Our Maths curriculum 4 – 10 years and beyond

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April 30, 2016

in Classical Education, curriculum, Early Learning, Kumon, Maths, Singapore Maths

After researching Maths curricula for a long time, I had settled on Singapore Maths for my children, enriched by Saxon Maths for additional practice and mastery. Having found excellent deals, I had prepared the following books to get started with my 4-5 year old:

  • Singapore Maths 1A, 1B, 2A, 2B (workbooks and word problems)
  • Saxon Maths 5/4 (once we have worked our way through 1B)
  • Kumon Addition Grade 1, Addition Grade 2, Subtraction 1 (for additional practice, since I like the simplicity of the workbooks)

We are working on Singapore Maths mainly with a bit of extra practice via Kumon worksheets already, albeit half-heartedly, but recently I was inspired by many new opportunities that I had not been aware of previously. Discussed at length in the excellent Atlantic article The Math Revolution, I became aware of several inspiring online schools that will likely give kids a far better edge in higher Maths, once the basics are in place via the programs we already use.

When outsiders think of Math, they often think of basic mental maths and operations, which are of course the first steps in Maths, but this has very little to do with the Maths that is tackled in Maths Olympiads or inside Maths departments at university. In the past, kids were largely dependent on inspiring teachers or scientist parents to learn about the higher realms of problem solving, but of course not everybody is that lucky. I remember when I was about 12 our Maths teacher handed the Maths Olympiad problems to some of us (the most gifted students in class) in case we were interested in participating, but he did so with no further instructions, just saying have a look and if you can solve them, you can send in your solutions. I had a look at them at home briefly, but having had no training whatsoever and having no-one to turn to, I quickly realised I had no idea how to go about solving them and decided not to pursue it. This happened to all the other “gifted” kids as well, bar one. One boy did participate in the Olympiad and got into the regional finals, though he did not get further (his younger brother however go into the national Olympiad team competing at the IMO). Once we were chatting about the Olympiad and I confessed to him that having looked at the questions, I had no idea how to solve them and never participated. And he told me matter of factly that his dad was a computer scientist and had always gone through all the practice problems with him in the past to familiarise him with ways of how to solve these types of questions and that was the only way he had learned how to solve them. That was a light bulb moment for me. I realised that he was simply lucky to have a dad who could teach him the tricks of the trade. And in the past, it was down to luck.

It is only now that I realise how deficient my Maths education has been (had I gone on to study Maths at university, as my high school teachers recommended, I would have probably found out in a painful way). I went to what I thought was an excellent school (a school offering free classical education, teaching us Latin, Ancient Greek, Maths, the three Sciences separately, we had Saturday school, many pupils competing in Olympiads etc.) and still, I understand now I never learned real Maths. I have no idea about number theory and mathematical proofs. I was great at Mental Maths and plugging in formulas, I even did extremely well in statistics and calculus (so it is not that we didn’t do advanced Maths topics), but I was simply excellent at basic Maths, logic and applying formulae. We never actually learned to prove anything or derive rules. I learned that x-squared becomes 2x when you differentiate – but did I ever really understand why? No. I graduated with an A+ in Further Maths and looking at more advanced curricula or Maths books now I cannot say that I have learned anything that would be considered actual Maths!

But things have changed since I went to school, luckily. One very interesting new school that runs physical after-school programs and summer camps from 1st grade as well as online classes  from 4th grade is the Russian School of Math. It is a very demanding enrichment program focused on problem-solving and derivation of formulas instead of plugging in numbers into formulas without understanding them. They also introduce Algebra far earlier than is commonly done. We will definitely look at their online school from 4th grade. A similar school has recently opened in London, UK, and I believe there are a variety of Maths circles in France, too.

The Art of Problem Solving, founded amongst others by San Francisco Maths professor Paul Zeitz, aims to train students in Olympiad type problem solving and runs online courses from Pre-Algebra to college level Maths and Olympiad training. For the younger students, they publish Beast Academy text books from 2nd grade (to be published in 2017) to 5th grade (3rd to 5th grade books are already available). They cover the same topics typically covered in the respective age groups, but on a deeper level with more challenging problems to solve, creating an enrichment rather than an accelerated curriculum.

So our long term plan for Maths at the moment is to continue with Singapore 1A through to 2B (reinforced by Kumon and Saxon Math practice) for another 1-2 years, and then switching to Beast Academy text books. And then from around 4th grade, enrol in the ¬†Russian School of Math. Exciting times ahead. Unfortunately we struggle with consistency, which is why progress is slow for the moment. I am also a believer in mastery and don’t want to move ahead while my kids still make basic mistakes. Unfortunately, because my eldest is only 5.5 years old, she does sometimes get answers wrong or get confused about the easiest things (like number bonds to 10), even though other times she answers much more challenging questions. So she may chant “17” when I ask what’s “8+9” but then say 6+3 =8 or the like. So I keep working on the basics of addition and subtraction to 20 and won’t move on to the next topic, whereas others might already be moving on. But I feel there is not much point in discussing place value or working with higher number until she gets the very basics. I do subscribe to the mastery approach and also the Singapore Maths idea of moving slowly and working with numbers to 10 until children really get how they work and what they mean. Hopefully, once those basics are finally in place, we can move forward to the higher realms of Maths, which will be far more exciting!

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