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Action Research in Mathematics: Providing Metacognitive Support (as a Heutagogical Technique) to Grade 3 Students

By Zoriana Myburgh

 

ABSTRACT

Self-determination, as one of the 21st-century skills, prepares students for our constantly changing world. Can metacognition help students become self-determined and is it worth starting to introduce metacognitive elements at an elementary school? Based on the current literature from teachers’ and administrators’ points of view, metacognition positively influences students’ performance and wellbeing. Therefore, there is a need to continue researching the effects of metacognition at a young age but from students’ perspectives.

The purpose of this research is to enhance grade 3 students’ metacognitive abilities to help them manage their learning. The data was collected using the students’ personal thoughts and emotions during semi-structured interviews and the researcher’s observation notes in order to summarise whether or not metacognitive interventions were helping students become self-determined. A lack of qualitative action research in existing literature highlighted the need for this research design.

It has been found that metacognition as a heutagogical technique can be used to improve students’ self-determination in an elementary school. Students mostly showed improvement in the Commitment category: goal-setting, self-questioning and self-monitoring. Less than half of the students showed the development of metacognitive skills in the Capacity category. Most of them already had some skills before the experiment started (e.g., strategies for solving problems, improvement strategies, and asking for help when needed). The Value category represented how students developed their metacognitive experience and supported the finding of the previous categories. Considering the significance of metacognitive development, teachers should constantly strengthen the metacognitive abilities of their students.

 


 

University of Southampton, 2021

FACULTY OF SOCIAL SCIENCES

ACTION RESEARCH IN MATHEMATICS:
PROVIDING METACOGNITIVE SUPPORT (AS A HEUTAGOGICAL TECHNIQUE) TO GRADE 3 STUDENTS

by Zoriana Myburgh

A dissertation submitted in partial fulfilment of the degree of

<MSc Education (online) PT>

by taught course.

You can view this dissertation in its entirety in PDF form here.

 


 

1. INTRODUCTION

Background of the Study

Due to constant and rapid changes in our society, the importance of lifelong learning is also increasing. People need to constantly evaluate their ideas and experience. This ceaseless “transformation of information, the creation, construction and renewal of knowledge, is at the heart of reflexivity” (Dyke, 2009, p. 295). Traditional learning models might not be satisfactory for current learners nowadays who look for greater independence and integration (McLoughlin and Lee, 2008). Taking into account COVID-19 pandemic restrictions all over the world and the availability of online learning resources, it’s essential for students to learn how to manage their learning. Furthermore, some of the jobs that we have now might be replaced by the time our primary students will finish school. In that case, it is necessary to teach 21st-century skills, namely critical thinking, self-determination, and socialization, that will help students adapt to these new requirements (Irgatoglu and Pakkan, 2020).

Being an elementary school teacher, I often noticed that when students are given a word problem to solve, they will say, “I do not know, teacher” or “Teacher, what to do here?”, or will patiently wait until the teacher scaffolds it, or someone else finds the answer. Can coaching students on metacognition as one of the heutagogical techniques solve this issue? The main goal of developing students’ metacognition is to make them autonomous and self-determined learners (Thomas, 2003). Self-determined learners set their own goals and learning paths, monitor timing, and reflect on their final outcomes.

Based on Self-determination Theory, students have three primary needs: autonomy, competence, and relatedness (Deci and Ryan, 2000). Autonomy means the freedom of choice and the wish to control the learning process. Competence refers to having the confidence and capabilities to complete a task. Relatedness is about working with others and feeling connected (Marshik, Ashton and Algina, 2017).

Definition of Terms

This paper will be based on three main terms: heutagogy, self-determination, and metacognition.

First, it is important to differentiate between self-determination, self-regulation, and self-efficacy as these three terms will appear in this paper.

  • Self-determination refers to individual motivation that is influenced by internal impetuses (Ryan and Deci, 2000).
  • Self-regulation is defined as self-management, the ability to control the thoughts and
    emotions that direct human’s behaviour (Panadero, 2017).
  • Self-efficacy is one of the tools of self-regulation and means the beliefs people have in achieving a task successfully (Bandura, 1977).

Self-determined learning is also known as heutagogy, a concept introduced by Hase and Kenyon (2000) and refers to student-centred learning “where the individual student’s interests and motivations create a focus area for new learning” (Jones et al., 2019, p. 1172) and the teacher acts more like a mentor in a classroom. One of the main heutagogical principles is self-reflection (Blaschke, 2012) which is known as metacognition. Metacognition is “thinking about thinking”, “cognition about cognition” (Pritchard, 2013, p. 27) or “our ability to know what we know and what
we don’t know” (Costa and Kallick, 2008, p. 24).

Metacognition is not only about planning and knowledge activation but also the intentional monitoring of students’ cognitive processes, reflection, time management, and self-evaluation (Bol et al., 2016) and determining new ways to proceed and learning from the experience (Edwards and Costa, 2012).

Metacognition is one of the 16 Habits of Mind (HoMs) developed by Costa and Kallick (2000) that are a collection of behaviours that can help students tackle different problems they encounter at school or in other settings. Students need more than just academic knowledge and skills in order to succeed. HoMs focus not only on how much students know but also on what they do when they do not know an answer (Costa and Kallick, 2008). Teachers can help them practice these behaviours by modelling them, immersing these habits in the school curriculum and culture, and constantly
checking their growth (Edwards and Costa, 2012).

Problem Statement

Considering that learning is a lifelong process, it is logical to start teaching self-determination skills as soon as possible (Palmer & Wehmeyer, 2003). Moreover, it is recommended by some researchers to start teaching self-determination at a young age as it will become more difficult at later stages (Danneker & Bottge, 2009). Stein (2018, p. 4) underlines that “effective teaching and learning [should] take place early on so that students can be successful in secondary school and beyond”. For instance, elementary school students can be taught how to set goals, make decisions, assess, and reflect on one’s own work. Knox (2017) emphasises that students who developed metacognitive skills can organise, examine, and assess their thoughts. However, there is not much qualitative research that investigates the impact of metacognitive support on elementary students, particularly in the context of mathematics. Most of the studies focus on quantitative data based on students’ performance. Previous literature was more focused on the teachers’ perspectives disregarding the views of students.

Self-reflection tasks are often treated as some extra time-consuming work for students, especially during mathematics classes because students do not see any value in them (Kiles, Vishenchuk and Hohmeier, 2020). Metacognitive skills that lead to self-determination are not instinctive and might be challenging (Bouldin, 2017). Considering that self-determination plays an important role in students’ well-being (Martinek and Kipman, 2016), it is important to dedicate this study to research the effects of metacognition on learners’ self-determination at a young age from students’ vision.

Fifteen grade 3 students (9-10 years old, 8 girls and 7 boys) took part in this experiment at an elementary school in Cambodia. Data from the participants were collected as semi-structured interviews with students recorded via Google Meets and the researcher’s observation notes taken during math classes. During the research period, all schools in Cambodia were operating online because of COVID-19 pandemic restrictions. The experiment lasted 9 weeks from April 29 to June 30, 2021.

Purpose of the Study and Research Questions

The purpose of this study is (a) to understand the necessity of a heutagogical framework from the perspectives of students during maths classes in an elementary school in Cambodia, and (b) to find out whether metacognition can help students become self-determined at a young age. Action research cycles will be used to examine self-determined learning in the context of mathematics at an elementary school. Action research can be conducted by teachers in their classrooms with the aim of refining pedagogy and student learning (Nasrollahi, 2015). Coding student perspectives and researcher’s notes will help understand the phenomenon of self-determination and the use of metacognitive elements, namely goal-setting, self-assessment, self-questioning, self-monitoring, responding to and reflecting on feedback, note-taking, problem-solving strategies, and improvement strategies, etc.

The aim of the study was supported by the following research questions:

Central Question: How can students’ needs be met using the heutagogical framework while teaching maths in an elementary school in Cambodia?
Subquestion 1: What tools and strategies should teachers use to implement the heutagogical framework?
Subquestion 2: How can metacognition as a heutagogical technique be used to improve students’ self-determination

By answering these research questions and gaining insight from students, we can better understand the conceptions and misconceptions about the heutagogical framework in an elementary school. We will see whether metacognitive elements in a lesson plan encourage self-determination based on students’ responses and the researcher’s observation notes. With this undertaking, elementary teachers might be inspired to design better lesson plans.

Organization of the Study

The structure of the study is as follows. The literature review provides the context for current research, explains the importance of metacognition as a heutagogical technique in the learning process from teachers’ perspectives. It was considered whether metacognition can be taught and what techniques work best based on the current empirical data. The methodology chapter explains the rationale for research design and the methods chosen as the most appropriate for this study. Plus, it gives an insight into how data was collected and analysed. The findings chapter presents the themes developed during the analysis of the collected data. The research outcomes are compared with the existing literature in the discussion chapter. Based on the research findings, implications for further research are suggested and conclusions are made.

 

2. LITERATURE REVIEW

Metacognition will be studied through constructivism and individualism leading to postmodernism. Literature was reviewed to examine the importance of metacognition as one of the heutagogical techniques and a Habit of Mind in the learning process. It was taken into account whether metacognition can be taught and what approaches on the current empirical evidence work best to enhance self-determination. Finally, some quantitative and qualitative tools to measure metacognition were analysed. The search was not limited to specific dates although preference was given to the last two decades.

2.1 Metacognition through the lens of constructivism, individualism, and postmodernism

From a constructivist viewpoint, metacognition is “the result of mental construction” (Pritchard, 2013, p. 18). According to constructivist theory, learning is a metacognitive process (Wray and Lewis, 1997). Reuer states that constructivism happens when students connect their experiences and ideas (Reuer, 2017). Constructivists claim that we learn better if we constantly build our understanding (Pritchard, 2013). Since metacognition is also about self-assessing and self-monitoring, it complements constructivism perfectly. Different people learn things differently. We, as teachers, might not know which approach will be the best for a specific topic for different students but we can encourage them to experiment with various methods and decide metacognitively how to approach and solve a mathematical problem. Pritchard (2013) also claims that if students are asked to share their approaches or evaluate their classmates’ ideas in a constructive way in a safe and supportive environment, it will eventually lead them to develop their processes of thinking and help them solve problems.

It’s important to understand the teacher’s role in this domain. Constructivism is often criticised because students are left “to teach themselves” (Hubbard, 2012, p. 160). According to heutagogy, teachers act more like coaches (Mohammad et al., 2019) and facilitators (Akyildiz, 2019). Akyildiz interviewed 40 educators from Turkey who implemented heutagogical frameworks within their classes and summarised that 30% of teachers reported that they had to reflect more if they wanted to progress with heutagogical education and 40% of them claimed that they lost power in the classroom. However, Horrigan (2018, p. 57) argues that “empowering students is not the same as a teacher losing power”. Can metacognition help students and teachers because both need to adapt to the 21st-century requirements?

Furthermore, metacognition is connected to the values of individualism, encouraging self-directedness and heutagogical principles in general. Working at one’s own pace and reflecting on one’s learning are paramount skills for students in order to transform into independent learners (Sart, 2014).

Seeing each child as an individual with their own personality, mental and physical capabilities is an example of individualism (Fevre, Guimarães and Zhao, 2020). According to constructivists, knowledge is built by an individual through the explanation and combination of different ideas (Hubbard, 2012). Thus, both the constructivist methods and the individualism of heutagogy lead to postmodernism because postmodernists believe that the goal of education is “teaching critical thinking, production of knowledge, development of individual and social identity, self-creation” (Hossieni and Khalili, 2011, p. 1307). This aligns with 21st-century skills discussed in the previous chapter. Following this philosophical approach, teachers as mentors guide students to come across new things and reflect on them on their own (Hossieni and Khalili, 2011), therefore, students alter from passive recipients of knowledge to active constructivists (Reuer, 2017).

2.2 Metacognition through self-determination, self-regulation, and self-efficacy

Self-determination and even heutagogy are not new terms in education but their importance in elementary school has emerged within recent years. Some findings suggest that nurturing metacognitive beliefs in kindergarten children will increase their behavioural self-regulation (Compagnoni, Sieber and Job, 2020). Therefore, teachers must “maximize the learning classroom climate for self-regulated learning” (Panadero, 2017, p. 23). Using action research cycles (Plan – Act – Observe – Reflect – Revise – Plan), the behaviour of students engaging in self-directed learning was investigated in Ireland (Newman and Farren, 2018). They claimed that reflections and critical self-analysis motivated students to become more self-directed. However, the authors believed that the terms “self-directed” and “self-determined” are interchangeable. This definitional vulnerability questions the validity of this study. Self-directedness is based on single-loop learning (correcting the mistakes without reflections) and self-determination is founded on double-loop learning (questioning beliefs and assumptions) (Peeters and Robinson, 2015).

Self-determination techniques are often analysed alongside metacognitive strategies because according to heutagogy, metacognition is a major characteristic of how people naturally learn (Blaschke, 2012). Moreover, “the autonomy and flexibility of heutagogical models are managed well when incorporated into a reflective practice” (Newman and Farren, 2018, p. 6). If learners reflect on their results through the problem-solving process and take their actions and beliefs into account, new learning situations can be adapted to various learning styles (Blaschke, 2012). Blaschke is talking about the double-loop learning model, the key principle in the heutagogical framework. It was examined in Indonesia among 48 middle-school participants who were split into two groups (Nur et al., 2019). Using questionnaires, pre-tests and post-tests students’ progress was measured. It was summarised that this constant reflection using a double-loop learning model positively affected students’ results. However, the analysis is lacking in rigour. First, it is not mentioned whether multiple observers were invited to this study and the duration of the experiment is not clear. Secondly, it is difficult to judge the validity of the data without the examples of pre-tests and post-tests.

Some researchers even consider metacognition as a general term combining other definitions, such as self-regulated learning, thinking skills, etc. (Perry, Lundie and Golder, 2019). Winne and Hadwin (2008) explored self-regulated learning and its effects on motivation from a metacognitive perspective and described it as a cycle: define a task, set goals, perform the task and metacognitively modify if needed. According to their study, self-regulated learners can use metacognitive strategies to monitor their goals and progress in completing them. Analysing this model, Greene and Azevedo (2007) noticed that metacognitive monitoring is a significant part of self-regulated learning. However, these authors together with Panadero (2017) in his meta-analysis, argued that it was unclear how the last phase worked in Winne and Hadwin’s cycled model, specifically they believed that metacognition should occur throughout each phase and not as an end product.

Students who are confident in their abilities, try to achieve their goals, look for academic help and self-reflect will show better performance at school (Martinek and Kipman, 2016). Martinek and Kipman (2016) argue that if supporting students’ autonomy increases students’ motivation, then self-determined learning will also improve students’ self-efficacy (self-confidence in succeeding in the task). Self-efficacy is one of the variables that influences self-regulated learning (Panadero, 2017). According to the Self-determination Theory, there are three basic needs: autonomy, competence, and relatedness. Therefore, if students have a choice and understand the purpose and relevance of the tasks, students’ intrinsic motivation will be increased (Ryan and Deci, 2000). Martinek and Kipman (2016) predicted that self-determination, academic self-regulation and self-efficacy (𝑆𝐸³) will have positive consequences on students’ subjective well-being (W). 131 students from an Austrian primary school completed questionnaires regarding this study called 𝑆𝐸³𝑊. It was concluded that 𝑆𝐸³ decreased noticeably from grade 1 to grade 2, but the general W did not change. Martinek and Kipman (2016, p. 130) assumed that the teachers did not provide enough autonomy to their students because they did not “trust in the learning abilities” of their students or felt “a loss of control” in actual students’ work. However, some researchers believe that using questionnaires in elementary school is not appropriate because of the students’ age and observer’s reports are essential in future studies (Morison et al., 2000). Others think that teachers do not have enough training on self-determined learning (Panadero, 2017).

Teachers’ behaviour as an example of self-determination is truly crucial. If students do not feel these supportive interactions, their self-determination might not be ignited. 2,587 students in the USA took part in a survey that examines how the social aspects of schools foster students’ self-determination (Adams and Khojasteh, 2018). Having applied quantitative methods, the authors concluded that the school climate does have consequences. At the same time, a similar experiment in the USA was conducted with 106 university students (Hayward et al., 2018). The authors used a mixed-methods research approach to examine how inner directedness (in particular, metacognition) will affect students’ motivation. For each experimental section instructors recruited three to five volunteers called Student Pedagogical Teams. Their role was to collect feedback from other students and to present it to their instructors. The instructors followed this repeating cycle: teach a class, receive feedback, modify the classroom activities, receive students’ feedback again, reflect on the results and plan the next task. Metacognition through self-assessment, reflections, and self-regulated learning promoted teachers’ self-directed professional development (Hayward et al., 2018).

2.3 Metacognition as a Habit of Mind

Metacognition is one of the Habits of Mind (HoM), “the characteristics of what intelligent people do when they are confronted with problems” (Costa and Kallick, 2008, p. 15). The authors of 16 HoMs, Costa and Kallick, believe that the main purpose of all HoMs is to create self-determined, lifelong learners. Therefore, students need to self-monitor and self-regulate to achieve this goal. This HoM is subjectively the heart of all Habits of Mind and a core of heutagogy. If an individual can self-regulate their thinking processes, they can choose other appropriate habits to succeed in the task. Based on the empirical evidence presented by Muscott, students who were trained in and demonstrated how to think about their thinking did better in assessments (Muscott, 2018).

There are two main components of metacognition: metacognitive knowledge (MK) and metacognitive experience (ME) (Flavell, 1979). MK is the strategy students use to solve problems and ME is about contact with the environment. ME could inspire both cognitive and metacognitive strategies necessary to solve mathematics word problems. “Cognitive strategies are invoked to make cognitive progress, metacognitive strategies to monitor it” (Flavell, 1979, p. 909). Efklides separated metacognitive skills (MS) from MK and ME. She defines MS as “procedural knowledge” (Efklides, 2006, p. 5). Students must get used to “linking and constructing meaning from their experiences” (Costa and Kallick, 2008). Costa and Kallick add two more components: inner awareness and the strategy of recovery. They explain it with an example of reading an unfamiliar story. When a person reads a text and suddenly loses the meaning, he/she will reread it and get back the connection to understand what is happening.

Costa and Kallick (2008, p. 63, fig. 4.1) developed five dimensions within which students can grow regarding Habits of Mind: meaning, capacity, alertness, commitment, and value.

 

By exploring meaning the authors mean that students understand the meaning of HoMs. Increasing alertness is about applying HoMs without being asked. Extending values is understanding why some HoMs are more applicable in specific situations so if the students extend the value of metacognition in mathematics, it might turn into a pattern of behaviour eventually. Expanding capacities is about developing various techniques when solving problems or making decisions. If students develop metacognitive strategies, they might be able to apply other HoMs more effectively. Building commitment is constant development in the use of HoMs when students progressively become self-determined. This dimension is closely related to heutagogy as students learn to self-manage, self-monitor, self-reflect, and set higher expectations for themselves (Costa and Kallick, 2008).

Wagaba, Treagust and Chandrasegaran (2016) were also trying to conceptualise the dimensions that characterise metacognitively-oriented learning environments: (1) metacognitive demands, (2) student-student discourse, (3) student-teacher discourse, (4) student voice, and (5) teacher encouragement and support. If we are talking about metacognitive demands, it is recommended to model metacognition and not assume that the students already know organisational techniques or how to set goals, collaborate, etc. but explicitly teach these metacognitive strategies. The student-student dimension refers to whether students think interdependently and discuss how they learn with their peers. Student-teacher interaction means whether students discuss how they learn with their teacher. By “student voice” the author means students’ contribution to lesson planning. That is especially important in heutagogy. Thomas (2003) argues if students have control over their learning tasks, it will be easier for them to meet their learning goals. Lastly, teacher encouragement and support might not influence students’ metacognitive abilities directly, but it might be the first step in developing those skills. As Gallucci (2006, p. 19) mentioned, “the heart of teaching is providing
students with the tools to make them more effective learners” and not just teaching the content.

2.4 Can metacognition be taught?

Some researchers argue that metacognition can be taught, and it might improve academic achievement (Muscott, 2018). The effects of metacognitive training on students’ achievement in maths were tested recently in the USA (Bol et al., 2016). 116 randomly selected participants who were split into two groups (control and experiment) took part in this three-week research. The authors concluded that this training in self-regulated learning (specifically, such skills as goal-setting, self-monitoring and self-reflection) improved not only students’ maths results but also their time management skills. However, the validity is questionable since this questionnaire is a self-reported measure and some students might have overestimated their use of self-regulatory strategies (Young and Ley, 2005). Their paper states that questions about self-regulation could be difficult for poorly self-regulated students.

A year earlier a similar experimental design was employed in Italy among 135 elementary school students (Cornoldi et al., 2015). By using regression analysis, the authors concluded that training in metacognition transferred positively onto students’ abilities to solve maths problems. Mathematical word problems are “complex cognitive tasks” (Cornoldi et al., 2015, p. 434) and apart from mathematical abilities, children also need reading comprehension, metacognitive abilities, and motivation. In this experiment, not only were activities focused on metacognition, but the students reflected on their beliefs about mathematics. Referring to this study, Davey (2016) also emphasised the importance of metacognitive training programmes. Having conducted a case study, she claimed that the teachers’ actions and words are crucial in developing students’ metacognitive abilities.

Mutambuki et al. (2020) combined metacognition and active learning and by applying a quasiexperimental design investigated the influence of both on the first-year undergraduate students in chemistry courses. By active learning, the authors mean frequent questions, discussions, problemsolving tasks, etc. Such metacognitive prompts as planning, reflecting, developing self-awareness, and making adjustments were mentioned in this paper. The authors concluded that active learning implemented with metacognitive instruction impacted students’ results in General Chemistry, “particularly on cognitively demanding chemistry concepts” (Mutambuki et al., 2020, p. 1832). Having 240 students in the control group and 270 students in the treatment group increased the validity of the findings. However, the two groups had different instructors with different teaching styles which could have influenced students’ learning in a course.

Belenky and Nokes (2009) took into account not only students’ performance but also engagement while using metacognitive prompts. Based on the questionnaires, low-achievers “showed better learning and transfer when getting metacognitive prompts” (e.g., How does the solution relate to what you did?) and high-achievers “showed better learning and transfer when getting the problemfocused prompts” (e.g., What is your goal now?) (Belenky and Nokes, 2009, p. 102). The study proves that manipulatives alone do not necessarily make students think and reason deeply, it is also the way they are engaged with them. Plus, students’ engagement does not depend on whether concrete or abstract materials are used.

As it was mentioned in the previous chapter, writing reflections can be met with resistance among learners. Though reflective journals are commonly used among researchers (O’Loughlin and Griffith, 2020; Ramadhanti et al., 2020), there are other audio or video tools to record self-reflections and at the same time engage students, for example, Flipgrid (Flipgrid, Inc., 2021), an online video forum platform. Flipgrid was recently implemented as a pilot study in the USA (Kiles, Vishenchuk and Hohmeier, 2020). In 2019 about 30-35.7% of students wrote reflections in journals and in 2020 87-93.4% participated in Flipgrid forums. 96% of students preferred to record short videos instead of writing journals. The authors believed that the casual nature of Flipgrid might have motivated students to share deeper reflections. It was concluded that this online platform has the potential as “a self-reflection tool used in combination with other pedagogical techniques to facilitate learning” but the depth of reflections should be explored further (Kiles, Vishenchuk and Hohmeier, 2020, p. 4).

As for students, changes for teachers might be difficult too. To promote metacognition during math classes, a teacher should model it first (Knox, 2017). That is why it is important to have professional development about this topic. Many teachers do not see the connection between mathematics, reading, and metacognition (Tok, 2013). Tok believes that it’s essential to grasp reading and mathematical skills in order to succeed. Both Tok (2013) and Knox (2017) argue that classroom instructions usually pay more attention to content rather than analysing the problem-solving process.

Noteworthy research was conducted in the USA for a similar duration (4 weeks) (Siegle and McCoach, 2007). However, the sample in this experiment was even larger (872 grade 5 students) and the aim was to investigate whether teachers who are trained in self-efficacy will have a better effect on students’ performance. It was also organised with a control group and a treatment group, but the teachers had professional development regarding metacognitive support in the latter. As a result, the students from this group were more confident and it had a positive effect on their self-efficacy.

Therefore, factors that support metacognitive development are (1) attention to learning goals (Buzza and Dol, 2015), (2) constant self-assessment, (3) reflection using different tools, (4) applying one strategy at a time (Davey, 2016). Meanwhile, (a) predetermined curricula, (b) predefined answers to open-ended questions, and (c) ineffective classroom management (Greene, Costa & Dellinger, 2011) can decrease metacognitive development and educators should be aware of that.

2.5 How to measure metacognition?

There are different quantitative tools to measure metacognition: the Metacognitive Awareness Questionnaire (Schraw and Dennison, 1994), the Metacognitive Awareness Inventory for Children (Jr. MAI) B Form (Sperling et al., 2002), the Motivated Strategies for Learning Questionnaire, (Valencia-Vallejo, López-Vargas and Sanabria-Rodríguez, 2019).

Wagaba, Treagust and Chandrasegaran (2016, p. 5379) argue that sometimes it’s hard to check how students are progressing metacognitively because most tests assess only cognitive abilities. Similar to the current study, action research was conducted but quantitative data analysis methods (Metacognitive Support Pre- and Post-questionnaires) were applied. Seventy-nine students took part in this study, but the number varied throughout the research cycles. Frequently, students reported that they didn’t discuss with their peers how they learned science because they either did not have an opportunity to do so or, as the authors stated, most of them were low achievers. The researchers concluded that some results could have been “misleading because many of the scales had generally high pre- and post- mean scores in the three cycles, therefore there was not much room to move up on the Likert scale” (Wagaba, Treagust and Chandrasegaran, 2016, p. 5392). They also believed that the 20-weeks cycle is too long to enhance the necessary changes and it is better to have the same topic and the same students in all three cycles. It is also recommended to find a better instrument to test metacognition in the classroom.

One of the tools to measure metacognition is called the Metacognitive Awareness Inventory for Children (Jr. MAI) B Form (Sperling et al., 2002). This questionnaire consists of 18 items (5-point Likert-type scale). It was adopted while studying metacognitive abilities among 150 gifted and 150 non-gifted students (Ogurlu and Saricam, 2016). Researchers claimed that gifted students possessed greater metacognition which should be considered while creating lesson plans. However, they mentioned social-desirability bias as a common vulnerability in questionnaires. Valencia-Vallejo et al. (2019, p. 15) also underlined that “the subjectivity of students’ answers is a limiting factor of self-reporting questionnaires”. Thus, further qualitative research is needed to observe metacognitive awareness among young gifted and non-gifted students, and it proves the importance of the current qualitative study.

Another fascinating research was conducted in Malaysia among 378 students to show the correlation between metacognitive abilities and achievement in mathematical problem solving (Zakaria, Yazid and Ahmad, 2009). A Metacognitive Awareness Questionnaire, modified from the one created by Schraw and Dennison (1994), was used in this research to prove that the higher students’ metacognitive abilities, the higher their results in a Mathematical Problem-Solving test. However, Muscott (2018) questions the authenticity of the problems used in this test. Employing quantitative methods, he concluded that HoMs, particularly HoM 5 Metacognition, have positive effects on students’ performance outcomes but an assessment tool to measure HoM competencies is still required.

Qualitative measuring tools use the coding of responses. The codes will depend on student answers or the researcher’s interpretation of metacognition. Responses might be scored as high, medium, or low levels (Strauss and Corbin, 1998). Stanton et al. (2015) used students’ answers to make deductions about their levels of metacognition and developed a coding system as Sufficient/Provides Evidence or Insufficient/Provides No Evidence. 245 undergraduate students in the USA took part in this experiment. Researchers coded all answers individually. Then, they discussed all findings together and came to a consensus for the final coding. Following this model allowed the researchers to get some valid data. It was summarised that metacognitive skills had an effect on learners’ performance and what is more important would assist them to become more self-regulated students in the future.

These findings support the significance of metacognitive training as a heutagogical technique among teachers and students to enhance cognitive abilities and mathematical reasoning. There is some strong empirical evidence that metacognition has positive effects on students’ performance, specifically in mathematics. However, there is still not enough evidence to prove its importance in elementary school, especially from the students’ point of view, which validates the purpose of this qualitative action research. In the next chapter, the research design and methods to solve this problem will be discussed.

 

3. RESEARCH METHODOLOGY

This study aims to explore the perceptions of students on the heutagogical framework while teaching maths at an elementary school in Cambodia. The study focuses on some metacognitive elements that can assist students to become more self-determined.

Central Question: How can students’ needs be met using the heutagogical framework while teaching maths in an elementary school in Cambodia?
Subquestion 1: What tools and strategies should teachers use to implement the heutagogical framework?
Subquestion 2: How can metacognition as a heutagogical technique be used to improve students’ self-determination?

This chapter aims to explain the research design and methods that were selected as appropriate to research the issue related to the research questions.

3.1 Research design

A lack of qualitative action research in existing literature highlighted the need for this investigation into self-determination through metacognition at a young age. Compared to traditional experimental studies, action research is an amalgam of theory and practice (research and action) that “focuses on specific situations and localized solutions” (Stringer, 2007, p. 1). It is a compass leading teacher in the right direction and helping them see changes in their practice (Simon and Wilder, 2018). Action research is “grounded in a qualitative research paradigm whose purpose is to gain greater clarity and understanding of a question” (Stringer, 2007, p. 19).

Action research was promoted in the mid-1940s with the purpose to solve some practical problems in everyday life. The goal was to distinguish the problem, try to change the situation, and check the results (Coolican, 2014). Since the main purpose of action research is to improve the practice of education by studying issues or problems (Creswell, 2012), it was decided to choose this research design to align with the purpose of the study. Self-determination is like “mini action research”. It also has a cyclical model: setting goals, attempting to achieve them, self-assessing and making adjustments (Zimmerman, 2002). Metacognition itself has a cyclical model too: planning, thinking about it and making changes if needed, reflecting, and making new plans based on the results (Costa and Kallick, 2008). Thus, it was the other reason for choosing action research as a research design for this investigation.

The main attribute of almost all action research models is the cycles, specifically that each cycle is based on the conclusions of the previous cycle (Edwards and Willis, 2014) which “guides teacher preparation and instruction” (Stringer, Christensen and Baldwin, 2010, p. 1). Sometimes they are named spirals or helices (Punch and Oancea, 2014). Edwards and Willis’ (2014) model starts with reflection: Reflect – Plan – Act – Observe, while Stringer’s (2010) model commences with the observation cycle: Look – Think – Act. Even though it seems straightforward, it is not as simple as it looks. There are no arrows between them so it is not a linear process and the researchers can go back to any cycle when changes or adjustments are needed. The “Act” stage also includes reflection and evaluation. Reflection is the key characteristic of each cycle, and the results indicate whether changes should happen or an additional cycle or “mini-experiment in practice” is needed (Wagaba, Treagust and Chandrasegaran, 2016, p. 5378). Since its purpose is not just understanding the problem but finding the solution, it is a suitable form of research for this investigation. Moreover, Nasrollahi (2015, p. 18667) noticed that Stringer’s model does not only involve teachers but also students “as action researchers collaborating in the action research process”. It is a standard model that has been similar to hundreds of other models created in the last eighty years.

The present action research will include these research tools: interviews with students and observations using the researcher journal. The research questions that require qualitative data to investigate students’ views justified the qualitative approach of this study. Interviews (qualitative methods) show the complexity of the data provided by participants (Creswell, 2012). At the same time, some quantitative methods, such as questionnaires, can be “inappropriate because of the child’s age” (Morison et al., 2000, p. 113). Qualitative methods and students’ involvement can provide more light on heutagogy in elementary schools and explore any misconceptions.

3.2 Setting and participants

Metacognition is one of the sixteen Habits of Mind (Costa and Kallick, 2008) adopted by the participating school in Cambodia. Thus, it provided an ideal setting to apply action research on metacognitive support in mathematics. Secondly, being a subject coordinator allowed the researcher to take action and adapt the math curriculum using metacognition as a heutagogical tool. Stringer (2007) underlines that conducting action research helps in curriculum construction and evaluation. Finally, as a participant-researcher, the researcher had a chance to work closely with the participants and gather data during math classes.

Previous research in self-determination in elementary school is mostly from the teachers’ (Stein, 2018) or school administrators’ points of view (Akyildiz, 2019) which indicates the need for the present study. Earlier, children were treated as “dependent” on others to guide them on what to do (Elden, 2013, p. 78). Later, Arnold and Triki (2017) argued that children might be participants in experimental research, however, the chance exists that students would only say what they think researchers want to hear instead of their honest statements. It is understandable that writing a high-quality study with children may be a noteworthy challenge (Ponizovsky-Bergelson et al., 2019), yet open-ended questions and encouragement can elicit some valuable data. Hoover (2018) recommends using short semi-structured individual interviews while working with young children. Semi-structured interviews “have in-built flexibility to adapt to particular respondents” (Punch and Oancea, 2014, p. 184) which is also preferable for interviews with children. Punch also suggests having natural settings and making sure that the language is age appropriate. All these recommendations were taken into account during this study. Interview questions can be found in Appendix III. Each interview with each student was not longer than 15 minutes, with three interviews during the experiment (the beginning, middle and end of the unit). Interviews were conducted via Google Meet, the platform used at school during online learning.

23 grade three students (9-10 years old) and their parents were informed about this research. 15 of them returned the signed consent forms, 8 parents did not reply to the email sent, so their children were not involved in research. In the end, 7 boys and 8 girls took part in the study.

All the students were Cambodian. Their native language is Khmer (the official language of Cambodia). The interviews were conducted in English as this is the language they use to study at this International School. This language barrier is why math in English might be particularly challenging and metacognitive strategies might be beneficial to them. All interviews were transcribed verbatim by the researcher.

Consent forms were sent on April 28, 2021, as soon as permission was granted by ERGO. Parents were called by the academic assistant from the school who informed them about an email sent. As soon as some consent forms signed by parents were returned, consent forms were sent to their children. Observations began as soon as both parents and students signed the consent forms. The first interviews were held on the same or following days as soon as the consent forms were returned:

29/04: S2, S3, S13, S14
03/05: S17, S21, S22
04/05: S16, S23
05/05: S5, S7, S8, S12, S19
07/05: S20

The second round of interviews was held on June 17-21. The third round was recorded on June 14-
15, 2021.

3.3 Data collection

The experiment lasted 9 weeks starting on April 29 until June 30, 2021. Three cycles of Stringer’s model were incorporated into three phases of instruction (Stringer, 2007, p. 9, fig. 1.1).

PHASE 1: PLANNING

1. LOOK (3 days)

Consent forms are sent to parents and students (Appendices I and II). The first semi-structured interviews with some students are recorded. Field notes are taken every day.

This first stage allows the researcher to collect data about participants’ perspectives and to define the problem.

2. THINK (1 week)

Data are organised, the answers are coded and analysed, and observations continue during this time. Metacognition Diaries (MD) and the final assignment that incorporated metacognition elements are created based on the results of the interviews and on the theory of the process of metacognition which consists of three dimensions – commitment, value, and capacity (Costa and Kallick, 2008). Even though the authors presented five dimensions in their book, and they are discussed in the previous chapter, the core of this study constituted only three dimensions. First, HoMs are included in the school curriculum since kindergarten, it is assumed that by grade 3 most of the students should know the meaning of 16 HoMs, thus, Expanding Meaning as a dimension was not covered by this research. Secondly, considering the age of students and the time constraints it would have been overwhelming for students to reflect properly on all five dimensions at the same time. Since the focus of this paper was self-directedness through metacognition, Increasing Alertness as a dimension was not included in this study.

3. ACT (1 week)

MDs are shared with the students in Google Classroom (Appendices VI, VII, VIII). The final assignment is explained to students (Appendix IV). Before being given to participants, MD and the final assessment were examined by our school curriculum coordinators who supported that both assignments can be used to monitor students’ metacognitive growth.

The Flipgrid platform is introduced to students. Students have a choice to either complete MD in Google Classroom or answer these questions by recording videos in Flipgrid (video diaries). To set the tone of reflection, at the end of each math lesson students have five to ten minutes of “silent thinking time” where they have a chance to reflect and answer the questions in the diaries or record the videos. Observations continue during this time. Organisational skills are taught by using checklists.

This part of implementing practical solutions distinguishes action research from other types of research. Stringer (2007, p. 142) calls it “the sharp end of the stick”. This is the part where the action happens.

 

PHASE 2: INSTRUCTION

1. LOOK (1 week)

The second semi-structured interviews are recorded to check what modifications should be made. Observations continue during this time. MDs and Flipgrid Videos are checked by the researcher. Most of the student answers in the diaries are short and not specific. Multiple students do not stay online until the end of the class and do not complete the MDs or do not record the videos.

2. THINK (1 week)

Answers are coded and categories are added or modified. Observations continue during this time. Reasons for students leaving online classes early could be family circumstances, bad Internet connection, no interest in the topic, other distractions. Student answers might be improved by providing more scaffolding and teaching how to set goals, how to monitor learning by using checklists and rubrics, how to take notes, etc. The benefits of reflections should be discussed with the students.

3. ACT (2 weeks)

This cycle takes longer because it is necessary to spend more time on interventions. All math lesson plans are modified and include metacognitive elements (Appendix V), namely goal-setting, selfassessment, peer feedback, HoM Discussion, assessing using a rubric, exit tickets, note-taking, post-assessment. Not all lessons include all these elements at once because of time constraints. It is decided to add metacognitive elements in the beginning and middle of the lessons so that all students have a chance to reflect before they leave the class. Observations continue during this
time.

 

PHASE 3: EVALUATION

1. LOOK (1 week)

The third semi-structured interviews are recorded on June 14-15 and observations continue during this week. All lesson plans continue to have metacognitive elements and students continue to write MDs or record video diaries on Flipgrid.

2. THINK (1 week)

Final interviews are analysed. Student MDs, videos and observation notes are reviewed, final codes and categories are added, the strengths and weaknesses of the experiment are identified. All core categories, abstract concepts and specific indicators were organised in a spreadsheet.

3. ACT (3 days)

General and brief results were discussed with colleagues during the subject meeting at the end of the school year. These continuous cycles of looking, thinking, and acting allowed the researcher to identify the necessity of metacognition as a heutagogical technique in fostering self-determination in young students.

3.4 Data analysis

Metacognition is not only about planning and knowledge activation but also the intentional monitoring of students’ cognitive processes, reflection, time management, and self-evaluation. That is why the participants frequently had chances to set goals in using HoM 5 Metacognition, self-reflect on whether they achieved those goals, monitor their progress in solving math problems, reflect on their progress using the rubric, apply different strategies in solving word problems and reflect on them. These topics were observed by the researcher and discussed during each of the three interviews. The analysis began after the data was collected from the initial interviews, starting from April 29, 2021, as soon as some parents and students returned the signed consent forms. From that point onwards, data collection (from the following interviews and field notes) and analysis occurred simultaneously. This approach has become a regular practice in qualitative research (Charmaz and Belgrave, 2015).

In order to understand the context, Stringer (2007, p. 100) suggests researchers should start with interviews and then move to other sources of information in the next cycles of action research. Observations written in the research journal were held during all three cycles of action research. The focus was on behaviours related to self-determination, particularly the metacognitive skills related to goal-setting, self-reflection, reflecting and monitoring the progress in solving math word problems, and the emotional aspect after solving problems (feeling of difficulty, feeling of confidence, etc.). As soon as the student showed some evidence of applying metacognition, it was recorded as a memo or a sentence. Thus, the protocols were kept for each student who signed the consent form. Observations were overt since both students and parents were asked to give their consent before the beginning of the study. The primary data were derived from interviews but observations further clarified or extended understanding of the issue being investigated. Punch (2014) underlines that combining interviews and observations is a good method that can lead to high-quality data.

Students’ interview data, as well as observation notes, were coded and analysed using a grounded theory approach. Creswell (2012) believes that it helps the analysts remain close to the data during the whole process. Codes and themes were developed, and connections were identified between different themes in order to generate conclusions. Based on the systematic design of the grounded theory, there are three types of codes represented diagrammatically by Punch and Oancea (2014, p. 238, fig. 10.4):

a) substantive (or open coding) is done at the beginning of the analysis to generate more abstract concepts,
b) theoretical (or axial coding) to see how data is interconnected, and
c) core (or selective coding) concentrates on core categories around which the theory is designed.

Charmaz (2006) emphasizes that it’s not a linear process and a researcher can go back to the initial data and make new codes at any moment of action research. Moreover, the grounded theory implies that the experiment doesn’t commence with an already formulated theory but rather “allows the theory to emerge from the data” (Strauss and Corbin, 1998, p. 12). Analysts are encouraged to (a) remain open to various opportunities, (b) produce a few options, (c) investigate different opportunities before selecting one, (d) use cycles to go back to the experiment and get a new vision, (e) believe
in the study, (f) circumvent shortcuts, (g) enjoy the research (Ezell, 2017, p. 72).

Information was collected, analysed, and compared until data saturation was achieved.

3.5 Ethics and risk assessment procedures

The approval to conduct this research was confirmed through the Ethics and Research Governance Online system of the University of Southampton. In order to start the study, it was obligatory to obtain confirmation. After that, the potential participants and their guardians were invited to take part in the study via email.

First, the Board of Directors of the participating school were informed about the study. Since the children are 9-10 years old, the consent forms were first signed by students’ guardians and after that, if the parents approved, they were sent to students. Both the guardians and the participants agreed that the interviews will be recorded. Confidentiality was guaranteed to all participants. The participants had the right to withdraw from the interviews at any moment before June 30. Personal information was anonymised during the transcription process and coded as Student 2, Student 3 etc. Since February 20, all schools in Cambodia moved to online learning, thus, both interviews and observations took place via Google Meet. Only the researcher had access to the audio-recorded data which were held on a University of Southampton file storage space and were destroyed after the transcriptions were complete. The transcribed interviews and the observation notes were stored on a password-protected University of Southampton file storage space too.

3.6 Validating findings

To avoid an incorrect interpretation of data, multiple methods of qualitative data collection should be used (Oliver-Hoyo and Allen, 2006). The accuracy of the findings was validated through the triangulation analysis:

– interview with students,
– observation notes,
– literature review.

Triangulation of data ensured the chosen key themes, providing an insight into self-determination from the students’ views. Punch (2014) also suggests getting feedback from responders. After the interviews were transcribed verbatim, the participants were asked to check them. Triangulation and member checking are the most common validation techniques (Creswell, 2012).

In the next chapter, the results of qualitative action research will be presented.

 

4. FINDINGS

4.1 Overview of the chapter

Using an action research framework, it was investigated how engaging in reflection can change grade 3 students’ behaviour, making them more confident in their abilities to solve mathematical tasks and motivating them to be more active and consistently remain self-determined. Data was collected over a period of 9 weeks from April 29th to June 30th, 2021 during a lockdown (all classes were online). The data analysis stage was conducted concurrently with data collection during the three cycles of action research.

This chapter presents the data collected during the interviews with the participants and the observation notes collected by the researcher while teaching mathematics. The participants were 15 grade 3 students (9-10 years old) in one of the private schools in Cambodia. The responses and the field notes were grouped into categories and analysed to answer the research questions.

Core categories, abstract concepts, and specific indicators (Punch and Oancea, 2014) were selected. Having analysed all interviews, it was clear that open coding and deductive analysis did not answer the research questions because they focused more on the categories selected rather than how students developed their metacognitive knowledge and skills throughout the unit. Therefore, during the axial and selective coding, inductive analysis was conducted, new codes were created based on the previous analysis.

The following core categories were decided on during the analysis and were based on the Habit of Mind Dimensions of Growth by Costa and Kallick (2008):

A. Commitment (ability to self-assess, self-direct and self-monitor in their development of HoM 5 Metacognition within the unit)
B. Value (ability to recognise the benefits and advantages of engaging in the HoM 5 Metacognition)
C. Capacity (ability to develop skills, strategies, and techniques through which they engage in the HoM 5 Metacognition within the unit)

Each core category covered three to five abstract concepts. The specific indicators are the same for each abstract concept in each category and coloured accordingly:

  • Indicator 1: not attempting to do (red).
  • Indicator 2: attempting to do (yellow).
  • Indicator 3: able to do successfully (green).

After reading each student’s response, it was categorised to a core category and then assigned to an abstract concept. After that, it was colour-coded based on the indicators above (Appendix IX).

4.2 Core category: Commitment

In general, most of the students showed the development of metacognitive knowledge. Four abstract concepts were defined during the analysis based on students’ responses:

1) Setting goals
2) Self-questioning
3) Self-monitoring
4) Responding to feedback

Show major improvement Show minor improvement Stay in red Stay in yellow/green Decline No progress can be detected (1 answer provided)
Setting goals 4 8 0 2 1 0
Self-questioning 3 1 4 2 1 4
Self-monitoring 5 6 0 4 0 0
Responding to feedback 2 2 0 0 0 11

Table 1: Core Category Commitment – Overall Picture during 3 Phases

* Major improvement – moved from red to green indicator.
* Minor improvement – moved from red to yellow indicator or from yellow to green indicator.
* Stay in red – did not show any progress.
* Stay in yellow/green – already had good self-determined skills at the beginning of the research.

More examples and notes can be found in Appendices X – XIII that complement Table 1.

4.2.1 Setting goals

It is interesting to find out how all students understood and could define the importance of setting goals during the first interviews but most of them did not set goals in mathematics or did it only when teachers asked them.

After completing the tasks with the metacognitive elements, some students shared their views on how goals helped them:

“don’t give up and try to solve a problem” (S17-P3),
“know what to do and you will not lounge, so you’ll be better” (S5-P3),
“learn and stay happy and, like, don’t get bored of learning” (S13-P3).

However, according to the field notes Students 5 and 17 were not persistent in achieving their goals during the unit. Other students believed that it was not necessary to set goals because they did not have time to do them (S20), or they were not important in maths because “you don’t have to calculate” when you write goals (S23-P3). Student 7 did not set any goals because she forgot about them. Based on the observation notes, she also missed some classes or did not complete most of the metacognitive activities before the third interview was held.

4.2.2 Self-questioning

The analysis of the interviews highlighted the importance of self-questioning. Some students were consistent throughout the unit and shared some questions they asked themselves: “is this answer correct” or “have I filled the checklist” or “do I have to start over again?” (S8-P1).

Others claimed that they did not ask themselves questions (S5-P1). However, during the last interview, they mentioned the importance of self-questioning “because if you don’t ask yourself, you might don’t know what to do” (S5-P3) or referred to past knowledge “because you can ask yourself…or just get some ideas from the past” (S20-P3). While during the first interview Student 3 said she would rather wait for the teacher to ask questions, later she noticed “my PT [Performance Task] is not that good so I change my PT, and so I ask question, ‘how good is my PT?’ “.

Another theme that emerged from the interviews is the lack of persistence: “I ask, ‘what do this task do?’ and sometime even I don’t understand… but sometime I guess” (S22-P3), or “I ask myself ‘Really?’ and go back and sit one more” (S7-P3) or the students simply replied they did not ask any questions (S2). Some participants claimed that they preferred to ask other people because “I don’t know about myself” (S12-P3).

4.2.3 Self-monitoring

Out of all the concepts, this was the only one where all students showed improvement by the end of the unit which is an important sign of self-directed learning. Starting from not using the diary “because I forgot about it” (S14-P1) to using it to find the unfinished assignments “When I go to checklist they will have a link to go in the work for math… it help us know what work that we still haven’t finish” (S14-P2). Field notes show that Student 14 participated more in the middle of the unit. According to the data collected from the interviews, Students 2, 3 and 16 already had good self-monitoring knowledge since Phase 2.

It was thought-provoking to listen to what students think about using rubrics (Appendices IV and V) and self-assessment in maths. Most of the participants highlighted that it was useful to have rubrics in the Metacognition Diaries:

“so Teacher can know which task they don’t really understand” (S22-P3),
“students write goals and look at rubrics to see what their grades and grade theirself and do important stuff on it” (S3-P3),

On the other hand, some students pointed out such issues as dishonesty, inability to use the rubric without knowing the correct answer, and overconfidence. Student 21 (P2) mentioned that some students might not be honest when they grade their own work: “they want a perfect score and then when they’re bad they just put four and they’re saying that, ‘I’m good, I’m good’ “. Student 19 (P3) pointed out that it is difficult to use the rubric when you do not know whether the answer is correct or not: “So, when kids do it, no one, he or she in the PT cannot predict if they’re correct or not”. And during Phase 2, he mentioned that he used the rubric when the teacher projected it but not on his own initiative “when you just post the assignment with the rubric under it, it’s very hard for you to make me watch rubric”. Student 20 (P2) also underlined that “it’s kinda helpful if you’re not good, but if you’re good already, you always grade yourself four, I think it’s not really that useful”.

4.2.4 Responding to feedback

This abstract concept was mostly based on the observation notes because students were not asked about feedback during Phases 1 and 3. The planning for the interviews was not done properly. The list of selected questions differed during three Phases. Students were asked specifically about feedback during Phase 2. After the analysis was done, it became evident that they should have been the same questions in all three Phases.

What some students said in the interviews did not match their behaviour during the observations. I believe it happened because they probably wanted to say what they thought the teacher would want to hear or they wanted to present themselves in a positive light (social desirability bias). For example, Students 17, 21 and 22 said that they often checked the feedback in Google Classroom but based on the observation notes, they did not reply to them. Having read the questions that the researcher asked about feedback, some of them could have been reworded or asked indirectly (how a third party would behave) so that students do not feel embarrassed. It proved to be effective while interviewing Student 23:

“Researcher: What advice would you give to students who just finished grade two and are moving
to grade three? …
Student 23: … I recommend them to use, study more math, use more link and make sure that do
more work than me, ‘cause I never do my work.
Researcher: Why not?
Student 23: You don’t remember at the last interview I said. I’m lazy, but now I do.
Researcher: I remember you said so.
Student 23: But now I do it.” (P3)

Most students understood that they had to check teacher’s comments and correct their mistakes “If I get feedback I try to make it better, for example, the math what is perimeter, I always do it then you always feedback me, that time I had [a perimeter of] more than 24 and then now I have [a perimeter] over 40” (S20-P2). Some of them checked and replied to comments frequently: “I check on the private comments and I finish some of your private comment and then after, later I will do the next comment and then after that I turn in the work” (S8-P2). Observation notes confirm this data too.

Other students explained why they did not respond to feedback. They either missed the notification “sometime I didn’t see my email to me” (S12-P2) or they were overwhelmed “I have a lot of email and then it comes a lot of email now” (S16-P2), or they still do not understand the feedback “sometime I just don’t understand the question” (S13-P2), or they forgot about it “sometime I forgot” (S14-P2). All these reasons are understandable for grade 3 students who moved to online learning a few months ago. When the students were studying onsite, real-time feedback was provided every day during classes. For example, when students completed a task, the teacher would return their notebooks and they had a chance to ask questions for clarification in person.

Even though some students understood that they could have asked for feedback “Maybe I can ask for feedbacks or I just, when I’m offline or I don’t have anything to do, I’ll just try a little more” (S7-P1), they could not identify why they had not responded to it: “sometimes I just miss it” (S7-P2).

4.3 Core category: Value

In general, most of the students showed the development of metacognitive experience.
Three abstract concepts were defined:

1) Making connections to real life and the future
2) Giving advice to other students
3) Emotional aspect after solving problems

Due to the subjective nature of this core category, it was not quantified as the other two.

4.3.1 Making connections to real life and the future

Almost all students could have connected the unit to real-life or to the future starting from the first interview, so these questions were not asked in further interviews:

“I know how to measure, like, when I don’t have a standard unit, I can use the non-standard unit” (S2-P1);
“we learn about litres… so, as a scientist, we have to put portion… to invent something” (S8-P1);
“because my parents own a business… they just [bought something] from China and we measure the stuff” (S13-P1).

Students who did not make clear connections between reality and the unit did not participate actively in class. They mentioned some general math connections, e.g., counting money (S5), multiplying something (S7) or calculating the cost of the units (S22) which were not relevant to the current unit.

4.3.2 Giving advice to other students

The purpose of this concept was to see if students can apply self-directedness to external situations.

When students were asked to recommend something to children who are moving to grade 3, these themes emerged:

  • Use HoMs when solving difficult problems “Persisting and Apply Past Knowledge to New Situations and Listening and Communicating with Clarity and Precision” (S8-P3);
  • Watch the recorded lessons and Youtube videos “I will tell them what to watch in the YouTube to help them a success in grade three” (S16-P3);
  • Read more books (S14);
  • Do extra research “search more about shapes and math because when you go to grade three, now you will learn about the fractions and rhombus, new shapes” (S20-P3);
  • Ask questions and no copying (S21);
  • Review difficult topics before studying in grade 3 (S22).

4.3.3 Emotional aspect after solving problems

This was the only abstract concept that was not colour-coded based on the specific indicators as they were not applicable here. The purpose of this concept was to observe whether emotions can have some effect on metacognition and self-directedness in general. Students were asked about their feelings directly during the interviews and some of them were also inferred from their answers or observations.

This category explained the answers to other categories. For example, a lot of Student’s 2 answers were simply “No” or “I don’t know”. Thus, in some cases, this lack of persistence could have contributed to less self-questioning and less note-taking.

Students 5, 8 and 20 did not get sad when they made mistakes (P1). They said it was a chance for them to improve more. However, as observation notes show, Student 5 lost his motivation during the unit and did not complete most of the graded tasks. Reasons might be different: family circumstances, no ability to become independent and control his learning or even that it was the last unit of the year, and he was simply tired. Meanwhile, Students 8 and 20 were developing their metacognitive knowledge and skills. Thus, while these reasons helped some students, they hindered
others.

During Phase 3, Student 7 was worried that she did not complete most of the tasks, but she also did not ask for help during the unit and missed a lot of online classes. Same as Student 14 who could not identify the difficult topics and thus, could not make an improvement plan. It is possible that lockdown impeded teachers’ ability to reach out more to students in need. In order to help students who struggle, the teacher could have initiated some interventions to learn more about the students’ circumstances.

Student 12 could identify the difficult parts of the unit and was very persistent to learn these topics. Her answers for goal-setting, strategies and self-monitoring concepts, and the observation notes combined into a complete picture to show improvement in self-directedness, similar to Student 13 who also showed enthusiasm to study more on her own. These are the students who were doing well before lockdown and continued doing well during online learning.

4.4 Core category: Capacity

In general, some students showed the development of metacognitive skills.
Five abstract concepts were defined:

1) Connecting metacognition to math
2) Applying different strategies when solving problems
3) Asking for help when needed
4) Taking notes
5) Improvement strategies

Show major improvement Show minor improvement Stay in red Stay in yellow/green Decline No progress can be detected (1 answer provided)
Connecting
metacognition to math
1 5 2 3 2 2
Applying
different
strategies
when solving
problems
1 4 3 5 1 1
Asking for
help when
needed
3 3 0 9 0 0
Taking notes 1 5 0 1 3 5
Improvement
strategies
2 3 0 7 3 0

Table 2: Core Category Capacity – Overall Picture during 3 Phases

* Major improvement – moved from red to green indicator;
* Minor improvement – moved from red to yellow indicator or from yellow to green indicator;
* Stay in red – did not show any progress;
* Stay in yellow/green – already had good self-determined skills at the beginning of the research.

More examples and notes can be found in Appendices XIV – XVIII that complement Table 2.

4.4.1 Connecting metacognition to math

About half of the students were able to connect metacognition to math at the end of the unit. Students could recognise the purpose of using Metacognition Diaries in class:

  • to understand the meaning of the HoM (S21-P3),
  • to help set goals and self-assess (S17-P2),
  • to talk about feelings, improvements, and plans (S16-P2),
  • to make it more challenging (S13-P3).

Student 12 connected it to the lesson when she solved word problems about time “because I really struggling about time so I need to think if I go backwards” (P3). Student 8 made a connection to the lesson about perimeter “so that we can express our opinion of our commitment over doing those tasks.” (P2). Student 23 recognised her internal doubts and uncertainty and understood that they need to be eliminated:

“I think about my thinking because if we don’t think about our thinking, for example, I think to do my work, but my mind, my half-mind say don’t know. So, it’s still no.
Researcher: So, what do you do then?
Student 23: I make that mind go together to get along.” (P3)

Some students still did not see a clear connection to math and said they only used it when completing Metacognition Diaries (S2-P3), when the teacher asked to do the tasks (S19-P2), or when recording videos in Flipgrid “I need to think what I need to say” (S20-P2), “it really help not to always write, we need to talk to people, to not be shy, to show your feeling and your answer, so, I think it’s good” (S13-P2). The students who completed only 1 Metacognition Diary or did not write at all (based on the observation notes) did not see the importance of thinking about their thinking:

“I didn’t think of that” (S14-P3),
“I don’t know how to answer this question” (S5-P3),
“I do not understand the HoM yet. It’s kind of difficult.” (S3-P3).

4.4.2 Applying different strategies when solving problems

The following strategies were mentioned during the interviews:

  • asking the teacher or listening how it was explained to other students (S3);
  • asking other family members (S21)
  • applying other HoMs:
    • Striving for Accuracy (S5);
    • Persisting (S16);
    • Thinking Flexibly (S17, 22);
    • Applying Past Knowledge to New Situations (S20).
  • completing the shortest tasks first: “Because I was like, ‘What, I still have more task?’, so I have to go do the small task so when I did the small task I will do the long task later” (S8-P2);
  • finding clues and drawing a model: “First, I need to find clues. And the second, I try to do a model but drawing a model is very easier” (S12-P1);
  • using a calculator (S13).

Five students showed some improvement during the unit. The rest of the students stayed on the same level as they were in the beginning and could not identify any strategies (S2, 7, 14) or said they would just guess the answers “sometimes following your gut you get it right” (S20-P).

I think this concept was not developed well during the unit. The prepared lesson plans did not include any specific strategies to help the students because of time constraints.

4.4.3 Asking for help when needed

Most of the students stated that if they did not understand the problem, they would ask their teacher (S3), family members (S21) or friends (S5).

Even though some students said during Phase 1 that they did not ask anyone “I do not need someone to help when it’s math” (S2), later they mentioned they would ask their relatives if they did not understand. Student 14 remarked that he was scared to ask the teacher “because I ask too much” (P1) and observation notes indicate that he rarely asked for clarification during the unit. This lack of confidence could have hindered his metacognitive skills.

Some students noticed that before solving some problems on their own, they would ask someone to help (S7, 8). Maybe studying at home during the pandemic is the reason for it. Meanwhile, Student 13 mentioned that she would try to solve the problem by herself first and then she would ask someone if needed “or when they’re not home, I would try to research a bit” (P2). Student 20 (P3) also mentioned that he would research by himself before asking anyone. During Phase 1 and 2, Student 22 understood that she needed to ask the teacher more often “but sometime I didn’t ask about, I just do it”. During Phase 3, she stated that she asked the teacher when she needed help which is also mentioned once in the observation notes.

4.4.4 Taking notes

Most students understood the purpose of taking notes: “we take a note and then when we go back to try finishing [a problem], we can copy instead of wasting our time on thinking too long” (S7-P1). However, based on the observation notes, this student did not follow her own advice. During Phase 3, she stated that she only noted on her whiteboard which tasks she had not finished yet. When students were asked to give a piece of advice to their younger peers, Student 13 (P3) suggested watching some videos on YouTube because “mostly people just watch it for fun, not education … so when they have free time they can watch it and take a lot of notes from the video and what do they understand from the video”. She also mentioned that she did not take any notes during Phase 1 and used to forget many things but during Phase 2 she took some notes in order to prepare for the quiz. It was interesting to see how one student understood that he needed to work on controlling his emotions during classes and mentioned that he took notes to remember it (S19).

Students shared how and when they took notes during this unit:

  • Whiteboards “Because if you do it like that, the answer is correct” (S2-P1). However, later he said, “I don’t know why I need to take notes” (P3). Similar answers were provided by Student 3.
  • Sticky notes “when you show example of one of the EQ [Essential Question], I have to go on the notes and write what you said, so when I go back to my EQ, I know what I, I can learn off that example” (S8-P3).
  • Notebook “get notebooks that I write lessons inside” (S12-P1).
  • Google Docs or Slides “when we did the clock hand I get a paper and then I write about the short hand and long hand and for this end this unit, for the polygon, I also write it in a Docs” (S16-P3). Meanwhile, during Phase 1 she remarked that she usually forgot to take notes.

Other students mentioned that they took notes when the teacher told them to do it but did not show the initiative themselves “maybe I’m not sure about this, maybe it’s wrong and why did I take note about it if it wrong” (S12-P3). Based on the interview and observation data, some students (14 and 17) did not show any improvement in this concept.

4.4.5 Improvement strategies

Generally, students could identify some specific improvement strategies, such as:

  • watching videos on Youtube or the recorded lessons (S12),
  • playing online games connected to the topic (S14),
  • applying HoM’s Listening with Understanding and Empathy (S17), Creating, Imagining and Innovating (S19) and Applying Past Knowledge to New Situations (S20),
  • asking more questions and participating during classes (S19).

Some students shared the view that they would like to have Metacognition Diaries when they study in grade 4 so they could set goals for improvement (S12). This student also said she would do the same extra activities as she was doing in grade 3. Even though she felt they did not help much, she could not identify how to change the situation. A quiet environment when studying online was also mentioned in one of the interviews (S13). In the previous interviews, this student also said she could have asked her family to prepare some extra tasks for her to practice or set a goal to improve. Student 20 emphasised that it was important to know what topics and PT we would study in advance so that he could prepare better.

Changing Behaviour

Another theme that emerged from the interviews was changing behaviour. One of the problems was joining online classes on time. Student 23 started to ask her grandmother to wake her up so she would know how to do the assignments. Student 3 wanted to stop doing the tasks without thinking. To change the situation, she would “[ask] in Hangouts and then just try to do it, one by one and be careful” (P3). Meanwhile, Student 2 could not provide explanations for how to change his behaviour.

Other students either could not define whether they needed to change anything (S5 and 7) or did not specify any improvement strategies apart from “practice about the lesson that I don’t understand” (S22-P3). Student 22 also did not feel she was getting better because she said she did not understand maths. Observation notes show that she missed a lot of classes or did not do the prepared tasks. Finally, some students underlined that they wanted to study at school because they did not have enough materials at home (S20).

These findings are thought-provoking and will be discussed further in relation to academic literature in Chapter 5.

 

5. DISCUSSION AND CONCLUSION

5.1 Overview of key findings

The research question of this study: How can students’ needs be met using the heutagogical framework while teaching maths in an elementary school in Cambodia? By students’ needs we mean self-determined learning needs. Following the Self-determination Theory (Ryan and Deci, 2000) and the findings from the current research, it is possible that students’ basic needs – autonomy, competence, and relatedness – can be met using the heutagogical framework while teaching maths in an elementary school. Having a choice in choosing their goals, self-monitoring, taking notes and
connecting metacognition to maths, eight students were able to control their learning process. Competence was practised by applying different strategies when solving problems and reflecting on improvement strategies. Relatedness was achieved by responding to feedback, self-questioning and asking for help when needed. The data were obtained from 45 interviews (3 phases – 15 interviews each) with students and constant researcher’s observations during online classes for 9 weeks. The data presented in this action research have shown that some metacognitive strategies are necessary at elementary school from students’ perspectives.

Students’ answers were grouped into three categories: Commitment, Capacity and Value – three dimensions of Habits of Mind developed by Costa and Kallick (2008). The majority of students showed improvement in the Commitment category: they often set goals for improvement, questioned themselves and monitored their learning. The results showed that most of the students found them useful, especially when studying at home. Less than half of the students showed the development of metacognitive skills in the Capacity category. Most of them already had some skills before the experiment started (e.g., some strategies for solving problems, improvement strategies, and asking for help when needed). The Value category represented how students developed their metacognitive experience and supported the finding of the previous categories.

5.2 Research outcomes in the framework of existing literature

The findings of this research have several themes that have been discussed previously in the literature review.

Research subquestion 1: What tools and strategies should teachers use to implement the heutagogical framework?

It was found that the following tools and strategies were used to implement the heutagogical framework:

  • goal-setting in Google Classroom (at least once a week),
  • using checklists, rubrics and self-assessments to self-monitor,
  • note-taking,
  • discussions at the end of the class,
  • recording video diaries on Flipgrid to share strategies implemented during the day and/or completing Metacognition Diaries.

Goal-setting

According to the findings, most students started setting goals regularly during the unit and found them helpful in mathematics. The data reported in this study support the results of Erwin et al. (2016) who claimed that self-determination in adults and children is different, but that some elements can be practised in elementary schools, namely goal-setting. They developed a model with four steps: assess, select, try it, and reflect. The focus was on goals and reflection strategies which promoted good results and consistent communication between parents and teachers. Goal-setting can eventually help students become independent. The learning goal orientation might be a starting point
in training self-determination (Compagnoni, Sieber and Job, 2020).

Rubrics

Students who showed high metacognitive knowledge and skills since the first interview noticed that rubrics were not as useful for them as they used to score high and did not feel any improvement. Other students also highlighted that some students might not be honest when they self-assessed and in that case, it was not beneficial. These disadvantages were previously discussed by Jamrus and Razali (2019) who believed that these constraints could be overcome if proper instructions and observations were conducted by a teacher. Moreover, rubrics should challenge students’ abilities,
but rubrics’ language should be age-appropriate (Costa and Kallick, 2000).

Checklists

Another self-monitoring tool that the students used was the checklist. Organising the thought processes and refining the thinking skills is essential for lifelong learners (Knox, 2017). Students found the checklist convenient while studying at home because they could quickly find the tasks and self-monitor. Nidus and Sadder (2016) emphasise the importance of teaching this art of noticing at school. They believe that when students learn how to use the checklist, they can focus on specific tasks, set goals for improvement, thus ask for more detailed feedback and evaluate their progress. The findings of this study about feedback support the results of a quantitative study of Molin et al. (2020) who found that there are positive effects of feedback from teachers or peers on both students’ metacognitive skills and motivation. According to them, responding to feedback is a key element of self-determination. Even though the findings for this specific abstract concept are not complete as the students were not asked about feedback during all three phases, it is still important to take their responses into account, specifically the ones connected to the lockdown.

Metacognitive Diaries (MD)

MD – reflective journals – as a tool of students’ self-assessment positively influenced students’ metacognitive experiences. Knox (2017) recommends journal writing and writing through the problem-solving process during math classes to define students’ mental processes while gaining knowledge. Following the action research framework in this study, students’ reflections were reviewed, and notes were made about their progress. It was also interesting to observe how some reflections reported in the Findings chapter moved from superficial to in-depth in Phase 3. By in-depth reflections, Costa and Kallick (2008, p. 235) mean “making specific reference to the learning event, providing examples and elaboration, making connections to other learning, and discussing modifications based on insights from this experience”. While most of the students from our study reported that they would like to have MD in further grades because “we can tell about the goals that we want to achieve and we can tell how we feel to the teacher and the score that we give to ourself if we give ourself a low score, the teacher will know that we don’t really understand it” (S16-P3), three students did not want to have MDs when they move to grade 4 stating that – “I can think of by my own and then study” (S2-P3). Recent research with elementary students supports the previous findings with university students (O’Loughlin and Griffith, 2020) and illustrate that not only students’ metacognitive skills were affected but also teachers had evidence of how students progressed during the unit. A similar experiment with reflective journals was recently designed in Indonesia (Ramadhanti et al., 2020). However, the questions in that study were grouped around such aspects of metacognition as awareness, evaluation, and regulation. Fifty students who were involved in Ramadhanti et al. (2020) study went through these processes and were able to become independent learners.

Video Diaries (Flipgrid)

Flipgrid (Flipgrid, Inc., 2021) was used as an alternative online video-response tool to self-reflect and facilitate discussions. Students were already familiar with the concept of journaling. This app was used as an alternative to MDs to increase students’ engagement. Students had a choice of how to answer metacognition questions: writing MD, recording a video on Flipgrid or both. Most of the students reported that they enjoyed using the app because it was something new and they could show their feelings, but student engagement has not dramatically increased. The findings of this study differ from those reported by Stoszkowski, Hodgkinson and Collins (2021) which indicate that participants provided more frequent and more critical answers when using Flipgrid. Although, it might happen because older students took part in that experiment, or the differing amount of scaffolding provided by teachers in various studies. Educators should understand that this platform is not a “magic bullet” to increase participation (Kiles, Vishenchuk and Hohmeier, 2020, p.1).

Research subquestion 2: How can metacognition as a heutagogical technique be used to improve students’ self-determination?

It was found that metacognition as a heutagogical technique might be used to improve students’ self-determination.

The findings of this study are in line with previous literature (Gourgey, 1998; Costa and Kallick, 2008). It proved that students who did not have a habit of thinking metacognitively might not show a lot of enthusiasm in the beginning, especially if they had been passive learners for some time. Panadero (2017) believes that interventions have different effects on students because of their educational level. Moreover, the learning environment played a significant role in developing metacognitive capabilities in mathematics, especially in the current lockdown situation. On the other hand, some students were able to recognise other HoMs during the interviews or even spontaneously during classes, according to the observation notes. The creators of HoMs believe that it is one of the strategies that students can use to build deep reflections in order to become lifelong learners (Costa and Kallick, 2008).

During our maths lessons, some students were able to choose what strategies worked well in achieving their goals or they could change their learning approach if needed. This ability to monitor and regulate is the nature of metacognition (Wagaba, Treagust and Chandrasegaran, 2016). Students reported such strategies as applying other HoMs, finding clues and drawing a model, completing the shortest tasks first, using a calculator, asking the teacher or family members. Nevertheless, when looking at the strategies reported by the students during the interviews, five students stayed in the same yellow or green indicator during three phases and same number of students showed major or minor improvements. Therefore, it is difficult to say whether they were the results of applying past knowledge or strategies offered by previous teachers, peers, family members or they were the strategies taught in this unit. Corresponding findings have also been reported by the studies of Davey (2016). Investigating metacognitive development in early years children, she underlined that even younger students can talk about strategies they implemented when facing a problem to solve. The only thing that is clear is that three students still stayed in a red indicator by the end of Phase 3. Perhaps, more focus should be provided on this area when creating lesson plans.

Different studies argue that if students are taught metacognitive strategies at school, they will perform better and even their general wellbeing will improve (Perry, Lundie and Golder, 2019). This study was not focused on students’ performance, but their emotions were taken into account in the Value Category. The findings support the studies of Gabriel, Buckley and Barthakur (2020) who concluded that motivational and emotional factors affect students’ abilities to self-regulate their learning. Mathematics anxiety is an obstacle to learn maths and might impede students’ engagement and the metacognitive processes in general. It was particularly observed during online classes when students could simply leave the meeting when they wanted or do not join at all. The reports in the findings chapter prove that the students who did that felt worried or stressed by the end of the unit because they did not know how to solve the tasks and since they did not have developed metacognitive skills, they could not self-regulate their learning.

5.3 Limitations of research

The researcher acknowledges several constraints of the study. First, it was difficult to set the tone of reflection while teaching online. Most of the metacognitive tasks were done at the end of the lesson and by that time half of the students left the meeting (bad Internet connection, family circumstances, distractions etc.). The results could have been different if teaching on campus. On the other hand, online settings can test self-directedness even better (Cano-Hila and Argemí-Baldich, 2021) so it probably shows that some students were not ready yet to monitor their learning.

Secondly, it would have been better to have this pilot in the middle of the year. At the end of the year, a lot of graded tasks had to be done and there was not enough time to do as many reflections as was planned. Costa and Kallick (2000) recommend that students should reread their journals from time to time to compare their thoughts and make an action plan. During this study, the students were asked to review their Metacognition Diaries but a lot of them did not do it because of the time limits. Adding to this, the scope of this research project was too broad for the timeframe in which it was conducted.

Finally, the concept of semi-structured interviews was partly misunderstood by the researcher. Some of the questions differed during the three phases, thus the progression might not be completely visible. Moreover, some of the questions could have been reworded to avoid different biases.

Overall, while the results of this study appear promising, they should be treated with caution due to the above limitations.

5.4 Implications for further research

The recommendations for other researchers have been made to provide an impetus to continue research on metacognition from students’ perspectives. The data collected could greatly support teachers and curriculum coordinators in finding solutions to overcome the issue of low self-determination in elementary schools. Stringer recommends being careful while creating the questions so that the interviewers do not integrate their ideas into the interviewees’ answers (Stringer, 2007, p. 65). Having analysed the data, it was noticed that some students’ responses contradicted what was observed in the class. Meanwhile, when they were asked indirectly (e.g., “What advice would you give to students who are moving to grade 3?”) they could make connections to themselves and their learning styles. Kaminska and Foulsham (2013) believe that this social desirability bias is caused because of students’ embarrassment and uneasiness if their answers do not match with teachers’ expectations. It is recommended to reword some questions if this research is about to be repeated. For example, instead of asking “Do you think the rubric that we used in class was helpful or just a waste of time?” it is better to ask “Would you recommend having rubrics like this in grade 3? Why or why not?”.

For teachers, it is crucial to inspire students, at every age, to find how they learn and what benefits them individually (Pritchard, 2013). That is why it is important to have professional development in teaching metacognition at this early age. Plus, further research can be carried out to demonstrate whether different teaching styles have an effect on how students develop metacognitive knowledge and skills.

Regarding future research, there is one more perspective worth investigating, that of the parents. First, parents have a big influence on their children’s achievements (Jezierski and Wall, 2019). Secondly, it is paramount to know whether the students apply these metacognitive strategies or other heutagogical techniques at home and whether their behaviour has changed because of it, especially during the lockdown.

5.5 Practical recommendations

Even though some educators believe that developing metacognitive skills is often difficult and time-consuming (Thomas, 2003), it is an important goal of education. There are a lot of techniques and strategies that teachers might implement to train students’ metacognitive abilities. Students should be given opportunities to learn how to set goals, assess their progress and take ownership of their learning.

However, teachers should not expect that students already know how to monitor their progress, plan and self-evaluate as all these skills should be explicitly taught and modelled (Perry, Lundie and Golder, 2019). We cannot expect elementary students to already have metacognitive knowledge and skills (Wagaba, Treagust and Chandrasegaran, 2016). One of the goal-setting strategies that worked during this study was to have students self-assess first and based on their results ask them to write what they can improve and how. It was important to model that our goals should be specific, achievable, and timely. Furthermore, it was repeated every time before the activity started that these goals are for them and not for the teacher so that students synthesize the importance of goal-setting.

Conducting discussions turned out to be one of the tools that promoted metacognition in the classroom. Following Costa and Kallick’s (2008) advice, some thought-provoking questions were designed for the MDs (Appendices VI-VIII). During these moments, students learned how their peers applied some strategies and grew in this Habit of Mind. If the students are studying onsite, it might be better to conduct discussions at the end of mathematics classes but if lessons are online, it is recommended to either ask the students to complete the journal in their free time or choose a
moment when most of the students are present.

It is crucial to demonstrate that solving problems is not only about finding the correct answer but about the process. Moreover, reflective writing might support students in determining their strengths and weaknesses in the topic. Costa and Kallick (2008) also suggest students should reread these journals from time to time, comparing what they have learned in the past and now. Based on the observation notes, teachers should encourage students to complete the diaries regularly to habitualize them. Perhaps teachers may complete the diaries as well as an example.

It is also important not to expect immediate results. Even though this study lasted 9 weeks, it was not enough to coach on metacognition. Students should have enough time to understand their learning processes and to develop a habit of reflecting on their learning and experiences.

5.6 Conclusion

This section is an overall conclusion of the current research. Previous studies from teachers’ and administrators’ perspectives summarised that implementing metacognitive techniques will positively influence students’ performance (Stein, 2018). Nevertheless, the lack of empirical studies from students’ points of view is still a concern in education.

The purpose of this study was to enable grade 3 students to reflect on their learning practices and habits by using metacognitive methods and to see whether it can help them become self-determined learners. Self-determined learners are students who can self-assess, self-direct and self-monitor their learning (Commitment Category), can recognise the benefits and advantages of engaging in metacognitive processes (Value Category) and develop skills, strategies, and techniques through which they engage with their peers (Capacity Category).

Metacognition is the foundation of lifelong learning. Action research cycles with constant reflections helped the researcher as an educator to learn what is best for her students and how to adapt to meet the 21-st century requirements. Based on the observation notes and interview data, most grade 3 students were able to find more motivation for learning mathematics, therefore became more engaged in the learning process. Hence, it might be useful to stimulate deep reflections at an early age. By increasing metacognition, students could find different strategies, apply them, and choose the most effective ones based on the situation. That’s why it is a heutagogical technique. However, some students still could not regulate their learning even after the metacognitive interventions were implemented.

Less than half of the students could connect metacognition to mathematics by the end of phase 3 and three students were able to do it before the experiment started. Four students either stayed in the red indicator or dropped from yellow or green. However, it is important to note that these students missed more than a third of online mathematics classes or did not do most of the metacognitive activities assigned during the unit.

The pandemic lockdown affected children’s learning. Even though there are a lot of physical and emotional limitations connected to the pandemic (Cano-Hila and Argemí-Baldich, 2021), it might be considered a perfect setting to practice metacognitive skills when students can set goals, monitor their learning using different checklists and rubrics, reflect on the feedback provided in Google Classroom and think about improving strategies while writing diaries. Hopefully, these positive aspects of online learning concerning metacognition should remain even after lockdown.

However, recent research in education showed that in fact, the lockdown increased the gap between high and low achievers: stronger students had more ability to concentrate on the tasks while weaker students were less able to focus (Spitzer, 2021). This study supports this statement because when we look at the findings, it is noticeable that the students with yellow or green specific indicators in Phase 1, continued to show progress in other Phases. But if they started in a red indicator and did not join classes or did not do the metacognitive tasks, they stayed in the same colour code. If students are studying at school, they are approximately equal in terms of metacognitive support provided by a teacher. Meanwhile, when studying at home, there are different family circumstances that can increase or decrease their metacognitive skills (e.g., eliminating distractions, helping with monitoring their progress, doing work with parents, etc.) (Cano-Hila and Argemí-Baldich, 2021). Another term used recently in research is “Zoom fatigue” when students are getting tired from overusing virtual platforms (Wiederhold, 2020). A few children reported during the interviews that they were overwhelmed with the number of emails and feedback on different platforms that sometimes they missed and did not reply to the teacher.

The study has revealed that such tools as Metacognition Diaries and video diaries on Flipgrid were effective from students’ perspectives to regulate their learning. This indicates that these tools might be useful in implementing the heutagogical framework. Based on students’ responses, rubrics were useful during mathematics classes by helping students improve their work or informing the teacher about their progress. However, such issues as dishonesty, overconfidence, and the inability to use the rubric without knowing the correct answer were also highlighted and should be taken into account by educators. Checklists, on the other hand, turned out to be very helpful self-monitoring tools during online classes.

Another summary related to the results of the study shows that although some students stated that they wrote goals, responded to the teacher’s feedback, took notes, it disagreed with the researcher’s observation notes. Even though MDs were not graded, the final assessment about HoM 5 Metacognition was included in students’ grade books. It could have influenced some students’ answers. Some students could have hidden what they did not know, and it is not the purpose of reflections (Ramadhanti et al., 2020). That is why it is better to have it not graded in further studies.

I would like to conclude this paper with the quote of Mark Van Doren, “The art of teaching is the art of assisting discovery” (BrainyMedia Inc, no date). As researchers and as practitioners this should be our aim and metacognition as a heutagogical technique might assist in it. What if teachers were more concerned about students’ abilities after graduation (e.g., problem-solving, decision-making, being a lifelong learner) rather than focusing only on the acquisition and end-of-year exams? Finally, the ultimate goal of education is to develop lifelong learners and, I would add, metacognitive and self-determined lifelong learners.

 

For references and appendices please refer to the full dissertation in PDF form.

Appendix I: Consent Form (Parents)
Appendix II: Consent Form (Students)
Appendix III: Interview Questions
Appendix IV: Final Assessment
Appendix V: Lesson Plan with Metacognitive Elements
Appendix VI: Metacognition Diary (MD) – Value
Appendix VII: Metacognition Diary (MD) – Capacity
Appendix VIII: Metacognition Diary (MD) – Commitment
Appendix IX: Coding Legend
Appendix X: Qualitative Analysis of Abstract Concepts – Setting goals
Appendix XI: Qualitative Analysis of Abstract Concepts – Self-questioning
Appendix XII: Qualitative Analysis of Abstract Concepts – Self-monitoring
Appendix XIII: Qualitative Analysis of Abstract Concepts – Responding to feedback
Appendix XIV: Qualitative Analysis of Abstract Concepts – Connecting metacognition to math
Appendix XV: Qualitative Analysis of Abstract Concepts – Applying different strategies when solving
problems
Appendix XVI: Qualitative Analysis of Abstract Concepts – Asking for help when needed
Appendix XVII: Qualitative Analysis of Abstract Concepts – Taking notes
Appendix XVIII: Qualitative Analysis of Abstract Concepts – Improvement strategies

 

LIST OF TABLES
Table 1: Core Category Commitment – Overall Picture during 3 Phases
Table 2: Core Category Capacity – Overall Picture during 3 Phases

 

LIST OF ABBREVIATIONS AND ACRONYMS
EQ = Essential Question
GC = Google Classroom
HoM = Habit of Mind
MD = Metacognition Diary
MK = Metacognitive Knowledge
ME = Metacognitive Experience
MS = Metacognitive Skills
PT = Performance Task
P = Phase
S = Student
S2-P1 = Student 2 – Phase 1
SLO = Schoolwide Learner Outcomes

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