Posted in A. Math, A. Math Tips, Metacognition, Pri Math, Sec Math

Metacognition and mathematical problem solving

Metacognition is a crucial element in problem-solving, which is itself a key component in mathematics learning. To monitor and regulate one’s cognitive processes in problem-solving, Polya (1945) describes a four-step method: first, one has to comprehend the problem by sub-dividing it into more manageable parts and recognize any given data, conditions and variables to be found; second, one devises or selects a strategy to find the connections between the known data and the unknowns to be found; third, one executes the plan, scanning, regulating and examining each step; and, finally, after obtaining the solution, one evaluates the results which may involve re-visiting the previously taken steps.

Building on Polya’s work, Schoenfeld (1987) describes effective mathematical problem-solving as being contingent on how one uses four types of knowledge/skills: (1) resource knowledge, which is knowledge about one’s abilities and cognitive processes including knowledge of how to perform tasks or procedures; (2) heuristics, which are specific problem-solving methods or strategies; (3) regulatory processes, which includes the organisation and selection of resources and strategies; and (4) beliefs, which includes perceptions of and assumptions about mathematics (Gama, 2004).

Ilyasa

 

Note: The above paragraphs are adapted from my minor research paper, Examining Supports for Metacognition in Singaporean Lower Secondary Mathematics Textbooks, NIE, 2011. All rights reserved.

Related links:

(1) Metacognition – The secret to learning and problem-solving;

(2) Metacognition enhances learning;

(3) Is Metacognition part of the Singapore Math curriculum?

 

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Posted in H1 Physics, JC Math (H2/H1), Pri Math, Pure Physics, Sec Math

Metacognition – The ‘secret’ to learning and problem-solving …

You don’t have to be ‘good in English but bad in Math’, or ‘good in Science but lousy in History or Literature’, or ‘good in Chinese but lousy in English’. It doesn’t have to be a one-or-the-other kind of thing. Every subject has its own way of learning and thinking about, but you can only discover it if you bring yourself one level up – think about the thinking itself, and think about how you learn. You can only learn how to learn if you think about learning. You can only learn how to think if you think about thinking.

Thinking about thinking has another name: metacognition, which formed the basis of my minor research work completed in 2011 at the NIE. A lot of research into metacognition centers around mathematical problem-solving, although metacognition can be applied equally well to other subjects. So for the purpose of illustration here, I will use math as the basis for our discussion about metacognition.

What is Metacognition?

In its simplest form, metacognition can be described as thinking about thinking (Wellman, 1985). Flavell (1976) has stated some examples of what constitutes metacognition:

I am engaging in metacognition if I notice that I am having more trouble learning A than B; if it strikes me that I should double-check C before accepting it as a fact; (…)if I become aware that I am not sure what the experimenter really wants me to do; if I sense I had better make a note of D because I may forget I; if I think to ask someone about E to see if I have it right. (p. 232).

The above sounds familiar, doesn’t it? Yes, you may have been practising metacognition sub-consciously, all your life, without realising it has a formal name, or without realising how important it is to learning and thinking.

Research in metacognition has examined various forms of cognitive processes by building on Flavell’s initial notion of metacognition as the monitoring, regulation and arrangement of thinking processes to achieve specified goals (Gama, 2004).

For example, Brown (1987) argues that metacognition consists of two components: knowledge of cognition, and regulation of cognition. The former involves being aware of one’s cognitive abilities through self-reflection while the latter pertains to mental activities such as monitoring and controlling one’s thinking processes in the course of learning or problem-solving. According to Brown, although these two types of metacognition are distinct from one another, they are usually used together in the same cognitive process as one type often utilises the service of the other (Gama, 2004).

Wishing you all the best in your studies,

Ilyasa

(hp: 97860411)

 

Note: The above paragraphs are adapted from my minor research paper, Examining Supports for Metacognition in Singaporean Lower Secondary Mathematics Textbooks, NIE, 2011. All rights reserved.

Related links:

(1) Metacognition and problem-solving;

(2) Metacognition enhances learning;

(3) Is Metacognition part of the Singapore Math curriculum?

 

TUITION CLASSES:

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ipbutton                    pributton

_______________________________________________________________

EDUCATIONAL SERVICES:

hwsupervbutton                   intensivebutton

alevelprepbutton                   olevelprepbutton

______________________________________________________________

By EX-MOE TEACHERS & EXPERIENCED TUTORS

@ BLK 644, BUKIT BATOK CENTRAL, #01-68. S(650644).

CALL 65694897 OR SMS 98530744 OR 97860411.

 

 

Posted in Pri Math, Pri Science

Pri 3 to Pri 6 Math & Science Tuition at Bukit Batok Central

 

For our latest timetable, click here =>  pributton

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ORIGINAL POST (OUTDATED):

 

The following subjects and levels are provided (each lesson is 1.5 hrs):

Pri 6 Math: Mon 4.00 pm – 5.30 pm, Wed 4.00 pm – 5.30 pm, Fri 4.00 pm – 5.30 pm

Pri 6 Science: Mon 5.45 pm – 7.15 pm, Wed 5.45 pm – 7.15 pm, Fri 5.45 pm – 7.15 pm

Pri 5 Math: Mon 4.00 pm – 5.30 pm, Wed 4.00 pm – 5.30 pm, Fri 4.00 pm – 5.30 pm

Pri 5 Science: Mon 5.45 pm – 7.15 pm, Wed 5.45 pm – 7.15 pm, Fri 5.45 pm – 7.15 pm

Pri 4 Math: Tue 4.00 pm – 5.30 pm, Thur 4.00 pm – 5.30 pm

Pri 4 Science: Tue 5.45 pm – 7.15 pm, Thur 5.45 pm – 7.15 pm

Pri 3 Math: Tue 4.00 pm – 5.30 pm, Thur 4.00 pm – 5.30 pm

Pri 3 Science: Tue 5.45 pm – 7.15 pm, Thur 5.45 pm – 7.15 pm

DETAILS:

Location: Blk 627 Bukit Batok Central #07-640

Tutor(s): Mr Jay Lim, Master of International Management, experienced full-time tutor.

Average Class Size: 3-6 students.

Fees Per Month:

Pri 5 or Pri 6: One subject, once a week: $100 per mth; One subject, twice a week: $160 per mth; Two subjects (3h), once a week: $160 per mth; Two subjects (3h), twice a week: $280 per mth; Two subjects, EVERY day (3h) Monday to Friday: $580 per mth.

Pri 3 or Pri 4: One subject, once a week: $80 per mth; One subject, twice a week: $140 per mth; Two subjects (3h), once a week: $140 per mth; Two subjects (3h), twice a week: $240 per mth; Two subjects, EVERY day (3h) Monday to Friday: $480 per mth.

Note: Lessons will begin on Dec 3 onwards.

For enquiries, call or sms to 97860411. To register, sms Student Name, Subject, Level and Day/Time to 97860411. Thank you.

Ilyasa

Posted in Personal

What makes my day …..

I’m doing relief teaching again today, at a school in Dover Road. I’m now in the library, waiting for the next class to begin at 2.25pm. Just now, after the Physics class ended, students for the next lesson started trickling in. One of them, a tall, lanky boy, looked at me and said,”Hey, weren’t you the teacher that took us for the Log class? That was 2010.”

Looking hard at him, I replied,”Yes, must be. And you look familiar too, except that I now remember you being shorter, but just as thin.” He smiled. “I really enjoyed that class.” “Me too”, I remarked before leaving.

Nothing pleases a teacher more than a meeting an ex-student who has benefitted from his or her teaching. Very often these students have grown up quite a bit and I don’t recognise some of them, but they would stop me in my tracks in a public place, or wave at me from afar and I would take some time to search my memory. Often I dont remember their names already, as so many batches have come and gone. Once a young man stopped talking to his girlfriend, stood up and said hi to me and we chatted for some 5 mins; I hope they are still together.

Sometimes I wonder where the rest have gone to, what they are doing now, and whether they are happy and successful, howsoever they define success. Some I found in facebook, and a few came back to help me tutor. Of the latter, three came in Sec 2, stayed until JC2, underwent NS, and now are undergrads, and I get to meet them every week and ask about their current lives. From all of them I learn about what matters to young people nowadays, their worries, their aspirations and their hopes for the future.

I hope parents spend more time with their children, for some of them tell me things they wouldn’t share with their parents. But I also often tell these youngsters to understand their parents, instead of always asking to be understood.

Parents have their own worries, fears and hopes too. I’ve advised parents before on how to handle their children, and vice versa, and when either party tells me things have become much better, that too, makes my day.

I also feel happy when I have induced a person to do self-reflection, because I do it everyday, in fact almost every moment, even when I’m teaching. That, I think, is the only way to improve. I mean, I don’t see how you can improve if you don’t know what you don’t know, and you also don’t know what you know. Thinking about your own thinking, often called metacognition, is very important in life. I’ll talk about this in another post.

Ilyasa

Posted in Group Tuition

Group Tuition for 2013 starts this Saturday Nov 17 onwards …

TUITION CLASSES:

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_______________________________________________________________

EDUCATIONAL SERVICES:

hwsupervbutton                   intensivebutton

alevelprepbutton                   olevelprepbutton

______________________________________________________________

By EX-MOE TEACHERS & EXPERIENCED TUTORS

@ BLK 644, BUKIT BATOK CENTRAL, #01-68. S(650644).

CALL 65694897 OR SMS 98530744 OR 97860411.

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ORIGINAL POST(OUTDATED):

 

Just to remind existing students and potential students that some group tuition classes (for various subjects) commence this Saturday. Pls click on Tuition Timetable from the menu bar in the home page to find out the details.

So if you have not registered but you intend to start tuition during the school holidays so that you can have a good headstart to the academic year 2013, please register now or as soon as possible. The class sizes are from just two to six students, so places are indeed limited (not limited by policy, but by actual physical constraints).

To register, sms Student Name, Subject, Level and intended start date to 97860411.

Ilyasa

 

Posted in A. Math, Headstart Classes, Holiday Classes

Sec 4 A. Math Headstart Programme – Differentiation

For our latest timetable, click here =>   secbutton

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ORIGINAL POST (OUTDATED):

 

The details of the 2-day, 6-hr programme are as follows:

Date/Time (choose one pair of sessions only):

(1) Sat 10 Nov (10 am to 1 pm) and Sun 11 Nov (10 am to 1 pm);

(2) Thurs 22 Nov (4.30 pm to 7.30 pm) and Fri 23 Nov (4.30 pm to 7.30 pm);

(3) Thurs 6 Dec  (4.30 pm to 7.30 pm) and Fri 7 Dec (4.30 pm to 7.30 pm);

Location: Blk 627, Bukit Batok Central, 07-640.

Class size: Max 6 students.

Investment amt: $150 total for both days (6 hrs).

Topics: Calculus – Differentiation & Its Applications

Tutor:  Mr Ilyasa; M.Ed (NIE), PGDE (NIE), BSc (NUS), A-Level (RJC); ex-sch teacher, full-time tutor (8 years) of PSLE, O and A Level Math and Physics.

To book a place in the programme, sms to or call Mr Ilyasa at 97860411.

Posted in A-Level, General Paper

General Paper: Tuition Timetable (2013)

For our latest timetable, click here =>  jcbutton

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ORIGINAL POST (OUTDATED):

 

(1) JC2 General Paper:

Fri 7pm to 9pm (Mr Virgilio);

Sun 9.30am to 11am (Ms Foo);

(2) JC1 General Paper:

Sat 5pm to 6.30pm (Ms Foo) ;

 

DETAILS:

Location: Bukit Batok Central

Tutor(s):

Ms June Foo, NUS graduate, NIE-trained, Master of Arts degree, ex-MOE school teacher (including GEP and JC), alumnus of MGS and RJC.

Mr Virgilio E. Hollen, SMU undergrad, experienced tutor for General Paper, supported by Current JC GP teacher who wishes to be anonymous.

To register, kindly call, or send an sms to 97860411, indicating the Student Name, Subject and Level.

Posted in Curriculum & Teaching

A mission for teachers …

“We who are teachers would have to accommodate ourselves to lives as clerks or functionaries if we did not have in mind a quest for a better state of things for those we teach and for the world we all share. It is simply not enough for us to reproduce the way things are.” (p.1)

– Greene, M. (1995). Releasing the Imagination: Essays on Education, the Arts, and Social Change. San Francisco: Jossey-Bass Publishers.

Posted in Curriculum & Teaching, Schools

A new mission for schools …

“The 10 jobs projected to be the most in-demand jobs in 2010 did not even exist in 2004. Thus, the new mission of schools must be to prepare students to work at jobs that do not yet exist, creating ideas and solutions for products and problems that have not yet been identified, using technologies that have not yet been invented.”

– Prof. Linda Darling-Hammond, Charles E. Ducommun Professor of Education, Stanford University, in the Straits Times, Aug 26 2009, p. A12.