Wednesday, December 15, 2010

Teacher Professional Development in Chile 12-18 Dec 2010

More than 80 teachers, in two classes, completed a 54-hour programme by Marshall Cavendish Institute (MCI) in Santiago de Chile. Tonight the institute hosted a dinner for them.

Even as MCI, a 3-month old institute, is kept busy developing a comprehensive teacher professional development programme for its Mathematics Academy which was launch in September, as well as doing the groundwork to prepare for the launch of three more Academies (Lesson Study Academy, Science Academy, Early Childood Academy) in 2011, it has began conducting courses for teachers.

The programme in Chile is for Ministry of Education Chile. The programme is part of MOE Chile's "Singapore Textbook Project" (Proyecto Textos Singapur), a 2011-2013 project where a representative sample of public schools in all p[arts of Chile were invited to receive the Spanish Edition of a Singapore texbook instead of the regular standard issue textbook. Participation is voluntary and sampled schools that did not opt for the Singapore textbooks were replaced with a similar school to maintain the representative sample. in 2011, Grade 1 and Grade 2 textbooks are available. In 2012, Grade 3. In 2013 Grade 4. The project will then be reviewed.

More than 80 teachers were selected to attended this leaders in mathematics education programme where they receive the necessary professional development to help them help about 10 - 20 teachers in their repsective regions.

They attended courses on Fundamentals in Singapore Math, Whole Numbers, Fractions, Measurements, Model Method, Differentiated Instruction and Activity-Based Lessons.

Sunday, October 10, 2010

Leaders and Educators in Asia Programme by Course by NIE International

Fifteen primary teachers from the Philippines will be in Singapore September to December to complete the Customized Training Programme (CTP) under the Leaders and Educators in Asia Programme (LEAP) which is a subset of the PGDE programme, where LEAP teachers do only specific components of the programme instead of the whole PGDE programme. It is specially designed to cater for the teachers’ needs based on their local context in Philippines.

I am fortunate I will be teaching both the mathematics content and pedagogy courses (a total of 50 hours to the group). The regular PGDE programme is slightly twice as long. Thus, I will have to identify critical aspects to develop the course and to capitalize on the fact that these are experienced teachers.

I have created a separate blog for this course at

Friday, October 8, 2010

NCTM Regional Conferences & Expositions 2010, Denver, Colorado 7-8 October 2010

US teachers who are interested in the problem-solving approach to teaching mathematics attended a presenttaion on the role problems can play in an early grades mathematics classroom.

In the afternoon, there was a different sessions on features of mathematics teaching in early grades in Singapore.

Saturday, October 2, 2010

Professional Development at Universidad Santiago de Chile

This is the Third Seminar on the Singapore Method in Mathematics Teaching organised by Universidad de Santiago de Chile (Usach). There were three presentations and one panel. I made two presentations. There were about 400 participants.

On Multiplication

On Assessment

Friday, October 1, 2010

Professional Development and Lesson Study in Chile

In my one week in Chile, there was a host of professional development activities for teachers from public, semi-private and private schools.

Presentation on Earlybird Kindergarten at British Royal School Santiago
coming soon

Presentation on My Pals Are Here! Maths at Andree English School Santiago
coming soon

Teachers who attended the sessions at Thomas Jefferson School, British Royal School (Conception), The Hebrew Institute and Mackay School (Vina del Mar) will find this presentation relevant.

Presentation on Pensar sin Limites at various schools can be found in another blog entry.

Lesson Study
I conducted an open lesson for Primary 2 (Multiplication) at Dagoberto Godoy School in Santiago for all the teachers from the eight primary schools in this semi-private school cluster.
coming soon

I also conducted an open lesson for Primary 2 (Addition and Subtraction) at Escuela Republica de Guatemala. Primary 1 and 2 teachers from 54 schools attended the session watching the lesson from a hotel and we had a discussion afterwards.
coming soon

Wednesday, September 29, 2010

Seminar on Assessment for Learning at The English Institute Santiago

Teachers from billingual schools that have been using MPH Maths for several years attended the course hosted by one of the schools The English Institute.

Pensar sin Limites Seminar at Colegio Inmaculada Conception

This presentation was made at various places - at schools that are trying out the Spanish edition of My Pals Are Here! Mathematics for the first time as well as potential users of the book in the coming school year.

Escuela Republica de Siria
Pedro de Valdivia School
St George's School
San Benito School
Alcantara & Alicante School

Also public seminars at Colegio Immaculada Conception

Check out this SlideShare Presentation:

Tuesday, September 28, 2010

Singapore Math in Chile (MOE Chile)

I gave this presentation at a seminar organized by Ministry of Education Chile to discuss how mathematics is taught in Singapore. It was held in Conception and later it was repeated in Santiago. The participants were mostly principals and curriculum directors.

I also had a meeting with the Curriculum and Evaluation team from the MOE.

About 200+ participants came for the Conception session. They were from the southern part of Chile.

Saturday, September 18, 2010

Singapore Math in the Netherlands

This si the third day and Singapore Math has gotten quite a bit of media attention - newspapers, radio and TV all giving it some airtime. I gave an interview to a national newspaper and a TV station.

Thursday, September 16, 2010

Wednesday, September 15, 2010

Singapore Math in the Netherlands

A group of 36 Dutch educators met for three day to participate in a programme to prepare them to support Dutch teachers who are using Singapore mathematics textbooks.

This is the Day 1 presentation.

Saturday, September 11, 2010

The Idea of Centre of Excellence (COE)

In Singapore, schools are grouped in clusters - called schools clusters. School clusters make up zones. All schools in Singapore belong to one of four zomes. In East Zone, they form a centre of excellence (COE). The East Zone COE for Mathematics organizes a one-day conference every year. This year they focus on mathematics games with students creating and presenting mathematics games at the event.

I gave a keynote lecture to teachers at this year's event on 6 September 2010.

Sunday, August 8, 2010

Mentari Upper Primary Number Sense

International School Saigon Pearl

Posted by Picasa

Teachers learn about the thinking and problem-solving orientation of Singapore mathematics curriculum. They also learn about Bruner, Skemp,Dienes as well as the spiral nature of the curriculum. The examples included materials from K-5 and are mosty from Math in Focus given that this is the series the school is using.

This is a one-day workshop covering half an academic unit.

Fundamentals of Singapore Math
1. The Focus on Thinking and Problem Solving
2. Bruner's Theory (CPA Representations)
3. Skemp's Theory (Conceptual and Procedural Understanding)
4. Dienes' Theory (Variability)
5. Spiral Curriculum

Tuesday, August 3, 2010

STU Workshop for Helping Children with Lower Primary Mathematics

In the photo, participants learn a simple game to help kids learn addition facts. One player says Salute and the other two hold up their cards as they salute each other. The one who says Salute tells the total of the two numbers he sees. The other players who cannot see their own number try to guess what number they are holding up.

Sunday, August 1, 2010

Professional Development for St Edward's School, Florida

The course covers the basics of SingaporeMath - problem solving, thinking, Bruner's CPA, Conceptual Understanding and Dienes' Variation.

Saturday, July 17, 2010

Pat's Schoolhouse Teacher Professional Development

This is the second time I teach a course for teachers from Pat's Schoolhouse centres. About 100 teachers attended the course.

At the end of the course, teachers who did the reflection mentioned among other things:

1. To always keep in mind that we are teaching kids rather than content. It is important to provide variations.

2. The magic tricks included in the course are interesting and can be used with the kids.

3. Another mentioned that she is reminded by the videos how important the way teachers speak to kids is.

4. The importance on being able to 'look at children' so that we are able to assess more accurately. The sticks activity, the card game and the Japanese video all demonstrated that a lot of thinking is involved on that part of the students.

5. A lot of Why? What do you think? It is important for kids to talk and share their views.

6. Teachers should model reading and good thinking.

7. CPA Approach. The focus on process than on computations. The games and websites are interesting.

8. Different materials are used for probelm solving. Letting kids figure out what is wrong and right.

9. A teacher mentioned that she is glad they have been doing the right thing!

10. The use of pictorial representation as well as real world context.

11. A precious lesson for another teacher is the use of variations. And thinking about how to challenge children.

Wednesday, July 14, 2010

National Conference on Singapore Math Strategies in Las Vegas

This session is on Early Grades Mathematics.

These are the slides for the sessions on Teaching of Fractions.

Monday, July 5, 2010

Primary 1 & 2 Mathematics

This was conducted at Teck Whye Primary School Open House 2010.

Slides will be available shortly.

The next presentation focuses on problem solving at primary one and two levels. It was conducted at CHIJ Our Lady Queen of Peace.

An Overview of Lesson Study

This is an introduction to lesson study. It has been conducted at various schools including primary school such as Da Qiao Primary and Compassvale Primary, schools cluster such as S1 Schools Cluster at Jingshan Primary School and secondary school such as Jurong West Secondary School. Minsitry of Education (Training and Development Division) is organizing this course on 9 July 2010. Two courses on more specific aspects of lesson study are planned for 27-28 July (primary) and 29-30 (secondary). See TRAISI for registration details.

The slides will be available shortly.

Sunday, June 27, 2010

Seminar for Parents

In Singapore, the PSLE is an important examination and parents are interested to know more about the examination.

Sunday, June 6, 2010

Rye City School District

I spent a day doing presentations on word problems and teaching of fractions to grades four, five and six teachers from schools in Rye City School District.

Dobbs Ferry School District

The Dobbs Ferry School District consists of three schools: Dobbs Ferry High School, Dobbs Ferry Middle School and Springhurst Elementary School. It is located in the quiet hamlet of Dobbs Ferry, NY, just 20 miles north of New York City. I visited Springhurst for a day and taught three classes, made a presentation on mathematics teaching to the teachers, and talked about the math program in the school to the parents.

Scarsdale Teachers Institute

This set of slides document the content of the weekend course on the use of anchor problems in enhancing teaching and learning of mathematics.

Tuesday, May 18, 2010

SingaporeMath in Action

Based on teacher education program in Singapore, about 90 Filipino educators made up the first class of Singapore Math in Action. Slides from four sessions are available here. The next Singapore Math in Action is scheduled for 24-25 September 2010.

For participants of the first class, these are the readings that you should complete to deepen your learning:

Read for Bruner`s ideas
Read also for Bruner. There is a link to Spiral Curriculum
Read for Skemp`s idea on understanding. This is his website and the paper on relational and instrumental understanding is found under the section titled Papers.
Read for Dienes` six-stage theory. And try to locate some reading, books or on-line, about perceptual and mathematical variability.

For participants who want to have a documentation of their learning beyond the certificate each has received, you are invited to submit something that you have tried out in your own classrooms based on Singapore Math in Action that you have attended. Details are in the e-mail sent to all participants of the course.

Questions posted at the seminar are found at

This session is on mathematical problem solving.

This session is on all things related to fractions.

Monday, May 10, 2010

Ateneo de Manila Summer Institute

This is the third year I have been here to teach the summer institute. This year I am teaching the middle school program where the teachers are teaching Grades 4 to 7. We began after a brief opening ceremony.

In the opening session, I tried to discuss Bruner's enactive, iconic and symbolic representations using division of whole numbers by fractions and long division algorithms. The teachers asked questions related to teaching of division of fractions by fractions, multiplication of decimals and operations involving negative integers. We ended the day with a game of 'either one or three'- in a game where two players take turn to remove exactly one or three paper clips from apile of clips and the winner is the person who remove the last clip(s) - what is the winning strategy?

What if the rule is changes to wither 'one or two'?

We begin Day Two with Dienes' Theory of Variation ... but not before I pose the class the Fido Problem. Tell you more later.

Saturday, May 1, 2010

Problem-Based Approach

The open-ended approach common in the Japanese mathematics classroom uses a single problem in a mathematics lesson. In training teachers at Bina Bangsa School - a family of schools in Indonesia that uses the Singapore curriculum - I introduced the idea of teaching new concepts, doing drill-and-practice as well as getting students to apply what they learn using a well-selected or well-crafted problem. Other than workshops and lectures, teachers also get to see such problem-based lessons - there was one on learning area (primary three) and one applying Pythagoras theorem to find distance bewteen points (secondary two). Teachers saw examples, they worked through afew such problems, I modelled a few of such lessons with them and one with students,they worked with other colleagues to design one such lesson which hopefully they will try out and see how studenys respond to the lesson).

In designing such lesson, teachers select a problem and solve the problem themselves to understand the processes and challenges involved, as well as to see the mathematics in the problem. They decide if the problem can be used to introduce a topic or to provide drills-and-practice or to provide opportunities for students to apply what they have learnt.

They also considered how students will solve the problem and how to use the solutions to help students construct knowledge.

Saturday, April 3, 2010

Fraction Addition: Dienes' Theory of Mathematical Variability

In the final lesson with my first year diploma students (they will go on to read at least two more mathematics education courses as part of their pre-service training), we had a chance to review the test they took and key learning theories.

I used examples from fraction additions to discuss theory of variability (Zoltan Dienes). How is 2/5 + 2/5 different from 2/3 + 2/3? Both are symbolic representation of fraction additions. But mathematically they are not the same. Dienes refer to this as mathematical variability. In 2/3 + 2/3, students need to have the knowledge of mixed numbers and improper fractions. Such knowledge is not needed in doing 2/5 + 2/5. These two tasks possess mathematical variability.

In Singapore, these are taught in different grade levels. 2/5 + 2/5 is taught in Primary 2 while 2/3 + 2/3 are taught in Primary 4.

How about 1/8 + 1/8? This is taught in Primary 3. Why is addition of like fraction (2/5 + 2/5, 1/8 + 1/8 and 2/3 + 2/3) are considered not the same and are taught in different grade levels? According to Dienes, there is mathematical variability among the tasks. The Singapore approach seems to suggest the need for students to be systematically introduced to each variation.

In 1/8 + 1/8, students need to know equivalent fractions. Mathematically the three tasks are not the same and this is mathematical variability that Dienes wrote about.

Is 5/8 + 5/8 a variation of the three tasks given above?

Saturday, February 27, 2010

Fractions: Equal Parts

The mathematics education course focuses on curriculum structure, teaching strategies including ICT and students' responses (errors). For example in the Diploma programme, the first course (of three or four) includes Teaching of Whole Numbers, Teaching of Fractions, Decimals and Percent, Teaching of Ratio and Teaching of Rate and Speed.

Student teachers also learn the Singapore curriculum framework, learning theories, scheme of work and lesson planning, Ministry of Education initiativces including the role of calculators and ICT.

In a lesson on Teaching of Fractions, teachers were presented with this problem - is a rectangle cut into four equal parts by its two diagonals?

There were student teachers who said that the parts are not all equal because the triangles are not 'the same' meaning not congruent. Subsequent whole-group discussion with paper rectangles and a pair of scissors led to four responses that are shown at the top of this page.

There was a response that suggested cutting each the the four parts into two triangles which are equal parts as they are congruent triangles. Each of the four parts is then clearly 2 eighths. See Photograph 1.

A second response is based on using the formula to calculate the area of triangle. On Photograph 2, it can be seen that B = 2h and b = 2H. The area of the two non-conguent triangles can be shown to be the same.

Another response includes cutting each of the four parts into two congruent triangles and rearranging the pieces to form congruent triangles. Thus, the triangle shaded black and the one shaded red in Photograph 3 can be rearranged to form congruent triangles.

Finally there was another response that is based on using two congruent triangles to form a rhombus. This resulted in two congruent rhombii. If the two rhombii are equal, it follows that half of one rhombus (one of the triangles) is equal to half of the other (the other triangle).

The student teachers were told that in mathematics classrooms, teachers use different models to show fractions. In the example, we use the area model - where we use area to represent fractions. There is also the length model (e.g. the bar model or line model) where length is used to represent fractions. Other models include the volume model (e.g. using a cylinder of water to show fractions).

In terms of curriculum structure, we learn that equal parts is an important concept in understanding of the fraction notation. In terms of common misconceptions, we see that some students may have the wrong idea that equal parts refer to congruent parts rather than parts with equal area.

In Singapore curriculum, fraction is introduced formally in Primary 2.

Sunday, February 21, 2010

Becoming a Teacher in Singapore

There are plenty of opportunities for professional development for teachers in Singapore. These four teachers from four different priamry schools were on teacher work attachment (TWA) scheme with Teachers Network and went to Cambodia in December 2009 to share with Cambodian teachers and educators interesting ways to teach primary mathematics. The second batch of teachers that went on TWA to Cambodia in June 2010 captured their experience at

How does one become a teacher in Singapore? You can finish the A Levels (Grade 12) or graduate with a polytechnic diploma and join a two-year course at the National Institute of Education (NIE) to be certified to become a teacher. You graduate with a Diploma in Education. There are opportunities to obtain a university degree if you do well at the end of the two years (that means you study for another two years for the bachelors degree) or return to school after teaching for a couple of years.

From 2012, Ministry of Education (MOE) will stop taking in non-graduate teachers so this programme will presumably cease to exist. As of 2009 about 50% of teachers in primary schools are not university graduates. In secondary schools, most teachers are university graduates.

If your grade twelve national examination (the A Levels) result is good or you have done extremely well in your polytechnic course, you gain admission into a four-year degree programme where you graduate with a bachelors degree in science or arts with education.

You can also come in for a one-year course (PGDE) if you already have a university degree.

As far as mathematics education courses are concerned, they are the same in all three programmes. It makes sense because everyone, whether you have a university degree or not, will be doing the same job - teach children mathematics.

For secondary school teachers, the diploma option is not available as MOE takes in only university graduates as secondary school teachers. Secondary teachers either read the one-year PGDE programme or the four-year degree programme.

Secondary teachers are trained to teach two subjects, unless you are teaching in junior college (grades eleven and twelve). In that case, you do Teaching of Mathematics (Secondary) and Teaching of Mathematics (JC). There is also Teaching of Lower Secondary Mathematics for those do not not have the prerequisite to teach upper secondary mathematics.

Primary teachers are trained to teach mathematics with one (less common for now)or two (presently more common) other subjects.

Sunday, February 14, 2010

Teacher Education in Singapore

The new focus of this blog is to share what we do in teacher training in Singapore. I will focus on the teacher education for primary school (elementary school) teacher who teach in grades one to six upon graduation.

The examples are limited to the courses I teach.

In this introductory entry, I write about some background information that is useful in understanding teacher education in Singapore.

All the 150+ primary schools in Singapore are all public schools. We do not have a private education sector. The variations that are now available in the secondary and junior college levels (grades seven to twelve) are not available in the primary levels.

Formal schooling starts in grade one. Students turn seven sometime during grade one. Pre-school education is varied and a small number of children do not attend kindergartens. Compulsory education is only for grades one to six. However, it is extremely rare for teenagers not to attend school although it is not compulsory to do so.

All our primary school teachers are public school teachers employed by the Ministry of Education before they study to become teachers. This is not common. In most places people study in faculties of educations in various universities in the country and they apply for a teaching job after they graduate with a teaching degree (e.g. bachelor of education). In Singapore, people apply for a teaching job before they study to become a teacher. Once they get the job, they will all study, at present, at one place - National Institute of Education (NIE) which is housed in one of the four universities in the country.

The photo shows one of my classes conducting a lesson for their colleagues. They have designed an activity-based lesson to teach pie charts. I was pleased they attempted to put into practice what they learn in the course on engaging pupils with meaningful activities.