We had the great fortune to hear Tina Seelig, the Executive Director of the Stanford Technology Ventures Program and an advisor to Start-Up Chile, speak on Friday. A neurophysicist by training, Tina is one of the most enthusiastic and charismatic speakers I’ve ever seen, and her 2.5 hour workshop seemed more like 30 minutes — it flew by!

Tina Seelig. image via Stanford dSchool

At the beginning of her talk, Tina showed us a slide that said 5 + 5 = ? Everyone quickly answered 10. “Wow, you’re so smart, ” she replied. Next, she said, “But what if instead of 5 + 5 = ? we asked our students ? + ? = 10? What’s the answer then?” If you reframe the question to focus on the end product, and allow for an infinite number of ways to get to that solution, that is the type of thinking that supports creativity.

The day after Tina Seelig’s presentation, I sat in the Cafe Literario Parque Bustamante, reading Sábado, the Saturday magazine of Chile’s largest newspaper, El Mercurio. On page 42 of the September 10, 2011 edition of Sábado, I found a remarkable article by Isabel Plant, “A Clases Con El Método Singapur.”

This article describes how Singaporean math curriculum has been adapted in 250 Chilean schools, and takes us into one second-grade classroom. What surprised me most is that I saw Tina Seelig’s example in this article.

I translated about 1/3 of the article from Spanish to English. Enjoy.

The Singapore Way

The students in second basic B are sitting in groups. In the middle of their tables, they have a bag filled with what look like Legos, but really are some of the tactile instruments that are included in the first step of the Singapore class: the concrete part. Touching the math with the fingers.

The Lego-like pieces are called Unifix and they will help the children calculate. Every table has a group leader, who, according to the teacher’s instructions, assign the blocks to the other students. The pieces, of all colors, cover the table and the little hands assemble them.

“I do pink and green!”

“Me, blue and white!”

“Hey, you’ve got all the blue ones!”

Chilean students in a Singapore Method class. Image via La Tercera (a different Chilean newspaper, published by the same company as El Mercurio)

The kids look like they are playing, but really they are working: they have to put together 10 pieces, and connect them, using a distinct combination of colors. 3 red pieces and 7 green, for example, or 6 pink and 4 orange, or other combinations like that. Next, the teacher, Tabita, asks one group at a time which distinct combinations they have created, and notes them on the board. They count together, out loud.

After finishing the exercise, they move on to the second part of the Singapore Method: the pictorial part, in which the student visualizes the mathematics, not just the numbers.

For this, second basic B should put away the Unifix and take out the book, “Thinking Without Limits,” from the Singapore Method, and open it to page 122. At the same time, Miss Tabita has this page on her laptop, in front of the class, and projects it onto the board. There, represented with pictures — packets with 10 sticks in each one — the kids begin to do every type of multiplication. The teacher writes it down and asks the students, until the multiples of ten have been understood and reviewed. The students advance rapidly, although maybe one doesn’t succeed in multiplying 6 times 10.

“The time to make mistakes is now,” says Miss Tabita.

“… because when the test comes, it’s too late,” says one student, very seriously.

The teacher moves on, while the students do the exercises from the book, to show distinct ways of calculating multiplication, from counting on one’s fingers, to doing it mentally, to the “technique of zero,” which is used in multiples of 10.

The kids, very involved, raise their hands like bullets, now that the correct response gives a star to the group. Through this exercise, they begin to understand that there are many ways to arrive at the same solution. One of the focuses of the Singapore Method is problem solving, not just the content.

Finally, in the third part, the students do math problems using what they learned (“If Gugo has 6 trucks with 10 wheels each…”). This is the abstract part, the metacognition, which comes only after they have already touched and visualized the mathematics. This is the part that tests whether the child is capable of retaining what she has learned and solving problems in her head.

The students receive a yellow card and a red card. “Raise your yellow card if you understood the class. And the red card if you didn’t understand something.”

A sea of yellow cards rises, with one red in the middle.

“I have one thing I don’t understand well, the zero technique, does it only work for multiples of 10?” asks one student.

Miss Tabita reviews the material. They do two more exercises from the book, then the put away the books, put away the cards, and are ready to go out and play.

Singapore Method Teacher Training Seminar, sponsored by Chile's Ministry of Education. Image via http://explorarm.com/seminario-metodo-singapur/

More information on Singapore Math in Chile:

• http://www.latercera.com/noticia/educacion/2010/10/657-296382-9-capacitan-a-profesores-de-matematicas-para-implementar-metodo-singapur.shtml
• http://explorarm.com/seminario-metodo-singapur/