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Maths Musings...

I find that our homeschool days tend to ebb and flow. Sometimes we are right into our English - novels and literature and writing. Sometimes we are totally loving our Science - physics and ecology and biology.

We are at the moment heavily into our maths. And our art. Maybe the two are linked somehow? Anyhoo, the kids are loving working their way through Khan Academy practice questions. The thing that amazes me about this, is that they often voluntarily (you know, by themselves with no pushing from me) log on and go "exploring".

For my kids, Wombat Girl in particular, but also for Video Boy, maths at school was excruitiating slow. At home, we can move at our own pace, revising where necessary. I generally set a few questions from each topic and we move along a fair bit faster than their age peers at school would be. We don't have to do "concrete" maths, with counters or manipulatives, because my kids are pretty good at abstract concepts.

But that's not really the great beauty of homeschooling maths. The real beauty of maths at home is that we can learn how to think mathematically. We have the time to appreciate and explore all the wonders of maths - the patterns and the links between things. The things that make maths important and real. Not just arithmetic or pronumerals or getting the answers right in the back of the textbook.

Because I taught maths at high school, I have had a couple of homeschoolers ask me recently about how to approach maths. Their kids were bored by having to do every question in their workbooks of their "year level". Their kids are starting to hate maths. And they wanted to know how to break that cycle. My advice was that if the kids "got" the concept there is no need to do 20 questions. They got it at 3. Take advantage of the end of chapter tests to check their understanding. There is no need to wade through a billion textbook questions to prove to some dude that they "get" it.

Maths and what maths should be like in schools (because, yanno, that's where most maths learning takes place) has been in the media lately. Andrew Hacker started a bit of a mathematics bru-haha (I've always wanted to use that word in a sentence) by claiming in the NY Times of all places, that schools don't need to teach algebra.

In the US, kids do Algebra and Trigonometry as subjects in High School (Years 10, 11 and 12). This is a little different to how Australian schools approach these subjects - Algebra is included in the maths syllabus from Year 7 when they start to use pronumerals and trigonometry in Year 8 where they learn about Pythagorus' Theorem. Only if kids choose higher level maths in Year 11 and 12 do they encounter calculus. But they spend a good three or four years wading their way through 'higher' maths concepts.

Now, I tend to agree with Mr Hacker. Even though my own kids are happily working their way through linear equations and are moving themselves onto quadratic equations and parabolas and edging closer to calculus (which I admit I have completely erased from my own memory banks and will have to do some 'learning alongside' when we get there!), I have also worked in high schools teaching maths. For the vast majority of kids (in our town, at least) they don't "get" algebra, won't use it, and in fact have a very negative attitude to maths.

For those kids, I think 'higher' maths is a waste of everyone's time. They do not learn to "think mathematically" like many of the opponents of Hacker's views claim. They are unlikely to learn from algebra data organisation, extrapolation, how to go step-by-step. These same kids who don't "get" algebra are also the ones who are not "getting" chemistry and physics. They may be sitting in the classes, doing the tests and moving onto the next year, but they certainly aren't "getting" it. So my personal opinion is that a lot of maths and science "content" in high school is a waste of time for a lot of students and they would be better off pursuing their passions and learning what they need.

But there are also issues no only with what kids are taught in maths class, but how.

You know I love TED videos. There have been a couple discussing how maths is taught in schools and how we might do it better:


I love these videos because they emphasize that maths is about much more than doing arithmetic and repetitious questions from the textbook.

And so we come back to Khan Academy. The main reason we are enjoying it is that it truly allows the kids to move at their own pace. They don't have to wait for me to be available to explain something or give them questions. They can have a go at the questions, if they don't get the concept they can get hints or look at a video, which they pause, rewind, or fast forward. If they get really stuck, then they can ask me (and maybe I'll be able to help - at the moment!).

But is Khan Academy really all it's cracked up to be? Is it really a revolutionary approach to maths and science learning in the classroom?  Critics say it is no better than textbooks because it puts instruction/explanation before questioning and problem solving:

Sure, if you use it as videos/lectures first, practice questions second - it is no better than boring maths class (except you can pause the vid to go to the toilet, something that is difficult to do to Mrs Smith). But we don't use it that way! Maybe because we are homeschool rebels? But we hunt through the lovely mindmap for a concept we are unfamiliar with or interested in (eg: conic sections). We try the questions. If we struggle we ask for hints and then as a last resort, use the videos. And I use the world "we" purposefully here - I (me) am working my way through maths I can't remember from school or haven't revised during my teaching/tutoring. I am learning new maths! I am loving it!

So how does this all relate to how we can do maths at home?

  • We can help develop a love of maths in our kids. We can help them appreciate the beauty and complexity in maths. Even if we hated maths at school and don't see maths as our own particular strong point. What better opportunity are you going to have to influence you children positively and maybe change your view of maths in the process?
  • Maybe as teachers/facilitators/co-learners, we can take the opportunity more often to ask problematic questions. Questions that need maths skills to answer. Questions that have relevance to life and living.
  • We can provide a range of tools to help our kids use maths - textbooks, Khan Academy, online learning, YouTube videos, manipulatives, everyday items. Whatever we need to help us solve the problem, we can provide. 
  • We can let go of "school" maths. We don't have to do every question in the textbook (or on Khan Academy). We can meet our kids were they are at. We can move at their pace (faster or slower than the rest of the "class"). 
  • We can explore ideas that aren't in the syllabus! Maths doodling? Fibonacci? Fractals? Dimensions? Yep - we can do all those and more. We can follow our noses and those rabbit trails and interests.

We could put a label on this approach - call it "unschooling", or "natural learning" or "differentiated instruction". But I prefer to think of it as just "learning". Finding ways to make it work for us. For us it includes some textbooks, some algebra. For other families, it may be maths manipulatives and measuring and practical finance. 

Maths is important. It is important to make sure as homeschoolers it is relevant and interesting and useful. It is important to find the best way to do make it those things in our own homes and lives.


  1. ~"So my personal opinion is that a lot of maths and science "content" in high school is a waste of time for a lot of students and they would be better off pursuing their passions and learning what they need."~

    I love this! Not everybody should be scientists and there will be highly educated scientists who are not be able to cut their own hair. Really it does not even make sense to educate everyone all the same. Before we started unschooling I had 1 child who *hated* math and another who was adding dice together(in her head) at 5. One has math "bagage" the other was brought up with math not being separate from living. I can see a *huge* difference between the 2. Now though Sky is loving many aspects of "math" from following her own interests and she doesn't even realize that's what it is. :)

    1. Absolutely! It can be so much part of our lives - I think of having "maths goggles" on - you can see patterns in things, before you know it, you are learning quadratic equations! Truly!

  2. This is such a fantastic, thoughtful post, Ingi! Wow. I started reading it yesterday, got interrupted, started exploring Khan academy this morning with my girl…she has a cold so went off to bed to read her book…then I remembered I hadn't finished your post, and I came back to learn more. A meandering, revolving version of "play, explore, learn," don't you think?!

    Maths is probably the only thing left in our homeschool house that still feels a bit like "school"—something we should do and need to get through, rather than something intrinsically interesting and fun. I would love for maths to feel seamless in our house, seamless with life. I'd love for our maths learning to feel as interesting and exciting as writing a story (which we love!) or playing music (love!) or doing art (LOVE!). Sometimes I think, "Well, it's okay; maths is just not our "thing." " Other times (most times) I know that's a load of hogwash (another great word!), and maths could easily be our "thing" as much as all our other passions are. Anyway, I'll just keep on trying, exploring, playing, encouraging, looking for the joy in it, finding the joy in it, the way you all do.

    Lovely post, Ingi. Thank you :)

    1. I think that maths is the one thing even unschoolers have a hard time getting their heads around. I think you can "strew" maths as well - have a look at Stephanie's math's strewing on Ordinary Life Magic. It can be more than just measurement in cooking! Wait until you see what my two have been up to with a little Vi Hart strewing!


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