Mathematics is often regarded as the most valued subject by parents and societies. Yet, one of the most common comments I hear from adults is how much they hated Maths at school. Often, when asked why, they start by saying they start by saying they weren’t very good at it. After beating themselves up about this a bit more, they eventually end up talking about a Maths teacher who, at some point, knocked their confidence and meant that they no longer understood what they were doing. This is a great shame as Maths has so much to offer as a subject, not so much in terms of the content but because of the way it develops problem solving skills. I’m also a firm believer that everyone can succeed and enjoy the subject, in their own way. There are a wide array of choices when it comes to Maths approaches and curricula, all with their strengths and weaknesses so let’s take a look at which could be right for your child.
Approaches to teaching and learning Maths
Maths teachers, tutors and schools employ a wide range of different approaches when teaching the subject.
The more traditional approach has been based on rote learning: the teacher stands at the board, explains a concept and the students copy that approach a large number of times until they are confident and ready to move on. This is largely the way I personally was taught and whilst it can have some value when it comes to last minute exam cramming, I never really understood why I was choosing a certain method or another. This meant I hit a ceiling earlier than I would have as I didn’t really understand what I was doing. It gave me a complete lack of versatility when it came to choosing methods or solving questions that I wasn’t familiar with.
Jo Boaler, one of the most distinguished advocates for modern Maths teacher, advocates for emphasizing problem solving and developing maths sense over exercises and drills which she states often leads to fear and anxiety. Developing students ability to solve a real life problem in numerous ways and using diverse methods can really enhance the development of the way numbers and mathematical concepts interact.
I’m a huge fan of the Singapore approach when it comes to teaching Maths. This approach was developed in the 1980s, following heavy research on global approaches to teaching the subject. It has resulted in Singapore frequently topping the benchmarks when it comes to mathematical proficiency. It is based on a few core concepts outlined below:
Mastery: there is a heavy focus on mastery, with students fully understanding a concept before moving on. I really like the idea of no student being left behind, with students being encouraged to support each other with solving problems using a wide variety of methods.
Conceptual, Pictorial, Abstract (CPA): in the Singapore Maths approach students start with solving problems using real life objects (concrete), they then try to represent this problem in diagrams and drawings (pictorial) before moving to solving the problem through calculations and equations (abstract). All the three methods are valid ways of solving problems and all students start with the conceptual.
Number bonds and bar modeling: number bonds allow students to form infinite connections between numbers and develop their number sense whilst bar modeling allows students to solve complex problems without the need for algebraic, abstract equations which often throw students.
In terms of assessment as well as approach, I’m a big fan of the International Baccalaureate’s Middle Years Programme. Whilst it can be over complicated at times, the programme has a nice balance between gaining core knowledge and investigation. There are four assessment criteria:
Knowing and understanding
Investigating patterns
Communicating: this is so useful for the development of mathematical notation and language
Applying mathematics in real-life contexts
Students are often presented with rich learning tasks and engage in group projects which are then assessed according to the criteria above without the relentless need for test after test.
Through teaching Maths for over 15 years, I’ve noticed a significant difference to the way students learn the subject. Some require more visual tasks, others require more auditory instructions whilst others require movement in the form of kinaesthetic activities. Adapting activities to suit the learning needs of each child makes such a difference when developing their confidence.
Other increasingly popular approaches include the flipped classroom, where students focus on learning and researching the core concepts at home, with the practice and application being carried out in the classroom. This allows students to go at their own pace and not lose confidence given by timed activities and a one size fits all approach to lessons.
Curricula choices
As well as approaches, there are a wealth of curricula to choose from at international schools. The following table outlines some of their key features, strengths and weaknesses:
Curricula | Features | Key strengths | Key challenges |
International Baccalaureate Middle Years Programme (MYP) | Based on developing evidence for 4 assessment criteria (knowing and understanding, investigating patterns, communicating, applying maths in real-life contexts). Two levels: standard and extended | -Balance between knowledge, investigation and problem solving -Emphasis on skills -School flexibility | - School implementation: complexity of programme means that quality of implementation and assessment can be patchy. -Confusing grading system -Big gap between MYP and DP (both approach and level) |
International Baccalaureate Diploma Programme (DP) | Two course with two levels at each to choose from (Higher Level HL and Standard Level SL): -Mathematics: analysis and approaches SL -Mathematics: analysis and approaches HL -Mathematics: applications and interpretation SL -Mathematics: applications and interpretation HL Mathematics analysis and approaches is much more focussed on theoretical maths with lots of algebra, calculus whilst applications and interpretation is much more applied with an emphasis on statistics and real life problem solving | -Every student studies maths as part of their Diploma. -Choice of courses -Focus on critical thinking and global awareness - Favoured amongst universities -Significant improvement in latest iteration of courses as more applied | -Some students will find even SL challenging -Very test based (80% of grade) -Whilst improved, still very knowledge focus with a huge list of course topics to cover so can be rushed for some students |
British A Levels | -Choice of AS level (1 year course) and A Levels (2 year course). -Schools choose an exam board with Cambridge A Levels being the most common at international schools Cambridge offers two qualifications within Maths: Pure Mathematics, Mechanics and Probability & Statistics Pure Mathematics and Probability & Statistics -Graded A* to E | -Papers split by mathematical area (eg Pure mathematics, Mechanics, statistics) -More depth and specialization | -Very exam based - Not all students choose to study Maths at 16-18 -Less balanced than IB programme -Very UK focussed |
British IGCSEs | International version of the GCSE qualifications, all 16 year olds take -Choice of providers: Cambridge and Pearson -Graded A* to G | -Rigorous programme -Huge range and choice of subjects -Reliable assessment -Often regarded as better preparation for IB DP or A Levels | -Too much focus on knowledge, more traditional -More examination based than IB -Still more UK based despite attempts to make more international |
American AP | Choice of 38 introductory college level courses. The exams are scored on a scale of 1 to 5 by college and university professors and experienced AP teachers | -Great preparation for university as courses college level -Count for college credits -More flexibility of course combination -Rigorous education | -Less breadth of education -More US focussed =>leans towards US university application -Very subject focussed -Not suitable for all students |
Whilst these are the most common, it is by no means an exhaustive list of curricula options at international schools. Other common national curricula adopted are: Australian, Canadian, Indian, Singapore, Chinese, French and German.
Maths tutoring
My approach to Maths tutoring blends different elements as well as strengths in the approaches to teaching the subject, to fit individual students. Some of my core practices are outlined below:
Forming strong, trusting relationships: getting to know the student beyond Maths really helps build a relationship of trust.
Mathematical confidence: going at a pace appropriate for the child is key. This is why some children really benefit from tutoring as it allows them to process and progress at a pace appropriate for them.
Deep understanding: the why behind Maths is so important, so students should be able to explain why a certain method works. Singapore Maths approach to Concept, Pictorial, Abstract is so helpful here.
The more methods the better: introducing challenges such as: how many ways can you solve this problem builds flexibility and depth of understanding.
Fun: through my career, I’ve always tried to embrace fun within the teaching of maths, be it through incorporating games or developing examples which relate to the student.
Failure: this appears a controversial one but I feel it is important to embrace failure and getting this wrong. Learning from these failures and moving on confidently can do wonders to children.
Use of technology: whilst the incorporation of technology as a whole has been mixed in terms of positive impact, I’m a firm believer that in Maths it has had a dramatically positive impact. The many great interactive tools which allow students to explore and experiment with mathematics have really brought school to life.
Conclusion
Given all these improvements in the teaching and curriculum development of Maths, I’m hopeful that future generations will look upon their experience of the subject in a more positive way. In the parties of the future, I’d love to meet young adults, see their eyes light up when I say I teach Maths and hear them cherish the subject, appreciating its challenges and the way it can enrich the mind. I’ll strive to do my part in helping that happen!
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