I am a student self-studying mathematics from Singapore's textbook at the 10th to 11th (Secondary 5) grade levels. When I finish these, I would like to continue following Singapore's curriculum. Which books (series) do you recommend. I plan to study advanced topics in depth, like statistics and calculus? I would like to follow the newest books, ones followed currently in Singapore by JC students.

Student in USA

In JC, students do not use a textbook because the lecturers provide their own lecture notes, like in the university. If you have not done Additional Mathematics, you may work on this - it is a book that includes trigonometry, calculus and other advanced topics. This is used in Grade 9 - 10 by advanced students. It is available from the same place you got your other books.

## Sunday, October 30, 2011

## Wednesday, October 19, 2011

### Percent

I hope you still remember me. Last time I contacted you regarding congruence and similarity. Now, my son is studying in Grade 8.

If you don't mind can you clear my confusion regarding one problem of percentage. I have difference of opinion with the mathematics teacher and I want to clear my concept. The problem is as follows:

When we are converting 2/5 to percentage we write as follows:

2/5 x 100% = 40%. ---------- (1)

The teacher says it is not necassary to write symbol(%) with 100.

2/5 x 100 = 40%. ------------(2)

You will notice that % is missing from (2). Can you please explain is it also the correct practice not to write the symbol % with 100. My view is that 2/5 x 100 will result in 40 and not 40%.

I am afraid that this mistake will results in marks being deducted in the IGCSE.

A father in Saudi Arabia

You are right 2/5 is equal to 2/ 5 x 1 and 1 = 100/100 which is written as 100%.

2/5 x 100 = 40 as you said. 40% is equal to 0.4 (not 40).

Perhaps the teacher knows that, in a lenient way or marking, candidates get full credit whether they did (1) or (2). But I am sure you rather your son learn what is mathematically correct rather what is minimally acceptable to earn a credit in the examination. Please advise your son to write the mathematically correct sentence. I also trust that you will help him understand why (2) is not correct (although it may still earn a credit in the examinations, according to the teacher).

If you don't mind can you clear my confusion regarding one problem of percentage. I have difference of opinion with the mathematics teacher and I want to clear my concept. The problem is as follows:

When we are converting 2/5 to percentage we write as follows:

2/5 x 100% = 40%. ---------- (1)

The teacher says it is not necassary to write symbol(%) with 100.

2/5 x 100 = 40%. ------------(2)

You will notice that % is missing from (2). Can you please explain is it also the correct practice not to write the symbol % with 100. My view is that 2/5 x 100 will result in 40 and not 40%.

I am afraid that this mistake will results in marks being deducted in the IGCSE.

A father in Saudi Arabia

You are right 2/5 is equal to 2/ 5 x 1 and 1 = 100/100 which is written as 100%.

2/5 x 100 = 40 as you said. 40% is equal to 0.4 (not 40).

Perhaps the teacher knows that, in a lenient way or marking, candidates get full credit whether they did (1) or (2). But I am sure you rather your son learn what is mathematically correct rather what is minimally acceptable to earn a credit in the examination. Please advise your son to write the mathematically correct sentence. I also trust that you will help him understand why (2) is not correct (although it may still earn a credit in the examinations, according to the teacher).

## Wednesday, October 5, 2011

### From a Dutch Homeschooling Parent

I'm a homeschooling mother from the Netherlands and I have used (and still use) Singapore Math for my children in all the years of their primary education. I can't rave enough about this method of math education: the books are great, the bar diagrams are marvellous - I wish I had learned mathematics this way in my time.

Now my oldest child is starting Secondary Education the upcoming year. In the Netherlands secondary education consists of 6 years and the level of math at the final exams is relatively high (higher than say, American High School level - to give comparison). However, instead of preparing my children for their final exams with Dutch secondary math books, I prefer to keep on working with Singapore Math. Even though I can't really compare Dutch and Singapore High School Math, I very much like the way Singapore Math has build a strong math education in my children in such a thorough and painless way.

But in my search for information I got a little confused about all the available series. There seem to be:

1) New Mathematics Counts Series

2) New Elementary Maths Series and

3) New Syllabus Mathematics

Would you be able to explain to me the difference between these series or can you give me an advice on what to use for the High School years of my children? I'm aware this is not the type of problem question you usually receive on your blog, but I very much hope you can answer me just the same.

For the primary years we're using the My Pals are Here Maths Series (Grades 1-6), and I'd like use the best available SM high school sequence. I prefer to use the series that is used in most Singapore and/or International High Schools. For example: I understand that for the primary years My Pals are Here Maths and Shaping Maths are the most common used series in Singapore and International schools: MPAH in 80% of the schools, Shaping Maths in 20% - roughly estimated.

Do you happen to know the ratio of the three above mentioned series for the secondary years (New Mathematics Counts Series / New Elementary Maths Series / New Syllabus Mathematics)? Or do you know any distinctive features?

It seems that all Singapore Math distributors, either in the US, UK or Singapore are all pushing the series that offers them the most profit, so I don't know who to believe in that area. Buying all the books for four children is quite an investment, so it would be a pity if I invested in the wrong series. I was even on the verge of abandoning Singapore Math for a curriculum called The Art of Problem Solving (http://www.artofproblemsolving.com/Store/curriculum.php) because I didn't have any clue of the right series. But then I found your blog, I hope you can find the time to answer me.

Thanks in advance for your effort.

A Parent in The Netherlands

In Singapore, some students study 4 years and others 5 years for their secondary education. They then move to another two years in junior college (some opt to go to a polytechnic instead). The first four years leads to GCE O Levels (Grades 7-10) and the last two years leads to GCE A Levels (Grades 11-12).

You are right - there are many textbook series for secondary levels. In fact, more than the three you listed. Essentially they are all the same. Internationally, most schools / parents use New Syllabus Mathematics (NSM) and New Elementary Mathematics (NEM) simply because these has been around for many years. NSM is still sued in Singapore schools. NEM is no longer used - the publisher sometimes did not submit them for review or update it to make it a 100% fit with topics in the revised curriculum. All our textbooks must be reviewed by Ministry of Education. In my opinion, NEM is of good quality too.

New Mathematics Counts (NMC) is designed for academically weaker students - the program is to be done over five, instead of four years.

NSM is designed for students who have a strong foundation in mathematics. That is why other than the four books, there is a fifth book that advanced students opt for in Grade 9/10 (they use this book over two year to supplement the main text). This is Additional Mathematics. Many kids in Singapore study this subject. By the time they complete Additional Mathematics, they would have done basic calculus. Generally, if your child do well using the Singapore textbooks, he/she should be ready for ay kind of test.

In brief, NMC if the child is struggling with math. NEM or NSM if the student is quite good in math. NSM has the option for advanced topics.

See http://atl.moe.gov.sg/ for textbooks used in Singapore. Titles with Sec 5N are designed for students who tend to struggle somewhat with mathematics - the topics coverage is the same but done over five instead of four years. Books listed as NT (Nornal Technical) are for students who are moving to vocational course after Grade 10.

Now my oldest child is starting Secondary Education the upcoming year. In the Netherlands secondary education consists of 6 years and the level of math at the final exams is relatively high (higher than say, American High School level - to give comparison). However, instead of preparing my children for their final exams with Dutch secondary math books, I prefer to keep on working with Singapore Math. Even though I can't really compare Dutch and Singapore High School Math, I very much like the way Singapore Math has build a strong math education in my children in such a thorough and painless way.

But in my search for information I got a little confused about all the available series. There seem to be:

1) New Mathematics Counts Series

2) New Elementary Maths Series and

3) New Syllabus Mathematics

Would you be able to explain to me the difference between these series or can you give me an advice on what to use for the High School years of my children? I'm aware this is not the type of problem question you usually receive on your blog, but I very much hope you can answer me just the same.

For the primary years we're using the My Pals are Here Maths Series (Grades 1-6), and I'd like use the best available SM high school sequence. I prefer to use the series that is used in most Singapore and/or International High Schools. For example: I understand that for the primary years My Pals are Here Maths and Shaping Maths are the most common used series in Singapore and International schools: MPAH in 80% of the schools, Shaping Maths in 20% - roughly estimated.

Do you happen to know the ratio of the three above mentioned series for the secondary years (New Mathematics Counts Series / New Elementary Maths Series / New Syllabus Mathematics)? Or do you know any distinctive features?

It seems that all Singapore Math distributors, either in the US, UK or Singapore are all pushing the series that offers them the most profit, so I don't know who to believe in that area. Buying all the books for four children is quite an investment, so it would be a pity if I invested in the wrong series. I was even on the verge of abandoning Singapore Math for a curriculum called The Art of Problem Solving (http://www.artofproblemsolving.com/Store/curriculum.php) because I didn't have any clue of the right series. But then I found your blog, I hope you can find the time to answer me.

Thanks in advance for your effort.

A Parent in The Netherlands

In Singapore, some students study 4 years and others 5 years for their secondary education. They then move to another two years in junior college (some opt to go to a polytechnic instead). The first four years leads to GCE O Levels (Grades 7-10) and the last two years leads to GCE A Levels (Grades 11-12).

You are right - there are many textbook series for secondary levels. In fact, more than the three you listed. Essentially they are all the same. Internationally, most schools / parents use New Syllabus Mathematics (NSM) and New Elementary Mathematics (NEM) simply because these has been around for many years. NSM is still sued in Singapore schools. NEM is no longer used - the publisher sometimes did not submit them for review or update it to make it a 100% fit with topics in the revised curriculum. All our textbooks must be reviewed by Ministry of Education. In my opinion, NEM is of good quality too.

New Mathematics Counts (NMC) is designed for academically weaker students - the program is to be done over five, instead of four years.

NSM is designed for students who have a strong foundation in mathematics. That is why other than the four books, there is a fifth book that advanced students opt for in Grade 9/10 (they use this book over two year to supplement the main text). This is Additional Mathematics. Many kids in Singapore study this subject. By the time they complete Additional Mathematics, they would have done basic calculus. Generally, if your child do well using the Singapore textbooks, he/she should be ready for ay kind of test.

In brief, NMC if the child is struggling with math. NEM or NSM if the student is quite good in math. NSM has the option for advanced topics.

See http://atl.moe.gov.sg/ for textbooks used in Singapore. Titles with Sec 5N are designed for students who tend to struggle somewhat with mathematics - the topics coverage is the same but done over five instead of four years. Books listed as NT (Nornal Technical) are for students who are moving to vocational course after Grade 10.

### Bar Models

This morning I taught Primary 4 students word problems using bar models. I expected the students to get a clear picture by it, but actually not. They were so impatient to compute directly, even without reading the question :( They just depended on my instruction whether to multiply or to divide. So, I'm thinking of an activity at the beginning to introduce the bar model to them - perhaps by making the bars using color papers.

Teacher in Indonesia

This is not unexpected if the students are already used to a computational approach. All they want to do is to compute. Without a clear understanding of the problem, they will not be able to identify the correct operations.

Bar modelling begins in kindergarten when a teacher models the story using the real things and later pictures of the real thing. Later, 5 unifix cubes / snap cubes are used to represent, say 5 sweets. By Primary 2, they begin to use a bar to represent quantities.

Your idea of using paper strips is excellent. I do it all the time.

You can also give problems without numbers.

Johan has more sweets than Siti.

How many sweets does Siti have?

After students show the correct bars for number of sweets Johan has (longer) and number of sweets Siti has (shorter), tell them Johan has 6 sweets more than Siti. Ask them to put in the new information on the bar models. Finally tell them that Johan has 14 sweets. Get them to solve the problem.

Hope this helps.

Teacher in Indonesia

This is not unexpected if the students are already used to a computational approach. All they want to do is to compute. Without a clear understanding of the problem, they will not be able to identify the correct operations.

Bar modelling begins in kindergarten when a teacher models the story using the real things and later pictures of the real thing. Later, 5 unifix cubes / snap cubes are used to represent, say 5 sweets. By Primary 2, they begin to use a bar to represent quantities.

Your idea of using paper strips is excellent. I do it all the time.

You can also give problems without numbers.

Johan has more sweets than Siti.

How many sweets does Siti have?

After students show the correct bars for number of sweets Johan has (longer) and number of sweets Siti has (shorter), tell them Johan has 6 sweets more than Siti. Ask them to put in the new information on the bar models. Finally tell them that Johan has 14 sweets. Get them to solve the problem.

Hope this helps.

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