Chapter 4: Findings. "Action Research in Mathematics: Providing Metacognitive Support (As a Heutagogical Technique) to Grade 3 Students"
Author: Zoriana Myburgh
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):
- Commitment (ability to self-assess, self-direct and self-monitor in their development of HoM 5 Metacognition within the unit)
- Value (ability to recognise the benefits and advantages of engaging in the HoM 5 Metacognition)
- 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:
- Setting goals
- Self-questioning
- Self-monitoring
- Responding to feedback
- 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:
- Making connections to real life and the future
- Giving advice to other students
- 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:
- Connecting metacognition to math
- Applying different strategies when solving problems
- Asking for help when needed
- Taking notes
- Improvement strategies
- 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.
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