Mathematics Teacher Education: Singapore Approach

Early Numeracy @ Rotterdam ECM101

2012-02-17T00:15:00.001-08:00

Visit our early numeracy blog.

The course is on-going. The materials will be uploaded after the course.

Singapore Math @ Vlissingen

2012-02-16T02:37:00.001-08:00

Overview of the Singapore Approach: Case of Fractions

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Singapore Math in Holland : Mathematics Teaching for the 21st Century at Bunnik

2012-02-15T22:38:00.002-08:00

This is a workshop conducted at Mathematics Teaching for the 21st Century Conference in Bunnik, a town in Holland.

Workshop on Bar Model Method

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This is the keynote lecture delivered at the same conference

Mathematics Teaching for 21st Century

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Singapore Math in Manila Feb 2012

2012-02-05T05:54:00.000-08:00

This is the presentation for Early Mathematics and Primary Mathematics.

EdCrisch Primary Mathematics MAP102

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EdCrisch Kindergarten Mathematics

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2012-01-04T16:56:00.000-08:00

MCI in Chile

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About 50 participants attended this one-day course which aimed at helping participants gained an understanding of the fundamentals of Singapore Math, including the use of bar models.

MAP101 and MAP111 are part of the course.

Seminar for K2 Parents

2011-11-09T22:39:00.000-08:00

Seminar for K2 Parents

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Singapore Math Administrators Symposium at Scottsdale, Arizona

2011-11-04T23:25:00.000-07:00

This is Yeap Ban Har's presentation on Day 2. The three-day symposium was attended by administrators including superintendents, curriculum directors and principals from different parts of the US.

Singapore Math Administrators Symposium Scottsdale

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Utah ASCD Conference

2011-11-04T00:29:00.001-07:00

Utah ASCD Conference

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AMSTI at Birmingham, Alabama

2011-11-01T13:54:00.000-07:00

The book I shared is monkey puzzle.

Some questions asked are discussed further at askbanhar

This is the presentation made at the event.

Alabama AMSTI

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Promise Academy Elementary School, New York

2011-10-26T01:11:00.000-07:00

I visited a charter school in New York and taught Grade 2 and Grade 3 classes.

The lessons were both on addition. As the students are the midst of the textbooks, it was not possible for me to know which lessons they were at on the day of the open lesson, I decided to teach lessons which are based on addition but is not part of the textbook lessons.

The purpose of the open lesson is for teachers to understand the fundamenatals of Singapore mathematics curriculum - in particular the big ideas and the problem-solving approach.

In Grade 2, the anchor task is to arrange five consecutive numbers (initially 1-digit numbers and later where the sum is 3-digit)in a cross formation such that the verical sum equals the horizontal sum.

In Grade 3, the anchor task is to make the greatest possible sum (ABCD + EFG) using given digits 1, 2, 3, 4, 5, 7, 8. Sometimes conditions such as less than 500 are given. Another digit is added to make the greatest sum for ABCD + EFGH but the sum has to be less than 10 000.

I also gave a plenary session to parents and teachers at the end of the day.

This is the plenary presentation.

Promise Academy Elementary School

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Third READ Conference in Eschborn, Germany

2011-10-24T11:46:00.000-07:00

Third READ Conference, Eschborn, Germany

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Visit AEA-Europe for conference in assessment

MENDAKI Courses for Parents

2011-10-14T23:00:00.000-07:00

The first course is for Lower Primary.

MENDAKI Course for Parents Model Method for Lower Primary

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This is for Upper Primary.

The Model Method for Upper Primary

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Regular Lecture in Shanghai's East China Normal University

2011-10-12T08:22:00.000-07:00

ICSMT Shanghai

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NSM Seminar in Jakarta

2011-10-10T10:52:00.000-07:00

NSM Seminar

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An updated slides with participants' responses will be uploaded later.

Masterclasses in The Netherlands

2011-10-04T08:22:00.001-07:00

These Masterclasses were organized by Bazalt for Dutch educators. The first one on Bar Modeling (MAP111) was attended by about 70 educators and the second one on Fundamentals of Singapore Math (MAP101) was attended by close to 150 educators. This is the second time Masterclasses are held in the country.

Masterclass Rotterdam MAP111

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Masterclass Utrecht MAP101

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Second Marshall Cavendish Global Forum on Singapore Mathematics

2011-10-03T02:39:00.000-07:00

Second Marshall Cavendish Singapore Mathematics Global Forum 2011

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This is the opening plenary lecture.

This year's forum was attended by representatives from different countries among them people from Ministry of Education and Department of Education. Minister of Education (Panama) and Minister of Education (Trinidad & Tobago) were among the delegates.

Surviving Math

2011-09-19T09:09:00.001-07:00

Surviving math

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Concord Primary School WOW! Questioning Techniques in Mathematics

2011-09-14T08:14:00.000-07:00

Workshop on Questioning Techniques in Primary Maths

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Lesson Study Symposium : Deepening Our Practice 13 September 2011

2011-09-13T16:35:00.000-07:00

Keynote Lecture

Lesson Study Symposium : A Da Qiao Primary School 30th Anniversary Event

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First New Teachers Conference in Manila

2011-09-10T05:55:00.001-07:00

First New Teachers' Conference, Manila, 10 September 2011

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BSc in Early Childhood Education

2011-08-24T17:25:00.000-07:00

Photo: PCF Kindergarten Kembangan having a research lesson

A group of more than 40 kindergarten teachers are studying for their bachelors degree with Wheelock College Boston. The course is held in Singapore under SEED Institute.

Visit the students' blogs at www.i-teach-k.blogspot.com

Enjoy.

Fun with Maths

2011-08-22T10:11:00.000-07:00

This professional development is run by Educare Pte Ltd for school teachers in Singapore.

Fun with Maths by Educare

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Professional Development for K-2 Teachers in Hawaii

2011-08-12T03:03:00.000-07:00

The slides for both days are now available.
The event was held at Pearl City Cultural Center in Hawaii.

Day 1

Pearl City Hawaii Lower Grades 11 Aug

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Day 2

Pearl City Hawaii Lower Grades 12 August

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Singapore Math in Hawaii Upper Grades

2011-08-09T08:45:00.001-07:00

The slides for the three days are available here.

Day 1

Pearl City Hawaii 8 August 2011

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Day 2

Hawaii Professional Development Day 2

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Day 3

Pearl City Hawaii 11 August 2011

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Seminar for Parents at Red Swastika Primary School

2011-08-03T09:14:00.000-07:00

Red Swastika School

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National Singapore Math Summer Institute Denver 2011

2011-07-26T11:39:00.000-07:00

All of Yeap Ban Har's presentation are available here.

Yeap Ban Har's Opening Keynote Lecture.

National Singapore Math Summer Institute, Denver

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The core elective session is included below.

National Singapore Math Summer Institute Denver 2011

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This is the session on lesson study.

National Singapore Math Summer Institute Denver 2011

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Lesson Study in Action

2011-07-24T00:47:00.001-07:00

Lesson Study in Action by Academy of Singapore Teachers

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Primer Encuentro de Formacion Docente

2011-07-12T02:16:00.000-07:00

A class of about 60 Chilean educators are completing the courses as part of Certificate in Mathematics Teaching (Primary) programme.

The presentation slides in all the three courses are now available.

MAP101

Primer Encuentro de Formacion Docente

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MAP201

Primer Encuentro de Formacion Docente MAP201

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MAP111

Chile July 2011 MAP111

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MCI-Worchester State University Singapore Math Institute Classroom Sessions by Yeap Ban Har

2011-07-07T02:40:00.001-07:00

The first one that I did on Day 1

MCI - Worchester State University Singapore Math Institute Classroom Session A2

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My second session on Day 1

MCI - Worchester State University Singapore Math Institute Classroom Session A3

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My second day classroom session.

MCI - Worchester State University Singapore Math Institute Classroom Session B7

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These are my two sessions on the last day. Look out for an enhanced institute next year. Register early as we plan to have only 150 seats available. Keep updates at www.marshallcavendish.com.sg\education\mci

MCI - Worchester State University Singapore Math Institute Classroom Session B20

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MCI - Worchester State University Singapore Math Institute Classroom Session B27

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MCI-Worchester State University Singapore Math Summer Institute

2011-07-06T23:28:00.000-07:00

Plenary Lecture 1 - Pedagogy. Dr Richard Bisk did the lecture on Content.

MCI Worchester State University Lecture 1 Yeap

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Plenary Lecture 2

MCI - Worchester State University Singapore Math Institute Plenary Lecture 2

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Plenary Lecture 3

MCI - Worchester State University Singapore Math Institute Plenary Lecture 3

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ARK Schools, London

2011-06-26T14:38:00.000-07:00

ARK Schools, London

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This course was held in London in June 2011.

MCI SIF PDA Thailand Project at Meechai Pattana School, Buriram, Thailand

2011-06-07T07:27:00.000-07:00

MCI-SIF PDA Thailand Project

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Bukit Panjang Primary School Parents' Seminar

2011-04-29T07:24:00.000-07:00

Bukit Panjang Primary School Parents' Seminar

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NCoN2011 Brunei 25-26 April 2011

2011-04-25T03:29:00.001-07:00

Keynote Lecture

NCoN2011

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Workshop

NCoN2011 Brunei 25-26 April 2011 Workshop

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Seminar for Parents: Bar Model Method

2011-04-22T16:57:00.000-07:00

Parents were introduced to the bar model method, covering basic problems to advanced ones. The rationale for the method was also explained.

This is the edited version of the presentation.

RGPS Seminar for Parents (Revised)

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Bazalt HCO Singapore Math in The Netherlands

2011-04-20T14:09:00.001-07:00

Rekenwonders Bazalt HCO

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Utrecht MasterClass by Bazalt & HCO

2011-04-20T14:02:00.001-07:00

This is the first course we offer to teachers. This course is designed to change mindset about what mathematics is and what roles teachers play in the class. Mathematics is a platform to develop thinking. It is not about memorization and following procedures blindly. In this course, teachers get to learn the key roles of visualization, patterns and number sense, plus all the human qualities that children develop when they are in our mathematics class. In Marshall Cavendish Institute, we believe that helping teachers change their mindset about teaching and learning is key to transforming the classroom into exciting places for learners.

MasterClass Utrecht

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Rotterdam MasterClass by Bazalt & HCO

2011-04-19T13:11:00.001-07:00

MCI MasterClass Rotterdam

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Experiencing Singapore Math Birmingham Edition

2011-04-15T14:35:00.000-07:00

AMSTI Event, Birmingham, Alabama

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This was held on 15 April 2011 and it was attended by more than 150 participants. Organized by AMSTI.

Summer Institute in Worchester State University, MA

2011-04-15T04:43:00.000-07:00

MCI-Worchester State University Singapore Math Summer Institute

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NCTM2011 Sessions

2011-04-14T09:01:00.000-07:00

The morning session was on making mathematics accessible to all learners.

NCTM2011 Morning Session

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The afternoon sessions went to show the bar model method in detail.

NCTM2011 Afternoon Session

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2011-03-12T03:22:00.000-08:00

Association of Mathematics Educators Seminar on PSLE Mathematics

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This seminar was organized by AME Singapore. The Association for Mathematics Educators is organizing a one-day Mathematics Teachers Conference 2011.

Seminar for Parents at PLMGS on PSLE

2011-03-05T23:08:00.001-08:00

Seminar for Parents at PLMGS on PSLE

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Parents Seminar on Heuristics at Chongfu School

2011-03-05T23:04:00.001-08:00

Parents Seminar on Heuristics at Chongfu School

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LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011

2011-02-14T12:43:00.000-08:00

LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011

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LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011

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Professional Development of Teachers in Singapore

2011-01-09T13:56:00.001-08:00

WALS2010 yeap

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Teacher Professional Development in Chile 12-18 Dec 2010

2010-12-15T21:47:00.000-08:00

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.

Leaders and Educators in Asia Programme by Course by NIE International

2010-10-10T14:05:00.000-07:00

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 http://leap4teachers.blogspot.com/

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

2010-10-08T05:23:00.001-07:00

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.

NCTM 2010 Regional Conferences & Expositions Denver 1

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

NCTM 2010 Regional Conferences & Expositions Denver 2

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Professional Development at Universidad Santiago de Chile

2010-10-02T04:07:00.000-07:00

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

University of Santiago de Chile Multiplication

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On Assessment

Universidad Santiago de Chile

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Professional Development and Lesson Study in Chile

2010-10-01T00:54:00.000-07:00

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

Seminar on Assessment for Learning at The English Institute Santiago

2010-09-29T17:25:00.001-07:00

Chile Assessment in Primary

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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

2010-09-29T00:32:00.001-07:00

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:

Seminar at Colegio Inmaculada Conception, Universidad Andres Bello &San Benito School Santiago

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Singapore Math in Chile (MOE Chile)

2010-09-28T01:08:00.001-07:00

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.

Chile MOE Seminar Spanish

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Chile MOE Seminar English

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

Singapore Math in the Netherlands

2010-09-18T01:32:00.001-07:00

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.

Singapore Math in the Netherlands Day 3

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Singapore Math in the Netherlands

2010-09-16T19:03:00.001-07:00

This Day 2 presentation is on the bar model.

Singapore Math in The Netherlands

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Singapore Math in the Netherlands

2010-09-15T19:30:00.000-07:00

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.

Rotterdam Day 1

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The Idea of Centre of Excellence (COE)

2010-09-11T08:20:00.000-07:00

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.

Games in Maths

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Transforming the Mathematics Classroom at Rajabhat Maha Sarakham University Thailand

2010-08-14T03:54:00.000-07:00

Mahasarakham Rajabhat University Day 1

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Mahasarakham Rajabhat University Day 2

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Mentari Upper Primary Number Sense

2010-08-08T20:08:00.000-07:00

Mentari Upper Primary Number Sense

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International School Saigon Pearl

2010-08-08T18:55:00.000-07:00

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.

Issp saigon

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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

STU Workshop for Helping Children with Lower Primary Mathematics

2010-08-03T05:03:00.000-07:00

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.

Professional Development for St Edward's School, Florida

2010-08-01T06:03:00.001-07:00

St Edward's School, Florida

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

Pat's Schoolhouse Teacher Professional Development

2010-07-17T05:05:00.001-07:00

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.

National Conference on Singapore Math Strategies in Las Vegas

2010-07-14T00:45:00.001-07:00

This session is on Early Grades Mathematics.

Session A4 K-1 Math

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

Singapore Math Session D2 and G2

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Primary 1 & 2 Mathematics

2010-07-05T21:25:00.001-07:00

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.

Lower Primary Maths Problem Solving

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An Overview of Lesson Study

2010-07-05T21:21:00.000-07:00

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.

Seminar for Parents

2010-06-27T09:02:00.001-07:00

How to Ace PSLE Maths

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

World Bank East Asia Regional Conference

2010-06-21T12:04:00.001-07:00

World Bank East Asia Regional Conference

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Rye City School District

2010-06-06T15:21:00.000-07:00

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.

Rye Fractions

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Rye Bar Model

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Dobbs Ferry School District

2010-06-06T15:19:00.000-07:00

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.

Grade 5 Lesson

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Scarsdale Teachers Institute

2010-06-06T02:46:00.000-07:00

STI Course A Closer Look at Singapore Math by Yeap Ban Har

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

SingaporeMath in Action

2010-05-18T04:17:00.000-07:00

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 http://www.simplypsychology.pwp.blueyonder.co.uk/bruner.html for Bruner`s ideas
Read http://en.wikipedia.org/wiki/Jerome_Bruner also for Bruner. There is a link to　Spiral Curriculum
Read http://www.skemp.org.uk/ 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 http://www.zoltandienes.com/ 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.

SingaporeMath in Action 1

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Questions posted at the seminar are found at www.askbanhar.blogspot.com

SingaporeMath in Action 2

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This session is on mathematical problem solving.

SingaporeMath in Action 3

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This session is on all things related to fractions.

SingaporeMath in Action 4

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Ateneo de Manila Summer Institute

2010-05-10T07:33:00.000-07:00

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.

Problem-Based Approach

2010-05-01T18:01:00.000-07:00

BBS April 2010 Singapore Math in Indonesia by BBS Maths Consultant Dr Yeap Ban Har

View more presentations from jimmykeng.

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.

Fraction Addition: Dienes' Theory of Mathematical Variability

2010-04-03T05:38:00.000-07:00

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?

Fractions: Equal Parts

2010-02-27T16:05:00.000-08:00

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.

Becoming a Teacher in Singapore

2010-02-21T03:50:00.001-08:00

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 http://twacambodia2010.blogspot.com/

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.

Teacher Education in Singapore

2010-02-14T23:17:00.000-08:00

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.

AKM101 Lesson 4

2009-09-04T20:45:00.000-07:00

We had four lessons and for the next few weeks we will be having online lessons. Today, we re-examine the issues of teaching mathemeatics versus teaching children. I am glad to hear many views including if the national examination assess good habits of mind and spirit of innovation and enterprise. It is popular rhetoric that all the things outlines in various initiatives are fine and good but the examinations do not value them and hence teachers do not place emphasis on them. That is what this course is about - for the participants to re-examine this beyond the popular rhetoric, to reconsider one's present point of view and points of views of the other participants and to examine the issues more deeply. Thus two questions - one, how to help students reach a certain level of achievement that will allow them to progress towards becoming a productive citizen of the country and the world and, two, as teachers, should we go all out to ensure highest grade possible, even at the expense of teaching the child values and developing his or her confidence to face the world or moulding their personality as a well-adjusted youngsters?

AKM101 Lesson 1

2009-08-14T02:58:00.000-07:00

We dealt with recent initiatives in primary mathematics. Today I used two case studies to get students to think how to bring to life words in initiative documents such as the curriculum document. The first case study was a problem that is different yet connect to a pattern that is taught in the curriculum. In the curriculum, children deal with patterns such as ABCDABCDABCD... type patterns where they are expected to be able to find the n th letter in the pattern. In this lesson, we did a very different pattern. Students were asked to propose solution methods and evaluate if the methods are generalizable or not. The second case study was on teaching area through problem solving, using a method that is commen in the textbooks. The students looked at the curriculum document and were asked to think about the rationale for teaching mathematics. Students were asked to make tetrominoes and compare them. Along the way, the basic concept of area and deeper concepts of area emerged. I was excited because the students were giving their views and opinions and asking questions on issues we discussed. I am looking forward to the next lesson. The students were asked to think about what is mathematics teaching all about according to the official documents and according to their own views - what it is and what it should be.

DCM200 Lesson 1

2009-08-14T02:53:00.000-07:00

Teaching of Area. I tried to show how teaching through problem solving can be done for students in Primary 3. We did Tetrominoes (Make different shapes using exactly four square tiles.), Quadrilaterals (Make different quadrilaterals using exactly three square tiles and two half-square tiles), Area is Five Problems (Use the geoboard to make quadrilaterals of area 5 square units.). We ended by exploring the Pick's Theorem using the findings of the last problem. I wished I had more time for the students to explore the relationship between area and number of 'dots'.

Las Vegas Lessons

2009-07-12T00:15:00.000-07:00

Latest: The slides for the keynote lecture for National Conference for Singapore Math Strategies are already available at www.singaporemathz4kidz.blogspot.com Other slides will be available at math.nie.edu.sg/T3 soon.

Riviera Hotel and Casino will be my classroom for four days. I will be teaching classes at the National Conference on Singapore Math Strategies for Grades K-6 with five other American teacher trainers. Several teachers are also sharing their experiences with the participants. I was told that there are 800+ participants from all but four states in the US with California having more than 100 representatives. There are also about 10 international participants from places as diverse as the Uganda, Mexico and the Philippines.

On Monday, I kicked the conference off with a keynote session with Char Forsten. The session is titled Singapore Math: Where East Meet West. I gave the audience the context in which mathematics is taught in Singapore. In particular, I touched on the emphasis on challenging problems in the PSLE, and the fact that most schools have their own problem-solving programme to supplement textbooks which focus on developing strong basics. I also spoke on high parental expectations and LSP and Foundation Mathematics as safety nets to make sure every student get help so that they do not fall too far behind. Many Singapore teachers conduct remedial programme in one form or another - some schools have structured remedial while others do them as and when the need arises. Finally, I touched on teacher education, before they enter the teaching service and when they are in service. I raised the point that perhaps it is possible for teachers to acquire pedagogical content knowledge and content knowledge by working through the student textbook.

Over the four days, I taught classes on a variety of topics ranging from word problems to visualization to lesson study and more. The participants were enthusiatic and appreciative despite the relatively large class size. On the first day, all the three classes I taught (visualization, questioning technique and challenging word problems) had about 200 people.

I will write about these classes. I will upload the slides for the keynote lecture as well as for the different classes at mathz4kidz.com and at math.nie.edu.sg/T3.

Other than this blog where I talk about the lessons I teach, you may go to http://www.singaporemathz4kidz.blogspot.com/ for general discussion on Singapore Math. There is a video gallery here. http://www.askyeapbanhar.com/ is where I post responses to questions I receive through e-mails. If you are interested in lesson study, go to http://www.singaporelessonstudy.blogspot.com/

Some Lesson Ideas for AYG2009

2009-06-30T03:12:00.000-07:00

There is a sample lesson plan on incorporating scoring in diving mathematics lessons. See http://www.adrianbruce.com/maths/diving/diving_math_lesson.htm I think scoring in diving is especially useful for Primary 4 topic on operations involving decimals and Primary 5 topic on average.

NSM101 Lesson on Probability

2009-05-23T03:12:00.000-07:00

I taught this lesson in Manila to a group of high school teachers using the New Syllabus Mathematics. The problem posed is to find the probability of drawing two cards with the same number, one from a stack of cards labelled 1 to 4 and another from another stack of cards, also labelled 1 to 4. Using the responses from eight groups, we were able to solve this problem that involved combined events using the knowledge of basic probability of single event. The responses included the use of listing, tree diagrams and table. I was quite satisfied we managed to use the responses to explain the multiplication rule.

Education in the US

2009-05-16T22:21:00.001-07:00

Secretary of Education Arne Duncan

Last week I went to Berkeley County, West Virginia, to begin an open, honest conversation about education reform.I wanted to hear ideas about how we can accomplish President Obama's goal of providing every child in America a complete and competitive education, from cradle through career.As we prepare for the reauthorization of No Child Left Behind, I want to hear from classroom teachers and other educators, parents and students, business people and citizens. What's working, and what's not? What do we need to do that we're not doing, and what do we need to stop doing - or do differently?

In the coming weeks, I will ask questions here. Topics will include raising standards, strengthening teacher quality, using data to improve learning, and turning around low-performing schools. I will be reading what you say. So will others here at the U.S. Department of Education.Today, I want to start with a simple set of questions: Many states in America are independently considering adopting internationally-benchmarked, college and career-ready standards. Is raising standards a good idea? How should we go about it?

Let the conversation begin!

Arne Duncan

Art & Mathematics

2009-05-15T20:18:00.000-07:00

Another interesting problems we solve at the Ateneo Summer Institute is the one in which the teachers created interesting pictures like rat, cat and flowers on geoboard. Later, I asked the teachers to predict which of the picture occupies the largest area. Interestingly, in both groups, teachers suggested counting 'dots left over' as an indicator of area. We later tested this theory by finding the area by counting squares.

Some of the pictures were easily dealt with because they were made up of squares and half-squares. Others were more challenging. I hope the teachers got the idea of how to sequence discussion in students' creation in a way they are kept challenged all the time. We moved from cases which were easy to find the area to cases which demanded more visualization.

Ateneo Summer Institute

2009-05-11T03:31:00.000-07:00

This is the second year I am teaching this course for early grades teachers (kindergarten to third grade). In today's session, we explore why we teach mathematics. We did a problem that also includes drills-and-practice based on subtraction. Typically subtraction algorithm is done in grades one to three all over the world. I hope the teachers were able to understand that if all the child is able to do is to do subtraction then we have failed. The teachers told me a a cheap calculator cost about 50 pesos retail, that's a little more than USD1. I am sure the wholesale price is even lower. The teachers agreed that a 50-peso calculator can do subtraction rather well. So, if a drill-and-practice exercise enable childrent o do subtraction perfectly then they are just as valuable as a 50-peso calculator. i tried to convey the message that helping children develop thinking and other human competencies are equally important, if not more improtant than developing the ability to perform the subtraction algorithm. A teacher said the activity took more time. I hope we will see that the time invested (50 minutes) is well-spent. In fact, I argue that this is necessary. Unless a task is an extended one, the thinking involved is not very deep and, hence, not significant.

In case you are not in the class today, the problem was to use one set of digit tiles (0 to 9) to make two 4-digit numbers such that the difference is as small as possible. In both classes, we had 25 as the smallest possible difference. The teachers were impressive and were able to make some connections - such as the thousands digits are consecutive. In the end, they found three possible solutions 4xxx - 3xxx = 25, 5xxx-4xxx = 25 and 6xxx - 5xxx = 25. Try it and let me know what other insights you manage to have.

A teacher asked how teachers can formulate such problems. A short answer is to attend courses like these as well as to lookt hem up in books and on the internet. A long answer is to change our beliefs what mathematics teaching is all about. Once that happens, all the tasks we create or choose will have features that allows students to develop good thinking abilities and habits.

Division of Fractions

2009-04-09T03:30:00.000-07:00

I have just completed nine periods of mathematics lesson on this unit with a class of primary five students who struggle with mathematics. I am teaching dividing fraction a/b by a whole number c which is often done using the invert-and-multiply method. Instead of using this method which I believe contribute to these students' difficulties with mathematics, I use an alternate method which based on simple reasoning ... if 4 divided by 4 is 1 then 4 fifths divided by 4 is 1 fifth. In cases when this is not obvious such as 2/3 divided by 4 we talked about changing 2/3 into 4/6. 4 sixths divided by 6 was then "easy beezy" as one student put it. It gave the students plenty of chance to revise equivalent fraction, which is fundamental to operations involving fractions.

I particularly enjoyed the third lesson when I gave each pair of students a fraction. If they thought that their fraction has the same value as the one I put up, they put it next to mine. In other words the board was filled with equivalent fractions which the students can then use to do various division.

e-Lecture on Assessment for Secondary Mathematics

2009-03-13T07:37:00.000-07:00

In this lecture, we cover the key ideas in test construction of a mathematics test for secondary students.

It is for pre-service teachers in Singapore.

http://videoweb.nie.edu.sg/captivate/AGs/MME/QCM521_531/test_construction/test_construction.htm

Research in Mathematics Education

2009-03-13T07:10:00.000-07:00

It was an interesting opportunity for me to teach a graduate course at Chiangmai University in March 2009. The 26 students are all studying for a master degree in mathematics education. Some part-time students are doing coursework and need to do an independent study and the rest are full-time students who have to write a thesis. The three-day course aimed to help students with the construction of a research problem.

We spent some time identifying problems related to mathematics education. As the students are all school teachers in primary (grades one to six), middle (grades seven to nine) and high schools (grades ten to twelve), it was not surprising that most of the problems are classroom-related. We spent some time for the students to understand that the research problem is a culmination of their own personal experience and the literature. Their experience with the local situation as well as literature that describes the situation in Thailand (e.g. the TIMSS report) as well as previous studies done in Thailand and elsewhere on related topics are used to generate the content of their research problem.

For example, a student wrote that the primary-level students lack the ability to solve word problems in the topic of time. For example, third graders have difficulty in solving word problems that give the starting time of an activity, the duration of the activity and require students to find the end time of the activity.

This is a problem from the local situation. However, the research problem was still not articulated. For example, the research problem could be to investigate the types of difficulties students have when solving such word problems. A related research problem could be to use the findings from the earlier investigation to design instruction or remediation to help students develop the ability to solve word problems involving time, and to investigate features of instruction or remediation that are able to help students develop this ability.

Teaching Mathematics Education Students in Chiangmai University

2009-03-11T02:59:00.001-07:00

Why are the students so cheerful in class? Because they are solving simultaneous equation with three unknowns - that's why? It is impossible that students were so cheerful in the mathematics class?

Each student raised a card to their forehead thus was not able to see their own card. Subsequently, each student stated the sum of numbers on their friends' foreheads. Say, A had 7, B had 9 and C had 3. A would have said 12, B 10 and C 16. If the value of the card that A had is a, B is b and C is c then b+c=12, a+c=10 and a+b=16. However, in this case A would have known the values of b and c. The only unknown is a. For secondary students this activity can be used to introduce the idea of solving equations. For primary students, it is a good exercise in addition and subtraction and, more importantly, reasoning.

"Despite resources that are unmatched anywhere in the world, we have let our grades slip, our schools crumble, our teacher quality fall short and other nations outpace us," Obama told the U.S. Hispanic Chamber of Commerce. "The future belongs to the nation that best educates its citizens, and my fellow Americans, we have everything we need to be that nation," he added. The U.S. leader painted the education drive as part of a broader push to promote economic growth in the face of a deep recession and the nation's worst financial crisis in decades.

"In a 21st century world where jobs can be shipped wherever there's an internet connection, where a child born in Dallas is competing with children in Delhi ... education is no longer just a pathway to opportunity and success, it is a prerequisite," he said.

These are words from the President of the USA. In the special lecture I had with all the undergraduate and graduate students of mathematics education in Chiangmai University, I hope the 100 of them in the room can teach 40 students well. In their many years as a teacher of mathematics, they are in the position to bring up a whole generation of citizens who can compete in this type of global economy.

We emphasized on the problem-solving approach, the focus on intellectual competence as well as the concrete/pictorial/abstract approach to teaching students. I was asked where teachers can find problems such as the ones I used in the session. I replied that the problems themselves are not as important as how the teacher uses it. I had demonstrated in the lesson how even computational procedures such as 2/3 divided by 4 can be taught to help students develop and improve their intellectual competence.

In any case there are many good problems on the internet and in moments of inspiration some teachers can come up with interesting problems. If you are one of them, please share na. (na is a particle in Thai to gently persuade someone to do something.)

Temasek Foundation Singapore & Population and Community Development Association Thailand Project

2009-03-01T07:11:00.000-08:00

Think of two numbers e.g. 4 and 5. We will do three steps.

In a variation which I did with second graders in New York, they picked two numbers from a stack of cards. They showed the first number but not the second one. Before that they had done the three steps with the two numbers.

Use the 4 and 5 to make 45. Use the 4 and 5 to make 9 (4 + 5). Finally find the difference between 45 and 9.

After demonstrating that if they tell me the first number then I will be able to read their mind for the second and do all the three steps and giving the right answer each time, we began to record the findings.

Many of the participants saw the multiple of nine trick. As I pressed for more observations, another interesting one is how the second digit in the answer is derived by subtracting the first number from ten.

I was reminded again that asking students to explore more ways to often result interesting and outstanding responses.

I did this problem with the teachers group as well as the principals group and on both days we got equally interesting responses except I was surprised that no one in the teachers asked for the reason why the trick worked. One did in the pricipals group.

Temasek Foundation Singapore & Population and Community Development Association Thailand Project

2009-02-27T11:47:00.000-08:00

In this Temasek Foundation funded project, Population and Community Development Association (PDA) in Thailand has put up a Train The Trainers (TOT) Project. The idea is that teachers and principals are trained in the curriulum and management system used at the Lamplaimaat Pattana School in Buriram, a school that has a track record on par with that of private schools in the nation. The one-day training on effective teaching and learning of mathematics served as a case study to help teachers think about curriculum implementation and for principals to think about how they can sustain and implement high-quality programmes.

It was encouraging too see even the school principals thinking hard to come up with the solutions to the problems posed to them. And did they have good and interesting ways of solving those mathematics problems! I hope the general message about shifting the focus from memorizing fatcs, carrying out procedures without understanding and doing tedious clerical tasks like computations to intellectual tasks like doing visualization, looking for connections, developing number sense, developing metacognition and enhancing communication came across during the seminar.

There were 200 participants on each of the two days. So, I was glad to have the opportunity to influence the thinking of 400 people who are in the position to do something to make the learning process in schools effective and enjoyable. There were also three teacher trainers from a teacher training institute in Luang Prabang, Laos.

Teacher Workshop @ Queenstown Primary School

2009-02-21T20:29:00.001-08:00

The workshop was on developing visualization in primary mathematics. An interesting point raised by one of the teachers is whether it was easy for students to visualize. It set me thinking and I then suggested that visualization may well has a cognitive component as well as an affective component. Another way to put it is that it has a skill component - can visualize or not - as well as a habit component - is the mind in the habit of seeing the same thing in different ways or not. Thus, can students see that 2/3 dividied by 4 is the same as 1/4 of 2/3, 1/2 of 1/3 as well as 1/6 of the whole depends both on the possession of the skill to interpret diagrams as well as the habit of being able to interpret the same diagram in different ways.

DCM201 MicroTeaching on Subtraction of Mixed Numbers

2009-01-29T07:51:00.000-08:00

It is promising that I see at least one very good lesson in every microteaching session. teaching is a complex activity that defies description in words. one has to see it being played out before one's eyes. I hope the trainee teachers in my group who are observers are capable of seeing good examples of instruction. This is why I assign them the roles of 'students' and 'observers'. On the days they are the 'observers' they can divert all their attention to witness the complex activity of teaching without being distracted.

In Rendra's ;esson, we saw the use of PowerPoint to model the subtraction process. I wished he had stuck to this. Unfortunately, he moved to doing the subtraction in abstract symbols too soon. In Naz lesson, which was brilliant, I saw him being able to handle the complexities of being a teacher bringing a lesson plan to life. In particular, the pictorial-abstract linkage was well done. He used the 'models' to explain the symbolic manipulation. The subtraction process can be made obvious using suitable straegies that trainee teachers should be able figure out. In Hafeez' lesson, the idea of regrouing was not modelled by the pictorial representation. The use of a strory was good. especially if the teacher can act the situations out by making voices for Mr Gopan and whoever else in the story. Also, the pizza was impressive,

DCM202 Challenging Problems (1)

2009-01-26T04:17:00.000-08:00

The problem is to find the tens digit when 2 is multiplied 2009 times. Most of the students were able to solve simpler problems to see a pattern. A strategy suggested was to try simpler cases until we get the same digit for the tens and ones digit. I was glad I gave the students time to establish the fact that the pattern will definitely repeat. That means they were expected to be able to explain the pattern. I felt that it was insufficient for students to solve the problem based on pattern observation alone. They should be able to show that the pattern is guaranteed.

DCM201 Division of Small Numbers

2009-01-22T12:28:00.000-08:00

Keng Sing's lesson using When The Door Bell Rang was enjoyable with cookies and plates for the children to act division out as sharing. It could be improved by applying the theory of variation. In all the examples the children were asked to act the situation out. In the later stages, the children could be asked to draw and use the cookies to confirm their ideas.

Rebecca's use of the cut-outs was suitable. I have suggested that the writing of the division sentence happens sooner in the lesson. And that was what Wei Wen did. In her lesson on division with remainder, she made careful links between the concrete with the pictorial and abstract represents well. One suggestion is to introduce the idea of quotient a little later.

DCM201 Multiplication of Large Numbers

2009-01-20T16:04:00.000-08:00

Multiplication of large numbers begin in Primary 3 with multiplication of a 2 digit or 3-digit number and a 1-digit number followed by that of a 4-digit number and a 1-digit number. Later, students learn how to multiply a 2-digit number with another 2-digit number. The last two are often taught in Primary 4.

Khai taught 3D x 1D. I am pleased that he used the base ten blocks to model the process of 231 x 3 as representing 231 as 200, 30 and 1. Later he modelled the multiplication process of the hundreds, tens and ones. It is satisfying to see part of Bruner's Theory in action. One way this lesson could be improved, I told Khai, is to separates cases that requires renaming (365 x 5) from those that do not (231 x 3) and teach them in separate lessons.

In another lesson of 4D x 1D, I was excited when I saw the teacher teaching children how to use 123 x 2 to do 2123 x 2. The simplicity of it was beautiful - the new lesson simplify requires Primary 4 students to do the multiplication of the thousands (2000 x 2) and add this to 123 x 2 (which was done the year before already). It would have been great if this was done for the entire lesson. In this lesson it was done too briefly for it to have much impact on children learning. A good example of Teach Less Learn More (students learn to make connections by linking 123 x 2 to 2123 x 2).

In the third lesson, Lawrence did an excellent job applying Bruner's Theory in linking concrete, pictorial and abstract representations of 2D x 2D. You got to be there to appreciate fully what I said but breaking 34 x 42 into 4 x 42 and 30 x 42 using the area model would help children develop visualization as they learn the algorithm.

It was a good session. All the three demonstrates the basic competencies of competent teachers. They were the first three, so you can understand the nerves. It was good to see how the rest of the students who acted as students and as observers in a 'pseudo' lesson study supported their colleagues. I look forward to 27 more lessons that will unfold in the next few weeks preceeding the practicum.

Stamford Primary School

2009-01-09T18:38:00.000-08:00

This was a workshop on mathematical problem solving. We spent most of the time on undertanding the importance of number sense, looking for patterns, articulation of thought and visualization. We also explores two ways to improve understanding of word problems - metacognitive reading and problem posing. Finally, we explore the what-if strategy as a post-solving strategy. In one of the problems, teachers are asked to look for relationship between and among a set of numbers generated in a mind-reading game. The idea is to tell kids that if they think of two digits (say, 5 and 2) and tell you only the first one, then you can rread their mind to get the secon digit and even able to use the digits to (a) form a number 52, (b) form another number 7, from 5 + 2 and finally (c) find the difference between 52 and 7 and be able to write that down on a piece of paper. All these without them having to tell you the second digit. So when the kid tells you 5, you can write 45 down. When the kid tells you 8, you write 72 and when the kid says 9, you write 81. What do you write on the piece of paper if the kid says 3. 27 is correct. How does it work. That was the problem the teachers solved. They came up with two strategies (1) multiply the number the kid says by 9 and (2) subtract 1 from the number the kid says and then making sure the sum of the digits in the answer is 9. Do you know why the trick works? Using this problem, teachers can see that problem solving involves the ability to see a pattern and generalize the pattern. Also, it involves putting our ideas into words as we try to describe our observations of how the three numbers are related.
This workshop was attended by n teachers.