Metacognitive Behaviour of Malaysian Students While Solving Mathematical Problems of Form Three Assessment (PT3)

Abdullah, Abdul Halim; Ahmed, Surya ‘Ain; Rahman, Sharifah Nurarfah S. Abd; Mun, Soh Hon; Mokhtar, Mahani

doi:10.1590/1980-4415v31n59a03

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Article • Bolema 31 (59) • Dec 2017 • https://doi.org/10.1590/1980-4415v31n59a03 copy

Metacognitive Behaviour of Malaysian Students While Solving Mathematical Problems of Form Three Assessment (PT3)

Comportamento Metacognitivo Dos Estudantes Da Malásia Ao Resolver Problemas Matemáticos Da Avaliação Do Formulário Três (PT3)

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Several studies on metacognition have sought to solve mathematical problems. However, in Malaysia, there has yet to be a study investigating the metacognitive behaviour of students in solving mathematical problems of Form Three Assessment (Pentaksiran Tingkatan Tiga - PT3). This study was conducted to identify the metacognitive behaviour of students while solving mathematical problems in PT3 and examine differences in metacognitive behaviour among successful students (SS), partially successful students (PSS), and unsuccessful students (USS). A total of six (6) Form Three students in a school in Johor Bahru participated in this study. The research instrument used was the actual set of 2014's PT3 questions. Data were analysed using the Thinking Aloud method with reference to Foong's Taxonomy (1993)FOONG, P. Y. Development of framework for analyzing mathematical problem solving behaviours. Singapore Journal of Education, Singapore, v. 13, n. 1, p. 61-75. 1993., and it was supported by analysis of the students’ written work. Results showed seven types of metacognitive behaviour exhibited by the students, depending on the types of questions given. The analysis also found that each category of students showed different types of metacognitive behaviour while solving their PT3 mathematical problems. The SS group could control their metacognitive behaviour in mathematical problem-solving more regularly and frequently, the PSS students behaved moderately, while the USS group demonstrated limited metacognitive behaviour. As the results indicated differences in metacognitive behaviour among students of different performance levels, teachers should help students with weakness in solving mathematical problems implement metacognitive behaviour to strengthen their mathematical proficiency.

Keywords:
Metacognitive Behaviour; Mathematical Problem Solving; Form Three Assessment (PT3)

M-Category	Metacognition
	M1 - Proposing Plans M2 - Identifying the Level of Question (Easy or Difficult) M3 - Re-examining the Development M4 - Identifying Mistakes M5 - Identifying New Knowledge Q1 - Asking Relevant Questions N1 - Being Rhetoric on Tasks that are Irrelevant with Words

STUDENT	SCORE	Z-SCORE	T-SCORE	LEVEL	CATEGORY
1.0	83.3	1.23009830	62.300983	Very High	Successful
2.0	80.0	1.10213140	61.021314	Very High	Successful
3.0	50.0	−0.06120440	49.387956	Moderate	Partially Successful
4.0	42.0	−0.37142730	46.285727	Moderate	Partially Successful
5.0	37.5	−0.54592761	44.5407239	Low	Unsuccessful
6.0	16.67	−1.35367040	36.463296	Very Low	Unsuccessful

Participants	Participant 1	Participant 2
Verbal Protocol	S3: “At first, for ASB he will get 35% times a thousand. ” S5: “From ASN, he will get 4% from 3500. ” S9: And then he asked, “…how much percentage is left from the dividend that had not been reinvested?”	S4: “Oh. Aaaaaa… Try to do it…” S6: “Ok, we do the ASB. ” S8: “And then with the ASN he got 4% dividend. ” S10: “Fatin has reinvested with a total of 102 from the total dividend that she received from the investment. RM, the total dividend that had not been reinvested… it's total…”

Participants	Participant 3	Participant 4
Verbal Protocol	S2: “Ok, at first, 100% minus 35% equals to 65%. So 65% is the balance. ”	S4: “Ok, so the question wants the dividend that was not being reinvested.”
	S3: “This means that 65% times 102 equals 66.3. ”	S7: “Ok, divide RM 102 by 1000, and then multiply it by 35%.”
	S17: “This means that 102 over 1000 times 100. ”
	S22: “Then, the balance percentage… 102 plus 350 over 1000. ”

Participants	Participant 5	Participant 6
Verbal Protocol	S13: “Then, the dividend's percentage. ”	S14: “The percentage of balance means it has to be deducted from the original percentage. ”
	S20: “Then, dividend. ”
	S21: “So, the percentage of the dividend is the one missing. ”

Participants	Participant 5	Participant 6
Verbal Protocol	S5: “The type of investment… He invested a total of 1000 in the ASB. The percentage of dividend is 5%.” S12: “1000 plus 102… equals 1102…”	S2: “1000 plus 102, 1102.” S5: “1000 minus 102 is equal to 898. 898 over 1000 times 100, 89.8%.”

Participant	Participant 4
Verbal Protocol	S1: “It's difficult…”

Participant	Participant5
Verbal Protocol	S38: “This is really difficult… I don't understand…” S47: “Ok, now I understand. ”

Participants	Participant 1	Participant 2
Verbal Protocol	S18: “This is correct already. ”	S12: “O.K. RM 388.”
Verbal Protocol	S20: “O.K. this is correct…”	S13: “I think this is right.”

Participant	Participant 3
Verbal Protocol	S18: “Eh… Haa… Maybe… ”

Participants	Participant 5	Participant 6
Verbal Protocol	S27: “I didn't get it…” S54: “Ok, done!” (While checking the answer).	S18: O.K. Correct.

Participant	Participant 5
Verbal Protocol	S32: “So, 102… Erm… Plus 3500.” S35: “102 plus 3500, 3602.” S36: “Divide 3602 by 3500, times 4 over 100. ”

Participant	Participant 1
Verbal Protocol	S12: “Wrong!” S13: “Wrong!” S15: “Eh, it's not!”

Participant	Participant 3
Verbal Protocol	S4: “Wrong!” S9: “Eh wrong!” S11: “Wrong. Wrong!” S12: “Over 1000, also wrong. ” S14: “650 over 1102 times 100%, uittt wrong…”

Participant	Participant 5
Verbal Protocol	S16: “Eh wrong!” S23: “Erm… Wrong!” S33: “Erm… Wrong!” S44: “Erm… Wrong, wrong.” S50: “Wrong!”

Participant	Participant 5
Verbal Protocol	S48: “140 minus 102 is equal to 38 ringgit.” S49: “So 100% times 140 over 38. ”

Participant	Participant 5
Verbal Protocol	S17: “35 over 100 times the unknown is equal to 1000. ” S18: “Unknown times 1000, times 100 over 35. ”

Participants	Participant 1	Participant 2
Verbal Protocol	S16: “What does percentage mean? Try again…”	S1: “What is the percentage of the balance … They were not reinvested?”

Participants	Participant 3	Participant 4
Verbal Protocol	S20: “This is a percentage … 35% times 1000?” S24: “The total of dividend? The total of this dividend … ” S25: “350 in percentage … 350 over 1000, times 100, right? ”	S3: “How much is the total dividend? ”

Participants	Participant 5	Participant 6
Verbal Protocol	S15: “If it is one thousand? ” S31: “How much is the percentage … that was not reinvested?” S46: “How much is the percentage of the balance… was not reinvested? ” S51: “Erm… What is the percentage? ”	S3: “How much is the percentage that was not reinvested?” S11: “What is the percentage of the balance?” S12 “What is the percentage of the balance?”

Participants	Participant 1	Participant 2
Verbal Protocol	S2: “Meaning?”	S2: “Hmmm… So, how?”

Participant	Participant 4
Verbal Protocol	S2: “How, eh?” S6: “ASB… investment… How?” S9: “Is this correct or not, eh?”

Participants	Participant 5	Participant 6
Verbal Protocol	S3: “How to do this? ” S4: “What kind of question is this? ” S7: “How to answer this? ” S9: “What question is this? ” S14: “Percentage of dividend, Oh no! How do we calculate this? ” S52: “Erm… How much did I deduct just now?”	S4: “What is this?” S6: “How am I supposed to know? ”

Metacognitive Behaviour	Successful Students (SS)	Partially Successful Students (PSS)	Unsuccessful Students (USS)
M1 Proposing Plans	Showed good M1 behaviour.	Showed good M1 behaviour.	Showed M1 behaviour which unrelated with the questions’ requirements, and it was clearly wrong.
M2 Identifying the Level of Question	Did not show M2 behaviour.	Showed M2 behaviour at the early stage of the problem-solving process.	Showed M2 behaviour at the end of the problemsolving process.
M3 Re-examining the Development	Showed M3 behaviour at the end of the problemsolving process.	Showed limited M3 behaviour throughout the whole problem-solving process.	Showed M3 behaviour in the middle and the end of the problem-solving process.
M4 Identifying Mistakes	Showed M4 behaviour immediately after reaching a certain solution.	M4 was shown throughout the whole problem-solving process, particularly in the earliest stage. Corrections were made. However, they were inaccurate.	M4 behaviour existed, and the students realised the mistakes. However, they did not come out with the correct answers.
M5 Identifying New Knowledge	Did not show M5 behaviour.	Did not show M5 behaviour.	Showed M5 behaviour. However, the new knowledge identified was wrong and failed to help the students in solving the problems.
Q1 Asking Relevant Questions	Showed limited Q1 behaviour throughout the problem-solving process.	Constantly showed Q1 behaviour throughout the problem-solving process.	Constantly showed Q1 behaviour throughout the problem-solving process. Similar questions were asked by students repeatedly.
N1 Being Rhetoric on Tasks that are Irrelevant with Words	N1 behaviour existed but was seldom displayed.	N1 behaviour was moderately shown.	Constantly showed N1 behaviour throughout the problem-solving process.

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