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TEACHING & LEARNING

For teaching notes, please click here.

Time Managment/Logical & Analytic Thinking/Effectivity

Time Management is an important topic for all subjects.  If you cannot provide yourself with 10~15 mins everyday for a subject, then you should not blame anyone else, but yourself, for getting poor academic results in that subject.

[Think about a student attending the most expensive tutorial center 5 hours daily, but not working out 10 Maths problems each semester by himself/herself, then you would understand the true meaning of time management.]

 

 

To make a school different from a private tutorial center, the 2 keys are: (a) apart from academics, (i) students also take parts in various ECAs at a school, and (ii) teenagers' growth and developments are part of their teachers' concern; and (b) students go to a school to learn how to learn (manage their learning) and go to a tutorial center to learn how to take examinations (skillfully).

If someone considers academic / examination abilities as the most important thing, then he/she should go to attend a private tutorial center instead of a school.

 

 

 

Learning Mathematics

Mathematics is a subject that requires learners to think logically & analytically.  Apart from working diligently, learners should understand the concepts and have clear target(s) before doing their works.  Here are some guiding steps to Mathematics learners when doing their revisions:

  1. To start with a topic, ask a few questions.  You are going to find the answers by going through the chapter.

  2. List out all the ways that you would use to get the answer.

  3. Go to the chapter summary to see if you miss any of thing important.

  4. According to what you wrote, work it out.

  5. When you get the answer(s), check it.  Is your answer reasonable?

  6. Further thinking: If you are asked to do the same question again, with another method, what would you do?

Below you may find two examples with topics from F.4 and Yr.1 (non-Maths) levels.

 

 

Kitty's Teaching and Learning Experiences in Mathematics
There is an interesting topic about sequences and their sums, named as "Arithmetic and Geometric Sequences and Series" in the syllabus.  It was a F.5 topic in the HKCEE level and a F.6 topic for HKDSEE level now.  Kitty got very great experiences with it.

 

 

Back in P.4, Kitty's first time learning this topic formally under a classroom setting.  Every of her P.6 Team members thought this topic's trivial.  Promoted to F.1, Kitty failed to be patient when her enhancement class teacher talked about it as a new topic, to the rest of the excellent students.  Her teacher told that it would be a good chance for her learning how to teach instead of just the content of the topic.

Until F.4, Kitty got the chance (given by the same teacher) to teach this topic to some excellent F.1 students.  When Kitty had to learn this topic "again" in F.5, she successfully learnt to be patient and not to interrupt her teacher during classes.  During F.6, Kitty was coorperating with a F.3 student (that's Kitty's greatest student) in teaching the same topic to another class of excellent F.1 students.

 

 

Even when Kitty is doing her PGDE now, she still loves this topic a lot & chose it as the topic for her homework - planning how to teach this topic again, but to the normal studnets.

Executive Coaching

Leadership  Program

Conflict Resolution

Business Coaching

"Quadratic Equations" from F.4

  1. What is a quadratic equation?  How does it look like?  What does each coefficient represent?  How to form / solve a quadratic equation?  (Higher level students may ask: Can this method be generated to cubic (or higher power) equations?)

  2. Forms: x^2=4, ax^2 +bx +c=0, (x-x_1)(x-x_2)=0, etc.; coefficients: b^2 - 4ac > 0 => 2 distinct real roots, etc.; solve by factorization, completing square, applying quadratic formula, etc.

  3. Anything missed: (e.g.) x=-b/a is the axis of symmetry, x_1 * x_2 is the y-intercept, etc.

  4. Solve x^2 -6x +8=0, by (a) factorization: (x-2)(x-4)=0 =>   x=2 or x=4
                                             (b) completing square: (x-3)^2 =1  =>   x=3-1=2  or  x=3+1=4
                                             (c) quadratic formula: x=[-(-6) +- sqrt((-6)^2-4(1)(8))]/2=3+-1=2 or 4

  5. Put x=2 and x=4 into the equation respectively, get LHS=RHS, done.

  6. Plot a graph of y=x^2 -6x +8 and a graph of y=0, find the intersections between them.

 

 

 

"Limits" from Yr.1

  1. What is limit?  How to express a limit?  Any symbols / rules that I need to pay attention to?  How to calculate lim_(x->2)  [(x^2 -4)/(x-2)] ?  (i.e. what is the value of (x^2 -4)/(x-2) when x tends to 2 ?)

  2. Limit of a function exsits if you get the same value by approaching from both LHS and RHS, etc.; for one-sided limit, there is a little "+" or "-" sign at the top right-hand corner of the value approaching to, etc.; to calculate/obtain a limit, we may do: simplification of fraction, apply l'Hospitals' rule, etc.

  3. Anything missed: direct substitution (students usually miss the simpliest thing when they learn more)

  4. Obtain value of  lim_(x->2)   [(x^2 -4)/(x-2)], by
                 (a) simplification: (x^2 -4)/(x-2)=x+2                   =>                    lim=4
                 (b) l'Hospitals' rule: lim_(x->2)   [(x^2 -4)/(x-2)] =lim_(x->2)   [(2x)/1]       =>        lim=4

  5. Checking could be done by graph-plotting.

  6. We can also get approximate value by putting x=1.9, 1.99, 1.999, 2.1, 2.01, 2.001 into the fuction.  Remember ?

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Examples

​© February 2016 by Man Ching Kitty Lee

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