Wednesday, December 29, 2010

Question About Use of Notebook

Hello teacher Ban Har, I am one of the teachers in the course to apply the Singapore method in Santiago de Chile conducted recently. I now have to help 13 teachers next week in using the Singapore method textbooks. I have a question: how to use a note book, apart from the textbooks?

Marcela, a teacher in Chile

Hola Marcela. As we did in the course, we often use one problem in the development part of the lesson. At this point, the students are not likely to be opening the textbooks. They would be given the problem and asked to solve it usually in pairs or groups. They are likely to record their solutions in the notebook. After about 5 to 10 minutes, they will be asked for their responses which are used by the teacher to help students develop the key concept. By the end of the development, if you have attended one of my lessons before, you will see the board filled with different ways to solve the problem. Students can record this in their notebook. Sometimes there is also a conclusion. They will also be asked to write this in the notebook.

At this point the teacher will ask students to do consolidation tasks from the textbooks. These can be done in the notebook.

At the end of the lesson, students can do their reflection (e.g. write a letter to a friend about the lesson) in the notebook.

The notebook is an important tool for students to learn how to organize ideas.

Tuesday, August 17, 2010

Question About 4 x 4 = ___ + 7

Second grade students have some difficulties with tasks such as 4 x 4 = ____ + 7. They are students in billingual school and use Spanish and English.

A teacher in Chile

It is expected that students who do not understand the meaning of the equal sign (=) to give 16 as the answer to 4 x 4 = ____ + 7. The teacher can ask students: "What is the value on the right hand side?" (16 + 7) which is 23 and "What is the value on the left hand side?" which is 16. They should realize that these are not equal.

You could read the number sentence this way: 4 x 4 is equal to 16 which is what plus 7.

The task requires a two-step process and students need some metacogntion to complete the task. Use drawing and concrete materials to help the students.

Sunday, August 1, 2010

Two Times More Than

There were some yellow balls and red balls in a box.
The yellow balls were 2 times more than the red balls.
The box had 9 red balls.
How many balls were there in the box?

Should the answer be 36 or 27?


This task is poorly phrased. I hope this is not a test item.
Firstly, the quatity to be compared is not clear. Is it the mass, volume, number or some other quantity that is being compared? In this case i believe it is the number. Thus, it should be written as: The number of yellow balls was 2 times as that of red balls. Alternatively, it can be written as : There were twice as many yellow balls as there were red balls.

I believe MOE has addressed this point some years back. At the NIE, this issue should have come up during discussions on test item writing component of the course.

There were some yellow balls and red balls in a box.
There were twice as many yellow balls as there were red balls
There were 9 red balls in the box.
How many balls were there in the box?

In this case, the answer is 27 balls.

We say x is twice as much as y. We say x is 2 more than y. We do not say x is twice more than y. We might say x is 20% more than y.

Thursday, May 20, 2010

Questions Posted at Singapore Math in Action Professional Development in Manila

These are some questions posted at the Singapore Math in Action by Keys Institute for Teaching & Learning.

Q: You said that Singapore Math does not focus on recalling procedures. But isn't math process procedural? Please explain the difference.
A: In the Singapore curriculum, procedural fluecy is important but must be learnt meaningfully. Thus, the long division algorithm is explained using base ten blocks. Or the division of a whole number by a fraction is explained using the grouping meaning of division (how many three-fourths are there in one whole?. Mathematical processes include the use of heuristics and thinking skills. They also include reasoning, communication and seeing connections. None of these are procedural in the sense that the invert-and-multiply strategy is procedural.Mathematics is about sense making rather than recalling procedures.

Q: Many schools in Manila have crowded curriculum. How do you suggest Singapore Math being implemented the way it should be implemented given that kind of national curriculum?
A: Some schools simply use the Singapore curriculum and make sure that by the end of six years their students have mastered all content in the Filipino curriculum. Others use it as a resource to help teachers teach whatever there are in the Filipino curriculum in a meaningful way and to give their students challenging problems to solve.

Q: How do you feel about supplementing the school's curriculum of U.S. Math with Singapore Math? Will it be confusing for the child or would it be helpful for the child to learn different ways of solving problems?
A: Mathematics is the same everywhere. Singapore mathematics textbooks use more visual approaches and can help students learn abstract ideas.

Q: How old are Grade 1 students in Singapore?
A: They turn seven during the school year. They start school in January.

Q: When do you recommend a school to introduce Singapore Math to their students?
A: Any program is best introduce right from the start - Grade 1.

Q: How do you feel about 4th Graders using finger-counting to arrive at addition facts?
A: This should not happen. First and maybe second graders may use finger counting to figure out addition. But these should soon become facts and be remembered. Games such as Salute! seen in the lesson conducted during the seminar should help students gain mastery and fluency in addition facts. See the photograph.

Q: How do you help kids adjust from traditional methods to Singapore Math method especially if they are already in a higher grade?
A: They will need to get use to the use of bar models to solve word problems and they need to get use to more challenging materials. Older students may need some closing of gap.

Monday, May 3, 2010

Singapore Math @ San Diego

This was the presentation made at Sheraton San Diego Mission Valley Hotel. Yeap Ban Har presented this in the afternoon. William Jackson presented the morning session.

Sunday, April 25, 2010

Presentations at USA in April

I gave quite a few lectures in Boston and San Diego. The slides are available at

Monday, April 19, 2010

On Lesson Study

I am a teacher in a primary school in Singapore, currently carrying out Lesson Study in our school. I would like to seek your advice on Research Themes.

I gather that to come up with the Research Theme, the team needs to look at the Ideal Profile of Students and the Actual Situation of Students. This, with the School's and Department's Vision and Mision, the team will construct the Research Theme or Research Focus. My question is once this is firmed up, it will form the basis of all future Research Lessons for Lesson Studies, is that right?

Do we need to come up with a different Research Theme for each cycle of Lesson Study or will the Research Theme be the one that all Lesson Studies be based on. For example, my team has discussed and came up with a Research Theme for Mathematics. Will another Research Theme need to be constructed for a different cycle for Mathematics or can we use this Research Theme we have decided on for all Research Lessons for Mathematics.

Ban Har writes: Based on the school's vision, focus of the curriculum and your students' profile, the research theme is constructed. You are on the right track. You will stick with the same reasearch theme for a while until your team feel that there are new areas that need attention.

Saturday, April 3, 2010

Teaching Perpendicular Lines

Question: Should I get students to use set square to draw perpendicular lines in the first lesson or should I give them non-standard tools such as a right-angled triangle?

Hazel, a pre-service teacher in Singapore

This chapter comes after the chapter on angles where students have learnt about right angles. I think before students are taught how to draw perpendicular lines, they need to know what are perpendicular lines so that they are able to check if two lines are perpendicular. I am like to have given them two intersecting lines as well as lines joint at a point and ask them to measure the angles between the lines and to say that those that meet / intersect at right angles are called perpendicular lines. In my opinion, the chapter in the textbook starts too abruptly to get students to draw perpendicular lines without actually being taught what perpendicular lines are.

I like Hazel's idea of introducing other non-standard tools that can be used to draw perpendicular lines. I think a good lesson could involve the students being given some common objects such as ruler, protractor, set squares, triangle tangram set, an index card, ice-cream sticks and asked which of these they can use to draw lines that are perpendicular to each other.

The lesson can conclude with the whole class checking responses that they have generated using the criteria they have learnt.

Sunday, February 14, 2010

Implementing Singapore Math & PD

Can you tell me more about the professional development programm for teachers?

This is an exciting year as far as PD is concerned. You may read about lesson study in Singapore at I will also write more on this in a separate entry on a later date.

Suffice to say Ministry of Education in Singapore place a lot of emphasis on professional development. There is a position (called staff developer) in schools where the person (head of department level) is in-charge of professional development of his / her colleagues. This person is one of the head teachers.

What are the things that we must me aware about when we're implementing the program at our schools?

Three things you may want to take note of:

It is best to start from the lower grades. Unless the students have a strong foundation, they may not cope well with the textbooks (which includes challenging problems) if they start in, say, grade five. The teachers also have an easier time adapting to the pedagogy.

Support from the principal and school leaders is very important.

Professional development of teachers must be considered.

Differentiation in Singapore Classrooms

A friend in another country who requested some information about what happens in Singapore schools. He wanted to know more about the differentiation process. How does this take place in the classrooms? He said that he read that there are lesson after schools for children who have extra needs.

Differentiation is a continuing issue in schools here. chools are always striving to best do this. No wonder there have been quite a few request to conduct in-house training on differentiated instruction.

I think there must be variations on how this is done. But as a system, there are at least two things that happens in every school. One, Learning Support Porgramme (LSM) is a differentiated instruction for primary one and two students who are not entirely ready for the regular instruction. In many schools, these pupils are pulled out from their regular classes and work with a teacher who works with fewer children (not more than 10). The regular class size is 30. The content is the same as the regular programme. However, pupils get more attention because of small class size and the teachers are in a better position to diagnose and remediate. They may also use slightly different pedagogy to enage these pupils - more concrete activities, perhaps.

Another is the Foundation Maths Programme at Primary 5 and Primary 6. This is content differentiation. The students review work from the first four years in an age appropriate way even as they learn a bit of new materials. This is to ensure that the students are ready to join one of the course of study in grade seven (secondary school). They use a different textbook and they are usually in one class. In some schools with very few students in the Foundation Maths programme, they will be pulled out to do maths with another teacher during the mathematics periods.

It is alos not uncommon for teachers to conducrt remedial lessons after 1 p.m. Most of our schools end formal curriculum around 1 p.m. The afternoon is reserved for other non-academic activities, field trips as well as remedial and enrichment lessons.

Singapore Math Training

I get a lot of questions about the possibility of getting training in Singapore Math. The answer depends on what you are interested to do and which country you are in.

If you are interested in graduate studies, NIE offers masters degree in many specialization, including mathematics education, primary education and secondary education (there are many other fields of specialization). We have foreign stduents who complete the course full-time in a year although a year and a half is not so tight. NIE has both coursework as well as coursework plus thesis option.

If you are interested in Ph.D., you need to be here in the initial part to complete your coursework and to work out your research problem with your supervisor. You may do the research here or in your home country. You will be expected to be back here in Singapore towards the end of the candidature and for your oral examination before the degree is conferred. If you are interested please email me I can link you up with potential supervisors.

If you are more interested in getting training for classroom teaching rather than graduate degrees these are some options.

Join NIE's post graduate diploma in education (PGDE Primary) where you get pre-service training in two or three subject areas including mathematics teaching. It is one year. If you are not interested in the diploma and just want to focus on mathematics then I think there is an arrangement for you to do this as a non-graduating student.

Join NIE's inservice course. There is a range of subjects available throughout the year. From lesson study to problem solving to action research. A 12-hour course runs over 4 weeks. (once a week).

In some countries, there are institutes already in place. In the US, there is a summer institute every year. Go to for details.

Some school districts run theirs. I have been to Scarsdale School District twice to teach a course in their own teacher institute. I believe in the last course there were teachers not from the school district who joined the course.

In places like the Philippines, Indonesia and Chile, the book distributors have been organising training seminars at least once a year.

If you are thinking of running such institutes in your country, I can put you in charge with the book publisher to explore this possibility.