Metacognitive Skills of Malaysian Students in Non-Routine Mathematical Problem Solving

Abdullah, Abdul Halim; Rahman, Sharifah Nurarfah S. Abd; Hamzah, Mohd Hilmi

doi:10.1590/1980-4415v31n57a15

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Article • Bolema 31 (57) • Jan-Apr 2017 • https://doi.org/10.1590/1980-4415v31n57a15 copy

Metacognitive Skills of Malaysian Students in Non-Routine Mathematical Problem Solving

Habilidades Metacognitivas dos Estudantes Malaios na Resolução de Problemas Não Rotineiros de Matemática

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Metacognitive skills play an important role in solving mathematical problems. However, there is a lack of empirical studies on the role of metacognitive skills in solving mathematical problems, particularly non-routine ones. Therefore, this study was undertaken to identify students' metacognitive skills and the impact of such skills on non-routine mathematical problem solving. By using a quantitative method, a total of 304 students in Johor Bahru district were involved in the study. A Self-Monitoring Questionnaire (SMQ) and a mathematical test were used in data collection. Data were analysed using descriptive and inferential statistics such as frequency, percentage, mean, the Mann-Whitney U test, and the Kruskal-Wallis H test. Results showed that the level of the students' performance in solving non-routine mathematical problems was very low. There was also a significant difference in the metacognitive skills among students with different performance levels in solving non-routine mathematical problems, and we concluded that these metacognitive skills should be emphasised in this process.

Keywords:
Metacognitive Skills; Non-routine Problems; Mathematical Problem Solving

Mean value	Description
1.00 – 2.33	Low
2.34 – 3.67	Medium
3.68 – 5.00	High

Scores	Performance Level	Frequency	Percentage (%)
0.00 to 33.88	Very Low	118	38.8
33.89 to 43.87	Low	69	22.7
43.88 to 53.88	Medium	34	11.2
53.89 to 63.87	High	25	8.2
63.88 and above	Very High	58	19.1
Total		304	100

Item

Question

Mr. Hamid had a tank full of water in his backyard to be used when the water was running out. The tank was cylindrical with a radius of √120 cm and a height of 2h. Then, in the absence of water, Mr. Hamid flowed the water out of the tank through pipe A and pipe B at a rate of 18πl/min and 20πl/min, respectively.
If pipe B was opened one minute after pipe A, how long did it take to empty the tank? Explain your answer.

A person was found to have spilt water.
Four people were there at that time: Amanda, Suziana, Iman, and Rafiq. They were questioned by one of the mothers.
Amanda: “It wasn't me who spilled the water”
Rafiq: “Iman spilled the water!”
Suziana: “It was Rafiq”
Iman: “Rafiq was lying”
If only one person was telling the truth, who actually spilt the water? Explain your answer.

Level	Solution criteria for students' answer
Very High	▪ Students outline and extract the key information from the questions into comprehensible forms (e.g., drawing a diagram, labelling) ▪ Students are able to scan existing knowledge properly (e.g., writing the formula) ▪ The steps shown in the solution are organised, clear, and understandable. ▪ There are measures for revision or correction identified (e.g., crossing out answers, traces of eraser, change of strategy) ▪ The final answer given is accurate with justification. ▪ Students are able to provide explanations for certain items in a proper and logical manner (if any).
High	▪ Students outline the answer and rewrite the key information in a comprehensible manner. ▪ The existing knowledge is displayed in the steps for the solution. ▪ There are calculation errors in the solution steps, but the methods used are correct. ▪ There are mistakes even though the revised steps have been identified. ▪ The final answer given is accurate but lacks logical explanation.
Medium	▪ Students outline the key information. ▪ The steps for solution shown are incomplete, and the solution methods are inappropriate. ▪ There are revisions done, but other steps for solution are not displayed. ▪ The final answer given is less accurate with unreasonable justification.
Low	▪ The key information is outlined but the students do not translate it into a comprehensible form. There are mistakes in extracting the information. ▪ The steps for solution shown are ambiguous and confusing. Moreover, the methods used are wrong. ▪ The given answer given is incorrect, and no explanation is offered.
Very Low	▪ Certain students simply outline the key information in the question without attempting to translate it into an understandable language/form. ▪ The written steps for solution are incorrect. ▪ There is no final answer. ▪ There are students who submitted their items without any writing (e.g., blank question paper)

		Mean Rank	H	d f	Sig.
Metacognitive Skill	Very high	263.28	217.649	4	.000
	High	260.38
	Medium	197.12
	Low	100.70
	Very Low	92.63

		Mean Rank Difference	U	Z	Sig.
Metacognitive Skills	1–2	2.49	681.500	−.435	.663
	1–3	44.74	27.000	−7.775	.000
	1–4	63.50	.000	−9.696	.000
	1–5	88.00	.000	−10.785	.000
	2–3	27.97	22.000	−6.190	.000
	2–4	47.00	.000	−7.390	.000
	2–5	71.5	.000	−7.855	.000
	3–4	46.23	120.000	−7.392	.000
	3–5	69.18	180.000	−8.087	.000
	4–5	7.86	3729.000	−.960	.337

UNESP - Universidade Estadual Paulista, Pró-Reitoria de Pesquisa, Programa de Pós-Graduação em Educação Matemática Avenida 24-A, 1515, Caixa Postal 178, 13506-900 Rio Claro - SP Brasil - Rio Claro - SP - Brazil
E-mail: bolema.contato@gmail.com

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