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.

Friday, March 16, 2018

Prague Session | 17 March 2018

CEESA Conference - Session 7
Bar Model in Solving Word Problems 

Yeap Ban Har 
Pathlight School and Anglo Singapore International School
Twitter @banhar

We will likely solve two or three of these during the session and the rest are ... your homework.
To be submitted at CEESA in Warsaw next year. Kidding ... we will make you stay back to complete all the problem before we dismiss you.

Warm Up Problems 

Let's have a go at one ...

Slightly challenging ones ...

A bit of exercise before you head home ....


Problem A

Problem B

Safe journey home to all!

Thursday, March 15, 2018

Prague Session | 16 March 2018

CEESA Conference - Session 1
Fractions - Why Do Students Find Them Difficult?

Yeap Ban Har 
Pathlight School and Anglo Singapore International School
Twitter @banhar

Let's solve two problems to see what is it that makes fractions difficult and what are the main ideas students need in learning fractions.

This discussion add to the learning experiences that we discussed at the pre-conference. The learning experiences are needed for all lessons. Today's 90-minute discussion focuses on things specific to learning fractions. 

A major culprit is the notation used to represent fractions. Do students know that the numerator is but a name? If the know that then everything else they need is from whole number ideas - except equivalent fractions.

Do we focus on the teaching of equivalent fractions.

Through Problem 1, we see the learning of equivalent fractions in a conceptual way that requires visualisation and meaning-making. Students lack of relational and instrumental understanding of fractions is one major obstacle in learning fractions.

While we obsess with additions and multiplication facts for whole number concepts, do we pay the same amount of attention to the basics in fractions which is renaming a fraction in multiple ways? In the learning of finding equivalent fractions, are students merely learning the procedures without any kind of reasonable understanding? Is the learning connected to previous knowledge or is it "multiply the numerator and denominator with the same number"?

In summary, problems with fractions can be fixed by teaching the fraction notation and equivalent fractions well.

That's all. 

As I said, this is one of the easiest problem in the learning of mathematics to fix.

Wednesday, March 14, 2018

Prague Workshop | 15 March 2018

CEESA Pre-Conference Workshop on Teaching Mathematics: Five Critical Learning Experiences
at International School of Prague

Yeap Ban Har 
Pathlight School and Anglo Singapore International School
Twitter @banhar

1. Some Data on Achievement (e.g. PISA)

Another well-known study is TIMSS

In this workshop, we will examine critical learning experiences that can result in adequate learning even amongst the weakest learners with the average learners performing at a high level while the learning of the most advanced learners are not compromised.

We will also get to observe a class at International School of Prague and hear about one initiative at the school from two colleagues.

2. Case Studies for Workshop

The first part was to experience the learning experiences ourselves. Two ISP colleagues showed us one way to use the physical space - students writing on the wall spaces around the room - to provide a better learning experience 

Some of the apps that I use in this workshop are from this list.

Pieces Basic is another free app that I used in place of the base ten blocks from BrainingCamp.

Case Study 1 - Sharing Art Paper
This journaling task requires evaluation between ideas.
It involves little use of the written words. Students use diagrams or artefacts (paper folding).

Case Study 2 - Flowers

In this journal entry, students are describing one method used to solve the problem. 
Here, students use mostly mathematical notations and a little bit of the written words.

Students must have the experience to explicate mathematical ideas in four forms:
- using things
- using pictures and diagrams
- using written words
- using conventional symbols and notations 

Case Study 3 - Dots

This is the class' homework - to figure out a pattern raise the relationship between the he area of the polygon with a dot inside and the number of dots. Did your investigation yield anything interesting?

Case Study 4 - BOAT

By putting three more points B, A and T create a quadrilateral BOAT.
Let's investigate the angles of this quadrilateral.

What do we notice?
How can we prove what we notice?

Key Questions - What are the critical learning experiences? What are the theoretical underpinnings? How can we provide students with these  experiences? What is your key learning today?

Additional Question - How do learning experiences relate to mathematical practices outlined in common core state standards in the US?