March 16 | Singapore

I did a brief presentation to some tutors teaching in the RoPE Programme in Mendaki.

Teaching Word Problem to struggling learners

I demonstrated a way to cultivate habits - read, understand, do as opposed to reading the entire story and be overwhelmed.

Fraction - an area of difficulty for struggling learners.

I talked about denominator as a noun.

RoPE tutors are managed by Zenitant Pte Ltd.

March 16 | Singapore

This seminar is for schools in Singapore that use New Syllabus Mathematics Series. In the first of two sessions we are have for them this year, we had a general discussion on lesson structure, learbing well and mathematical models in three topics.

Slides to come 

March 11.12 | Connecticut (Westport)

With colleagues from Westport School District

Presentation Slides to come  

March 9.10 | Connecticut (Greenwich Public Schools)

Slides are here.

We open with some international comparative achievement tests data.

For the Grades K-3 session, the morning was devoted to studying the complete lesson structure

1. Anchor Task
2. Journaling
3. Reflection
4. Guided Practice
5. Independent Practice

How does the first thirty minutes look like?
How do we do an Anchor Task based on a Learn in a textbook
We also see how to select one of the three Learns in a textbook and use the other two as Reflection.

In the afternoon we saw three models of teaching word problems including those that focuses on calculation and bar models.

Slides for Grades 4-8 Session are here.

We looked at the three-part lesson structure and the different ways to teach word problems - problem posing, rewrite word problems told orally in one' sown words, presenting. word problem sentence by sentence and modeling reading word problems - we saw examples of each.

March 7 | Alexandria

We had sessions on Anchor Tasks and Guided Practice, both of which are learning activities as well Chalkboard Writing and Mathematics Journal.

The slides are here.

We had a side discussion on assessment. For Math in Focus users, the way the Chapter Tests and Mid-Year Examinations and End-of-Year Examinations are set up are not consistent with parental expectations because of differences in the grading system in Singapore and the US. MiF Trainers found that the proportion of unusual / challenging problems in different chapter tests are different, sometimes more, sometimes less. So in a test with five points for those problems, students get 20 when he is good on all tasks except novel items. On another test, only 2 points are allocated, this student gets 23. The measurement differs by 3 points on a 25-point test. That's a difference of more than 10%.

We discuss one way to overcome the problem.

March 6 | Danbury

March 5 | Danbury

Day 1 Slides are available here.
We focused on teaching problem solving rather than teaching to solve a problem. We looked at classroom practices and teachers actions to cultivate mathematical practices.

We looked at  grade five word problem and a grade four lesson on addition if unlike fractions. We also looked at a grade one subtraction lesson and a kindergarten lesson on triangle and a pre-kindergarten lesson on counting small numbers. We ended the day with a lesson on word problem for grade two.

The key focus is on the use of a single problem (Polya) solved over an extended period of time (Piaget). The students work in groups (Vygotsky) using concrete materials and visuals (Bruner) and explain their ideas in a whole class discussion using informal language (Dienes). The focus on concepts and conventions on top of just knowing the procedures in mathematics (Skemp) was demonstrated.

March 4 | New York (Bedford Central School District)

The slides for the teachers session are here.

Grade 3 Lesson on Fractions

Plan | I taught a 30-minute lesson based on this Put On Your Thinking Cap. I left Problem 1 and the Workbook Task for the next half an hour - Guided and Independent Practice. 

For this lesson, I planned to use Problem 2 as the Anchor Task. The Anchor Task was  - Here is a cake. (Students received a bar model cutout to represent the cake, cut into thirds) Nohair got 2-ninths. Spiky and Curly got the rest. How much if the cake did each of them get? Find as many ways as you can. 

Compare this version to the one in the book. What's the difference, if any? 

Differentiation for Struggling Learners - one condition was left out (Spiky got more than Curly). Also a concrete bar model was given to the students.

Differentiation for Advanced Learners - The bar model was cut into thirds so that students get to extend their solutions to cases such as 2/9 + 1/3 + 4/9. They are also encouraged to check if it is possible to include sixths or fifths.

Outcomes | 

It was suggested that students use a table to organize their responses. They were later scaffolded to realize that they work systematically. 

Grade 5 Lesson | Weston Intermediate School

At the end of our Open Lesson, a student asked me where he can find further practice problems. 

This is for him and his friends in the great grade five class at Weston Intermediate School.

Problem 1

Jonathon had $48. He spent a third of it on a gift for his mom and three-fourths of the remainder on a gift for his dad, Whose gift cost more? By how much?

Problem 2

Jonathon spent half his money on some stationery and one-fourth of the reminder on a pen. As a result he had $2.40 left. How much was the stationery?

Watch out this space for further practice problems.

March 2.3 | Connecticut (Weston Public Schools)

All the lessons are 30 minutes long.


March 2
Grade 3 Open Lesson @ Weston Intermediate School
Materials used include a strip of paper divided into thirds.


Grade 4 Open Lesson @ Weston Intermediate School
Materials used include the hundredths grid taken from internet.


Grade 5 Open Lesson @ Weston Intermediate School
Materials used include a strip of paper for bar modeling.


March 3
Grade 6 Open Lesson @ Weston Middle School


Grade 8 Open Lesson @ Weston Middle School


Grade K Open Lesson @ Hurlbutt Elementary School


Grade 2 Open Lesson @ Hurlbutt Elementary School