A few thoughts on Math education + Resources

TL;DR

Audience : parents of children aged 6 through 13.

First half: thoughts on priorities, and worldviews that affect Math education.

Second half: Physical (books) and Digital resources that may be of interest to parents.

Are you a Math person?

Are you a “math person” or are you “so not a Math person”?

I think its worth reflecting on this question because even the way it is framed impacts Math education, and how parents and teachers sink into an either-or. This binary way of thinking originated in the West, and is actually unnatural to the Asiatic mind. But given the cultural power of language, sit-coms and pop-culture, it has now seeped deep into the modern mind. That’s unfortunate, because it runs counter to what neuro-science has been telling us for the past 20 years or so. The myth that some people simply don’t have the aptitude for certain subjects is scientifically inaccurate and negatively impacts education and everyday life.

I think most children are perfectly capable of fine mathematical reasoning. They just need the right environment at home and at school.

But is Math even important? Maybe not?

Another interesting phenomenon I’ve observed is that many highly educated Indian parents – themselves having excelled in STEM fields in the conventional but not-altogether-bad Indian schooling systems are quite laissez-faire about their kids’ math education. The idea of not putting any pressure has become, in practice – a complete hands-off version of “its ok if s/he wants to photograph flowers when he grows up”.

Onward march of said student (courtesy: AI)

Great, but to invert – is it a bad idea to want to inculcate and even, ensure – that a child has a rounded education?

A broad liberal-arts education includes a reasonable grounding in the sciences – and mathematics is the first of the sciences, the very kernel. I feel parents ought to lookout for their children’s educational and learning outcomes in a holistic sense, and that should perhaps include developing good mathematical reasoning.

The risk of declining interest

If the child’s interest wanes – at any age, it is almost always due to some combination of the class environment and the teacher. We parents have to at least observe declines in interest – and remedy these at the very earliest. If left unchecked, these declines soon allow you to discover a child who will identify with the sitcom-dialogue version of “I’m not a math person” – and parrot that ad-infinitum to parents who’ve already embraced lily-photography or some such endeavor as a viable life pursuit.

At its root, I genuinely believe all children can develop a strong number sense, do elementary arithmetic in their minds, and develop an aesthetic for beauty in Math.

All that’s required is that throughout their school experience they are consistently nurtured by teachers who work with them with love, patience and encourage a growth mindset^[1]Boaler’s book Limitless Mind distills decades of reflection and wisdom on this. Beliefs and mindsets need to be nurtured early on in any home / school setting.*.

I realize the near-impossibility of the condition I just mentioned. Good teachers are a rare breed; good teachers of Math even rarer. Which is why, to some extent, the responsibility of consistently nurturing beliefs and mindsets actually rests on parents. (oops?)

While we parents cannot, generally assume the role of a Math teacher, I do feel that is helpful for us to appreciate directionally, at least – what might help our children over their school-going years.

Lockhart’s essay

I think a key first reading for parents in regards to their children’s math education is Paul Lockhart’s essay A Mathematician’s Lament. At least the first two or three pages.

Who is Lockhart? In a single sentence – he is a reclusive, gifted, self-taught mathematics teacher and scholar. This essay he wrote in 2003 was a poignant critique on the dismal status of Math education in America at the time. The essay was widely circulated in mathematical circles and touched a deep chord with educators worldwide. In the words of Keith Devlin**,

“In my view, this book, like the original essay it came from, should be obligatory reading for anyone going into mathematics education, for every parent of a school-aged child,,. You should read what he says and reflect on his words. This [book] is already a recognized landmark in the world of mathematics education that cannot and should not be ignored.”

Here’s a link to the essay (25 pages, maybe worth printing), and here’s a short review of Lockhart’s book.

In 2014, Lockhart went on to publish the book “Measurement” – an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work. His most recent work is “Arithmetic“. If you appreciate thinking from first-principles, these are excellent works. Both these books are for interested parents, or potentially for students aged 12 or older.

Where we are today

The world is a work-in-progress. It appears that we don’t yet have the resources for our children that meet Lockhart’s aspirations for beauty, elegance, simplicity, and aesthetic in what he suggests is the “Art” of Mathematics. But we’re getting there.

However, all of my research (and by no means, exhaustive) for these characteristics have led me to Vedic Math – which glows with these traits silently. I feel like I missed out on its aesthetic, its sense of wonder and joy as it was just completely outside the scope of our clinical curriculum. When I was younger, I spent considerable time learning the Trachentenberg system of speed math – and enjoyed it. But I now see this system – and the Abacus system – as beautiful, but tiny ponds when contrasted with the infinite blue ocean that is Vedic math.

Vedic math in India has been largely hijacked for its most crude utilitarian ends – scoring well on competitive exams. I’ve really struggled to find good books for children. There’s a gurukul based in south India (the Anaadi foundation) that is attempting to create a dharma-based curriculum from the ground-up – they’ve now come out with a beautiful set of books on Bharatiya Ganita & Integrated Indian Scisences. They’re beautifully typeset, engagingly written and surprisingly inexpensive. The books that they’ve released so far (as of 2023) are for children aged 8-11.

There’s also Kenneth Williams, a British-origin teacher & SME on Vedic Math who has written several good books. The most suitable ones are the The Cosmic Calculator series. One challenge I’m seeing with these is that they may not be books that kids will likely pickup and want to work with on their own. This is a key criterion for me – is the material so good that it can sustain a child’s interest on his own?

This leads me to what I currently feel are the best set of resources for kids aged 6 through 13.

While I think these resources are amazing, I don’t view them as tools to help a child succeed in competitive exams. The end, if any – is simply the pursuit of beauty. Mathematical reasoning is far more valuable than the ability to score in exams (though that too has its value).

Are there actually resources that encourage children to reason well and imagine widely? Yes. I try and cover them below, and I’ll update this page over time.

Superb Resources for children aged 6 to 13

Books by Beast Academy.

In the US, there is now a well-known organization called The Art of Problem Solving – they started out creating innovative new math curricula facilitating the thoughtful reflection for students already gifted in Math, but then realized over time that they were doing things so differently – that they were actually doing wonders for a much wider range of student capacities.

AoPS teachers were actually encouraging creative student work in Math, and they continue to build on their learnings and programs all the time – see the AoPS academies, for instance. A few years ago, they decided to put their best efforts into strengthening the foundations for younger children. Hence the books under the Beast Academy brand. These books don’t break Math into neat silos, they’re written engagingly – for kids, they have math stories interwoven throughout and are just fun to work with. In several contexts, they approach ideas in ways that are clearly taken from Vedic Math, but executed with great simplicity. We’re doing these books ‘in parallel’ with whatever’s being done in school – on a ‘whenever possible’ basis, no fixed timelines. Once she sits down with the current book, she’s on auto-pilot – no higher recommendation to another parent is required than this 🙂

Only downside – they’re only available in the US. Look them up – the publishers have put up the ToC for each, excerpts from different sections etc.

[June 2024 update: I was positively elated to discover that Dan Meyer uses the Beast Academy books for his own kids – see this. Dan is one of the most thoughtful math-educators in the world today & has a wide following in the education community. Find him on X here. I’m also a subscriber to his substack.]

Online platforms – Struggly, Tutor

There are now dozens of Math platforms for students of all ages, and I probably haven’t tried most as they mean more screentime, which I generally like to keep to a bare minimum.

However, by happenstance, one of the founders of Struggly (co-founded by Jo Boaler @ Stanford, head of Math education, author of Limitless Mind & several books) reached out to me cold under the BlueLotus.vc umbrella, so I ended up trying that platform out with my daughter. She absolutely loved it, and this is now a staple ‘fun’ activity at home (for her), whenever time permits.

See “How it Works” on their homepage. We have an annual subscription and find it worthwhile.

Another recent experiment is Synthesis‘ Tutor.

This is a new math platform being offered by the startup that took off from Elon Musk’s Astra Nova school. Still early days here, but very promising work. The word Tutor here is key; a good tutor gets the syllabus done, a great tutor can open up unimagined latent possibilities. That is one of the takeaways from one of the most interesting essays I read in 2023 by Erik Hoel and it was titled ‘Why we stopped making Einsteins’, with the subtitle ‘Aristocratic tutoring I: Explaining the decline of genius‘ [This essay generated 240+ comments & was followed up by a part II & III – also riveting reads]. Now, I don’t believe anyone should be in the business of making Einsteins (every child has a soul & unique purpose in the world etc), but Hoel’s essay makes persuasive arguments on how some of the most incredible minds of the past century or two have been tutored – personally – often by someone really good. Given that it is next to impossible to actually find a great good human tutor to spend time with our kids when there is a window of opportunity, I thought it may be worthwhile to try out platform.

Synthesis’ Tutor manifests as a conversational AI speaking with your child as s/he grasps new ideas and challenges. It is taking a completely different path from Struggly, but it has done some ground-breaking work that I find worthwhile.

Two Key ideas for parents of children aged 6 to 13

I’d like to end with just a couple of suggestions. There are two key ideas which I believe have a very high RoI. A bit of effort put in early lasts literally – a lifetime. There’s no rewind button once these are put in place.

  1. Number sense & love for numbers is foundational.

Encourage this, nurture this – whenever you can.

All tributaries and branches of math rest on a foundation of solid number sense. If you observe how students ascend the curve of knowledge in Vedic math (study how they build on ideas), you will see that there is a strong emphasis on developing familiarity with numbers, and being able to play with them. If a student does develop a strong number sense, learning advanced ideas later comes without much effort; and to invert – without this number sense – everything can become a struggle until the eventual sign-out of ‘I am not a math person’.

 2. The Tables must be learned – till 10×10.

A great chunk of the comfort and confidence which students develop and build on, in their early years stem from simple things – like knowing their tables ‘by-heart’. There is no sin in committing these to memory, and while schools may or may not care for this, in the Indian tradition of mathematics at least – it is common-sensical to ‘just know’ the tables – thoroughly. By ‘just know’ I mean – to be able to recall instantly – from memory, without pauses or stuttering. It is worthwhile to practice this with our children.