Singapore Math Training

I get a lot of questions about the possibility of getting training in Singapore Math. The answer depends on what you are interested to do and which country you are in.

If you are interested in graduate studies, NIE offers masters degree in many specialization, including mathematics education, primary education and secondary education (there are many other fields of specialization). We have foreign stduents who complete the course full-time in a year although a year and a half is not so tight. NIE has both coursework as well as coursework plus thesis option.

If you are interested in Ph.D., you need to be here in the initial part to complete your coursework and to work out your research problem with your supervisor. You may do the research here or in your home country. You will be expected to be back here in Singapore towards the end of the candidature and for your oral examination before the degree is conferred. If you are interested please email me banhar.yeap@nie.edu.sg I can link you up with potential supervisors.

If you are more interested in getting training for classroom teaching rather than graduate degrees these are some options.

Join NIE's post graduate diploma in education (PGDE Primary) where you get pre-service training in two or three subject areas including mathematics teaching. It is one year. If you are not interested in the diploma and just want to focus on mathematics then I think there is an arrangement for you to do this as a non-graduating student.

Join NIE's inservice course. There is a range of subjects available throughout the year. From lesson study to problem solving to action research. A 12-hour course runs over 4 weeks. (once a week).

In some countries, there are institutes already in place. In the US, there is a summer institute every year. Go to http://www.sde.com/conferences/singapore-math/index.asp for details.

Some school districts run theirs. I have been to Scarsdale School District twice to teach a course in their own teacher institute. I believe in the last course there were teachers not from the school district who joined the course.

In places like the Philippines, Indonesia and Chile, the book distributors have been organising training seminars at least once a year.

If you are thinking of running such institutes in your country, I can put you in charge with the book publisher to explore this possibility.

Why Does My Child's Score Drop Suddenly in Primary 5?

A parent shared her concern with me recently. Her daughter did well in Primary 1 to 4, scoring above 90% in her examinations. She has been coaching her daughter all these years. In her recent SA1 (mid-year examination) in Primary 5, her score dropped "incredibly to just 62%". In a mock test for CA2, she got "just 56%". The parents said she is "scared stiff" and is "perplexed as to how this can happen".

Maybe an explanation of examination structure will shed some light. Up to Primary 4, the proportion of extended problem solving where the tasks tend to be complex, multi-step or novel and students need to show their steps is relatively small. Typically, up to Primary 4, many schools' examination papers allocate 40% of the score for MCQs, another 40% for short-answer questions and 20% for long-answer tasks, the type that tend to be complex, multi-step and sometimes, novel. In upper primary the proportion changes to 20% MCQs, 30% short-answer questions and 50% long-answer questions.

The student concerned is presently scoring about 60%. This means her foundation is strong. This is clear from the fact that in earlier grades her scores had been about 90%. She is capable of problem solving but the type that is now common in upper primary is still a challenge to her. She like many primary five students are still developing this capacity.

My advice is to give her confidence by guiding her through such problems. Ask her scaffold questions so that she can she the intermediate steps that are not obvious to her now. Perhaps in the problems that she uses the model method, the models are more complex now and require strong visualization skills.

Whatever it is do not be overly anxious (I know this is hard for most parents to do) because the anxiety will transfer over to the child and this will not help. Get her to see that her basics are strong. This is probably evident from her test papers. Let her see that the problems she cannot handle are actually rather challenging. Then start her with the simpler ones first. Move to the more challenging ones. Try this and see if you can move her to about 70%. A score of 70% to 80% indicates that a child is within the A grade at the PSLE. Students capable of complex problem solving will move into the 90% range. If I am not wrong the national average for number of students who score A and A* (i.e. above 75%) is about 45%.

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 http://www.singaporemath.com/Math_Works_Coursebook_5A_p/mwc5a.htm. There are two textbooks (5A and 5B for Grade 5) and two workbooks per grade level.

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.

Maria

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).

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?