To the extent that learning maths is more about sharpening the logical thinking, there must be more preferred ways to structure the methods and milestones in the achievement of the learning goals in math. The evidence on the ground – the poor performance of children in maths, across the world – also dictates that there must be some fundamental missteps in the teaching of maths. We may be teaching maths in ways which need to significantly change – the current ways of teaching maths is not the best.

We, the authors, have been specifically working on improving the teaching and learning of maths for over five years through several discreet and ‘whole school’ innovations. Sandeep, one of the authors, also developed unconventional ways of teaching maths to his ‘home educated’ daughter, who is fairly ‘comfortable with the language of maths’ and appeared in Class X International Maths examination of IGCSE as a private student.

Here are the more important suggestions to reinvent the teaching and learning of maths, as distilled over the past half a decade:

- Physical (and digital) objects till Class IV – All of maths must be seen, felt and be easily manipulated; the objects used in maths education must be part of everyday living and easily accessible for repeated usage and extension into new situations.
- Methods to be avoided till Class IV – All of maths should be the ‘long way’, e.g. addition without carry over; patterns must be apparent, numbers and operations must be visually possible.
- Mental maths till Class IV – Children must be inculcated into thinking mathematically and to make it work, only up to two or three digit numbers may be used. Occasional worksheets may be used for holidays or weekends. Assessments should also be largely verbal.
- Homework content till Class IV – Maths homework may be mental maths, i.e. no written work at home except occasional worksheets. Reading ‘mathematical stories’ and writing mathematical solutions in mother tongue (or English) should be the major part of homework.
- Class V to be the bridge between mental and ‘method’ maths – Methods must be introduced as a matter of discovery out of the mental maths logic and not pronounced as given. Class V and VI are indeed the crucial years in learning maths.
- Homework, practice and class work – Homework for continued familiarisation is vital in maths; maths is not a socially important communicative language and needs distinct opportunities for practice and revision. It must be natural to expect wrong solutions in maths homework and homework should not involve tasks that may call for tutoring help. Classwork should involve exercises normally meant for homework to enable maths teachers to observe each students’ work, every day.
- Remedial in plain English – Remedial practice may be conducted in plain English, i.e. the solutions to the questions must be written in English words rather than mathematical signs; it works wonders in getting the thinking aligned.
- Reading mathematical books – There are a growing number of maths books without much of signs and formula. Ideally, the maths textbooks should be ‘readable’ like science books, i.e. with lots of text in communicative level language.
- Conversations and stories in every period – The language content in maths classrooms has to significantly multiply. Math must be made to be discovered everywhere the way science is to be ‘seen’ in every day routine.
- Teaching, assessment, reporting, remedial and self-learning of maths to be around well delineated concepts. Maths is a rigidly hierarchal subject and it must be taught in a way that hierarchy is respected

in teaching and learning by anchoring them around individual concepts. - Class-less syllabus access – Students must be allowed and encouraged to dig deeper in domains/concept families of interest beyond their actual class syllabus. Math and science are ‘logical subjects’ and cannot be sliced into rigid class-wise compartments.

It may be obvious that the 11-point agenda of change reads almost like the re-birth of maths education.