The alternative is unthinkable."
The Math Journey of a Leading Nation From a Global Perspective
Day Four* of a U.S. Math Teacher's Travel Journey to Singapore
3 September 2010
The Singapore Mathematics Journey and Framework
by Lueh Yueh Mei
Ministry of Education, Singapore
The 1960s and 70s was a time of nation building. In 1965, students took the first Primary School Leaving Exam (PSLE) - the exam students must pass at the end of 6th grade. Only half of the students passed and one-third of primary (elementary) school students did not progress to secondary school.
The 1980s was a time of industrialization. This is when the Curriculum and Development Institute was formed. One of the main accomplishments of the institute was the Primary Mathematics Project team, which developed Singapore's world famous Primary Mathematics curriculum. These quality materials which included textbooks, workbooks, teacher's guides and other helpful materials, helped teachers to teach more effectively using the concrete, pictorial, abstract approach. The model method for solving word problems was also developed.
The 1990s brought globalization. This is when Singapore began its "Thinking Schools, Learning Nation" initiative to promote critical thinking and problem solving in the schools. In 2001 a review of the math curriculum led to the creation of more time and space for "engaged learning," an attempt to make learning more meaningful, relevant and useful.
All of these efforts resulted in Singaporean students' rise to the top of the world in math and science. Up until this time, the Ministry of Education controlled the textbook business and the only textbook in use was Primary Mathematics. In 2001, Ministry of Education opened up the textbook market to commercial textbook publishers. 2007 brought the "Teach Less, Learn More" initiative with the goal of providing more innovative teaching methods.
Formal mathematics education in Singapore begins in 1st grade where math is students "main diet" and teachers try to make it tasty "like McDonalds, so children want to eat it." Mathematics courses are compulsory for 10 years in grades 1-10. The math curriculum is centrally planned in order to provide guidance to teachers, but flexibly implemented at the school level because schools and teachers know their students best. This allows teachers to customize their teaching to meet the needs of all learners.
At the junior college level (grades 11-12) math is not compulsory but over 90% of students take math anyway. This is a testimony to the fact that children like math and are confident in it. By contrast, only a minority of students take non-compulsory mathematics classes in the U.S.
The Singapore mathematics framework is both the "compass and lens" of the math program and gives both direction and a means to reflect on and modify mathematics instruction. The framework is described by the now familiar pentagon illustration below.
Although the pentagon was introduced in the 80s, it is still relevant and in use. By looking at the pentagon you can see that the focus in Singapore math is on developing problem solving abilities, including applications to real life and other fields. It is dependent on five interrelated components - concepts and skills (which are foundational), proficiency in processes, metacognition (monitoring one's own thinking), and students' attitudes toward math, which addresses the affective domain.
The Ministry of Education (MOE) works with publishers and the NIE to train teachers. When changes are made to the math curriculum every six years they are careful not to throw out the previous curriculum but review it, build on it and make small changes. This allows the MOE to stay relevant and responsive to changes based on trends in math education. When changes are made, feedback from schools and teachers are taken into account. This consultation allows communication and creates buy-in from teachers.
When developing textbooks, the main considerations are content and approach. The content must be age appropriate, relevant and meaningful. This means that at the elementary level math should not be not too abstract, and it should relate to childrens' daily experiences. Also, coherence important and design teams work together to develop a 12-year syllabus that is carefully sequenced so that both teachers and students can see the connections across grades.
Another important characteristic of Singapore math is a spiral approach that revisits and develops topics, and ensures coherence. This spiral approach is different than most U.S. textbooks that simply review the same topic again and again each year. (In Singapore math textbooks, topics are not repeated but reviewed in the context of higher-level topics. When children learn addition of fractions with unlike denominators, for example, there is an automatic review of addition with like denominators. A whole chapter on this is not necessary therefore as often happens in U.S. textbooks.) The pedagogical approach or methodology of Singapore math is called the CPA Approach. CPA stands for concrete, pictorial, abstract, which means that lessons begin with hands-on activities followed by pictorial representations that help children make create meaning of abstract concepts.
The new curriculum and the ability of commercial textbook companies to develop alternative textbooks allows for variety. However, the textbook authorization process is extremely rigorous in order to ensure quality, affordability and variety. (In Singapore the MOE sets a cap on how much textbooks can cost. This is because parents buy the textbooks so they must be affordable. Singapore math textbooks cost a fraction of what typical hardcover American behemoth textbooks do. One result of this is that Singapore textbooks don't contain a lot of fluff or extraneous and useless information like U.S. textbooks do.) Currently six different titles from three different publishers have been approved for use in schools. The MOE also produces additional resources such as books on the model drawing method and other helpful resources.
Teachers play a key role in mathematics instruction and learning. Teachers must be well equipped to teach and are encouraged to "upgrade themselves." The MOE has a "communication plan" that provides workshops to inform teachers of changes, modifications, and adaptations in the curriculum. The MOE partners with the NIE to provide preservice and inservice training to teachers. Through these efforts, teachers are "entitled" to get 100 hours of quality professional training per year. Singapore has also created a national platform where teachers can share their professional knowledge with each other.
In Singapore, the journey to improving math instruction continues. Singapore has both "a lot to share and a lot to learn" from other countries. The process of continual review ensures rigorous and useful materials and resources. These materials are prerequisite to improving teaching, learning, and achievement. "In Singapore, we value our teachers because without them the curriculum does not get implemented." And programs are provided to fulfill teachers' needs and build their capacity.
Global Perspectives on Singapore Math
by Dr. Marito Garcia, Economist, World Bank
Why teach math? Because math improves your earnings as well as the macroeconomic growth of the country. Dr. Garcia says he can prove that with data. The business section in the Strait Times reported today that economic growth in Singapore might surpass the 15% projected forecast. (By contrast, China's economic growth is 9-10% and in the Philippines, 8%.)
Dr. Garcia struggled in math as a student. In college he took economics, which required math and needed remedial lessons. (This was comforting for me to hear because I also majored in economics in college and struggled in math.) Nevertheless, Dr. Garcia has done a lot of work in education during his 15 years and the World Bank because the World Bank is the largest funder of education in the world, providing $2.5 billion of funding that governments borrow to improve their education systems per year.
The World Bank is also a knowledge base, spending billions of dollars on research on how to improve education worldwide. They gather information, transform data into knowledge, knowledge to advice, and advice into action. The World Bank's studies on the world's education systems found that Singapore is an "outlier," outperforming itself relative to income. Therefore the World Bank brings ministers and other representatives from many nations to Singapore to study their educational system.
In order to have an educated citizenry governments must provide access to education first. But World Bank's data show that the quality of education has a higher impact on economic growth than the number of years of education. There is no relationship between economic growth and the number of years of education. There is a direct relationship, however, between economic growth of a nation and growth in mathematics test scores according to the TIMSS data. And Singapore is way on top!
So why teach math? The reason we want students to improve their mathematical abilities is because the data show a direct connection between improvement on math scores and economic growth. World Bank data shows that for every one standard deviation increase in math scores there is an increase of 12% in income. Economic growth depends on quality of education, not the number of years of education and these returns are even higher in developing nations. A recent study realized in the U.S. and Chile found this relationship was even higher in Chile than in the U.S., so developing countries have even more to gain by educating their populace mathematically.
has a higher impact
on economic growth than the number of years of education."
Singapore is a shining example of this phenomenon. When we look at the data we see that Singapore is an outlier or "positive deviant." We see this trend also in other East Asian countries such as Korea, Taiwan, China, Malaysia, and Thailand. There has been an economic miracle in Asia over last 25 years. This was facilitated by effective mathematics education. Better math scores equal higher economic growth.
If we ignore the quality aspects of education we are underestimating importance of education. In economic growth, quality trumps quantity so we need to not only improve the number of hours kids are in school but the quality of their education. According to a 2007 study by Hanushek and Woessma, educational quality plus good institutional environment equals higher economic growth.
Singapore will spend $8 billion in education this year for 725,000 students, which is about $11,000 per student. Kenya by contrast spends $153 per year per child. The U.S. spends about $16,000 per child. (This made me think that we're not getting much of a return on our investment.) Dr. Garcia says that he puts his money where his mouth is by asking his clients in African countries to visit Singapore and create links with centers for excellence in Singapore. The government of Nigeria, for example, receives funding from the World Bank to develop links with Singaporean educational institutions and learn Singapore math methodologies.
Some thoughts about the talks . . .
After hearing all of these presentations, I am more impressed than ever with what Singapore has achieved in mathematics education. Singapore's economic growth can be directly tied to its success in mathematics. During one of the breaks, I had a personal conversation with "Prof Gopi" in which he told me that standing back and watching the rest of the world improve in math education is not an option for the U.S. While politicians in our country spend their time in partisan bickering and nothing gets done, other nations like Vietnam, Thailand, and Malaysia are not standing around and waiting for us to get it together. It's time that we take a serious look at what high-scoring nations like Singapore are doing, from the excellent education they provide their students to the way they train their teachers, and make the investments and changes needed to ensure that all of our citizens become proficient in mathematics and the future economic forecast is bright. The alternative is unthinkable.
3 September 2010
Link to Day 1 - Part 2 - "The Professional Lives of Teachers in Singapore"
Link to Day 2 - "The Teacher Model In Singapore: What Matters Most"
Link to Day 3 - "The Creativity & Critical Thinking Initiative"
Bill Jackson is Scarsdale NY Math Helping teacher and author of the exclusive series featured in The Daily Riff, "Singapore Math Demystified!", along with his "Travel Journal" series about teaching and learning in Japan.