Chapter 2 Literature Review. "Action Research in Mathematics: Providing Metacognitive Support (As a Heutagogical Technique) to Grade 3 Students"
Author: Zoriana Myburgh
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 (𝑆𝐸3W). 131 students from an Austrian primary school completed questionnaires regarding this study called 𝑆𝐸3 . 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 quasi-experimental design investigated the influence of both on the first-year undergraduate students in chemistry courses. By active learning, the authors mean frequent questions, discussions, problem-solving 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 problem-focused 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.
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