# Why Additional Maths (A Maths) is important for entering Medicine:

Pathway: A Maths (O Level) –> H2 Maths (A Level) –> NUS Medicine

Quote: While NUS and NTU Medicine does not (officially) require H2 Maths (ie. ‘A’ level Maths), some other (overseas) Medical schools might. And not having H2 Maths might (unofficially) disadvantage your chances, even for NUS and NTU.

Therefore (assuming you intend to fight all the way for your ambition), your safest bet would be to (fight for the opportunity) to take both H2 Bio and H2 Math. The ideal Singapore JC subject combination for applying to Medicine (in any University) is :

H2 Chemistry, H2 Biology, H2 Mathematics

Quote: pre-requisites for nus medicine will be H2 Chem and H2 bio or physics.

as for what’s best,
H2 math is almost a must since without it you’ll be ruling out a lot of ‘back-up courses’

## Mathematics is not a spectator sport (How to study Maths for Humanities students)

Studying Mathematics is totally different from studying Humanities, this is the reason why humanities students often don’t do well in maths. But with the right studying techniques (i.e. practising doing mathematics), humanities students can be very good at maths. Together with their creativity and good memory, humanities students have the potential to achieve the top grades in maths exams.

I have taught Pure Literature students and found that they definitely have the potential to do well in Maths once they learn the correct method of mathematical studying and thinking, and how to approach solving Maths questions.

One of the top mathematical physicists, Edward Witten, majored in history and minored in linguistics! (http://en.wikipedia.org/wiki/Edward_Witten)

# Mathematics is not a spectator sport

Even if you understand every word in lecture and in the textbook, the only way to really learn mathematics is by doing mathematics.  Sometimes this means doing even more than the assigned problems.  (See “time committment” above.)  This is how to avoid the common pitfall of “understanding everything in class but blanking out on the exams.

I realize this isn’t welcome advice, and I admit that I haven’t always followed it myself.  But in years of teaching (and 20+ years of learning) mathematics I haven’t found any shortcut.

## Why are China students so good at Math & Sciences?

Quote:

I’m sure many secondary school/Junior College students have know some China scholars in your schools scoring results that are seemingly impossible to reach (90+ for H2 Maths etc.) But when asked what’s their secret to scoring so well, they said they just study & memorize the same way any other student would do before exams.

I heard from my seniors that China scholars usually study till 2 am every night, but I don’t buy into that. I think they’re just exaggerated rumors to explain their excellent grades. Some of my friends say that China’s education gave them really solid foundation, such that they can grasp concepts much faster than the rest.

Anybody know their secret to doing so well?

It seems like the secret of the China scholars is “practice makes perfect”!

http://ideas.time.com/2013/08/20/dont-just-practice-over-practice/

The Time magazine even recommends Over-Practicing (http://ideas.time.com/2013/08/20/dont-just-practice-over-practice/)

# Over-Practicing Makes Perfect

The brain can get by on less energy when you overlearn a task
Read more: Over-Practicing Makes Perfect | TIME.com http://ideas.time.com/2013/08/20/dont-just-practice-over-practice/#ixzz2mQyatOKF

## Math, Science, Reading Scores Show U.S. Schools Slipping Behind

Math, Science, Reading Scores Show U.S. Schools Slipping Behind

Posted: December 10, 2010 PRINTER FRIENDLY VERSION: PDF

The United States received a stark wake-up call this week with the release of international test results showing students in other countries are surpassing American students when it comes to math, science and reading. China and Australia outperformed the U.S. in each of the three subject areas tested.

The results of a major international education assessment show that American students are lagging behind many other countries in crucial skills like reading, math and science.

“The United States came in 23rd or 24th in most subjects. We can quibble, or we can face the brutal truth that we’re being out-educated,” said U.S. Education Secretary Arne Duncan.

Test compares U.S. to other countries

The PISA tests how advanced students are in science, math and reading compared to their peers around the world.

The test, known as the Program for International Student Assessment (PISA), directly assesses how prepared teenagers are in math, science and reading compared to their peers in other countries.
The test is translated into each country’s language, and officials from the participating countries are able to review questions before students take the exam to make sure each test is fair and unbiased.

In the U.S., the participating schools and students are randomly selected. On average, about 4,500 students are tested in each of the participating countries.

## China and Finland lead the way

Chinese and Finnish students scored highest on the PISA test.

Each PISA subject area is scored on a scale where 500 points is the average. The results announced this week show many countries outperforming the U.S. Here’s a sample:

Math: China 600, Germany 513, United States 487 (31st place)

Reading: China 556, Korea 539, United States 500 (17th place)

Science: China 575, Finland 554, United States 502 (23rd place)

 The results of a major international education assessment show that  American students are lagging behind many other countries in crucial skills like reading, math and science.

## Shifts must be made in education system to prepare young for future: Heng Swee Keat

SINGAPORE: Education Minister Heng Swee Keat has said that two important shifts must be made in the education system in order to prepare the young for the future.

In a Facebook post on Friday evening, Mr Heng said firstly, the education system must help the young acquire deep skills and integrate theory with practice through applied learning.

Secondly, the system should make it easier for students to continue learning in their areas of strength and interest, and encourage lifelong learning.

Mr Heng said the education system needs to better link the interest and strengths of students to jobs of the future.

He explained that when students develop a deep interest, when their imagination is captured, they can go on to do wonderful things.

## New Additional Maths Syllabus (Syllabus 4047) TO BE IMPLEMENTED FROM YEAR OF EXAMINATION 2014

http://www.seab.gov.sg/oLevel/2014Syllabus/4047_2014.pdf

There are some minor changes to the A Maths Syllabus in 2014. Wishing everyone taking the new syllabus all the best!

Main Differences

– knowledge of $a^3+b^3=(a+b)(a^2-ab+b^2)$ and $a^3-b^3=(a-b)(a^2+ab+b^2)$ is needed

Topics Removed:

– Intersecting chords theorem and tangent-secant theorem for circles removed

– exclude solving simultaneous equations using inverse matrix method

## O Level E Maths and A Maths Tuition starting next year at Bishan

O Level E Maths and A Maths Tuition starting next year at Bishan
————————–
View Mr Wu’s GEP Testimonial at

https://mathtuition88.com/group-tuition/

Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system.

He would like to teach these techniques to students, hence choosing to become a full-time Mathematics tutor. Mr Wu has developed his own methods to check the answer, remember formulas (with understanding), which has helped a lot of students. Many Math questions can be checked easily, leading to the student being 100% confident of his or her answer even before the teacher marks his answer, and reducing the rates of careless mistakes.

Mr Wu’s friendly and humble nature makes him well-liked by students. Many of his students actually request for more tuition by themselves! (not the parents)

O Level E Maths and A Maths Tuition starting next year at Bishan, the best location in Central Singapore.

Timings are Monday 7-9pm, Thursday 7-9pm. Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free.

Register with us now by email (mathtuition88@gmail.com). Vacancies will be allocated on a first-come-first-serve basis.

Thanks and wishing all a nice day.

## Additional Maths — from Fail to Top in Class

Really glad to hear good news from one of my students.

From failing Additional Maths all the way, he is now the top in his entire class.

Really huge improvement, and I am really happy for him. 🙂

To other students who may be reading this, remember not to give up! As long as you persevere, it is always possible to improve.

## Information about Mathematics Department Courses (Nanyang JC)

H1 Mathematics

H1 Mathematics provides a foundation in mathematics for students who intend to enrol in university courses such as business, economics and social sciences. The syllabus aims to develop mathematical thinking and problem solving skills in students. A major focus of the syllabus will be the understanding and application of basic concepts and techniques of statistics. This will equip students with the skills to analyse and interpret data, and to make informed decisions. The use of graphic calculator is expected.

H2 Mathematics

H2 Mathematics prepares students adequately for university courses including mathematics, physics and engineering, where more mathematics content is required. The syllabus aims to develop mathematical thinking and problem solving skills in students. Students will learn to analyse, formulate and solve different types of problems. They will also learn to work with data and perform statistical analyses. The use of graphic calculator is expected.

This subject assumes the knowledge of O-Level Additional Mathematics.

Over the years, I have collected some information that I hope will help  students, particularly beginning math students, to improve their study  and learning habits.  An important part of what you learn at college is  how to learn, so that you can carry that on for the rest of your  life.  Find out what works for you and what doesn’t.

These observations are centered around first-year calculus courses, so not  everything may apply to you, but even more advanced students can benefit  from some of them.

One source of confusion for students when they reach college and begin to  do college-level mathematics is this:  in high school, it is usually pretty  apparent what formula or technique needs to be applied, as much of the  material in high school is computational or procedural.  In college,  however, mathematics becomes more conceptual, and it is much harder to  know what to do when you first start a problem.  As a consequence of this,  many students give up on a problem too early.

If you don’t immediately know how to attack a problem, this doesn’t mean you  are stupid,

 If you already know how to do it, it’s not  really a problem.

or that you don’t understand what’s going on; that’s just how  real problems work.  After all, if you already know how to do it, it’s not  really a problem, is it?  You should expect to be confused at first.   There’s no way you can know ahead of time how to solve every problem that  you will face in life.  You’re only hope, and therefore your goal as a  student, is to get experience with working through hard problems on your  own.  That way, you will continue to be able to do so once you leave  college.

One of the first steps in this is to realize that not knowing how, and the  frustration that accompanies that, is part of the process.  Then you have  to start to figure out the questions that you can ask to help you to break  down the problem, so that you can figure out how it really works.  What’s  really important in it?  What is the central concept?  What roles do the  definitions play?  How is this related to other things I know?

## EDUC115N: How to Learn Math (Stanford Online Maths Education Course )

I will be attending this exciting online course by Stanford on Math Education. Do feel free to join it too, it is suitable for teachers and other helpers of math learners, such as parents.

EDUC115N: How to Learn Math

In July 2013 a new course will be available on Stanford’s free on-line platform. The course is a short intervention designed to change students’ relationships with math. I have taught this intervention successfully in the past (in classrooms); it caused students to re-engage successfully with math, taking a new approach to the subject and their learning.

## Concepts

1. Knocking down the myths about math.        Math is not about speed, memorization or learning lots of rules. There is no such  thing as “math people” and non-math people. Girls are equally capable of the highest achievement. This session will include interviews with students.

2. Math and Mindset.         Participants will be encouraged to develop a growth mindset, they will see evidence of  how mindset changes students’ learning trajectories, and learn how it can be  developed.

3. Mistakes, Challenges & Persistence.        What is math persistence? Why are mistakes so important? How is math linked to creativity? This session will focus on the importance of mistakes, struggles and persistence.

4. Teaching Math for a Growth Mindset.      This session will give strategies to teachers and parents for helping students develop a growth mindset and will include an interview with Carol Dweck.

5. Conceptual Learning. Part I. Number Sense.        Math is a conceptual subject– we will see evidence of the importance of conceptual thinking and participants will be given number problems that can be solved in many ways and represented visually.

6. Conceptual Learning. Part II. Connections, Representations, Questions.        In this session we will look at and solve math problems at many different  grade levels and see the difference in approaching them procedurally and conceptually. Interviews with successful users of math in different, interesting jobs (film maker, inventor of self-driving cars etc) will show the importance of conceptual math.

7. Appreciating Algebra.        Participants will learn some key research findings in the teaching and learning of algebra and learn about a case of algebra teaching.

8. Going From This Course to a New Mathematical Future.        This session will review the ideas of the course and think about the way towards a new mathematical future.

## 积少成多: How can doing at least one Maths question per day help you improve! (Maths Tuition Revision Strategy)

We all know the saying “an apple a day keeps the doctor away“. Many essential activities, like eating, exercising, sleeping, needs to be done on a daily basis.

Mathematics is no different!

Here is a surprising fact of how much students can achieve if they do at least one Maths question per day. (the question must be substantial and worth at least 5 marks)

This study plan is based on the concept of 积少成多, or “Many little things add up“. Also, this method prevents students from getting rusty in older topics, or totally forgetting the earlier topics. Also, this method makes use of the fact that the human brain learns during sleep, so if you do mathematics everyday, you are letting your brain learn during sleep everyday.

Let’s take the example of Additional Mathematics.

Exam is on 24/25 October 2013.

Let’s say the student starts the “One Question per day” Strategy on 20 May 2013

Days till exam: 157 days  (22 weeks or 5 months, 4 days)

So, 157 days = 157 questions (or more!)

Each paper in Ten Year Series has around 25 questions (Paper 1 & Paper 2), so 157 questions translates to more than 6 years worth of practice papers! And all that is achieved by just doing at least one Maths question per day!

A sample daily revision plan can look like this. (I create a customized revision plan for each of my students, based on their weaknesses).

 Topic Monday Algebra Tuesday Geometry and Trigonometry Wednesday Calculus Thursday Algebra Friday Geometry and Trigonometry Saturday Calculus Sunday Geometry and Trigonometry

(Calculus means anything that involves differentiation, integration)

(Geometry and Trigonometry means anything that involves diagrams, sin, cos, tan, etc. )

(Algebra is everything else, eg. Polynomials, Indices, Partial Fractions)

By following this method, using a TYS, the student can cover all topics, up to 6 years worth of papers!

Usually, students may accumulate a lot of questions if they are stuck. This is where a tutor comes in. The tutor can go through all the questions during the tuition time. This method makes full use of the tuition time, and is highly efficient.

Personally, I used this method of studying and found it very effective. This method is suitable for disciplined students who are aiming to improve, whether from fail to pass or from B/C to A. The earlier you start the better, for this strategy. For students really aiming for A, you can modify this strategy to do at least 2 to 3 Maths questions per day. From experience, my best students practice Maths everyday. Practicing Ten Year Series (TYS) is the best, as everyone knows that school prelims/exams often copy TYS questions exactly, or just modify them a bit.

The role of the parent is to remind the child to practice maths everyday. From experience, my best students usually have proactive parents who pay close attention to their child’s revision, and play an active role in their child’s education.

This study strategy is very flexible, you can modify it based on your own situation. But the most important thing is, practice Maths everyday! (For Maths, practicing is twice as important as studying notes.) And fully understand each question you practice, not just memorizing the answer. Also, doing a TYS question twice (or more) is perfectly acceptable, it helps to reinforce your technique for answering that question.

If you truly follow this strategy, and practice Maths everyday, you will definitely improve!

Hardwork $\times$ 100% = Success! (^_^)

There is no substitute for hard work.” – Thomas Edison

## How to avoid Careless Mistakes for Maths?

Many parents have feedback to me that their child often makes careless mistakes in Maths, at all levels, from Primary, Secondary, to JC Level. I truly empathize with them, as it often leads to marks being lost unnecessarily. Not to mention, it is discouraging for the child.

Also, making careless mistakes is most common in the subject of mathematics, it is rare to hear of students making careless mistakes in say, History or English.
Fortunately, it is possible to prevent careless mistakes for mathematics, or at least reduce the rates of careless mistakes.

From experience, the ways to prevent careless mistakes for mathematics can be classified into 3 categories, Common Sense, Psychological, and Math Tips.

Common Sense

1. Firstly, write as neatly as possible. Often, students write their “5” like “6”. Mathematics in Singapore is highly computational in nature, such errors may lead to loss of marks. Also, for Algebra, it is recommended that students write l (for length) in a cursive manner, like $\ell$ to prevent confusion with 1. Also, in Complex Numbers in H2 Math, write z with a line in the middle, like Ƶ, to avoid confusion with 2.
2. Leave some time for checking. This is easier said than done, as speed requires practice. But leaving some time, at least 5-10 minutes to check the entire paper is a good strategy. It can spot obvious errors, like leaving out an entire question.

Psychological

1. Look at the number of marks. If the question is 5 marks, and your solution is very short, something may be wrong. Also if the question is just 1 mark, and it took a long time to solve it, that may ring a bell.
2. See if the final answer is a “nice number“. For questions that are about whole numbers, like number of apples, the answer should clearly be a whole number. At higher levels, especially with questions that require answers in 3 significant figures, the number may not be so nice though. However, from experience, some questions even in A Levels, like vectors where one is suppose to solve for a constant $\lambda$, it turns out that the constant is a “nice number”.

Mathematical Tips

Mathematical Tips are harder to apply, unlike the above which are straightforward. Usually students will have to be taught and guided by a teacher or tutor.

1. Substitute back the final answer into the equations. For example, when solving simultaneous equations like x+y=3, x+2y=4, after getting the solution x=2, y=1, you should substitute back into the original two equations to check it.
2. Substitute in certain values. For example, after finding the partial fraction $\displaystyle\frac{1}{x^2-1} = \frac{1}{2 (x-1)}-\frac{1}{2 (x+1)}$, you should substitute back a certain value for x, like x=2. Then check if both the left-hand-side and right-hand-side gives the same answer. (LHS=1/3, RHS=1/2-1/6=1/3) This usually gives a very high chance that you are correct.

Thanks for reading this long article! Hope it helps! 🙂

I will add more tips in the future.

## Recommended Maths Book:Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail

This book is a New York Times Bestseller by actress Danica McKellar, who is also an internationally recognized mathematician and advocate for math education. It should be available in the library. Hope it can inspire all to like Maths!