Thursday, July 23, 2009

Foundation Mathematics

I really enjoyed your presentations at the conference in Vegas. I'm curious about one of the books you mentioned and perhaps where I could find it. You said there is a book for the Foundations Mathematics Program.
Karen, 5th grade math teacher in Austin, Texas
By the end of Primary 4, students who have not acquired adequate basic foundational knowledge are recommended to do an alternate program. This is referred to as Foundation Mathematics, offered to Grades 5 and 6 students. Less than 10% of Singapore students do this program. This program help students review a lot of Grades 1 to 4 materials in an age-appropriate manner with some Grades 5 and 6 topics included. This program is suitable for US Grades 5 and 6 students who have not had Singapore Math background. The books are available at There are two textbooks (5A and 5B for Grade 5) and two workbooks per grade level.

Saturday, July 18, 2009

Language Issue

When we teach mathematics, we introduce two foreign languages to our learners (pretty hard for them) - the language of mathematics and the English language, because here in the Philippines, English is our medium of instruction. Other issues came out, that learners would learn best if they would use their mother language. I think this is one of the major issues now, not only here in our country but also globally. An example is Malaysia.
Jeniffer in the Philippines
There is no guarantee that using one's mother tongue results in high achievement in mathematics. Japan and Korea use Japanese and Korean to teach mathematics and their achievement is high (e.g. in TIMSS). Thailand and, until early 2000s, Malaysia use Thai and Malay to teach mathematics and their achievement is not high. Singapore use English, not the students' mother tongue and the achievement is high. There are other more important factors than the medium of instruction. In my opinion, if the medium of instruction is used right from Grade 1, students will just pick it up. Students from non-English speaking homes may need some additional help. In Singapore, we have Learning Support Programme in Grades 1 and 2. I feel that Malaysia should not say that their attempt in using English to teach mathematics has failed. If their politicians have read Michael Fullan's Six Secrets of Change, they will understand that when a change is implemented there will be a dip in performance before it increases again. I feel that they should have given the change a longer time to happen before deciding to abandon it. Incidentally, I had the good opportunity to listen to Michael Fullan this morning at a conference in Las Vegas. He was giving lectures to US principals who are attending the differentiated instruction conference.

Two Questions

May I know your stand on these issues, "Stop Teaching by Telling'' and "The Principle of Equity (in mathematics classes)."

Jenny, a teacher in the Philippines
Often teachers teach by one of these methods: telling, coaching, modelling and providing. There is probably a place for each technique. Generally, I would urged teachers to help students develop conceptual meaning of procedures they learn. For example, to lean 3 divided by 1/2, I would suggest teachers use pattern blocks or pictorial representations and ask students questions such as "How many halves are there in 1 whole? So, how many halves are there in 3 wholes?" From there students can see that the answers are 2 and 2 x 3, respectively. They understand why 3 divided 1/2 is the same as 3 x 2.
By using differentiated instruction, teachers are able to provide every child with equal opportunity to learn. For example, in practising multiplication, teachers may allow struggling students to use concrete materials to derive multiplication facts while challenge able students to spot patterns in the multiplication tasks or to use basic multiplication facts 7 x 7 and 7 x 5 to do say 7 x12.

Concrete Representations in Mathematics

My co-teacher asks me to e-mail you because she attended a conference in Manila, the Philippines in May 2009. What are the different processes in teaching concrete ideas in mathematics? Thank you so much.


I assume you are asking about the use of concrete representations to help students learn abstract mathematical ideas. This is the CPA Approach, as we call it in Singapore.

It is important to match the cognitive processes required in handling the abstract idea with the cognitive processes used in handling the concrete materials. For example, in doing addition within 20 (say, 7 + 5), one abstract ideas we want students to have is 'making 10'. Students should be able to visualize that 7 + 5 is the same as 10 + 2 (making 10 from 7 by moving 3 from 5). A suitable concrete activity is to use tens frame. Use two tens frames - one with 7 counters and another with 5 counters. Then get students to move 3 counters from the second frame to the first. The cognitive processes match.

The photograph shows tens frame made by public school teachers involved in the LEAP Project in the Philippines (December 2008, Ateneo de Manila University).

Wednesday, July 1, 2009

Model Method

I'd like to ask about this problem:

Ahmad and Mei Ling saved $800 altogether.
A quarter of Ahmad's savings was $65 more than a fifth of Mei Ling's savings.
How much more money than Mei Ling did Ahmad save?

Please explain the answer using model

Tendo, a teacher in Indonesia

For some reason the photograph does not show up.
Draw a unit bar for a fifth of Meiling's savings. So, a quarter of Ahmad's saving is this unit bar plus a bar that stands for $65. Now draw the whole amount of Ahmad's savings (four units plus four $65) and the whole amount of Meiling's savings (five units). These add up to $800, right? That means nine units plus $260 is equal to $800. Can you finish it up?