Wednesday, May 2, 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.
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 ....
Friday, March 23, 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.
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.
SUPPORTING STUDENTS in WORD PROBLEM SOLVING
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
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.
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?
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
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.
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
CEESA Conference - Session 7Bar Model in Solving Word Problems
Yeap Ban Har
Pathlight School and Anglo Singapore International School
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