“5-Year-Olds Can Do Calculus” by Maria Droujkova -collecting comments

What if we figured out ways for young kids to play with ideas from calculus, algebra, and other mathematical subjects beyond arithmetic? Last week, The Atlantic published Dr. Maria Droujkova’s interview, “5-Year-Olds Can Do Calculus” by Luba Vangelova. It started a broad international discussion, with follow-up interviews by Canada’s “Globe and Mail” and UK’s “The Times,” and translations into Japanese and Russian by news agencies. Droujkova and her colleagues at Natural Math are aggregating major themes from the comments:
  • How can we create and sustain environments where kids are free to learn, and adults are free to help them?
  • Can young children understand abstractions? Can they deal with the formal language of mathematics? If they can, will it hurt their development in some way?
  • Many grown-ups believe that young math will finally give them a second chance at making sense of algebra and calculus.
  • But what about calculating and memorizing? We need more research on balancing concepts and technical skills.
  • What can young kids actually do with algebra or calculus? How can they play with these ideas, or apply them to their daily lives?
  • Many people recognized our activities as similar to what they are doing with their kids – or what their parents did with them. What difference does this casual, everyday early math make for kids whose parents understand and love mathematics?
Some discussion and follow-up links:

An email to Elizabeth Truss MP (waiting for a reply)

Dear Ms Truss,

I am a Secondary Mathematics Specialist Leader of Education and was lucky enough to be amongst the group of teachers who travelled to Shanghai this January. I am very pleased to hear that you made it to Shanghai this week to see for your self how teachers and pupils work.

I am disappointed that several crucial facts seem to have been overlooked in the reports I have read about your visit so far.

Firstly, I agree that there are lessons to be learnt from the Shanghai model of education. I was thoroughly impressed by the professionalism and commitment of both pupils and teachers when I visited China (although I saw no teaching in Shanghai itself).

Teachers collaborate to produce lessons and worksheets of an extremely high quality. They carefully chose the best questions that contain a new idea or adaptation to a demonstrated problem. The worksheets quickly move students through a series of challenges and this “imitation” was mentioned a number of times as a reason behind pupils success. I also saw examples of multiple choice homework sheets where every question was a hinge question (as defined by Dylan Wiliam). This climate of not asking questions for the sake of it, to fill time or to simple practice things again and again was refreshing. I noticed that lessons were always pitched at the highest level. Hence ‘extension’ activities were very rarely (if ever) needed. Instead pupils who didn’t understand had to seek help outside of normal lesson time (for which they had the self-motivation).

This teacher collaboration and teaching to the top, rather than the middle, is something I am developing following the visit.

However, I hope whilst observing these kinds of ideas that you have also taken careful note of the lesson commitments of maths teachers in Shanghai. It’s all very well saying that we need to adopt ideas from Shanghai but I very strongly believe that the fundamental reason behind their success is the huge amount of time they have to plan, prepare and reflect. Every teacher we spoke to taught no more than two lessons a day (many had those two lessons with the same class). Teachers plan lessons together, reflect on their pupils learning together and are able to give same day feedback to pupils. Every single maths teacher was a subject specialist from primary through. ‘Weak’ teachers don’t seem to exist due to this careful joint planning, reflection and support. As a previous AST, head of department and assistant head, current SLE and as someone who runs workshops (KS2 – KS5) for teachers around the country the biggest barrier to teachers working in a similar way is there are simply not enough hours in the day and not enough teachers to teach the classes (even if we made classes larger).

There are cultural differences that mean many Chinese students have different attitudes towards maths and family support that many students I teach do not. However, I strongly feel that if we collaborated more, developed suitable resources (not necessarily along the Shanghai designs) to suit our students, understanding and results would improve. Through this collaboration we would be able to support those teachers not comfortable with their mathematics and meet the needs of our pupils.

I realise that this doesn’t fit a nice easy (and cheap) way to solve the issue of problems in maths education that you are searching for but it would be the right thing to improve results and mathematical understanding. It’s also not a short term commitment.

I have worked with poor teachers and teachers who do not have commitment to the pupils they teach. However the very large majority of teachers I have ever worked with have wanted the very best for their pupils, have tried to teach to the best of their ability and tried to produce stimulating and challenging resources. Sadly a large number of these have also suffered with stress, depression and anxiety. Many have also left the profession as it was simply too much. I myself have had moments where I have doubted my ability, considered a different career but I cannot imagine ever not being a teacher.

shanghai night

I would be keen to discuss this with you further, if you have an interest.