Saturday, December 27, 2008


There are probably two aspects to helping teachers use technology in teaching (mathematics). One is the use of technology. The other is the human qualities that must be developed through the use of technology. As technology takes over the nitty gritty of machine skills, instructional efforts can then be directed to developing human qualities. For example, as the calculator takes over tedious computations, students can perform many computations effortlessly to observe patterns and make generalization.

Sunday, November 16, 2008

Wednesday, November 12, 2008

Teaching Second Grade in Edgewood School in Scarsdale USA

For the first 15 minutes, I was worried as the children did not seem ready to engage in some difficult thinking. I had asked them to pick two 1-digit numbers from a stack of cards. Rohit volunteered and picked 3 and 3. I told them that the 3 and 3 were used to make 33 and 6 (3 + 3) and then the difference 33 - 6 was found. We used the 100-chart to help with the subtraction.

Another girl picked 8 and 6 and again we used those to form 86 and 14 and found the difference 86 - 14. I told them that even if I could not see the second number, I can still work out the difference!

This is a multi-step process problem. The children seemed lost in the many steps. They were not entirely ready for this and I had to do something to help them remember what the problem was all about. Some constantly thought that I was guessing the second number (i.e. 6 when the girl picked 8 and 6), instead of the answer to the third step - after using 8 and 6 to form 86, 8 + 6 = 14 and finding the difference between 86 and 14.

(I used the term difference very early in the lesson. I would not have done this in Singapore as I am aware that we introduce this term only in Primary 3. But I thought these kids being kids in U.S. would know the term. Clearly it was a wrong assumption - second graders who know subtraction may not comprehend the term difference.)

To help them remember, I constant got them to refer to the cases we have tried how the three numbers 86, 14 and 72 were obtained.

Each of the four groups were then invited to picked two numbers but not show the second one. I then wrote down the final answer for each case. We then checked and each time the answer was correct.

I asked the children to tell how the magic worked.

There was an early suggestion from Rohit and the boy in front of him that the answer was obtained through multiplication. However, as they had not yet learnt the multiplication tables, they struggled with this. I invited the children to checked if the answers was in their 'book of magic' which was just their exercise books which happen to have multiplicaton tables.

I gave some hints and many children could see that the tens digit in the answer is related to the first digit they chose. Someone else described that the sum of the digits in the answer is 9.

I asked Michael, who struggled with the task and seemed to start to lose interest in the lesson, to come out and helped me. Later, he told the Principal that he was nervous when he was called. I guided him and in the end he could see that the digits add to 9. He seemed more engaged after that.

I let the children try the trick among themselves and, just before we ended, gave them a few examples to try.

We had a roomful of teachers observing the children. It was a modified lesson study of sorts. The photographs of the lesson and a discussion of the mathematics will be posted here in the near future.

I did the same problem with teachers at Stamford Primary School in Singapore. The teachers came up with two ways - multiplying the first digit by 9 as well as to reduce the tens digit by 1 and making sure the sum of the digits in the final answer is 9. They could also explain method that multiply the first digit by 8 or by 10.

Friday, October 24, 2008

Teaching in Chile on YouTube

This is a video clip (in Spanish) to document my experience teaching a class in a public school in Chile. It was a third grade class, solving a problem based on addition of three one-digit number. I have taught similar lessons to second grade Thai students and first grade Singapore students.

Monday, June 30, 2008

Why Cavemen Drew on Cave Walls

Pre-historic cavemen already knew what the human brain is not good in - it is not good in memorizing large amount of information and it is not good in doing procedures. They drew on cave walls to help them retain information. They created simple machines to carry out procedures. Mankind's subsequant endeavour in inventing paper and creating more and more powerful computer storage devices as well as our attempt to invent increasingly complex and sophisticated machines only tell us one thing - the human brain is not superior in memorizing and doing procedures. Making children learn mathematics by memorizing and doing procedures result in two things - they don't do well or they struggle, only to do well superficially. Our brain is a visual brain. Our brain is good at spotting patterns and trends and coming to a general conclusion. Get children to visualize. Get them to look for patterns and make connections when they learn mathematics. These are their strengths. In turn, these abilities become increasingly more and more powerful. Mathematics is about visualization and looking for patterns. Mathematics is not about memorization and procedures.

Sunday, June 29, 2008

Teaching in Chile

The children were asked to arranged numbers one to five in a certain arrangement such that the total of the three horizontal numbers and the total of the three vertical numbers are the same. Later, the sets of numbers were changes to two to six, three to seven and four to eight. Each time, the children were asked to tell what the common total was. For each set of numbers, there were three possible totals. Finally, the children were asked to predict the possible totals if the sets of numbers were five to nine and ten to fourteen.

During my visit to Universidad del Pacifico, I had the good fortune to use this problem with a third-grade class in a public school and a fourth grade class in a private school, both in Chile. I have taught many lessons using such and other problems to primary school children in Singapore. In the public school, the children were less confident. In the private school, they were more so. In Singapore, some classes were closer to the class in the public school and others were more similar to the class in the private school. In some of these classes, the children had stronger basics. In others, the basics were not quite in place yet. In Singapore, the children spoke in English. In Chile, they spoke mostly in Spanish. Singapore students often performed well in international comparative study. Chilean students, less so.

But the potential of the Chilean children was not any less than that of Singaporean children. The Chilean kids were as engaged as the kids in Singapore. They were just as enthusiastic in trying to solve the problems. Their faces lit up when they managed. They looked puzzled when two of their friends gave conflicting information. They discovered for themselves who was right. They did all these and more, just like Singaporean kids.

I learnt that kids everywhere have the same potential. I believe that given the same opportunities kids everywhere will reach the same pinnacle.

EL Mercurio News

Sunday, June 15, 2008

About mathz4kidz

mathz4kidz implements programs that are consistent with the philosophy of SingaporeMath. The vision of mathz4kidz is Where A Child Grows to Be Creative & Critical Problem Solvers which emphasizes holistic development of children through a rigorous mathematics program. The overarching ACT framework directs the development and implementation of teaching materials. ACT refers to the three key competencies that mathz4kidz hopes children will develop - Attitude, Communication and Thinking. mathz4kidz's long-term goals include to develop research-based mathematics programs based on SingaporeMath.

About SingaporeMath

SingaporeMath has gained an international reputation for helping average students attain high achievement levels and enjoy mathematics. Some prominent features of SingaporeMath includes the emphasis on complex problem solving and concept development through the concrete-pictorial-abstract approach. A prominent feature of SingaporeMath is simple explanations for difficult concepts.

SingaporeMath's emphasis on the development of students' intellectual competencies is consistent with the importance placed on nurturing knowledge workers and people who can participate fully in an increasingly technological world. Textbooks based on SingaporeMath have been adopted in many countries around the world. As of this year, there is even a Standards Edition of a K-5 textbook series based on SingaporeMath.

TIMSS has consistently found that Singapore students perform well in mathematics. A 2005 study by American institute for research (AIR) found that SingaporeMath Grade 6 problems are "more challenging than the released items on the U.S. Grade 8 National Assessment of Education Progress (p.xiii)". It was also found that SingaporeMath "are rich with problem-based development (p.xii)" instead of focusing on the mechanics of mathematics and the application of definitions and formulae to routine problems. A 2007 article in Educational Leadership concluded that "using the bar model approach, Singapore textbooks enable students to solve difficult math problems - and learn how to think symbolically ".

This emphasis on visual methods in SingaporeMath could be a contributing factor to why Singapore students are able to sustain their achievement level from Grade 4 to Grade 8.