According to this Straits Times article, JCs offer "broader options" and a quicker route to a university degree.
Our view is that "all roads lead to Rome", no matter which path you take, if you work hard and persevere, you will reach the destination eventually. A downside of the current JC system is that "triple science" i.e. Physics, Chemistry, Biology combination is no longer allowed. Nor is Further Maths in the syllabus anymore (heard that it may be making a comeback though). This is bad news for those passionately interested in science, since they may have to drop one science subject that they love.
Do also check out our post on Which JC is good?
Another article here showcases different students who chose different paths. For those who are interested in early childhood education, a polytechnic route may be more direct, as mentioned by student Mark Lim.
Some good points about the JC route is that the maths syllabus there is more rigorous, especially if you take the H2 maths syllabus. It would provide a solid foundation for university maths, like multivariable calculus. As a tutor for university students, I have realised that students without H2 Maths background would struggle for the university maths modules, since it is hard to learn calculus over a short time in university. Check out what is H1, H2, H3 maths in this article.
Students who wish to know more about the psychology of learning math can check out the below book by Barbara Oakley. This century has been said to be the most important century since the beginning for mankind for Math. Nowadays everything we use in daily lives, from smart phones, computers, has something to do with Math!
Sunday, 18 January 2015
Using Computer to Teach Maths: Good or Bad? (Discussion)
The topic of using computer to teach mathematics is a controversial one. Yes, there are many benefits of using computers for calculation, but also some drawbacks.
Conrad Wolfram (in the above video) presents an excellent case of using computer to teach mathematics. This is really a good idea, to be honest. (The caveat is that Conrad is linked to the company Wolfram founded by his brother Stephen Wolfram. Wolfram is a computational math software company.)
Personally, I feel that once a student has mastered a skill to a certain degree, for example solving quadratic equations, there is no point making him/her solve quadratic equations ad infinitum over and over again. Using a computer/calculator that can solve quadratic equations is perfectly acceptable.
On a higher level, once a student knows how to compute eigenvalues/eigenvectors of a matrix, there is really little point in calculating eigenvalues by hand, which can be really tedious.
However, on the other hand, manual/mental calculation is an essential skill that is at the foundation of mathematics. Many mathematical theorems, no matter how abstract, have roots in calculation. To come up with a theorem, many mathematicians do extensive calculations to come up numerical evidence that a theorem is probably true, then try to prove it. Riemann came up with his famous Riemann Hypothesis after some calculation that the real part of the non-trivial zeroes of the Riemann Zeta function is always half. If you are interested in learning more about the Riemann Hypothesis, this book Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
is an excellent introduction to the subject for laymen.
Finally, manual calculation, despite being tedious and cumbersome, is also a skill. As a maths tutor over the years, I have seen some subtle changes in the average mental calculation skills of students after the calculator was permitted in Grade 5 (11 years old) in Singapore. Students who have memorized their time tables and used to mental calculation would have no problem telling what is 8x7, and what is 50-36.20, mentally. However, there are some students who are too used to calculators who may not be able (or willing) to calculate the above sums mentally. However, we must note that there are many great mathematicians who are poor at mental calculation. Grothendieck, one of the top mathematicians in the 1900s, once claimed that "57 is a prime number". As a result, 57 is known as a "Grothendieck prime".
What do you think about using computer to teach maths? Please write your comments below!
Also, check out this controversial book by Stephen Wolfram:
Although criticized by many for "pretending that he is the inventor of standard ideas and facts in computer science", there are some merits to this book. Galileo proclaimed that nature is written in the language of mathematics, but Wolfram would argue that it is written in the language of programs and, remarkably, simple ones at that. Sounds interesting...
Saturday, 17 January 2015
AES: Advanced Encryption Standard
This is a very nice, relatively short and sweet video about AES: Advanced Encryption Standard.
It is currently one of the most secure ways of encrypting data, and is used by the US government.
AES has swept away old faithful DES, and is now the workhorse of
business and government cryptography. Our entire civil order relies on
its integrity. Here we explain how it works, and discover how a string
of simple crypto primitives combine to such a robust cipher for which no
mathematical compromise was ever published.
Also, check out this book on Cryptography, Understanding Cryptography: A Textbook for Students and Practitioners
, rated rather highly by many people on Amazon.
It is currently one of the most secure ways of encrypting data, and is used by the US government.
Also, check out this book on Cryptography, Understanding Cryptography: A Textbook for Students and Practitioners
, rated rather highly by many people on Amazon.
Friday, 16 January 2015
Parents go for Maths Tuition
Source: http://mypaper.sg/top-stories/parents-go-tuition-help-their-kids-20150108
AS HE copied the solution to the maths problem sum onto his worksheet, he realised that he was lost.
Primary school mathematics is tough.
But this was not a primary school pupil struggling with the question. He was a father of two in a course on primary school maths.
He was one of several parents going for "tuition" so they can better understand what their children have to deal with in school.
On Dec 6, Mohd Yusof Maruwi, who is in his early 60s, and his wife, Sanisah Ismail, 45, attended an eight-hour session on solving primary school maths problems. It was held at a multi-purpose room at Muhajirin Mosque.
- from http://mypaper.sg/top-stories/parents-go-tuition-help-their-kids-20150108
Kudos to these highly commendable parents, who have taken the initiative to learn Primary School Maths to teach their children!
Despite sounding slightly ridiculous at first, tuition for parents is actually a good idea, especially if one of the parents (e.g. the mother) is a stay-at-home parent. This is because no matter how often a child goes for tuition, the tuition teacher can't accompany the child 24 hours, whereas the parent can.
Also, if the parent can do maths, it inspires the child and builds confidence. Imagine how demoralised a child may feel if the Maths problem is so difficult that even his beloved father and mother whom he/she looks up to can't solve it!
As a former Primary School Maths Tutor (I have since moved on to tutoring at secondary level onwards), I have to admit that some of the PSLE questions can be real tough. Even as a math graduate from NUS with years of experience, and an A* for PSLE Maths, I have to crack my brains and put on my thinking cap just to solve a PSLE question using elementary methods like model drawing. No wonder children will find it tough!
Also, some of the questions are designed to be tough for students using the traditional recommended method of model drawing. Examples of these kind of questions is when the model is 3 units, but the question requires dividing the 3 units into two. This leads to "half a unit" which is problematic, unless the student knows what to do (subdivide each unit into two smaller parts). Hence, students equipped with just the standard skill set of "draw model" naturally will find it very difficult to solve the problem.
A student who has mastered algebra at primary 6 level actually has a huge advantage over his peers. Most PSLE questions can be reduced to pair of linear simultaneous equations with two variables. This is amazingly easy to solve for those who have mastered solving such equations. However, this is a highly controversial method in pedagogy, since there are many who insist that algebra should not be taught so early.
If parents do not have the time or budget to go for tuition (also tuition teachers who teach parents are still currently rare), the next best thing is to read a maths book. Books like Step by Step Model Drawing: Solving Word Problems the Singapore Way
, written by Singapore Math expert Dr Yeap Ban Har, will enlighten parents on the divine art of drawing models. Model drawing will be able to solve 80%-90% of all PSLE Math questions, other than those questions specially designed to be anti-model, or model-unfriendly.
For the remaining 10% of problems (usually the last few problem sums) that are anti-model, trying to use the model method will lead to epic frustration. An algebra-model hybid approach using "u" for units, and "p" for parts would most likely be the ideal solution. A book like Practical Algebra: A Self-Teaching Guide, Second Edition
, would be what parents need to refresh their memory on Algebra.
Another fantastic book suitable for parents:
Finally, do check out a list of GEP Books for parents who are interested in preparing their child for GEP: http://mathtuition88.com/2013/11/11/recommended-books-for-gep-selection-test/
AS HE copied the solution to the maths problem sum onto his worksheet, he realised that he was lost.
Primary school mathematics is tough.
But this was not a primary school pupil struggling with the question. He was a father of two in a course on primary school maths.
He was one of several parents going for "tuition" so they can better understand what their children have to deal with in school.
On Dec 6, Mohd Yusof Maruwi, who is in his early 60s, and his wife, Sanisah Ismail, 45, attended an eight-hour session on solving primary school maths problems. It was held at a multi-purpose room at Muhajirin Mosque.
- from http://mypaper.sg/top-stories/parents-go-tuition-help-their-kids-20150108
Kudos to these highly commendable parents, who have taken the initiative to learn Primary School Maths to teach their children!
Despite sounding slightly ridiculous at first, tuition for parents is actually a good idea, especially if one of the parents (e.g. the mother) is a stay-at-home parent. This is because no matter how often a child goes for tuition, the tuition teacher can't accompany the child 24 hours, whereas the parent can.
Also, if the parent can do maths, it inspires the child and builds confidence. Imagine how demoralised a child may feel if the Maths problem is so difficult that even his beloved father and mother whom he/she looks up to can't solve it!
As a former Primary School Maths Tutor (I have since moved on to tutoring at secondary level onwards), I have to admit that some of the PSLE questions can be real tough. Even as a math graduate from NUS with years of experience, and an A* for PSLE Maths, I have to crack my brains and put on my thinking cap just to solve a PSLE question using elementary methods like model drawing. No wonder children will find it tough!
Also, some of the questions are designed to be tough for students using the traditional recommended method of model drawing. Examples of these kind of questions is when the model is 3 units, but the question requires dividing the 3 units into two. This leads to "half a unit" which is problematic, unless the student knows what to do (subdivide each unit into two smaller parts). Hence, students equipped with just the standard skill set of "draw model" naturally will find it very difficult to solve the problem.
A student who has mastered algebra at primary 6 level actually has a huge advantage over his peers. Most PSLE questions can be reduced to pair of linear simultaneous equations with two variables. This is amazingly easy to solve for those who have mastered solving such equations. However, this is a highly controversial method in pedagogy, since there are many who insist that algebra should not be taught so early.
If parents do not have the time or budget to go for tuition (also tuition teachers who teach parents are still currently rare), the next best thing is to read a maths book. Books like Step by Step Model Drawing: Solving Word Problems the Singapore Way
, written by Singapore Math expert Dr Yeap Ban Har, will enlighten parents on the divine art of drawing models. Model drawing will be able to solve 80%-90% of all PSLE Math questions, other than those questions specially designed to be anti-model, or model-unfriendly.For the remaining 10% of problems (usually the last few problem sums) that are anti-model, trying to use the model method will lead to epic frustration. An algebra-model hybid approach using "u" for units, and "p" for parts would most likely be the ideal solution. A book like Practical Algebra: A Self-Teaching Guide, Second Edition
, would be what parents need to refresh their memory on Algebra.Another fantastic book suitable for parents:
Finally, do check out a list of GEP Books for parents who are interested in preparing their child for GEP: http://mathtuition88.com/2013/11/11/recommended-books-for-gep-selection-test/
Monday, 12 January 2015
Winnie The Pooh Maths Olympiad Question!
Check out this interesting Math Olympiad question on Winnie the Pooh and sweets!
Question: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1411q.pdf
Solution: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1412a.pdf
Featured Book on Maths Olympiad:
Competition Math for Middle School
Written for the gifted math student, the new math coach, the teacher in search of problems and materials to challenge exceptional students, or anyone else interested in advanced mathematical problems. Competition Math contains over 700 examples and problems in the areas of Algebra, Counting, Probability, Number Theory, and Geometry. Examples and full solutions present clear concepts and provide helpful tips and tricks. "I wish I had a book like this when I started my competition career." Four-Time National Champion MATHCOUNTS coach Jeff Boyd "This book is full of juicy questions and ideas that will enable the reader to excel in MATHCOUNTS and AMC competitions. I recommend it to any students who aspire to be great problem solvers." Former AHSME Committee Chairman Harold Reiter
Question: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1411q.pdf
Solution: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1412a.pdf
Featured Book on Maths Olympiad:
Competition Math for Middle School
Written for the gifted math student, the new math coach, the teacher in search of problems and materials to challenge exceptional students, or anyone else interested in advanced mathematical problems. Competition Math contains over 700 examples and problems in the areas of Algebra, Counting, Probability, Number Theory, and Geometry. Examples and full solutions present clear concepts and provide helpful tips and tricks. "I wish I had a book like this when I started my competition career." Four-Time National Champion MATHCOUNTS coach Jeff Boyd "This book is full of juicy questions and ideas that will enable the reader to excel in MATHCOUNTS and AMC competitions. I recommend it to any students who aspire to be great problem solvers." Former AHSME Committee Chairman Harold Reiter
O Level Top Scorer 2015
Although MOE has ceased publishing the names of O Level Top Scorers, there is still some general statistics about O Level Top Scorers.
This year (2015), 83.3% of students scored 5 or more passes, which is the best performance in the past 20 years. Congratulations to all who did well!
According to this article in 2012, Lim Min from Crescent Girls’ School and Zhong Yingyi and Chai Yung Ci from CHIJ St Nicholas Girls’ School scored 10 A1s in the exams (11 A1s inclusive of mother tongue language). This is a very commendable effort by these O Level top students.
Another source from Kiasuparents shows that Cedar Girls' Secondary School is a consistent producer of O Level Top Scorers, with some having a total of 11 A1s in a single sitting. Seems like currently many of the O Level Top Students come from girls' schools. This may be due to the fact that girls are less playful and more likely to do their revision consistently, a huge advantage in terms of acing exams.
The Top Student in O Levels from Chung Cheng High School (2011) is Zeng Ding who has scored a very commendable 8 A1s (EL, HCL, CL, EMath, AMath, Chem, Bio, Comb Humanities) and 1 A2 (Phy).
Congratulations to all these O Level Top Students, especially those receiving their results in 2015! For those who are not top students, but tried their best, they too deserve a round of applause for their hard work and dedication.
Featured Book:
The Secrets of Top Students: Tips, Tools, and Techniques for Acing High School and College
Unlock your academic potential with tips, tools, and techniques from some of the best students in the country.
This year (2015), 83.3% of students scored 5 or more passes, which is the best performance in the past 20 years. Congratulations to all who did well!
According to this article in 2012, Lim Min from Crescent Girls’ School and Zhong Yingyi and Chai Yung Ci from CHIJ St Nicholas Girls’ School scored 10 A1s in the exams (11 A1s inclusive of mother tongue language). This is a very commendable effort by these O Level top students.
Another source from Kiasuparents shows that Cedar Girls' Secondary School is a consistent producer of O Level Top Scorers, with some having a total of 11 A1s in a single sitting. Seems like currently many of the O Level Top Students come from girls' schools. This may be due to the fact that girls are less playful and more likely to do their revision consistently, a huge advantage in terms of acing exams.
The Top Student in O Levels from Chung Cheng High School (2011) is Zeng Ding who has scored a very commendable 8 A1s (EL, HCL, CL, EMath, AMath, Chem, Bio, Comb Humanities) and 1 A2 (Phy).
Congratulations to all these O Level Top Students, especially those receiving their results in 2015! For those who are not top students, but tried their best, they too deserve a round of applause for their hard work and dedication.
Featured Book:
The Secrets of Top Students: Tips, Tools, and Techniques for Acing High School and College
Unlock your academic potential with tips, tools, and techniques from some of the best students in the country.
Author Stefanie Weisman was a top student all her life, graduating first in her class from Stuyvesant High School and Columbia University and getting degrees in both history and computer science. But it wasn't because she was a "natural" or smarter than everyone else -- it was because she had developed powerful and time-saving techniques for studying, taking notes, writing papers, taking tests, and much, much more, which anyone can put into practice!
Sunday, 11 January 2015
The Math of Noah's Ark
Source: Creation Ministries
Was Noah's Ark round? A scholar Dr Irving Finkel claims that the Noah's Ark was actually round, based on a translation of a small Babylonian tablet, named the Ark Tablet.
A replica of "Noah's Ark" according to Dr Finkel.
A ship modeled after the biblical description of Noah's Ark, "Johan's Ark", in the Netherlands
However, there is a rebuttal by Creation.com, which involves some mathematical arguments.
The Ark Tablet has the following verse: "Draw out the boat you will make on a circular plan; let her length and breadth be equal, let her floor area be one field, let her sides be one nindan high.". The phrase "length and breadth" be equal clearly suggests a square base rather than a round base. More calculations involving the surface area of bitumen needed to coat the Ark suggests that a square based ark is more consistent with the calculations, rather than a circular base.
Read more about it at: http://creation.com/real-noahs-ark?utm_media=email&utm_source=infobytes&utm_content=sg&utm_campaign=emails
Was Noah's Ark round? A scholar Dr Irving Finkel claims that the Noah's Ark was actually round, based on a translation of a small Babylonian tablet, named the Ark Tablet.
A replica of "Noah's Ark" according to Dr Finkel.
A ship modeled after the biblical description of Noah's Ark, "Johan's Ark", in the Netherlands
However, there is a rebuttal by Creation.com, which involves some mathematical arguments.
The Ark Tablet has the following verse: "Draw out the boat you will make on a circular plan; let her length and breadth be equal, let her floor area be one field, let her sides be one nindan high.". The phrase "length and breadth" be equal clearly suggests a square base rather than a round base. More calculations involving the surface area of bitumen needed to coat the Ark suggests that a square based ark is more consistent with the calculations, rather than a circular base.
Read more about it at: http://creation.com/real-noahs-ark?utm_media=email&utm_source=infobytes&utm_content=sg&utm_campaign=emails
Singapore IB Top Student
Source: http://www.straitstimes.com/news/singapore/education/story/singapore-among-top-asia-pacific-region-ib-exams-20150105
Out of over 2000 students who sat for the IB exams, Singapore produced 66 perfect scorers! (45 points) One of them is Seah Jun Jie, 18, who switched from the Express stream to the Integrated Programme (IP) in Secondary 3.
Australia is a distant second with 31 perfect scorers.
On average, Singaporean IB students scored 36.43 points.
Read more about the IB HL Math: http://mathtuition88.blogspot.sg/2014/12/ib-hl-math.html
Also, here is a Hitler parody on YouTube about "Hitler takes the IB HL Math Test". It is pretty funny, but gives an insight on the type of questions that can appear in the IB HL Math Test, for instance, a question on f(x+y)=f(x)+f(y), which has no numbers! This is related to something called Cauchy's functional equation!
Please note that this video is not created by me, and only watch it if you have a sense of humour!
IB Mathematics Higher Level Course Book: Oxford IB Diploma Program
Out of over 2000 students who sat for the IB exams, Singapore produced 66 perfect scorers! (45 points) One of them is Seah Jun Jie, 18, who switched from the Express stream to the Integrated Programme (IP) in Secondary 3.
Australia is a distant second with 31 perfect scorers.
On average, Singaporean IB students scored 36.43 points.
Read more about the IB HL Math: http://mathtuition88.blogspot.sg/2014/12/ib-hl-math.html
Also, here is a Hitler parody on YouTube about "Hitler takes the IB HL Math Test". It is pretty funny, but gives an insight on the type of questions that can appear in the IB HL Math Test, for instance, a question on f(x+y)=f(x)+f(y), which has no numbers! This is related to something called Cauchy's functional equation!
Please note that this video is not created by me, and only watch it if you have a sense of humour!
Featured Book:
IB Mathematics Higher Level Course Book: Oxford IB Diploma Program
Saturday, 10 January 2015
H2 Maths Syllabus and Formula Sheet
H2 Maths Syllabus and Help Sheet (MF15)
This is the latest updated H2 Maths Syllabus and Formula Sheet, for the year 2015.
H2 Maths Syllabus: https://mathtuition88.files.wordpress.com/2015/01/9740_2015.pdf
H2 Maths Formula Sheet (Printable): https://mathtuition88.files.wordpress.com/2015/01/listmf15.pdf
Hope it helps!
Official Source: https://www.seab.gov.sg/pages/nationalExaminations/GAL/School_Candidates/2015_GCE_A.asp
Featured Book:
Understanding Analysis (Undergraduate Texts in Mathematics)
Review (on Amazon.com):
Once in a while, a book comes along that is so wonderfully written, the reader reflexively searches for other books by its author. Understanding Analysis is a prime example of this rare breed (Unfortunately, this is Abbott's only book as far as I know: write more!).
Undergraduates often begin analysis courses with dread and finish in a state of utter confusion,knowing the definitions of key phrases, and sometimes even being able to supply proofs for some elementary results, but having no intution as to why the main theorems are pertinent.
Featured Book:
Understanding Analysis (Undergraduate Texts in Mathematics)
Review (on Amazon.com):
Once in a while, a book comes along that is so wonderfully written, the reader reflexively searches for other books by its author. Understanding Analysis is a prime example of this rare breed (Unfortunately, this is Abbott's only book as far as I know: write more!).
Undergraduates often begin analysis courses with dread and finish in a state of utter confusion,knowing the definitions of key phrases, and sometimes even being able to supply proofs for some elementary results, but having no intution as to why the main theorems are pertinent.
Thursday, 8 January 2015
Topics taught in JC 1 / JC 2 H2 Maths
What are the topics taught in JC1 H2 Maths?
What are the topics taught in JC2 H2 Maths?
Source: http://jcmath.wiki.hci.edu.sg/JC1+%26+JC2+Topics
Ans:
It differs from school to school, HCI teaches the topics in the following order below. The order may be different for different schools, though. Some topics definitely have to be taught first, for instance Differentiation is taught first before Integration almost all the time. After these two are taught, then students can move on to learn Maclaurin Series and Differential Equations.
What are the topics taught in JC2 H2 Maths?
Source: http://jcmath.wiki.hci.edu.sg/JC1+%26+JC2+Topics
Ans:
It differs from school to school, HCI teaches the topics in the following order below. The order may be different for different schools, though. Some topics definitely have to be taught first, for instance Differentiation is taught first before Integration almost all the time. After these two are taught, then students can move on to learn Maclaurin Series and Differential Equations.
JC 1 H2 Mathematics Topics
- Sequences and Series
- Graphing Techniques
- Inequalities and System of Equations
- Functions
- Differentiation and its Applications
- Integration and its Applications
- Vectors
- Binomial Expansion
- Maclaurin Series
JC 2 H2 Mathematics Topics
- Differential Equations
- Complex Numbers
- Permutation and Combination
- Probability
- Binomial and Poisson Distributions
- Normal Distribution
- Sampling
- Hypothesis Testing
- Linear Correlation and Regression
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