In the last episode I wrote about how the home school approach we have taken allows us to draw upon the best curricula from around the world. It’s a system that ensures we are ‘certified’ by the Australian educational system, but not limited by it. It’s a bit sad that we have to compensate for the educational system here, but the reality is that the performance of Australian schools has become horrifying. By the time Australian kids hit fifteen, their literacy skills are a full year behind their Singaporean peers.

For the remaining parts of the crash course I’m going to dig into the resources we use to backfill our daughter’s education. This edition focuses on Mathematics.

Kumon (Japan)

I have written a little about Kumon before. The short version is that Kumon excels at forming ritualized daily habits around focusing your child’s attention. But Kumon doesn’t cover all the elements of a modern maths curriculum, such as geometry, measurement, statistics or any of that good stuff. When we combined it with the resources below, we got a lot of value out of Kumon – mostly from the conversations we had around coaxing our daughter into completing a booklet each day. It established solid study habits, and it’s not just the general idea of small units of daily practice – I like how the Kumon marking system helps students correct and learn from their mistakes. It’s not cheap though; Kumon costs $1680 per year (with a $100 signup fee), but along with all the material it also includes weekly access a tutor.

New Syllabus Primary Mathematics Textbooks (Singapore)

I never imagined I would get excited by mathematics textbooks, but the New Syllabus Primary Mathematics series from Shinglee is brilliant. They have put lots of research and design into creating a text that helps young children teach themselves mathematics. Using a combination of clear diagrams and simple text, they carefully introduce mathematical notation and concepts.

Shinglee have executed a spiral curriculum perfectly. Earlier concepts are revisited with increasing complexity throughout the series, each reinforcing previous experience and leading the students onto more advanced techniques.

The series is split into two types of books: each lesson starts in the textbook, where students follow along as concepts are described and shown. A complete first example is shown and then a second example is presented with the same pattern as the first but only partially complete – students are required to fill in blanks and complete the second example themselves. Often the textbook will have practice questions, which is usually where I check-in to see if my daughter has got the hang of things. Then it is onto the matching workbook lesson, where students practice the newly introduced concept with some exercises.

At the end of a section, they have something called a ‘Mind Workout’. These are great little problems that require the creative application of skills they have picked up so far. While the exercises in the workbook are designed to develop core skills and can be clearly matched back to the textbook, ‘Mind Workouts’ shake it up completely. They stretch the student into applying these core skills in novel ways to solve interesting problems.

Picture of pages from the year 3 shinglee New Syllabus Primary Mathematics textbooks

At the outset, I spent a fair bit of time teaching our daughter to use the books, how to follow along the descriptions and examples in the textbook and how that information can be used to find solutions to problems in the workbook. But we are now at a stage where it perfectly matches our guided learning philosophy. Most of the time our daughter can follow along a lesson on her own. Every once in a while she hits a difficult patch and needs some extra help. But most of the time she plods along at her own pace. It costs about $215 to get a year level’s worth of the New Syllabus Primary Mathematics textbooks.

IXL (America)

We largely have a preference for analogue teaching resources and all that excellent tangible stuff. IXL is one of the first digital systems we have been very selectively adding to the mix. It’s an adaptive learning system that is constantly monitoring progress and generating just the right exercises to help your child develop their skillset. This means our daughter gets just the right number of problems she needs to master a new skill before moving onto the next. IXL also includes examples that help students do the self-directed thing and does a pretty great job at identifying and explaining where a student makes any mistakes. It all makes for a great tool that we can use for targeted practice in areas where our daughter might be struggling.

IXL also has an excellent internal map of adjacent skills, a bit like pre-requisites that will help children develop the underlying skills to address problem spots. This makes it a great tool for a more freeform exploration of Mathematics. Our daughter will often dive deep into activities and areas she finds fascinating.

IXL costs $155.40 for a year’s subscription and they have done an excellent job aligning it with the Australian curriculum and localising it so that things like money problems are shown in Australian currency.


We interleave short sessions of each system throughout the day. For example, our daughter starts her day with Kumon, does something different, circles round to the Shinglee texts, works on other things and eventually comes back to IXL. There is eventually overlap, but the content is presented in very different ways and on any one day she is getting a ton of variety. She might be working on two-digit multiplication in Kumon, solving word problems with division in Shinglee and doing time-related exercises in IXL.

Only as I was writing this article did I realise how much we were spending on maths resources. I guess it is a topic that our family values, and to butcher the words of Galileo, ‘Mathematics is the language of the universe’. But if we were on a tighter budget and looking for supplemental mathematics material, I would just sign up for IXL. It doesn’t explain things quite as well as the Shinglee texts, but if you had the time to put in the extra legwork you could transplant the Kumon philosophy into IXL. You could totally approximate the three systems at the cost for IXL alone.


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