Future of Mathematics in Junior Colleges

I’ve been teaching H2/ H1 Mathematics for 6 years and the past year papers clearly indicates that they are interested in finding out if students do understand their learning. In my opinion, Mathematics can be studied in several ways, mainly by technical means or academic means.

Technical means will be a students sitting down in Starbucks and do questions from the same topic for the entire day. Some extreme cases will be those that asks me directly for answers keys and regurgitate the model answers. To me, this is unhealthy as students are very limited to the type of questions they are capable of handling. And judging from the past year papers, they will end up with a B only.

Academic means will be a students understanding and appreciating the concepts of how to handle this topic. As I previously shared, H2 math classes that I conduct focuses a lot on handling the concepts, i.e., learning the topic by understanding. And then applying this learnt concepts to solving the questions. This enables students to stretch their abilities. Not to mention, students must also understand that the questions don’t test topically. We see from this question that A-level can mash and test a few topic in one question. So students must be able to look at H2 Mathematics as a subject, instead of topics.

I feel that in 2-3 years time, the syllabus might have an overhaul again. Also the old syllabus of F Mathematics and C Mathematics is very good, and more can be done for H2/ H1 Mathematics by bringing some of the removed topics. Similarly, the lack of focus given to Statistics in H2/ H1 Mathematics is simply sad. And I do think that it will not be long before Ministry of Education begins to introduce Statistics as a subject and Pure Mathematics as another. These two subjects might be stand alone subjects too, allowing students more focus and variety. We already see this being done with H2 Computing, albeit little success.

When this changes take place, students who religiously mug their Ten Year Series, read them will definitely suffer a lot. Thus, I always advise students to keep questioning what they are learning and to ask sparingly.

P.S. I recently gave a few students an assignment: to at least ask me 7 questions weekly. Be it conceptual questions or a practice question.

Difference between H1 Math and H2 Math

Prior to going Junior College, we always hold JC talks at various location to discuss with post O-levels students what to expect in JC. So many were confused with H1 Mathematics and H2 Mathematics. Let’s compare and contrast H1 and H2 Math in A-levels. And is H1 truly easier?

Content difference between H1 and H2 Math

Firstly, H1 Mathematics is 50% content of H2 Mathematics. Topics such as Vectors, Complex Numbers, Differential Equations, etc are not taught to H1 Mathematics students.

Is H1 Math easier?

In short, yes.

But will questions will be easier? No! I think there is a common misconception that H1 Mathematics is easier, only the studying part since students have lesser things to study. However, difficulty of the questions are not being halved or scaled down.

Exam difference between H1 and H2 Math

H2 Mathematics involves two 3-hr papers where paper 1 tests on pure mathematics while paper two comprise of statistics and pure mathematics. The overall composition for pure mathematics and statistics is 70\$ and 30% respectively. H1 Mathematics, on the other hand, has one 3-hr paper which consists of 60 marks on statistics and 35 marks on pure mathematics.

Now many students are also concerned about the prospects of taking either subject. Personally, I strongly encourage students to take H2 Mathematics as it does prepares them for University well. Believe me, unless you are going into Medicine, Law, Architecture or Dentistry FOR SURE, you probably cannot escape from Math entirely. So the know-how will definitely help.

Pre-requisites wise, I know some students that do not have Additional Mathematics background from secondary schools who managed to get an A for H2 Mathematics. So if they can, why not you? But these students put in double the effort as they know they are already lagging behind. My advice in general will be that, if you don’t have additional mathematics background, think carefully about H2 Mathematics. No doubt it is beneficial and crucial to meeting many university entry requirements, but JC is less than 2 years and you must ask yourself if you are ready and disciplined enough. 🙂

Many of my ex-students know that I send them this link post A-level. Prior to 2012, it was a link to a shared pdf that contains the suggested solutions that I rushed out, for both paper 1 and 2, in like an hour. In 2013 & 2014, I shared them on another site, Singapore Learner. I also rushed the suggested solutions out in an hour to put in up online.

I just want to clarify, I am not sadistic and want students to feel bad or torture them mentally by sharing my solutions. Furthermore, I do make a handful of mistakes while rushing them and I learn from them too. My main objective is to also collect different responses and provide a simple platform for discussion. Alternative methods by other tutors or students were being able to be shared there too. This helps me to improve. 🙂

Last but not least, having done the paper also allows me to respond and discuss with my students about it actively. At the same time, I can better prepare them for Paper 2.

A-level vs IB Mathematics

I’ve been giving several JC Talk at various tuition centres, students mostly ask me the difference between A-level vs IB. I’ll simply share my opinions on Mathematics.

Difference between A-level Math and IB Math

For A-level, there are two categories namely H1 and H2. Content wise, H1 is 50% of H2. H1 students sit for a 3H paper while H2 students sit for two sets of 3H paper. Students without A’Math background will be more comfortable with H1, though I do have a few students doing H2 without A’math background; they really shed blood and sweat for their A. H2 is definitely more helpful with your university transition. The sad truth is that Math is quite hard to avoid in University.

For IB, there are three categories namely, Math Studies (MS), Standard level (SL) & Higher level (HL). They are of increasing difficulty as their name suggests.

My favourite way of explaining their difference is that A-level is deeper and more narrower while IB is wider but less deep. It will be unfair to compare HL to H2 as they are exposed to different amounts of content. Students should google the content and see if the topics interest them. Pre-University education needs sufficient amount of interest to excel, and as 17 years old, they should be learn to take the responsibility of such decisions.

MF15 can’t be more useful!

The only cheatsheet every student can bring into the exam hall.

What is MF15?

It’s the formula sheet every H2 Math student needs to know about.

View PDF

I thought we can look at the MF15 and also highlight a few common mistakes that students make in exams. 🙂

Firstly, the trigonometry formulas are all given in exams. Most students however, do not know what they have. I strongly suggest students spend time to know what they have. And if you’re interested, you should really learn how to derive the sum to product formula from the product to sum formula. You can read more here.

Secondly, the integration formulas that students see in MF15, are not as innocent as they look. Many students overlook the fact that the coefficient of the $x$ is ONE! You can read up more here. too.

Lastly, the r-formula is given. Students should know how to use it at the least. Also the properties of the Binomial and Poisson distribution are given (if you’re J2 and still need to refer to know the E(X) and Var(X), you should be worried too).

And if you’re not using TI-84, I strongly suggest you learn how to read the T-Table and Z-Table.