Monday, July 30, 2018

Danvers, MA | 30 July 2018

Elective - Journal 

Different journal types based on two different lessons.

Session for 6-8 | Rational Numbers

Session for K-2 | Visualization

Thursday, July 26, 2018

Singapore | 26 September 2018

In my presentation to parents, I pointed out what is really important in secondary mathematics.

See here for Notes that are updated on regular basis

I pointed out the importance of 'reading' mathematical expressions such as (-6) : (-2) and 1 : 1/3.

Seattle | 23.24 July 2018

See presentation slides and summary here

Thursday, July 12, 2018

Kansas City Course | 12 July 2018

A Day with Grades 6-9

I did the course on Rational Numbers and Algebraic Thinking for this group on Day 3 of the event. 

We look at the use of models to help students learn mathematical ideas. In cases that are difficult to model we employ reasoning to help students use what they can model to figure out what they cannot.

For fractions, we focused on division by fractions. 

Again we compare the use of model as well as model + reasoning.

Along the way we had a bit of fun.

Algebraic Thinking 1 - Generalization - coming soon 

Algebraic Thinking 2 - Use of Variables - coming soon 

105 people went on a trip. 4/5 of the adults and 2/3 of the children took several yellow buses. The remaining 29 took a red bus.

Kansas City Course | 12 July 2018

Advanced Learners 

More slides later
or at 

Wednesday, July 11, 2018

Kansas City Courses | 11 July 2018

Enquiries about 
think! Mathematics 
a textbook with anchor tasks based on latest research on how teachers use textbooks and how students respond to different tasks

US Office

Or contact the Singapore office 

Kansas City | K-2 Journals
We looked at four journal types. 

I invited the class to think about the roles of journals as 'homework' - class started 15 minutes late because the keynote ended late. And it was 4 p.m. and the Teachers have been in sessions since 8 a.m. Greg is a slave-driver so he packs the day for the participants 😂.

After 4 there's still yoga and all sorts of dancing, if you are the dancing type. Me, I went for Chicken Katsu and Sake with a couple of friends.

But here are the highlights of the one-hour elective session.

Follow-Up Videos to Watch
Schools talking about the use of journals.

Also see for other additional videos

These are a few examples of journals from schools in Thailand (Anglo Singapore International School) and South Africa (King David School).

Source | Anglo Singapore IS - a glimpse into how a child counts 100
There is evidence of counting groups but is it groups of ten?

Source | Anglo Singapore IS - upon completing a practice worksheet students are asked to sort those that they have to do regrouping and those that they do not need to.

Source | King David School - this student was responding to "Draw a Friend who is 7 paper-clips tall". Like all kids his age, he drew a Friend and crossed his fingers.


Thursday, July 5, 2018

Altrincham and St Albans Course | 5.6 July 2018

Math Learning Center
Pencil Box
Bamboo Paper

Opening Problem
We discussed ways to support struggling learners and ways to challenge advanced learners.
We looked at anchor tasks and some conditions of learning.

What's advanced thinking in mathematics? 

Wednesday, July 4, 2018

Wednesday, June 27, 2018

London Course | 27.28.29 June 2018

Case 1 | 7+3+2

Case | Multiplication 

Wednesday, May 2, 2018

Singapore Seminar | 18 April & 2 May 2018

As part of Pathlight School's school-parents partnership model, we try to empower parents. In my role, it is to empower them to help their kids with the academics.

This year, I focus on (surprisingly) mathematics.

Parents are encouraged to return to this blog post as I will be adding content throughout the year.

We discussed how to learn calculations at a level beyond the procedural in the April seminar.
In May, we looked at word problems.

Spiky, Curly and Smiley had the same amount of coins. Curly and Smiley each had a mix of two types of coins, 50-cent coins and 10-cent coins. Curly had nine 10-cent coins and Smiley had fifteen 10-cent coins. Spiky had only 50-cent coins.

(a) Of the three children, who had the most money and who had the least?
(b) What is the difference in the total value of Curly and Smiley's coins?
(c) Smiley used all his 50-cent coins to buy some food. He then had $10 less than Spiky. how many coins did Spiky have?

We did this problem to understand the role of qualitative thinking in mathematical problem solving. The hard part in problem solving is usually the qualitative thinking, rarely the quantitative computation which can be done by a calculator anyway.

For those who did not attend 😤 (detention class, no, joking), please solve this problem before I continue...

After a hard day's work a group of parents were made to solve this problem, which is a version of a recent year's Primary School Leaving Examination (PSLE) task.

Sorry 😬

We hope the food compensate for the hard thinking some of us had to go through at eight at night.

I shared a few routines parents can teach their children.

Read. Draw? Calculate?
Do not encourage kids to reach the entire paragraph, unless he is a gifted reader. 

Who is is in the story? What is it all about?
These are easy entry points to a challenging problem and gives kids confidence.

Read the first sentence.
Is it easy to understand?
Can I already calculate?
Can I draw (a model)?

Then move to the next.
This read-and-do routine helps kids to manage information and not be overwhelmed by the complexity of the story.

Can you imagine the story?
All the three are holding a bowl of coins, all the same number. Suppose all are fifty-cent coins. 

Imagine Curly giving up one 50-cent coin and receive one 10-cent coin. What happens to her amount of money? By how much? 

Is that right ... Curly had nine 10-cent coins. I imagine her giving up 9 fifty-cent coins in return for the 9 ten-cent coins. How much less money does she has than Spiky? 

I share are techniques in scaffolding. I discourage parents explaining solutions to their kids | Scaffold and Model, Not Explain

To be continued ....

Wednesday, April 11, 2018

Friday, March 23, 2018

Manchester Course | 23 March 2018

The problem-solving courses focuses on teaching basics as problem solving as well as teaching of solving of word and puzzle problems.

Can drill-and-practice be done in the spirit of problem solving?

We saw how teaching times tables, as well as algorithms like long  division and subtraction with renaming as problem solving.

Spiky spent one-quarter of his savings on a present and one-sixth of the remaining money on a toy for himself. As a result, he had £32 left.

Solving a simpler problem ...
Spiky spent one-quarter of his savings on a present and one-third of the remaining money on a toy for himself. As a result, he had £32 left.

What-if ....?
Spiky spent one-quarter of his savings on a present and one-quarter of the remaining money on a toy for himself. As a result, he had £32 left.

In teaching word problems, I demonstrated my usual "guess my next word" routine in teaching word problems. 

What are the advantages of this strategy?

The class came up with this list ...

1. Teaching habits of mind of handling small chunks of information
2. Teaching kids to be not helpless - Can we calculate already? Can we draw?
3. Leaving out numbers in initial problem or when reading

Monday, March 19, 2018

London Course | 19.20.21 March 2018

Session 0
Some achievement score data and what they means ...

Session 1 Addition

Session 2 Subtraction 

Session 3 Multiplication 

Minister Nick should have taken advice from our class today. When you feel not confident about your answer, just check it quickly using one of these methods that can be done mentally and fairly quickly.

These are examples of Phase 2 strategies from Baroody's three-phase model of learning times table.

Challenging Advanced Students

1. What if ....? 

What if the fraction of the remainder is a quarter instead of a third?
What if the toy's price is an exact amount to the nearest one pence?
What should the remaining amount be instead of £32?

2. Journals

Instead of descriptive journals, students can do evaluative or investigative journals, for instance.

3. Write a Note, Invent a Method, Pose a Problem

Saturday, March 17, 2018

Prague Session | 17 March 2018

Session 5 

The demands on young people in the marketplace are different to say four decades ago. Do our kids have the right competencies and mindset about what they are expected to be able to do in jobs that can give them a reasonable quality of life?

Practice is variation not repetition. See the theory of variability by Dienes.
Practice is important as a consolidation tool in mathematics learning.  
Not drills which is characterised by repetitive work.
Not rote memorisation.
So how do kids learn multiplication facts.

Thank you, class, for helping Nick.
He will be grateful to you guys.If he is listening.

But can we do drills.
Well, let's see.

Spoiler Alert: The answer is yes but how it can be done in an acceptable, even productive way, that can lead to learning in the true sesame of the word.

Colleagues think that this drill activity is productive because 

A. competencies like .... are developed
B. productive mindset like .... are developed

So, drills are acceptable if they can lead to high-level competencies and productive mindset otherwise it is illegal to do drills.

I am glad you had fun.