Yesterday was the last session of the Maths Exploration after school class. We explored many mathematical concepts in a fun and hands-on way. We made 2D shapes by folding a simple A4 sheet, measured and represented data, flew paper planes, and made some beautiful string art! Have a look at our explorations on the blog.
2015 Principal’s Sabbatical Report “Singapore Mathematics”
By Wayne Bainbridge
Singapore Maths is used by the top four consistent math nations in the world, as measured by TIMSS (Trends in International Maths and Science Study) – Singapore, South Korea, Hong Kong and Japan. Since its development in the late eighties, and its revision in 1992, Singapore has surged to the top of the world maths achievement and also severely reduced its underachievement tail. It is used in a number of countries on a school by school basis and in the United States by private schools, charter schools and homeschoolers. In 2014, an Australian version was launched in Australia, titled Prime Maths and made available in New Zealand in 2015.
How does it differ?
- Concepts are introduced at an earlier age and covered in depth till mastery.
- Fewer topics are covered in greater depth.
- It is marketed as a complete package with a teacher’s book, course book and practice book.
- It is sequentially based on previous knowledge and mastery.
- Teacher’s professional learning is embedded within the teacher’s book and course book, plus the Bar Model Method “Mathematical Problem Solving”.
- Problem solving is central for teaching and learning.
- It is a ‘cook book’ package which provides a consistent pedagogy which covers topics in depth leading to mastery.
- The teacher’s guide includes comprehensive lesson plans with notes to support each page in the student books to show teachers how to effectively teach each lesson.
- The concrete materials for manipulative learning are as simple as paper clips and ice block sticks.
- Each chapter of the books has a review which provides summative assessment.
The New Zealand Scenario
The TIMSS Year 4 results between 1995 – 2011 show that while the results in Singapore, Hong Kong and South Korea all went up, Australia rose then plateaued, the New Zealand scores actually declined between 2003 and 2011.
Many New Zealand teachers became disillusioned by frequent changes to the Numeracy Project, rewriting of booklets and changes in testing. Many expressed the view that maths in New Zealand had been ‘dumbed down’. Mathematical concepts previously introduced in primary schools were delayed till intermediate or even secondary level, such as fractions, long multiplication, division and the use of algorithms.
Our approach has been described as a scattergun approach with the same topic spread out across different years, rather than being covered in depth to mastery. Scholastic, publishers of Prime Maths, believe Singapore introduces mathematical concepts from one to three years earlier than New Zealand and Australian schools.
New Zealand teachers feel unsupported in their maths learning and fall back on a variety of online resources which they need to search, download and incorporate into their planning which takes considerable time and effort. Because Singapore Maths is a complete package including professional knowledge, planning and summative review it is clearly advantageous. The publishers commissioned Lester Flockton to prepare a comparison between New Zealand curriculum objectives in relations to Prime (Singapore Maths) objectives to show how the latter fits into the New Zealand Maths Curriculum.
The Primary Mathematics Teaching and Learning Syllabus: Singapore Ministry of Education 2012 clearly outlines the philosophical underpinning of Singapore Maths.
Teaching is for learning; learning is for understanding; understanding is for reasoning and applying and, ultimately problem solving.
Teaching should build on students’ knowledge; take cognisance of students’ interests and experiences; and engage them in active and reflective learning.
The Singapore Ministry of Education firmly believes teachers need support to deliver the curriculum and this is built into the course books used. The two underlying principles are expanded upon.
Teaching Principle 1: Problem Solving
“The learning of mathematics should focus on understanding, not just recall of facts or reproduction of procedures. Understanding is necessary for deep learning and mastery. Only with understanding can students be able to reason mathematically and apply mathematics to solve a range of problems. After all, problem solving is the focus of the mathematics curriculum.”
“Mathematics is a hierarchical subject. Without understanding of pre-requisite knowledge, foundation will be weak and learning will be shallow. It is important for teachers to check on students’ understanding before introducing new concepts and skills.”
The teaching of problem solving is well illustrated by the following extract from Prime Course book 2 – after 3 years at school. Note the scaffolding:
Some factors which may contribute to the success of Singapore Maths in Singapore
- Children don’t start school until they are seven, so may be ‘more ready’ for formal learning.
- Teaching is a highly respected and well paid profession in Singapore.
- Teachers are entitled to 100 hours of low cost or no cost professional development each year (but not necessarily release based).
- All teachers are trained at the one site, the National institute of Education.
- Singapore has performance pay.
- Like many Asian countries, teachers and schools in Singapore are both highly respected and highly supported. With no social welfare systems, a parents ‘pension’ or post retirement living is somewhat dependent on the success of their child or children. Parents support their children’s education, after school tutoring is the norm, complaints are rare, any disciplinary issue is well supported by parents.
- There is an expectation that children will do well and parents make sacrifices to ensure their child’s success.
- Attendance at parent interviews is usually 100%.
- ICT to support learning is provided.
In such a positively supportive environment, with a well-trained, well respected and well paid teacher workforce, the ‘complete package’ provided by Singapore Maths is perhaps more likely to be successful then it might be in countries like New Zealand and Australia which don’t have the advantages of strong societal support and respect for teachers and schools. Teachers speak with respect and pride of the support they get from their Minister and their Ministry. The present Prime Minister Hsien Loong Lee was formerly Education Minister (note; Singapore is virtually a one party state with high conformity to societal norms. Dissent is not normal).
What does a Singapore Maths lesson look like?
It looks remarkably like a New Zealand classroom lesson although classroom decorum and teacher interaction are a little more formal. In junior levels, a lot of use is made of concrete materials – plastic beads, paper clips, ice block sticks etc. There is an emphasis on children working together and children learning from each other. No doubt, some teachers may be textbook bound but those I saw ‘roved’ as in New Zealand classrooms working with individual groups while the other groups collaborated and problem solved together. Incidentally, class sizes are larger than in New Zealand with classes up to 40 students, the same size as I saw in Shanghai and Beijing.
Much is made about the reliance in Asian countries on textbooks. In the Singapore context, textbooks were used as an adjunct to the learning. The lesson started with a ‘Headworx’ type exercise of patterning, counting on, counting back and a reminder of yesterday’s lesson.
Three groups were operating but the teacher intends to move to four groups:
Group One worked on a follow up from yesterday’s lesson using the practice book.
Group Two worked on a game, then another follow up activity (but not book based).
Group Three worked with the teacher using the course book and were directed to tomorrow’s follow up activity from the practice book.
When I asked the teacher what was the most useful part of the approach and materials, she was a little perplexed because this was all she had known. However, when prompted she felt the consistent lay out of the books with a review section ‘Let’s Remember’ at the beginning of each
topic chapter; explicit learning intentions for each lesson; ‘Let’s Do’ which is a learning section done with the teacher followed by ‘Let’s Do’ practical application and then solving word problems. The consistency of each lesson based on the structure of the book have familiarity and confidence to the children. They could also use the language of instruction very well. The lesson was similar to a New Zealand style lesson and the textbook was used as part of the follow up range of activities.
Because of the haphazard nature of the New Zealand mathematics curriculum, the lack of coherent resources and in my opinion, poor pre-entry training leading to limited teacher mathematical knowledge, the structured ‘package’ approach provided by Singapore Maths with emphasis on in- built teacher knowledge, strongly suggest that this resource should be more closely evaluated by the New Zealand Ministry of Education, with a view to its introduction and implementation into New Zealand primary schools.
- Flockton, L. (n.d.). PRIME Mathematics and the New Zealand Curriculum. Retrieved from http://scholastic.co.nz/schools/teaching/pdfs/PRIME_Maths_in_the_NZ_context_Lester_Flockt on.pdf
- Lightfoot, L. (2009, July 2). Box clever: Singapore’s magic formulas for maths success. The Independent.
- PRIME Mathematics : Teacher Guide, Course Book, Practice Book. (2014). Singapore: Scholastic.
- Yoong Wong, K., & Hoe Lee, N. (2009). Singapore education and mathematics curriculum. Mathematics Education, The Singapore Journey world Scientific Publishing.
- Yueh Mei, L., & Vei Li, S. (2014) Mathematical Problem Solving – The Bar Model Method: A Professional Learning Workbook on the Key Problem Solving Strategy Used by Global Top Performer (Prime Professional Learning). Singapore: Scholastic.
“A report to be launched by the Minister of Education today criticises the way pupils are taught maths and calls on parents to demand a return to basics.
The paper, written by a researcher for the New Zealand Initiative (NZI) business group, criticises a $70 million Government maths project for failing to improve results and says teachers’ maths abilities are letting children down.
“Too many children are not learning the basics off by heart at school. And, paradoxically, this is what is holding them back from developing a more complex understanding of maths,” the report said.
Its release follows several recent local and international studies, including a Herald investigation from 2013, that found New Zealand children’s maths abilities are on a downward slide. The latest, released by the Ministry of Education on Friday, said scores drop dramatically between ages 8 to 12, with too many of the older children failing to grasp fundamentals such as fractions and decimals.”
Today Room 9 celebrated Pi Day, an annual celebration commemorating the mathematical constant π (pi). Pi Day is observed on March 14 (or 3/14 in month/day date format), since 3, 1 and 4 are the three most significant digits of π in the decimal form.
We read the story “Sir Cumference and the Dragon of Pi” and after that did our own investigations with various sized circles to see if we could get Pi. At the end of this we learnt the formula to work out pi equals the circumference divided by the diameter of the circle.
We made a paper chain that represented Pi and completed number searches related to Pi.. We also designed our own Pi T Shirts.
We ended the day with a competition to see who could remember Pi to the greatest decimal place. The winner was Walt! What an awesome effort!