition referring to children having an awareness of their own cognitive
processes and how they regulate them. As a result of research, the Singapore
curriculum (Ministry of Education Singapore, 2012) developed a framework (see
figure 2) in which ‘metacognition’ is deemed a main component. Children can be
given the opportunity to develop metacognitive strategies which can assist children
with their awareness of their cognitive processes and how to regulate this. In line
with mathematics, the use of metacognitive strategies can support children with an
overall approach to a problem, facilitate in selecting an appropriate strategy,
monitor their own progress and where necessary assess and revise their approach
(Garofalo and Lester, 1985; Foong and Ee, 2002; Teong, 2003). Developing
children’s metacognitive strategies enables them to become independent learners,
assess situations and be resilient with their learning. The emphasis on
metacognition in the syllabus implies that children understand what metacognition
is and what it looks like in their learning, however if other countries are to adapt
the Singapore approach then they too need to make children aware of
metacognition. The school in which this research project took place, were beginning
to make children aware of metacognition and developed learning characters to help
develop a common language for learning across the school and made it suitable to
each year group (Teaching and learning policy, n.d.). Research conducted by Yeap
and Menon (1996) noted that metacognitive strategies were used by children when
faced with an unfamiliar problem. This suggests that begin to regulate their own
learning when the outcome to the problem is not obvious.
Problem-solving is very complex and difficult for some to understand. Research has
been carried out into the role of metacognition in accordance with problem-solving
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(Garofalo & Lester, 1985; Montague, 1992; Schoenfeld, 1987). In particular, Flavell
(1976) investigated how knowledge of a task and strategy can be used to monitor
and regulate one’s own abilities. A child’s understanding of the task or question can
impact their ability to select an appropriate strategy to aid them but also their
ability to reassess the situation and be resilient with themselves. Evidence from
Schoenfeld (1985) suggests that children who are good problem solvers used
metacognitive strategies more effectively than those who struggled with solving
problems. Thus, the explicit inclusion of metacognition within the Singapore
Curriculum (2012) framework highlights the importance of metacognition in the
teaching and learning of mathematical problem-solving within its curriculum.
Schoenfeld’s (1982) work was a big step in the direction of highlighting aspects of
the problem solvers behaviour in which metacognitive aspects are likely to be
present or conspicuously absent (Garofalo and Lester, 1985). Garofalo and Lester
(1985) states that one way to study the role of metacognition in the problemsolving process is to identify a framework or model into which metacognition can be
incorporated (similar to the Singapore framework, 2012). There have been several
models of problem-solving performance, like Polya’s (1957) four phase model of
problem solving (understanding, planning, carrying out the plan that may serve
successful problem solving. Unfortunately, metacognitive processes are considered
only implicitly (Garofalo and Lester 1985) unlike the mathematics curriculum in
Singapore (Ministry of Education Singapore, 2012).
How can children use metacognitive strategies if they do not know what they are?
Montague (1992) claims that children will benefit from training first. Hutchinson
(1986) and Wong et al (1986) suggest implementing the use of self-questioning
which may lead to increased metacognition. The notion that problem-solving can be
broken down into representation and solution is a metacognitive strategy. It is a
higher order strategy that involves discrete heuristics. While they are not necessary
to find a solution, they can facilitate in finding a solution. Self-instructional training
requires considerable direct teacher time initially, the increased positive self-talk
leads to independent and improved math performance (Meichenbaum, 1977).
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Children actively involved in self- talk maintain the strategy. Incorporating the
principles of self-instructional training may be an effective intervention for those
children having trouble with problem solving.
2.4 Conclusion
The purpose of the review was to identify the research that has been conducted
into how reasoning and problem-solving is taught, the best practice that is currently
being used and to identify any gaps in this area. There has been much research and
discussion conducted into reasoning and problem-solving. Since Polya (1957), more
research has been carried out as it has become an intrinsic part of the mathematics
curriculum in several countries (The Common Core Standards, 2010; GB. DfE,
2013). In particular the Singapore curriculum (Ministry of Education Singapore,
2012) places reasoning and problem-solving at the core of its mathematics
curriculum and how to ensure children can reach mastery level in mathematics. It is
clear from the research reviewed that reasoning and problem-solving are key
elements in mathematics and in life. Metacognition and self-regulation play a role in
children being aware of their own thinking and learning process and having the
skills to approach a question and identify an appropriate strategy to use.
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Chapter Three: Methods and Methodology:
3.1 Ethics
When undertaking a research study, there are ethical implications which need to be
considered and adhered to (BERA, 2018). In accordance with BERA (2018), the
name of the school is kept confidential. Before reaching out to participants, I
submitted an ethics form. These documents were submitted, reviewed and
authorized by the ethics committee at Nottingham Trent University. This ensured
that my research investigation considered both the British Educational Research
Associations ethical guidelines for educational research (BERA 2018) and NTU’s
code of ethical practice for research (NTU 2017).
Ethical considerations assure that the researcher is aware of what is moral,
permissible and correct in terms of conducting viable research (Farrell, 2005). The
privacy of participants must be considered in terms of confidentiality and
anonymous treatment within data (GDPR, 2018), and therefore all data contained
within this research project is anonymised to protect the school and participants
identities (Farrell, 2005).
In order to ensure I was being ethical, I created a letter that outlined my role as a
researcher, the purpose of my research and their children’s rights as participants.
Within the letter it was noted that participants may choose to engage in research
but then later decide to withdraw. In this case, each participants parent was made
aware that all data involving their child could be removed from the research and
destroyed (Groundwater et al, 2015). This was made possible by having the
participants choose a pseudonym to ensure all data was kept anonymous. However,
it was later deemed unnecessary to send out individual letters and instead a note
was added onto the homework letter. The data collected will be shared with the
research school and the children throughout the process. Once all research is
completed, the research school will be given the opportunity to read the final study
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and a dissemination poster created for staff and participants outlining the results of
the research. A finished copy can be found as appendix 11 and 12.
3.2 Research strategy
Action research (AR) underpinned my methodological approach to this study,
allowing for reflections and analysis of data to be completed throughout (Robert
and Dick, 2003). Various data collection tools were used throughout this study
including work scrutiny, observations of the children, interviews with the children
and child questionnaires all of which are outlined within the ethics protocol
(appendix one). AR is a form of research used within education. It is an effective
method used by professionals conducting research as it focuses on a collaborative
approach to advance learning while having professionals in control of their practice
(McNiff and Whitehead, 2010; Cain, 2011).
Figure 3- Action Research Cycle
The AR cycle, as seen in figure 3 (Milton, Shumbera & Beran, 2010) outlines how
AR can be used by the researcher to identify the problem within the classroom or in
the literature. AR is an effective and appropriate approach to this study as it
enables the researcher to constantly gather and interpret data, identify next steps
and allows for reflections and adaptations to take place throughout each of the
cycles. This approach permits for careful considerations of the data collected and
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for the researcher to identify common themes but also any failings of the data.
Contrastingly, Scott and Usher (2011), call attention to the fact that while AR offers
opportunities for reflections to take place these findings are not always
transferrable.
3.3 Methodology
Epistemology is the study and acquisition of knowledge which can be broken down
into two sub approaches of positivism and interpretivism (Neuman, 2003). Whilst
both these approaches have their strengths and weaknesses, most of my study
underpins interpretivist values due to the nature of data and the methods used to
collect it. The main method of data collection used within this research study
consisted of semi- structured interviews and observations of the children, which
according to Clough and Nutbrown (2012) emphasise an interpretivist stance as
these methods permit the researcher to understand knowledge and construct
meanings through careful analysis.
I opted for a mixed method approach to gather the data surrounding my research
topic, in order to allow for better evaluations (Anning and Ball,2008). A mixed
method approach to research involves at least one qualitative and one quantitative
method of collecting data in a research project (Bergman, 2008). Qualitative
methods such as interviews and observations allow for individual experiences and
beliefs to be acquired. Whilst quantitative methods such as questionnaires and
surveys are effective because they can be given to larger numbers of participants
and are also less time consuming.
Educational research aims to improve the teaching and learning process; therefore,
children should be at the centre of the research, taking into consideration their best
interests. It is important to note when undertaking research with children, the
researcher must gain the consent and co-operation of school staff and parents
(Cree et al, 2002).
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3.4 Triangulation
Triangulation is the process of comparing and contrasting theories, data generated
through different methods, and different perspectives introduced by using
investigators who have differing assumptions about research (Denzin, 2009). The
use of triangulation during the research project facilitated in ensuring all data
collected was valid allowing for confidence in research data and it provides a clearer
understanding through cross checking from more than two sources. The idea of
triangulation validating data is in line with Bazeley and Kemp (2012); Greene
(2007) and Greene et al (1989).
3.5 Methods
As part of my research I had to devise a way of gathering my data in order to
provide an answer to my research question.
Historically, research was conducted on children, rather bringing the children into
the research (Darbyshire et al 2005; Mayall, 2000; O’Kane, 2000). Until recently,
children were viewed as objects to be studied. This was due to children being
viewed as unreliable, incompetent and were not viewed as experts in their own
lives (Barker and Weller, 2003;Kellett and Ding, 2004; Mauthner, 1997; Bergström,
Jonsson and Shanahan, 2010). In recent years, children have become more valued
in educational research and are now being seen as active participants who can shed
insight into the research process (Coad and Evans, 2008; Harcourt and Sargeant,
2011).
It is widely referred to in literature that interviews are an effective method used for
collecting qualitative data in educational research (Atkins et al, 2012). As with most
data collections there are advantages and disadvantages. In regard to interviews,
they are a method that allows the research to engage with the research participants
in group and individual settings. They offer face to face interactions and freedom of
speech that cannot be obtained through questionnaires and focus groups (Atkins et
al, 2012). Another advantage of using interviews as a data collection method is that
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they are flexible (Wilson, 2016) and can facilitate gathering view and opinions,
personal narratives and other varieties of information. Cohen et al (2011) states
that interviews should be conducted in a comfortable and informal setting, chairs
should be organised so that the researcher and participant are not face to face as
this can signal confrontation rather than a conversation. When conducting the
interviews, the chairs were side by side angled towards each other. In order to
ensure interviews are successful, it is useful for the researcher to ease the
interviewee into the conversation and establish their comfort zone (Cohen et al,
2011). Atkins et al (2012) and Cohen et al (2011) highlight how the use of
interviews allows the interviewer to probe, retrieve in-depth responses and the
opportunity for clarity where necessary. The opportunity for clarity is not available
when using data collection methods such as questionnaires.
After researching the benefits and limitations of using interviews, I opted to use a
semi-structured interview as a framework to identify points of comparison in the
data collected from different children within the group. Semi-structured interviews
were conducted with all the children within the group. This enabled me to
encourage participants to talk to ensure their insight was obtained (Atkins et al,
2012). In some cases, the interviews were conducted on a 1:1 basis, while other
times the semi-structured interviews took place as a group during a task. They
lasted approximately 5-10minutes and all responses were recorded through
notetaking. Interview conducted on a 1:1 basis allowed the participants to be more
comfortable and freer with their opinions, especially when discussing their negative
feelings and attitudes. However, note-taking comes with disadvantages such as,
time constraints and not being able to write down their responses in time, therefore
missing out of key pieces of information. Throughout the study, participants made
reflections that could be triangulated with observations and interview responses to
ensure validity and reliability of the evidence, especially in cases where key pieces
of information were missed. An advantage of a semi- structured interview (Cohen
et al, 2011) had to be weighed against the need to respond flexibly to each set of
responses and the freedom to explore points further where necessary. When
conducting interviews, the data needs to handled in a way which follows the ethical
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research framework and ensure the confidentiality of those involved (Atkins et al,
2012; BERA, 2018).
Powney and Watts (1987) describe the term ‘informative interview’ as an interview
in which the end goal is to gain the insights of a particular person (or persons)
within a situation (p18) as opposed to the ‘respondent interview’ (Powney and
Watts, 1987) where all control and initiative rest with the interviewer.
A multi-method approach allows the researcher to gain a deeper and broader
perspective (Huang et al, 2016). A multi-method approach is effective because
children often have difficulties expressing their views and feelings through words.
Therefore, a variety of non-verbal data collection methods can be used to motivate
the children. Observations are a professional practice used when working with
children of all ages (EYFS, 2007). They help to assess children’s progress, identify
next steps but also identify their experiences and attitudes through non-verbal
communication. Rolfe (2001) considers observations to be a useful tool to detect
behaviours and examine how their behaviour changes. Observations can either be
quantitative or qualitative (Mukherji and Albon, 2009). Within this study
observations were qualitative and were used for exploratory purposes. Observations
can be conducted in the moment and requires no advanced preparation. On the
other hand, the researcher needs to decide what should be recorded as not
everything will be relevant to the research (Mukherji and Albon, 2009).
The documentary analysis, responses from interviews and the observational data
was then triangulated in order to clarify the children’s perspectives (Denzin, 2009;
Sharp, 2012; Roberts-Holmes, 2011). My pre-established rapport with the children
and the familiar classroom context ensured confidence (Mukherji and Albon, 2010;
Cohen, Manion and Morrison, 2017).
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3.6 Sampling
Due to the nature of my small-scale study, I only required information from a small
group of children. The sample of children chosen for the study was representative;
meaning they are a mixture of genders, months of births and represent the mix of
children within the class. Children within the sample are also a range of abilities and
have English as an additional language (EAL). Throughout my research project the
children will be active respondents; they will be providing responses to questions
through interviews and mathematical discussion. The children will articulate their
feelings and reflections throughout the process.
After choosing my sample for the research project, children were asked to give
informed consent (without coercion, threat or persuasion) (BERA, 2018). Children
within the sample were deemed competent by gatekeepers to understand the
purpose of the research project and their right to withdraw from the project at any
time (Alderson and Morrow, 2004).
Research will be obtained during assembly time to allow anonymity as other
members of staff and children are not present. All research tasks will take place
somewhere the children are familiar with; allowing the children to feel comfortable
and open to expanding on their responses.
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Chapter Four: Results and Discussion
4.1 Research cycles
The process of action research cycles used to obtain research are outlined in
appendix fifteen. The overview highlights how each cycle builds upon the last and
how the data was analysed throughout (Scott and Usher, 2011).
4.2 Reconnaissance
In order to correctly pitch my first research cycle to the right level, I undertook a
reconnaissance period. The reconnaissance period allowed me to discover the
children’s ability to solve reasoning and problem-solving questions. It also enabled
me to gain an insight into how the children felt when faced with these types of
questions and the strategies they would use to enable them to solve it. During the
reconnaissance stage, the children were reminded of the 4R’s (resourceful squirrels,
reciprocal ants, resilient rhinos and reflective owl) (Teaching and learning policy,
n.d.) these will be used to develop children into becoming self-regulated learners
who use metacognitive strategies regularly. The children are aware of the 4R’s as
they are part of the research schools teaching and learning policy (n.d.) and the
4R’s are constantly referred to within lessons.
It became clear after an analysis of the children’s initial work that they were of
varying abilities in mathematics. Jeff is of a high mathematical ability and was able
to complete the task and generate an answer in his head. On the other hand,
Margret who is of a lower ability, made mathematical jottings to aid her in solving
the task. The initial task consisted of a sample of questions taken from a year 6
reasoning SAT’s paper.
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4.3 Attitudes and beliefs towards reasoning and problem-solving
Shaughnessy (1985) implies that a person’s confidence in themselves as problem
solvers or their beliefs and feelings about mathematics can have a prohibitive effect
to attack problems in a productive way. From my initial observations of the focus
group and the semi-structured interviews conducted during the reconnaissance
stage (appendix three), it became apparent that all of the children do not like
reasoning questions as they expressed negative attitudes towards them. When
conducting the interviews, open questions were used to allow the participants to
express their views (Elci, 2017). When asked how they felt when the words
‘reasoning’ and ‘problem-solving’ were used, four out of the five participants replied
with negative views. Babatunah stated, “some reasoning questions are really long,
and it is too much information to take in”. On the other hand, one child appeared to
enjoy reasoning and problem-solving as they offered the child more challenge
(appendix fourteen). After analysis of the evidence collected so far, it was noted
that these negative attitudes were more towards reasoning than problem-solving.
Princess Leia stated, “I don’t mind problem-solving, but I hate reasoning because of
the explaining side that come with it” (Appendix fourteen).
Above all, children’s beliefs can influence their attitudes to learning (Ministry of
Education Singapore, 2012; Shaughnessy, 1985). During the reconnaissance stage
the children undertook a self-audit (appendix two) which helped me to gain an
understanding of their attitudes towards reasoning and problem solving,
categorised by confidence, effort, enjoyment and value (Hwang et al, 2017). The
figure below is a graph which shows the results of the children’s self-audit at the
beginning of the research, and similar questions were used post research to
evaluate their progress.
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Figure 4- Attitude graph from reconnaissance stage
Figure 4 shows a graph of four categories and the results from the reconnaissance
stage, which are based upon the children’s responses. The X-axis shows the
categories, and the Y-axis shows the children’s responses. For example, when
looking at those who expressed having a high confidence in reasoning and problem
solving there was only one child out of the six who said they were confident in
themselves and their abilities when faced with these types of questions. Following
on from the analysis of the self-audits, it was important to consider how to develop
the children’s confidence due to the link between confidence and reasoning (Hwang
et al, 2017).
In order to develop the children’s confidence, they were provided the opportunity to
work in groups, they were not given a time limit (Elci, 2017) and were given the
opportunity to take part in mathematical discussions to help develop their
reasoning vocabulary and efficiency throughout each cycle. Observations were
completed throughout each cycle, I observed that being able to practice reasoning
questions and having the opportunity to discuss how to solve the problem step by
step and then engaging in discussion as to how they can justify, explain and reason
as to how they got there. By sharing ideas, the children were becoming more
confident and were learning from one another.
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Figure 5- Attitudes graph from end of research
After four action research cycle, the children completed the self-audit again to
determine if their attitudes and beliefs had changed. Figure 5 is a graph showing
their attitudes towards reasoning and problem-solving. There is a general
improvement across all categories, those who had overall lower responses have
made progress. There is a significant increase in confidence with the exception of
one making progress and displaying more confidence in their abilities to use a
variety of strategies to help with the reasoning and problem-solving process. It is
worth mentioning that one child who still expressed having low confidence at the
end of the research could be caused by their absences from cycles two and three,
however I cannot be sure this is the reason behind their lack of confidence.
Findings based on several data sources- children’s responses to the self-audits that
were completed at the beginning and end of the project, their responses during the
exit cards and their interviews at the end of the project- suggests that as the
children’s confidence grew so did the effort they put into their work and they began
to value mathematics. Results confirm that having a positive attitude towards
mathematics can positively impact performance and attainment.
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Based on the results obtained, in my future practice I will continue to develop
strategies to develop children’s confidence, make learning enjoyable and introduce
the use of key word prompts for reasoning questions and provide positive
reinforcement where applicable.
4.4 Problem-solving and heuristics
Throughout the reconnaissance stage and cycle one, I observed Jeff completing the
two-step word problems without making any form of jottings to aid him in the
process. However, as the problems grew more complex it became clear that
carrying out the calculations in his head was leading to mistakes, therefore a new
strategy was needed. Babatundah suggested that Jeff use jottings (mathematical)
to help keep track of each stage of the problem. Throughout the rest of the cycle
Jeff made use of this new strategy by writing numbers down as he was calculating
mentally, which in turn allowed him to carry out a calculation more effectively. He
also began using the formal written method (GB. DfE, 2013) to assist with long
multiplication problems. At the end of cycle one the children completed their
reflections, within these the children noted the strategies that noticed themselves
using (figure 6). For example, one child observed that they were underlining key
words, while another child used jottings. Within these reflections, the children also
expressed their attitudes and feelings towards the problems they were given,
linking to the overarching theme of negative attitudes affecting children confidence,
enjoyment and achievement (Schoenfeld, 1985; Ma and Kishor, 1997; Hwang et al,
2017).
Figure 6- children's reflections from cycle one
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The Common Core Standards for Mathematics (2010) and the Department for
Education and Employment (1998) emphasise that children should be taught
mathematical methods explicitly such as the formal written method (GB. DfE, 2013)
but should also be encouraged to develop their own methods. A child who is
mathematically proficient is able to consider varying methods and decide upon a
method best suited for the problem.
As a result of the reconnaissance stage and cycle one it became apparent that the
children within the group were constantly using the same strategies for every type
of problem they were faced with. While in some cases this was effective, in others it
was not, and this led to their lack of resilience and confidence towards reasoning
and problem-solving questions. Macintyre and Forrester (2003), state that the focus
shouldn’t be on a specific strategy but on the ability for the children to be flexible in
terms of which strategy they will employ for a given problem. I opted for this
approach when introducing the children to heuristics.
The children had never heard of the term ‘heuristics’ before so I began by showing
them a child friendly poster (appendix five) which displayed several types of
heuristic strategies and offered the children a brief explanation as to what they are.
The poster was used as a starting point to ease the children in, it is a resource that
can be reused and is a visual prompt that can be referred to. Heuristics are
strategies that the children can use when solving problems. They can be used
alongside other strategies and when the solution is not obvious. The children were
given 10 minutes to look at the poster, discuss amongst themselves and ask
questions. Following on from the initial discussion a more in-depth conversation
was had going into detail about each heuristic strategy can be used and the types
of questions these can be applied to.
5 mathematical questions relating to reasoning and problem solving were then
placed on the table for the children to work through. They were under no pressure
to use the heuristic strategies recently introduced to them. Through observations
(appendix four) and examining the children’s work it became clear that Jeff
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continued to use the strategies that he was used to (working out in his head with
the occasional jottings) whilst the other five children attempted to use heuristic
strategies such as visualising the problem and working backwards. The end of
session discussion showed that the children were thinking about a variety of
different strategies at their disposal before they began to work out the answer.
During this discussion it was made clear that the children are not confident in using
heuristics and therefore would not use them consistently. In order to support the
children with using heuristics in later cycles, modelling and the opportunity to work
in pairs were used to increase the children’s confidence and have the opportunity to
discuss which tool is best suited for the problem. The children were showing signs
of beginning to use self-regulate their learning. This was evident through the way in
which they approached the problem, selecting the appropriate strategy and
monitoring their progress throughout (Garofalo and Lester, 1985). From
observations it was apparent that the children were also showing signs of selfregulating their learning because they were able to reflect on the performance by
checking their work, self-questioning and through discussions with peers and
myself and justify their responses building on their reasoning (Hutchinson, 1986;
Wong et al, 1986).
Figure 7 highlights that by the end of the research project 2 out of 6 participants
viewed the use of heuristics as a tool to be a good problem solver (Polya, 1957;
Schoenfeld, 1985). This suggests that the children are aware of the benefits of
using different strategies such as heuristics and the impact they can have on the
problem-solving process when the solution is not clear. If the opportunity arose to
continue the research further, I would continue to develop the children’s confidence
in using heuristic strategies, explore in depth the benefits of using them and how
they can be used in relation to specific types of questions.
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Figure 7- the use of a heuristic strategy
4.5 Metacognition and self-regulation
Creating an environment in which children are aware that everyone makes
mistakes and that they are part of the learning journey can facilitate a
metacognitive environment. The research school uses the 4R’s in order to create a
metacognitive environment, alongside using the concept that everyone can learn
from mistakes (Teaching and learning policy, n.d.). An environment rooted in
mutual respect will allow the children to feel comfortable in sharing ideas, making
mistakes and willing to express their feelings or attitudes towards the research
being conducted. The research school’s teaching and learning policy makes
reference to ‘learning powers’ which the children referenced frequently throughout
each of the research cycles (Teaching and learning policy, n.d.).
During the reconnaissance stage and cycle one the children exhibited a lack of
resilience to keep on trying and to use a range of strategies to support them with
this. This was evident throughout non-verbal cues such as a slumped body position
and facial expressions. In order to overcome this, the children were encouraged
to work together to solve problems and during cycle three, they were made
aware of different strategies that could be beneficial to them during the problemsolving process.
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The children were ‘resourceful squirrels’ as they were constantly looking for new
strategies, they could use to assist them which is why the introduction of heuristics
in cycle three was positive and retained by the children. This is evident in appendix
six where it is noted that all the children worked reciprocally and observations
taken during cycle two (appendix four), these data sources indicate that the
children felt more comfortable and willing to attempt problems when they were able
to work together to discuss each stage (Polya, 1957). Notes made during
observations conducted in cycle two evidence how the children are beginning to
self-regulate and reason, “questioning each other’s thinking” (appendix four).
The children worked reciprocally through all of the research cycles, turning to each
other for support through mathematical dialogue. They were supported in becoming
reflective learners by being provided opportunities for the children to reflect
through discussion or by writing it down. It encourages children to be reflective of
their own learning, learn from their mistakes and what they are taking away from
session (Flavell, 1976).
Due to unforeseen circumstances the research project was cut short and therefore
sufficient data was not able to be collected in relation to the effects metacognitive
strategies can have on the reasoning and problem-solving process. However, based
on the research that was obtained, I will facilitate children in becoming independent
learners and develop their resilience (Garofalo and Lester, 1985). With this
resilience children will continue with reasoning and problem-solving questions even
when the solution is not obvious. Having mathematical resilience will positively
impact on the children as it can help develop their self-regulation techniques, their
ability to assess situations and problems and build their confidence, all of which
impacts positively on children’s achievement within mathematics (Hwang et al,
2017; Garofalo and Lester, 1985).
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Chapter Five: Conclusion
The aim of this study was to develop metacognitive and self-regulated learning
approaches to improve children’s mathematical reasoning and problem-solving
capabilities. Experience and literature have highlighted that reasoning and problemsolving is a problem area for many primary aged children. Metacognition and selfregulation are concepts involving children being aware of their own thinking and
learning process and taking charge of it (Hattie and Clarke, 2018; Flavell
1976;1981).
This study indicates that metacognitive and self-regulation strategies can improve
children’s attitudes towards reasoning and problem solving, which in turn improves
their work outcome. Evidence suggests that children’s attitudes towards reasoning
and problem-solving can have a huge impact on their abilities in these areas. At the
beginning of the research children displayed and expressed negative attitudes
towards reasoning and problem-solving emphasising their lack of confidence and
lack of effort within lessons. By incorporating the 4R’s and the use of learning
language within the research cycles children were able to develop their
metacognition and self-regulated learning approaches. Cycle two and the use of
heuristics provided an opportunity for the children to be ‘resourceful squirrels’ and
‘reflective owls’ through their choice of strategy and monitoring their progress by
questioning whether the strategy was successful or if they needed to try something
else (Hattie and Clarke, 2018).
Further enquiry is needed into how to measure reasoning, how do educators know
when a child is ready to move on. Subsequently, reasoning is ever changing and
requires consistent development. A gap in the literature and the research is the
effectiveness of metacognitive and self-regulated strategies in improving reasoning
and problem-solving.
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Research methods were successful in producing data which enabled me to a range
of evaluations and interpretations (Anning and Ball, 2008). Observations produced
rich data, interviews and questionnaires allowed me to gather several opinions and
attitudes at once. Semi-structured interviews allowing more freedom and flexibility
with their responses (Cohen et a, 2011).
The research project was hindered by a global pandemic which meant that I was
not able to collect a large amount of data and I was not able to complete all
planned research cycles. On the last day I was in my research school, I was only
able to obtain two participants follow up questionnaires, exit cards and interview
which examined how their attitudes and abilities towards reasoning and problemsolving have changed and the impact metacognition and self-regulation had on this.
In the future, I aim to conduct this study again with my own class. However, this
time it would be over a longer period of time and consist of a larger number of
participants to identify any patterns and whether or not the development of
metacognitive and self-regulated strategies are more effective in smaller settings.
Analysis of the data indicates that metacognitive and self-regulated approaches can
not only impact the children’s attitudes and confidence but also improve their
reasoning and problem-solving. Of the children present (two out of six participants)
during the final research cycle they demonstrated overcoming the difficulties
previously experienced in persevering, for example, becoming stuck and repeatedly
giving up due to their lack of confidence thus impacting the effort they were
exerting. Due to the study being cut short I was not able to determine whether the
participants demonstrated movement in their mathematical reasoning and problemsolving abilities from where they started. However, based on what I observed
during each of the sessions the participants gained a positive attitude towards
reasoning and problem-solving leading to increased motivation, active engagement
in the learning, increased confidence and enjoyment. When all combined, in my
opinion can only lead to higher achievement.
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I feel that since carrying out this study I am more competent in my understanding
of the role reasoning and problem-solving play in and outside of the classroom and
have a deeper understanding of what metacognition and self-regulated learning is
and how this applies to the classroom. I am able to create an environment which
fosters the use of metacognitive and self-regulated approaches, implementing them
and the benefits they can have on children.
I am now confident in using a variety of approaches to promote an understanding
and positive attitude around reasoning and problem-solving.
For learners I would recommend the use of the 4R’s as this can not only have a
positive impact of their mathematical ability, but it can also be used in other
aspects of education and life. Being able to constantly reflect on their learning,
discuss next steps and areas of development, persevering and thinking of different
approaches will allow learners to continue to make progress.
The results of my research study were shared with the participants and staff within
the research school through the use of dissemination posters which were emailed
out (appendix twelve and thirteen). The research school can make their own
decisions based on the results. In the future, with my own class I will expose
children to metacognitive approaches as early as possible. In regard to reasoning
and problem-solving, continue to create an environment that enforces the concept
of learning from our mistakes. I will ensure there are a range of different strategies
and resources which are at their disposal and allow them to self-regulate their own
learning by choosing an approach that best fits them and their way of learning.
As a Newly Qualified Teacher (NQT) I will make a conscious effort to ensure I allow
children time to respond when asking questions, offer a range of resources and
strategies that can assist their learning. I will endeavour to provide opportunities
for the children to reflect on the learning taking place and ask themselves question
to regulate their learning e.g. what is going well? What could I do to improve?
[Word count: 8009]
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Appendix List
Appendix One- Ethics protocol
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Ethics protocol
NTU’s clearance for this project is conditional upon the conduct of the research being ‘within an ethicN0679999
of respect for any
persons involved in or touched by the research’ (BERA 2018 p.6). This protocol sets out the key ways in which the
research design has taken into account BERA’s most recent guidelines for the ethical conduct of educational research.
Please note: ‘The [BERA] guidelines are intended to promote active and concrete responses following from a
deliberation of the issues. (BERA 2018 p.3).
Your protocol should be shared with and discussed with appropriate colleagues in the setting in which you wish to
undertake your research, as part of gaining agreement for the focus of your research and gatekeeper consent for your
intended research design (see paragraphs 54-58)
British Educational Research Association [BERA] (2018) Ethical Guidelines for Educational Research, fourth edition,
London. https://www.bera.ac.uk/researchers-resources/publications/ethicalguidelines-for-educationalresearch-2018
Project title:
How can I develop metacognitive and self-regulated strategies to improve mathematical reasoning and problem
solving?
Project aims:
How can I best support children in developing their reasoning and problem-solving?
What are the best strategies to use?
What is the best practice?
How can metacognition be used to support children?
Responsibilities to sponsors, clients and stakeholders:
Research methods: maximising intended benefits and minimising potential risks
Responsibilities to participants:
Avoidance of harm arising from participation in research
The aim of my research is to see how reasoning and problem-solving can be improved through the use of metacognition
and self-regulation. What are the strategies that are already in place to support children’s development in this area of
maths?
The evidence I am collecting will be collected through observations, interviews with staff and children, questionnaires
and children’s work.
Data collection method
Perceived benefits of chosen method
Potential disadvantages of chosen
& scope of use
for this research project
method and
actions to ameliorate them
Interview with members of staff
To gain an understanding of what the Time to meet with members of staff
staff know about the teaching of
to discuss reasoning and problemreasoning and problem-solving and
solving and how metacognition can
the best strategies to use to support
be used to support this.
the children.
In order to ameliorate this, I need to
schedule in advance with staff who I
wish to meet with and being flexible
and organising my time around the
teacher.
Interviews with children
Gauge what the children understand
No concept of the impact this has on
about the processes they go through
their learning and how it can be used
when given a reasoning and
to help them. Use phrases that the
problem-solving question. What do
children are familiar with e.g. their
they need to do first? What can they
learning powers.
use to support themselves in their
learning?
Questionnaires for the whole school
Find out how the staff feel about
Not having the questionnaires
teaching reasoning and problemhanded back in, questions are not
solving and the strategies that they
specific enough, not enough room for
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Children’s work and reflections
School policies, INSET days and staff
meetings
have put in place to support the
children learning.
What strategies do they find the
most effective? What impact do they
think metacognition and selfregulation can have on reasoning and
problem-solving?
To gain an understanding of how the
children feel about reasoning and
problem-solving questions and the
emotions they bring up. What
strategies do the children already use
when faced with these types of
questions.
Have an understanding of the
information that has been shared
with the staff and the training they
have received.
them to give deeper explanations.
Providing the teachers with the
opportunity to meet at a later time to
discuss in more detail and allowing
an extra page for teachers to make
additional comments.
Children not being able to articulate
their views and responses.
Responsibilities to participants:
Voluntary informed consent, the right to withdraw and incentives
Members of staff and children have the right to withdraw from the research at any time. Before any research takes
place, the teachers and children need to give informed consent for observations, copies of children’s work, interviews
and questionnaires. Staff, children and parents will be asked to sign a consent form prior to the start of data collection.
Responsibilities to participants:
Transparency and feedback
Members of staff have the right to read any of the research that I have collected from them.
Responsibilities to participants:
Privacy, anonymity, and confidentiality & data storage and disclosure
The research and evidence that is collected will be anonymised and kept confidential. It will be stored in a confidential
location, where access is restricted.
Responsibilities to the community of educational researchers
Responsibilities for publication and dissemination
Scope, format and integrity of reporting research outcomes
Allowing members of staff access to the research that I have collected and providing them with a copy of my completed
dissertation.
Version 1 DP NIE NTU 13/09/2018
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Appendix Two- Self audit
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Appendix Three- Interview Questions for children
1. How do you feel when I mention reasoning and
problem-solving?
2. What strategies do you use to help with these types
of questions?
3. Do you like reasoning and problem-solving?
4. If not, why?
5. How did you find the activity?
6. How did you approach it?
7. How do you feel now?
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Appendix Four- Cycle two observations
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Appendix Five- heuristics poster
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Appendix Six- Cycle three observations
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Appendix Seven- Children’s reflections from cycle three
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Appendix Eight- 4R’s poster
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Appendix Nine- End of research questions
Q1. Do you like math?
Why or why not?
Q2. Describe your math skills?
Very poor
poor
average
good
very good
Q3. What is reasoning and problem-solving?
Q4. Only geniuses are capable of discovering or creating
mathematics?
Q5. Getting the correct answer to a problem is more important than
knowing how to solve the problem?
Q6. Describe how well you solve math problems.
Q7. What makes some really good at solving math problems?
Q8. What is the hardest part about reasoning?
Q9. What would help you become a better problem solver and
reasoner?
Q10. Are some parts of a problem, as it is written down, more
important than others? How can you tell which parts are the most
important?
Q11. What questions do you ask yourself while you are reading a
math problem?
Q12. After you have read and understood the problem, what else
must you do to still complete it successfully?
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Appendix Ten- Exit card
What have you learnt?
What did you like most?
Was there anything you didn’t like?
What will help you reason and problem solve in the future?
How do you feel about reasoning and problem-solving now?
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Appendix Eleven- Dissemination poster to staff
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Appendix Twevle- Child friendly dissemination poster
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Appendix Thirteen- Independent study proposal
PED4 2019-2020
Independent Study
PRBA34102
Independent Study Proposal (500-1000 words)
Researching and developing an aspect of professional practice.
Your completed proposal should be shared with your supervisor in your first
individual tutorial.
Proposed area of study (and working title)
How can I develop metacognitive and self-regulated strategies to improve mathematical
reasoning and problem solving?
Key research questions
o
o
o
o
How can metacognition impact children’s reasoning and problem- solving?
What strategies are there to support the teaching of reasoning and problem solving?
What impact does reasoning and problem solving have on children mathematical
understanding?
Can metacognitive strategies improve children’s ability to solve reasoning and
problem-solving questions?
Rationale for your chosen focus including your personal motivation for this
choice:
I have chosen to focus on reasoning and problem-solving as it is an area of maths that is
covered in every school. It’s a fundamental aspect of the maths curriculum. My placement
school has an interest in metacognition and the impact it can have on children’s learning.
Understanding the professional context (within your school)
How will you familiarise yourself with the current context of your chosen focus
within your school? (e.g. inspection reports/performance
data/observations/interviews with pupils or key colleagues)
Interviews and conversations with the senior leadership team who led the staff meeting but
also organised an inset day based on metacognition. Looking at the school teaching and
learning policy which outlines how the 4R’s are used within the classroom. Interviews with the
children about their understanding of the 4R’s and what they believe the reason behind them
are. How effective do the teachers within the school find this approach and then impact they
are seeing within their class.
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Maths policy
Working walls in terms of maths
Reasoning and problem solving- integral, extension etc
Understanding the wider professional context
How will you familiarise yourself with wider professional thinking and innovative
practice in your chosen focus?
(e.g. inspection and research reports /curriculum frameworks/ international
perspectives)
Use google scholar and the library to find out about international perspectives based on
metacognition and self-regulation in maths and the impact this is having on children in regard
to reasoning and problem solving. Looking through journals and research papers around the
subject.
What strategies are being used to support reasoning and problem-solving? Library one search,
google scholar, NCTM and international perspectives (Australian and American curriculum) to
see how reasoning and problem-solving is being taught and how best to support children in
this. What are the problem areas that children might face? Is there any evidence to suggest
metacognition can support the learning (journal articles)?
o
Enrich articles
Keywords for literature search
o
o
o
o
o
o
Strategies
Mathematical reasoning and problem solving
Heuristics
Resilience
Metacognition
Self-regulation
An outline of key research and reading in this area (key themes identified
from literature read so far including reference to journal articles)
Identify as starting points a minimum of three key texts (including journals) that
you expect to use to support your study.
o
o
o
Emotions- children often feel anxiety, helplessness and worry when faced with
reasoning and problem solving questions. (Tornare, E., Czajkowski, N.O., Pons, F., 2015.
Children's emotions in math problem solving situations: Contributions of self-concept,
metacognitive experiences, and performance. Learning and Instruction, 39(C), pp.88–
96. 10.1016/j.learninstruc.2015.05.011)
Metacognition and self-regulation- what are they, how do they link Verschaffel, L.,
Depaepe, F., Mevarech, Z., 2019. Learning Mathematics in Metacognitively Oriented
ICT-Based Learning Environments: A Systematic Review of the Literature. Education
Research International, 2019, p.19. 10.1155/2019/3402035.
Dignath, C., Buettner, G., Langfeldt, H.-P., 2008. How can primary school students learn
self-regulated learning strategies most effectively? Educational Research Review, 3(2),
pp.101–129. 10.1016/j.edurev.2008.02.003.
Reasoning and problem solving:
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o
o
Buchheister, K., Jackson, C., Taylor, C.E., 2017. Maths Games: A Universal Design
Approach to Mathematical Reasoning. Australian Primary Mathematics Classroom,
22(4), pp.7–12.
Stein, M., Burchartz, B., 2006. The Invisible Wall Project: Reasoning and Problem Solving
Processes of Primary and Lower Secondary Students [online]. Mathematical Thinking
and Learning, 8(1), pp.65–90. Available at:
http://www.tandfonline.com/doi/abs/10.1207/s15327833mtl0801_4.
Evidencing practice in the professional context.
Research Strategy
Identify the key data collection and other methods that you will use to gather
evidence for your study.
Identify any ethical issues you can predict and how you will address these.









Observations of children and teachers
Interviews with senior leadership, teachers and children
Questionnaires for teachers to complete
INSET day notes
Staff meeting notes
School policies
Displays
Copies of children’s work
Photographs- children not being able to have their photo taken for safeguarding
reasons. Allowing for consent from parents and children before taking any pictures
In order to keep my research ethical, I will provide staff and children with a letter of consent,
have a conversation with them about what I am wanting from them and give them the
option to withdraw at any time. All research will be kept confidential and names will be
anonymised.
Evaluating impact on learning and teaching
Identify how you will evaluate the success of your project in terms of supporting
the children’s learning and your teaching (i.e. identify success criteria).
o
o
o
o
o
Children are able to justify their choices for the resources they use
Children are able to explain how they got to that solution and what they did to get
there
Use reasoning to explain their answers
Are able to discuss how their feelings towards reasoning and problem-solving have
changed over the weeks
Are able to reflect on their mathematical resilience
Indicate the
o key colleagues or adults
o focus children
who will support your evaluation of the project.
(provide a description of the sample here, not the names of individuals)
o My own reflections after each session
o Have the children reflect on the process
o Involving adults in how children tackle it and how they articulate their strategies
Project plan/timeline
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Briefly outline your project plan with a clear indication of your proposed timeline.
Speak to the headteacher- 20th January
Consent forms- 20th January
Create and organise interview questions and questionnaires- 23rd January
Organise focus groups- 27th January (providing consent forms are back in)
Reading around concept- completed throughout dissertation
Lit review finished- 21st February
Research analysis- 13th March
Conclusion- 20th March
Dissertation completed and handed in- 1st April.
Student number: N0679999
Name: Staci McCourty
School representative signature:
NTU Supervisor signature:
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Appendix Fourteen- Children’s responses to questions in appendix three
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Appendix Fifteen- Overview of research cycles
Reconnaissance stage:
o
Children’s attitudes towards reasoning
and problem solving
o
Their understanding of strategies that
they use
o
Initial assessment
o
Observation of focus group
Cycle One:
o Interviews with the children
o Observations of focus group
o Task- two step multiplication word
problems. What strategies do the
children use to figure out what they
need to do first and then the step that
follows
o Murder mystery investigationinvolves problem solving and the 4R’s
(reciprocal ants). Do the children still
continue to learn and develop their
skills? What are they getting out of it?
How does this impact their attitudes,
confidence and effort?
o Children’s reflections- have the
children’s attitudes changed? What
can I use from their reflections to
inform the next cycle?
Analysis:
o Children do not enjoy reasoning and
problem-solving questions
o Feelings of worry and anxiety when faced
with these questions due to low confidence
o Find them boring
o Strategies that the children use are
mathematical jottings and working out in
their heads
o Higher attaining children in maths would do
everything in their head, whereas lower
ability would make jottings.
o Negative attitudes towards reasoning and
problem-solving, closed off body language,
lack of effort when completing the initial
assessment
Analysis:
o Enjoyed the murder mystery problem
solving task and were able to explain how
they figured out each section of the task
o Children worked well as group
o 2/6 struggled with the word problems as
they were two-step
o Continued to use strategies such as
underlining key words, jottings and working
it out in their heads
Interview:
o Want more investigative problems
o Prefer when the questions are given to them
in different ways e.g. not all SAT’s like
questions
o The discussion that occurs during the
activity allows the children to bounce
ideas/strategies back and forth
o For those less confident they prefer to work
as a group as it offers reassurance
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Cycle Two:
o Introduction of heuristics through
discussion and the child friendly poster
o
What are they are how can they help?
o
Reasoning and problem-solving
questions
o
Children’s reflections
Cycle Three:
o The use of mathematical games
o Investigations which encompass
mathematical aspects
o Can children apply heuristics strategies
o How do they feel about the task?
o Do games allow for children to develop
mathematical skills?
o Are the children more engaged in the
session?
o Do they exhibit signs of self-regulated
learning?
Cycle Four:
o Exit cards and self- audit (same as
reconnaissance
o
Exit interview
o
Conversation with participants and
research school on how the results will
be shared
Analysis:
o when working on the questions
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children tried to make use of the new
strategies taught to them
o referred back to the poster (visual and
will not be put up on the walls)
o Discussed in pairs which strategies they
found to be successful for certain types
of questions
o One child continued to use his own
strategies (this is fine as long as it is
effective)
o One child said they would continue to use
these strategies if they can remember
them
Analysis:
o Children were more engaged and willing to
participate in the activity
o Enjoy working with other people
o One child shows negative and closed off
body language- might be down to the
games and learning or because of who they
are paired up with
o Different to what they are used, they like
the change
o During the investigation- children
attempted to use heuristic strategies where
possible
o Both activities promoted mathematical talk,
engaged in mathematical reasoning by
justifying their choices.
o Reflected on the process during discussion
and reviewed strategies (self-regulating)
Analysis:
o
Cycle four was changed at the last minute as a
result of the pandemic
o Only 2/6 participants were present on the last
day of school
o I conducted an exit interview with the two
children to determine how their attitudes
towards reasoning and problem-solving have
changed but also how their abilities have
improved- they have grown in confidence;
attitudes have improved slightly and will
continue to if these approaches are continued
o How did they feel about participating in the
research, what did they learn from the
experience, are they going to continue to use
any of their strategies?
o
Self-audit: the two children appear to have
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improved in all four aspects e.g. confidence,
effort, enjoyable and value.