Two new students joined us ytdy, one from Monfort Sec and one from SCGS. Apparently, I tutored the latter’s cousin a few yrs ago, all the way from Sec 2 to JC2 in Math and Physics, and who is now a first year undergrad; just learnt that he scored 2 A’s and 2 B’s in his A-levels (he might have told me about it); anyway, that proves my point, that you can come from a ‘neighbourhood’ sec sch and then go to a ‘low-ranked’ JC and still do well at the A-Levels. Contrast this with the two ex-IP students that I helped this year to re-take their A-Levels. So students out there pls wake up; no one owes you good grades.
The three tutees agreed to revise some sec 3 topics instead of me teaching them a Sec 4 topic. So for this class (Sat 2.15 to 3.45pm), I will only start teaching Differentiation in Jan 2013. So ydty two of them covered Indices, Surds and Log while the remaining one wanted to revise Trigonometry. Every time, I find joy in proving to students that Logarithms is a VERY EASY topic. Once you understand what a logarithm is, everything about it becomes very easy (I’ve posted another article on Log; pls do a search on it, under A Math study tips I think).
Trigo is a much harder topic, especially the proving of some Trigonometric Identities. However, there are heuristics to use in solving the latter, and these techniques work 95% of the time. I like ‘proving’ qns because there is no answer to find, and students normally dislike such qns precisely because there is no answer to find. But I can’t blame them; imagine spending 6 yrs of your life in pri sch only learning how to find answers, so students become obsessed with finding a numerical answer, and eventually get defeated by qns that ask them to prove something already known.
Related pages:
Is metacognition part of the mathematics curriculum in Singapore?
One of the aims of mathematics education in schools in Singapore is to enable students to acquire thinking and problem solving skills and to make effective use of these skills to formulate and solve problems (MOE, 2007).
The existing curriculum framework for mathematics designed by the Ministry of Education (MOE) lists metacognition as one of the components on which the development of mathematical problem solving ability depends.
According to the MOE (2007), metacognition can be defined as the realization of, and the ability to regulate one’s thinking processes, in particular the choosing and application of problem-solving strategies. The MOE believes that it is important to provide students with metacognitive experience in order to help them develop their problem solving abilities.
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 and problem-solving;
(3) Metacognition enhances learning;
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Metacognition enhances learning
Various studies have revealed that metacognition helps to enrich students’ learning in different domains. For example, it has the potential to increase students’ capacities for independent learning (Ganz & Ganz, 1990).
Research also shows that knowledge of metacognition, such as being familiar with one’s strengths and weaknesses and searching for ways to overcome the latter, contributes to more effective learning (Bransford, Brown, & Cocking, 1999). Research also suggests that metacognition improves one’s chances of success when it comes to completing activities that rely heavily on thinking processes (Garner & Alexander, 1989; Pressley & Ghatala, 1990).
Many studies in metacognition have concluded that those who have advanced metacognitive abilities are more adaptable and steadfast in problem solving (e.g., see Artzt & Armour-Thomas, 1992; Swanson, 1990). Studies have also shown that one’s ability to plan and monitor a problem-solving process requires several metacognitive skills such as regulation and evaluation of thought processes (Mayer, 1999), and the use of metacognitive skills has the potential to identify the more able students from the less able ones (Pellegrino, Chudowsky & Glaser, 2001).
In addition, research has shown that one’s individual and group learning skills can be improved through the acquisition of metacognitive competencies (White & Frederiksen, 2005). Recent studies have also revealed that students who often fail to choose appropriate strategies, monitor or regulate their work, or articulate their thought processes are more likely to perform poorly in mathematics (e.g., see Lucangeli & Cabrele, 2006; Carlson & Bloom, 2005).
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 and problem-solving;
(3) Is Metacognition part of the Singapore Math curriculum?
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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).
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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EDUCATIONAL SERVICES:
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By EX-MOE TEACHERS & EXPERIENCED TUTORS
@ BLK 644, BUKIT BATOK CENTRAL, #01-68. S(650644).
CALL 65694897 OR SMS 98530744 OR 97860411.
Sec 4 A. Math Headstart Programme – Differentiation
For our latest timetable, click here => 
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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.
A. Math Reflections & Study Tips
(1) Simultaneous Equations
Generally an easy topic, but beware of certain kinds of questions such as:
(a) Questions involving reciprocals of x and y, such as
Solve 3(1/x) + 1/y = 1; 1/(x^2) + 1/(y^2) = 5
Ans: x = 1, y = -1/2 or x = -5/2, y = 5/11
Do not make common denominators and cross-multiply; the better technique is to let p = 1/x and q = 1/y.
(b) Questions involving coefficient matrices that are singular (determinant = 0), such as
Given that x and y satisfy the simultaneous equations mx + (m-1)y = 10 and (m-2)x + 3my = 20,
(i) if the equations have no unique solution, find the values of m; (ans: 1/2, -2)
(ii) if the equations have no solution, find the value of m.(ans: 1/2)
(adapted from Additional Math, EPB Panpac, p. 13)
(2) Indices, Surds & Logarithms
Generally an easy topic, except for students who do not understand or memorize the laws of indices and logarithms properly. I find that quite a number of weak students do not know the meaning of logarithm, thus not appreciating and enjoying the topic. Weak students do not realize that while Indices is concerned with the answer or expression obtained when a power is applied to a base number, Logarithms is about the power itself; the power that is needed to be applied to a base to give a certain number.
For eg, why is lg1000 = 3? ‘Evaluate lg1000’ or ‘What is lg1000?’ is the same as asking, “What is the Power that must be applied to the number 10 (the base) to obtain 1000?” Since 10^3 = 1000, therefore the answer is 3.
Weak students almost always make one or more of the following mistakes, thinking that (i) logA x logB = logA + logB, (ii) log(A + B) = logA + logB, (iii) logAB = logA x logB, (iv) (logA)^n = nlogA, (v) logAB^n = nlogAB, (vi) (a^m)^n = a^(m+n). All these are wrong.
How to be good in Indices and Logarithms? READ AND UNDERSTAND THE LAWS OF INDICES AND LOGARITHMS CAREFULLY. Yes, there is such a thing as READING MATH, not just practising Math.
(3) Quadratic Functions & Equations
Some of the points to note are:
(1) Understand that alpha and beta by themselves also satisfy the quadratic eqn because they are the roots of the equation! So it’s not just abt finding the sum and product of roots;
You must be able to solve questions like:
If α is the root of the equation x^2 = 2x – 1, show that α^4 – α^2 = 2α – 2.
(2) Understand that the discriminant (b^2 – 4ac) is less than or equal to zero when the question involves the phrase “for which the function is never positive or never negative”;
(3) Understand that sometimes you are required to solve an inequality involving the discriminant but at other times the inequality involves the function itself;
(4) Understand how to complete the square to determine the maximum or minimum value of a quadratic function;
(5) Recognise that “real and distinct roots”, “real and equal roots”, and “no real roots” have other names that express the same meaning.
TO BE CONTINUED ……….. (by Mr Ilyasa)
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Sec 4 Physics, A. Maths One-to-One Tuition
For our latest timetable, click here =>
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ORIGINAL POST (OUTDATED):
Objective: Intensive Revision or Crash Course for O-Levels 2013
Focus: Understanding Key Concepts, Problem-Solving Techniques, Difficult Topics
DETAILS:
Available Time Slots:
Mon 4pm – 7pm
Thur 1.30pm – 4.30pm, 8pm – 10pm
Fri 6pm – 8pm
Sat 9am – 11am
Investment Amt: $80 per hr
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.
Location: Blk 627 Bukit Batok Central #07-640
Average Class Size: 2-6 students
For appointment, call or sms to 97860411. Thank you.
Beware the critical years in math education …
Be aware that there are Mathematics gaps that need to be handled with care:
The following is derived from my eight years of teaching mathematics from
Primary 1 level to JC 2.
1st Gap – From Lower Primary to Upper Primary:
Somewhere in Primary Three problem sums that require the drawing of simple
models begin to appear and in some schools, this happens in P2 and even P1.
However, these problems tend to be simple enough so as not to cause problems for
students who don’t draw models. Generally, parents report their children doing
badly and losing interest in math in P4. This is because in P4, complex problem
sums begin to appear. It also coincides with the appearance of Decimals. Thus
students who have not mastered Fractions as well as simple models by the end of
P3 will find P4 a tough and demoralising year, with some probably staying away
from Math for the rest of their lives. However, in P4, Section C (problem sums)
still only take up about 20% of the marks, so pupils will still survive and
scoring above 75% is not a problem for the hardworking student who is not
careless.
However, this ecstasy is short-lived. In P5, Ratio, Average and
Percentages start to appear, on top of decimals and fractions, and only the
well-taught and discerning student will understand that they are all roughly the
same thing in different forms. To add to the agony, Section C in P5 takes up
about 45% of the total marks! It is a very big jump from P4; students can no
longer afford to just concentrate on their short questions in order to score a
Band 1. P5 is the year that separates the men from the boys (or the women from
the girls). In P6 or PSLE, Section C’s weightage is increased to about 55%,
wiping out all remaining students who have not mastered complex problem sums and
non-routine questions. That is NOT the bad news yet. The worse news is, the
joy of quite a number of students who scored A-star in math at PSLE is also
short-lived (I have encountered quite a number of students doing badly in
secondary math even though they scored A-stars or A’s at PSLE).
2nd Gap – From P6 to Sec 1:
Why is it that some students can score A-stars or A’s at the PSLE yet become average or even failures in math at the secondary level? The answer lies in two words – Algebra and presentation. It’s unfortunate that even at the upper primary level, students are not taught to form and solve equations using algebra, and they are also not taught how to present their answers in logical and coherent mathematical statements. Thus I find that many Sec 1 students provide math workings that will not earn full marks by ‘O’ level standards, and these habits are hard to change. Inability to use algebra properly also means inability to master important fundamentals such as algebraic expansion, factorisation and manipulation, resulting in poor performance at the upper secondary and JC levels.
Whenever I ask an upper secondary or JC student to state the main reason why he thinks he’s doing badly in math, the reason given is almost always that he had difficulty handling algebraic concepts and formulae while in Sec 1 and Sec 2. Thus parents and students need to comprehend fully the importance of mastering algebra in the lower secondary years.
3rd Gap – From Sec 2 to Sec 3:
Even students who perform well in Sec 1 and Sec 2 may suddenly suffer a drop in their math performance by the middle of Sec 3. This is largely due to the full impact of Additional Math and the pure sciences taking place and finally being felt by students around that time. A. Math can be a shock to some students who are not used to algebra-intensive questions with solutions that are one-page long. Trigonometry in A. Math is also substantially more difficult to grasp than it’s counterpart in elementary Math.
4th Gap – From Sec 4 to JC 1:
H2 Math is more shocking to new JC students than A. Math is to new Sec 3 students. H2 Math is significantly more difficult than A. Math and from my experience, students who do not get an A1 for A. Math will have a hard time even in completing their JC tutorial worksheets. This is because on top of having to write out solutions that are often more than one page long, students have to familiarise themselves with a new graphical calculator. Many topics in H2 Math are also completely new to students, such as Complex Numbers, Series and Sequences and Probability Distributions, just to name a few. H2 Math is also difficult for most students because some parts of its topics are taken from the former subject Further Math, which was meant for only top students in Math. Thus it is not surprising to find many students failing in Math tests in their first year in junior college. From my experience, two topics in H2 Math that most JC students complain about are Complex Numbers and Vectors. This is largely because these topics speak their own language.
My main point is – Concerned parents must monitor their children’s
mathematical development extra closely when the kids go through the above
stages.
Good luck.
Best Regards,
Ilyasa
Related Links:
FREE SEC 1 MATH TUITION AT SINGAPORE LEARNER!
Integrated Programme subject combination and promotion criteria
What happens at the end of Y4 IP?
Tips on how to Excel in Integrated Programme
What to do if you are failing in Integrated Programme?
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Sec 4 A. Math Group Tuition @ Bt Batok by qualified and exp. tutor
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ORIGINAL POST (OUTDATED):
If you are struggling with A. Math for the coming O-Levels and you need guidance for certain topics, the following tuition slots are suitable for you:
Day/Time: Mon 4.30 to 6 pm, Wed 4.30 to 6 pm.
Location: Blk 627, Bukit Batok Central.
Class size: 2 to 5 students.
Investment amt: $50 per session.
Tutor: Mr Ilyasa; M.Ed (NIE), PGDE (NIE), BSc (NUS), A-Level (RJC); ex-sec teacher (3 years); full-time tutor of O and A Level Math and Physics (8 years). To see his detailed resume, click here.
To book a tuition slot, sms to or call Mr Ilyasa at 97860411.
Ad hoc Individual Consultation for Math and Physics …
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EDUCATIONAL SERVICES:
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@ BLK 644, BUKIT BATOK CENTRAL, #01-68. S(650644).
CALL 65694897 OR SMS 98530744 OR 97860411.
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ORIGINAL POST (OUTDATED):
I understand that there are students who don’t need long-term tuition but are weak in certain topics and they just need to consult a qualified and experienced tutor about these topics since exams are near. I’ve re-organised some of my tuition slots this June hols, so now I have a few free slots that can be used for ad hoc or short-term, individual consultations for the following levels and subjects:
PSLE Math, Sec 4 Math (E/A/IP/IGCSE), Sec 4 Physics, H2/H1 Math.
Fees per hr: JC – $80, Sec – $60, Pri – $50. (Pay per lesson)
Contact no: 97860411
Timing of lesson: Call or sms to arrange.
Location: Blk 627, Bukit Batok Central (near West Mall, 3 min walk from Bt Batok MRT or bus interchange).
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.