Tuesday, 28 January 2014

Eye on the Ball, Please! Part 3


This is the third part of a series of my termly plans.  The first two parts are:
  1. Ball #1: Language Arts
  2. Ball #2: Mandarin

Ball #3: Mathematics - Addition and Area
The way that we have been learning mathematics here seems to be increasingly topic- or themed-based rather than curriculum-based, which suits us fine.  We started off following a maths curriculum, which worked very well, but was starting to get a little tedious for Tiger.  Once we started experimenting with learning-what-we-want-to-learn-when-we-want-to in maths, the approach feels a lot more logical and natural to us and is what we do now.

This term we are going to focus on two topics:
  1. addition
  2. area

What About Gaps?
It seems that many homeschoolers are uncomfortable with the idea of not following a curriculum in maths.  Usually their biggest concern is gaps in their children's maths skills or knowledge.  Following an established curriculum certainly gives some people -- notably adult and children who are naturally predisposed to a systematic, highly organised way of learning -- a sense of security that they have "covered everything" that a child of a certain age/level needs to know.

The way that I handle the question of gaps is very simple:  I make a mental note of it when I notice it, then I find an opportune time to introduce it.  The next question then is, what is an opportune time?  Well, my definition of an opportune time is:
  • when I have gathered the necessary teaching materials/resources; or
  • when the topic ties in with another area that we are studying, e.g. there are many cross-curricula opportunities to be created around the topic of geometry, symmetry, tessallations, Islamic art, etc; or
  • immediately - we are prepared to drop everything else if it is a matter of urgency to learn a certain topic.  So far, we haven't come across any situation that requires us to adress our mathematical deficiencies immediately.

My confidence in our approach comes from the realisation that:
  1. Time is on our side.  Tiger is only nine years old so he still has quite a few years to go before he has to worry about standardised tests or entrance exams.  I might start panicking if we were still on the topic of addition when he is 19 years old.
  2. Tiger is capable of buckling down to do the work when it becomes necessary.

Once I got over my initial fear of gaps (yes, I experienced much doubts and fears in the early days as well), I have come to view the learning of mathematics to be more than the acquisition of multiple sets of facts, short-cuts, and formulae.  It is a language of its own.  As soon as I realised that mathematics is a language, I decided that, as with any language-learning, establishing a strong foundation is very important.  Just as a strong language user needs to have a contextual base to understanding and mastering the subtlties of any language, a strong maths user needs to have be able to apply mathematical skills and knowledge for them to become meaningful.  Merely memorising mathematical formulae without the experience of applying them to solve real problems (as opposed to clinically designed textbook problems) is akin to memorising English idioms without knowing how to use them in the right context.

What About Practice and Mastery?
Having explained (I hope) above why I'm ok with Tiger's maths progress not following exactly in the same order or at the same pace as determined by any curriculum, you can see why I can tolerate us dwelling on any topic -- addition comes to mind immediately -- forever.  However, the time that we spend on any one topic is not used on repetitive drills or learning the same set of skills at the same level over and over.  An example is the latest addition game that we played.   Different maths skills were used at the same time to solve that set of problems -- addition, long multiplication, counting, number sense.  When we play maths games or riddles like the example that I have just referred to, both Tiger and I can easily and clearly determine whether he has any gaps in his knowledge (in which case we will work at closing those) or where his gaps are (so that we can direct our effort more effectively)

A tool that I find to be effective for practice is the Khan Academy's maths section.  I've mentioned before our sporadic use of the website whenever we feel Tiger needs to have more focused practice on any topic.  Most recently, we discovered a new feature on the website called Mastery Challenge, which is very similar to a series of short composite tests on various maths topics.  Tiger doesn't mind working on a few rounds of these each day.

To me, it works in the same way as what we have been doing at home to identify gaps and areas of improvement. For example, one of the recent challenges shows that Tiger needs more work on the long division (which we had touched upon briefly in November but not formally worked on yet).  With this information, Tiger watched the two-digit division video:

and worked through the example alongside the video, before attempting several rounds of two-digit divisions on the site.  Working on these exercises enables Tiger to solve a recent maths challenge, but it is not the way in which I would like him to learn long division (even though he certainly can do them mechanically now), so we will spend some time later in the year to learn division in a more visual, hands-on way.

I don't claim that our method of learning maths is superior to any other method, but it is one that suits Tiger's need for variety, applicability, and minimal repetition.


  1. Adding, subtracting, multiplication and division are the majority of what kids learn in elementary math education. If you cover these four basics and Tiger gains good number sense and learns to think mathematically, I think you are way beyond having any gaps. I love your approach and think that my son has been watching the same Khan Academy video.

    1. Thank you for your vote of confidence, Julie. :-) It took me a while to be fully comfortable with how we are doing maths. Every now and then we notice that Tiger needs to learn certain concepts to solve a puzzle/challenge, then that's when I think about gaps. :-) Other than that, we are quite comfortable with how things are working.

  2. You've articulated your maths philosophy very well, Hwee.

    I have a similar approach to "gaps" - we see them as fun opportunities to learn something new.

    I'm not nearly as comprehensive and organised as you are but I think, as you point out, that's a reflection of what works for the combination of personalities in our family. And I like knowing that in much of the time they're not doing maths, my kids are doing other things (often onlin) that develop their mathematical skills.

    1. Thank you for your encouragement, Lucinda. I'm not sure our day-to-day maths learning is quite as comprehensive and organised as it appears here, but I try not to be overly chaotic. :-)

      The main reason I write this series of posts is to help me focus on a few things that I'd like us to stay on track with, precisely because there are too many ideas swirling in my head that I am forcing myself to make good choices.

      I also think that maths is all around us, so it is very difficult to NOT be doing something that is related to maths in our normal, day-to-day living. :-)

  3. We have been doing a similar approach with L and it has been working so very well. But this year I tried her back on some formal maths, just to see how she did and she froze. Yet she had been answering mathematical questions and really understanding how numbers worked.
    Sigh, I wish I had the confidence to have the confidence in this approach (if you know what I mean?) It has worked so well for her, and she was starting to say maths was one of her favourite subjects (!), but I had her yawning yesterday, with the formality of text book learning. I'm definitely not fully comfortable yet, and I have to admit to feeling a sense of relief when C told me she'd prefer to do Saxon than living maths. L definitely suits living maths, but I don't want to fail her...

    1. I know what you mean, Claire. I suppose you can try to alternate between textbook-maths and living maths for L until both of you find a comfortable way forward that works for both of you. There's no hard and fast rule as to which way is better. It's often a matter of constantly adjusting and tweaking your approach until you are happy with it.

      However, from what you've written about L, it appears that she is actually very mathematical, but not in the schooly-maths way. Maybe you can try a 50-50 approach with her (50% formal maths, 50% living maths) first, then gradually adjust the balance once you're more confident of her ability.


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