Mathematics of Sudoku

Sudoku, a number-placement puzzle, is a logic-based game consisting of 9x9 grids with 3x3 sub-grids. The objective of the game is to fill up all the grids so that each column and row, and each of the nine 3x3 sub-grids contain all the digits between 1 and 9. Thus there should not be repeated digits in each 3x3 sub-grids or each column and row.

An example of a completed Sudoku puzzle:

There would be empty grids in some of the grids in each puzzle given. The solver would then have to fill up the grids.

Try solving this:

Our Brand of Maths



At Southern Cross School in Santiago, Chile, first- to fourth-grade pupils became more interested in their mathematics lessons after the school started teaching Singapore maths. -- ST FILE PHOTO: NURIA LING

At Southern Cross School in Santiago, Chile, first- to fourth-grade pupils became more interested in their mathematics lessons after the school started teaching Singapore maths.

Says head of the elementary school Shannon Watt: "They are more engaged and more active and asking more questions now."

Singapore's maths syllabus - developed by the Ministry of Education with a strong focus on problem solving and using model drawings - has been adopted in a number of South-east Asian countries and the United States.

And it has also slowly made its way to South America.

Chile, Colombia and Panama have adopted the syllabus over the past few years.

This year, Chile will introduce a new Mi Mathematica textbook series to all public school pupils at Grade 2, the equivalent of Primary 2. The series, based on Singapore's method of teaching - was jointly developed by Singapore publisher Marshall Cavendish and Chile's Ministry of Education.

Singapore maths attracted international attention after Singapore students consistently outperformed their peers in global assessments such as the Trends in International Mathematics and Science Study (TIMSS).

In the latest TIMSS 2011 International Results in Mathematics, Singapore pupils scored highest among fourth-grade pupils from 63 countries and were the second-best scorers, after South Korea, among eighth-grade, or Secondary2, students.

Although Singapore maths has been widely praised, there was some resistance from parents and teachers in Chile when the syllabus was first introduced.

Ms Watt says that at Southern Cross, which introduced it in 2010, parents did not understand the programme and were not comfortable with it. "(So) we did clinics with parents, just as we did with the students, and now they like it and they see the strength."

Teachers, too, needed to be trained. Ms Paulina Estrada, the academic coordinator for Innovacion Tres, a consultancy working with seven schools in Chile, says: "The mathematical level of our teachers is not good, they have to study and prepare more to understand the programme."

"But our students now want to have classes in maths," she adds. "They love talking about and explaining mathematics concepts."

Dr Yeap Ban Har, who has given talks on Singapore maths overseas and is principal of the Marshall Cavendish Institute - the education arm of the publisher, providing teacher training programmes - says foreign educators see the advantages of the syllabus. "Generally, they are always amazed maths can be learnt in a way where memorisation, rote procedures and tedious calculations are not central," he says.

In North America, acceptance of the Singapore approach is also growing. Introduced to the US market in 1998, Singapore maths is now taught in more than 3,000 schools across the country.

The state of California approved the syllabus in 2008 and Oregon in 2010. Schools elsewhere have independently picked up the syllabus for their students.

In April, a new edition of the Primary Mathematics textbook, which fulfils the requirements of the Common Core State Standards Initiative, will be rolled out.

The initiative is a joint effort by most US states to provide consistency in what is expected of students. This means 45 of the 50 states, plus the District of Columbia, will have the option to teach Singapore maths.

Seattle's Schmitz Park Elementary School has been using the syllabus from 2008 to great effect, says its principal Gerrit Kischner.

While less than a quarter of fifth graders usually qualify to take advanced maths in the sixth grade, at his school, two-thirds will make the cut. "That's more than the school with the gifted students," he says proudly.

By Melissa Sim U.S. Correspondent In Washington

Straits Times