Monday, December 9, 2013

Professional Development for Moanalua Compex, Oahu in Hawaii

Teachers from the elementary schools and Moanalua High School met for a one-day professional development to update teachers' knowledge in teaching mathematics with a focus on differentiated instruction.

Main Presentation 

Venue of Professional Development Day of Moanalua Complex

Questions - to be updated

Wednesday, December 4, 2013

Sunday, November 17, 2013

Mathematics Education Conference 2014

This one is in Europe in an interesting location. I am sharing this information forwarded to me by a colleague based in Poland, Dr Alan Rogerson (originally from the UK).

Saturday, November 9, 2013

STI Course #4466 A Closer Look at Singapore Math with Ban Har Fall 2013

Course Instructor's Contact

Day 1 Summary

Day 2 Summary

... to be updated soon ...

Watch As I Was Going to St Ives video here

Watch Jack and the Beanstalk video here

Professional Development at Edgemont School District

Thursday, November 7, 2013

Seminar for Parents at Edgemont School District, New York

The Blake School, Minneapolis

Division of A Number by a Two-Digit Number
(Grade 5)

For full story, read The Blake School.

Photo Credits - The Blake School

Seely Place Elementary School, New York

An open lesson based on Math in Focus (Book 4A Lesson 3.5)

The anchor task in the book is:
Mr. Benson and Mr. McKenzie have $4,686 altogether. Mr. Benson’s share is twice as much as Mr. McKenzie’s.

Introduction - Students were asked what could a number such as 4,686 represents.

Development - Problem was presented. Spiky and Curly share $4,686. Curly has twice as much as Spiky. If this strip of paper represents $4,686, show the amount that Spiky and Curly get.

In this lesson the students gave four responses.

Method 1 - (length) We used a ruler and found out it is 6 inches long. So 4" for Curly and 2" for Spiky.

Method 2 - (parts) We folded the strip into three parts. Spiky gets 1 part and Curly 2 parts.

Method 3 - (fraction) We divided the strip into thirds. Spiky gets 1 third and Curly, the rest.

Method 4 - (misconception) I divide the strip into 2. Since Curly gets twice as much, he gets two parts.

Several students disagreed and stood up to say why that reasoning is not correct. Generally the sentiments were .... "That means Curly gets 2 and Spiky gets zero! That is not twice!!"                                                                                                                                                                                    

Monday, November 4, 2013

The Blake School - Summary

Presentation Slides Information Night for Parents

Lesson Planning - Anchor Task

Lesson Planning - Differentiated Instruction

Grade Level Sessions
Teaching of Percent for Middle School

Sessions on Lesson Planning at The Blake School

Lesson Planning with a focus of anchor task and problem solving

Lesson Planning with a focus on differentiated instruction
(coming soon)

Sunday, November 3, 2013

Visit to The Blake School (Day 1)

This is my second visit this year to The Blake School in Hopkins, MN.

Day 1 - I am scheduled to meet with the teachers in middle schools. I will be teaching two classes a Grade 6 lesson on percent and an Algebra 1 lesson. The focus of the discussion with the teachers are (1) Lesson Planning with Anchor Tasks and Problem Solving and (2) Percent.

There is a two-lecture series on lesson planning. The presentation is available in a separate entry.

Day 1 is scheduled to end with a seminar for parents at Parent Information Night.

Tuesday, October 15, 2013

Resource List for Singapore Math

Lesson Study

I have a blog at

Singapore Math

Erikson Institute | Marshall Cavendish | Shinglee

Erikson Institute in Chicago did a series of videos on early numeracy in Singapore.

Look at Marshall Cavendish's video gallery for videos on Singapore Math and other things connected to Singapore education.

Shinglee which publishes one of the main secondary textbooks used in Singapore has a video to explain Singapore Math at the secondary levels (Grades 7 - 10).

Shinglee also has a video to explain its implementation in the Philippines. In it, I describe what Singapore Math is.

Some talks done in London - The CPA Approach - Model Method - Number Bonds - Singapore Maths -

Success Story in UK - Watch the video

A related video by a British educator - Didactics Matters

Maths No Problem has a collection of videos on Singapore Maths.

Advanced Lesson Planning

At Keys Grade School, I worked with a group of teachers (and parents!) on lesson planning.

We focused on using DuFour's Four Critical Questions. Read more about the four critical questions in his article on PLC. Or watch him explain it on a video.

We embed differentiated instruction and assessment into lesson plans.

We did two examples - early fractions and subtraction of mixed numbers.

Seminar for Parents in Manila

At Keys School Manila

Friday, October 11, 2013

An Exercise in Re-imagining the Classroom

This 1.5 day workshop is for all teachers at Anglo Singapore International School to help the school brand its programmes and achieve its mission and vision.

Thursday, August 22, 2013

Weston Public Schools 22-23 August 2013 MAP111 Bar Models in Primary Mathematics

The course for teachers of Grades 2 to 6 classes (23 August)

The course for teachers of Grades 7 and 8 classes (22 August).

Wednesday, August 21, 2013

Weston Public Schools 22 August 2013 MAP101 Fundamentals of Singapore Math

This was covered in 2012 sessions.

The sessions is 2013 is an mix of review and extension.

Session 1
Fundamentals of Singapore Math for Grade 3, 4, 7 and 8

Photographs of the session are available here.

Friday, August 16, 2013

Wheelock College EDU330 Elementary Mathematics at SEED Institute

The 8th BSc cohortor completed their module on elementary mathematics today. I t is good to see that a degree in early childhood requires students to know something about primary level mathematics. I have been teaching this course for several years now.

One of the tasks the students did in class was to write story problem for 3/4 divided 1/8.

Some do not show the required division 

There are 3/4 of a pizza left at a party. 
Sam cut 1/8 of the the remaining pizza into equal parts.

Advil calculated the division correctly (8) but wrote 

Peter has 8 pizzas.
He ate 3/4 of it (them).
How many slices did he eat?

This could have been correct if it was

Peter cut a pizza into 8 equal slices.
He ate 3/4 of it.
How many slices did he eat?

Adil's story is answered by doing 3/4  x 8.

Saturday, August 10, 2013

Masterclass for New Syllabus Primary Mathematics in Manila

In this invite-only class to train a core group of Filipino educators to provide professional development for teachers using a Singapore mathematics textbook series aligned with the Philippines new K-12 Initiative, the focus is on helping teachers understand the Problem-Solving Approach, the CPA Approach as well as the three-part lesson format with some references to Differentiated Instruction, Assessment and Model Method.

Photographs of the sessions are available here.

Technology tools used during the sessions include NLVM and Ultimath.
The apps used on the iPad include Bamboo Paper, Geo Board and Thinking Blocks, all available from Apple Store (free apps).

Friday, August 2, 2013

Professional Development at Island School

The course is on Problem-Solving Approach and CPA Approach.

Photographs are available here.

We discussed anchor task:
(1) extended time over one problem
(2) use of concrete materials
(3) collaborative format

Anchor Task : Think about ways to do 32 - 19

NSMSI Open Grade 5 Lesson in Westminster Colorado

Today I taught two open lessons to one group of 'volunteer' students (they gave up a day of their summer because their parents made them come; thanks, guys), Many did not know each other before today. This is the best option we have given that the conference was held during the summer break and yet we want to provide teachers with some opportunities to observe learning in action.

Lesson 1 was a problem-solving lesson on algebraic thinking designed to show teachers the implementation of anchor tasks. The anchor task for this lesson is taken from Primary Mathematics Grade 6 textbook for algebra but for the fifth graders, we did not move to formally writing expressions. The problem is to arrange five consecutive whole numbers in the arrangement seen in the photos such that the vertical sum and horizontal sum are equal. Students articulate the general pattern they saw using words. They saw several patterns. With little guidance, one student saw that "in a population, if there are more even numbers then the numbers in the middle are even". With some help a girl saw that one of the totals can be obtained by "times-ing 3".

Anchor Task

Guided Practice

Lesson 2 is the first lesson on finding 1/2 of 3/4. Students used paper folding to discuss the anchor task. Two main ideas emerged - halving the entire 3 fourths and halving each of the fourths.The focus today is to review a fraction of a whole number and using it to do say 1/2 of 6 eighths as 1/2 of 6 apples.

This open lesson is for teachers to study the three-part lesson format and differentiated instruction.

A student later articulated that what helped were (1) the paper and (2) the 'advice' which is essentially is instruction between desks or differentiated instruction - different kids got different advice based on their current level of understanding.

It was gratifying to see a good student who started off using the procedure to get 3/8 got the conceptual idea during independent practice.

Independent Practice

Wednesday, July 31, 2013

National Singapore Math Summer Institute at Westminster Colorado Day 2

This is my presentation on Day 2 which is to show how to use Singapore Math to implement Common Core State Standards.

Skemp's idea of relational understanding and instrumental understanding reminds us that there is no dichotomy between procedural and conceptual understanding.

We referred to three big ideas today - Generalization, Visualization and Number Sense.

Three ways to subtract (1) subtracting 3 from 4 and subtracting 7/12 from 9/12 (2) subtracting 3 from 3 and 7/12 from 1 (3) having everything as twelfths

Share 2 pizzas between 3 friends (1) 6 thirds shared by 3 (2) 6 fourths and 6 twelfths shared by 3

Students learn procedure alongside the concept.

Monday, July 29, 2013

National Singapore Math Summer Institute at Westminster Colorado Day 1

Day 1 Lecture 1 by Yeap Ban Har on Mathematical Practices

Day 1 Lecture 2 on Model Method
Photographs at Facebook

Presentation on Bar Models

Day 1 Concurrent Session 1 / 2

Friday, July 26, 2013

Shinglee Publishers Mathematics Textbook Launch

The latest edition of the secondary mathematics textbook for Singapore schools was launched yesterday. I am proud to be the consultant to this textbook series that has been around since the 1980's. It is one of the two textbook series approved for use in secondary schools for the latest syllabus for the Express course. For the first time, Shinglee also published one of the two textbooks for the Normal Academic course.

This is the presentation made at the book launch which doubled up as a professional development afternoon for the teachers.

Wednesday, July 17, 2013

SDE's National Conference on Singapore Math Strategies

I presented on two days. On the 17th I do a course on fractions and on the second, I do four short sessions on various topics. In 2014, I present on 9th and 10th July.

Photographs of the 'whiteboard' are available on MCI's Facebook.

Presentation Slides from Day 2 (Fractions)

Updated presentation slides for Day 3 Sessions

The Venue - Sands Convention Center

Tuesday, July 16, 2013

Math in Focus Summer Institute at King of Prussia

Lecture 1 - Visualization

Lecture 2 - Generalization

Example 2 - Generalization

Example 3 - Generalization
Bar Model - Problem 1

Bar Model - Problem 2

Bar Model - Problem 2

Lecture 3 - Bar Model
Look out for solutions to homework problems.

Monday, June 24, 2013

Progressive Classroom Designs Institute at Danburry, Connecticut

Photographs at my Facebook.

Day 1 Presentation is available here

We saw (1) CPA Approach (2) Spiral Approach (subtle variation from day to day lessons).

We heard Bruner, Dienes, Vygotsky and Skemp.

We spoke of several ways to challenge advanced learners in basic skills lessons

Can-You-Explain / Write-a-Note-to-Absent-Friend Strategy
Write-A-Story Strategy
What-Is-The-Mistake Strategy
Taking-Perspective Strategy

Photographs of the lessons including solutions to Homework tasks are available here

Day 2 Presentation is available here

Thursday, June 20, 2013

M4thodology Institute - Workshop on Challenging Word Problem

Problem Set is available here.

The solutions to the Challenging Problems are here.

The solutions to the Homework will be available later.

Problem 1 Emma and Farid Problem

Problem 2 Chairs and Tables

Problem 3 Apples

Warm Up Problem for Textbook

Review of Problem from Lecture on Assessment

Wednesday, June 19, 2013

M4thodology Institute at The Bolles School (Grades 3-6 Session)

Photographs of the board and charts are available here.

Day 1

Opening Lecture on Role of Mathematics

Breakout Session 1 on Anchor Task (see notes below)

Breakout Session on Anchor Task
Notes on Anchor Task Breakout Session

Day 2

General Session on Assessment

General Session on Challenging Word Problems - Problems used in the session is available. See for solutions to the eight problems for the session including the three homework problems.

General Session on Generalization and Links to Algebra

Breakout Sessions on Fraction, Ratio and Percent

The discussion on Fractions is here.

Problem for Ratio

Problem for Percentage Change
Day 3

General Session on Visualization

General Session on Questioning Strategies
There are also additional summary notes in the blog entry for the K-2 Institute.

Breakout Session on Multiplication and Division (see below)

Breakout Session on Measurement and Area where we did one word problem lesson, one basic concept lesson (area of triangle) and one drill-and-practice lesson (based on Pick's Theorem on the geoboard grid).

In the Closing Forum, we look at the Japanese features of effective mathematics lesson (Shimizu, 2013). The slide is available in another blog entry.
Lesson to Develop Formula for Area of Triangle

Lesson to Apply (Measurement)

Lesson to Consolidate (Area)