Giving my Unschoolers a Maths Test

I had this brilliant idea. Well, I thought it was a pretty
good idea until this morning. It was all to do with maths. How do you prove
your children are covering the required maths syllabus, and achieving the necessary
outcomes, when they don’t use a formal maths program? I’ve been thinking about
this for a while.
My husband is a school teacher. Every year his year 3 and 5 students
have to sit the dreaded NAPLAN test. (National Assessment Program – Literacy and
NAPLAN tests the sorts
of skills that are essential for every child to progress through school and
life, such as reading, writing, spelling and numeracy.

So I had this idea: if my girls do the maths part of the NAPLAN
test and pass, then I can say they have age appropriate maths skills. (They would be in years 3 and 5 if they attended school.) I could
file the results in my records book as proof they are learning maths despite
the lack of a formal program. I could continue tempting them with real books
about real maths, finding maths games for them to play, looking for every
opportunity to expose them to real maths in our everyday life…
So I asked Andy to bring home some NAPLAN papers, and this
morning I asked the girls if they’d like to do the test. I can’t say Sophie and
Gemma-Rose jumped up and down with excitement when I explained what they had to
do. But they were agreeable. They’d never done a test before. This was a new
Ten minutes into the new experience, Gemma-Rose had had
enough. She was making a lot of unhappy noises. She did lots of huffing and
puffing. She was clearly unimpressed. I don’t think she saw the point to all
the questions. Sophie just got down to work.
Some time later they’d both finished. I marked Sophie’s
paper first. She smiled as I gave a tick to one question after another. Then
she got a few wrong, and by the time I got to the last page, she was crying.
“But you did okay,” I assured Sophie. “You got 85% right.
That’s good.”
But Sophie wasn’t convinced. She is used to working at a
problem until she gets it correct. Today her time was over. She couldn’t go
back and try again. Her final score is unchangeable. No one cares if she puts
in further work and perfects her score and learns from her mistakes. That’s the
way of tests.
By this time, my enthusiasm for the test had waned
considerably. I had two unhappy girls and I hadn’t even marked Gemma-Rose’s
“Let’s forget the test,” I told Gemma-Rose. “We don’t need
to mark it.”
But Gemma-Rose surprised me by saying, “You might as well
mark it and see what I get.”
So I marked the paper and she got 77%, which didn’t please
her or displease her. Marks don’t really mean much to her.
What do I do next? Am I tempted to pull out the maths textbooks so the girls can fill in the gaps in their maths education? Or am I satisfied with the results? Will I be giving them further tests at regular intervals to prove they have age appropriate maths skills?
As I mull these questions over, I wonder about the value of testing. I am sure that the ability to take a test is a skill of its
own. Working out problems in real life has nothing to do with how you fill in a
paper under a time constraint. I’ve also just realised that students usually revise before a test while the material is fresh in their minds. My girls only got a few seconds warning. So was the test really fair?
“Shall we start studying for the next test?” I ask Sophie
and Gemma-Rose. “We could grab those textbooks off the shelf and start work.”
They look at me. Am I serious? No. I’m smiling. They look relieved.
It would be so easy to take those textbooks and insist the girls
use them. Maybe everyone wonders why I don’t do this. I could satisfy the
educational authorities. My girls would learn maths and I wouldn’t have to
worry about proving it.  Easy.
But I know I would be saying, “I don’t trust you to learn
what you need to know. I need to interfere just in case. I am more concerned
about outside expectations than I am about you. I don’t really believe in the
principles of unschooling.”
Will I be giving the girls any more tests? I spent years trying to remember things just to pass tests… and then forgetting… I want something better for my children. No. I won’t be giving
them any more tests. 
So I will continue strewing maths in front of the girls, and I will take delight in their delight as they learn. 
And I will look for another way to satisfy the educational authorities. 

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  1. Reply

    Well this is a timely post for our family, Sue! I've been busy sitting at the computer researching living maths AGAIN. Unfortunatley I am having trouble letting go, but one of my children really needs a different approach. Thanks for your post which has given me a little more confidence.


    1. Reply


      Maths is tricky, isn't it? It seems to be the last thing we hang on to when we decide to unschool. Maybe we just can't see how the alternative ways of teaching maths will be as successful as the traditional approach. Perhaps we think it's too much of a risk to unschool this subject.

      I finally let go when I realised that the girls were dreading maths lessons. I decided that if they hated maths they wouldn't learn much anyway. So we changed our way of doing things. And now they do like maths and are confident in their ability to manipulate numbers etc.

      Even though the girls didn't enjoy doing the tests, the results do show they have adequate maths skills compared with their peers at school. I don't think I'll repeat the test experience though!

      I hope you find some living maths resources your son enjoys. If you find anything wonderful please share!

    2. Reply

      Well last night I found a great quote which I have since written in the front of my home ed. record book.

      "Larning can only happen when a child is interested. If he's not interested it's like throwing marshmallows at his head, and calling it eating." unknown.

      Based one this I have been throwing a whole lot of marshmallows!

    3. Reply


      I love that quote!

      Sophie said something similar (but not in such a poetic way!): How Children Learn According to Sophie…

      Yes, we really are wasting our time if a child's interest is not engaged.

      I can remember times when we just went through the motions of learning maths. I knew Gemma-Rose wasn't really learning anything because she hated it, but it looked like she was 'doing' maths and I could record it for the BoS in my records book. It was a big waste of time! It wasn't real learning at all. So I've thrown a lot of my own marshmallows, Tricia!

      Thanks for sharing!

  2. Reply

    Unfortunately, we are required to test anually in Minnesota. But we do not have to submit schooling plans. I have one who tests wonderfully and 2 who test horribly…we just keep plugging along!

    1. Reply


      I guess we are fortunate not to have mandatory testing each year. I'd forgotten that some US states require this.

      Do you find testing time stressful? I wonder what happens if your children fail the tests. Are there tests for all subjects? And do you have to teach a certain syllabus so your children are successful at those tests? Lots of questions! Sorry, but I'd be interested to hear more.

      Thanks for your comment!

  3. Reply

    I don't like the standardised tests, either, Sue. They seem to be a contradiction of all our principles and I don't think they're a fair assessment. It would be such an easy way to satisfy the requirements, though.

    I've thought about making up my own end-of-term test of our own work just to give exam practice. The thought came when one of the older girls said that exam practice would have been useful experience. I thought it also could help with the end-of-term assessment that our authorised person likes to see.

    Congratulations to the girls for their good marks! Isn't it interesting how homeschooled children aren't happy with less than perfect? Our children think like that, too.

    God bless, Sue:-)

    1. Reply


      Yes, I agree that testing contradicts our education principles and don't give a true assessment.

      I do know that some schools teach English and maths in a way that ensures their students have the best chance of success when test time arrives. They drill the kids in Naplan-like questions, explain all the language and give lots of practice tests. This is all so the students get good marks and raise the profile of their schools. Anything outside the Naplan syllabus is given low priority. It's really teaching for a test.

      My girls didn't even see a Naplan paper until yesterday and they weren't familiar with the language used in wording the questions. I am surprised they did so well. But I don't think the marks mean much really. I know Gemma-Rose has gaps in her maths knowledge. She isn't happy with telling analogue time for example. But in other areas, I am sure she is well ahead of school children. It just depends what's on the test paper on the day.

      Yes, our children don't get exam practice. Duncan soon learnt though once he got to uni. Did your older ones adjust quickly too? Taking tests is just another skill. Maybe school children have a bit of an advantage for a while until our kids get the idea and catch up. But you are right, maybe some practice would help. Do you think it is necessary to give exam practice to younger children, or do you think they can pick it up easily enough in the later years of school?

      Some of our children have done music and musicianship exams which have given them a taste of what exams are about. They know all about having to do their best on the day, and only having a certain amount of time to display their skills.

      If you go ahead with the end of term assessments, please share. I'd love to hear if your tests are successful.

  4. Reply

    Curious about this. We fall on the unschooling side of things, but I do a variety of math curricula. The living math stuff seems to work well for basic everyday math, but I don't see how you ever get to Algebra and higher.

    The fact is, most people don't use higher math every day, but not having it seems to shut off any future in math or science. I know you have kids that went on to college, how did that work for them?

    Thanks so much!

    1. Reply


      The younger girls are not using maths workbooks or a formal program but they are learning a lot of maths regardless. I am strewing all sorts of maths resources in front of them. For example, recently we've read a book about fractions and another about times tables. The girls have been dipping into some maths gizmos and learning about decimals. I remembered we still have a Brainpop subscription and so yesterday we did some browsing and watched a video on decimals. We did some reading about cubism and then had a chat about 3D shapes. I have a big box of coins that needs sorting and counting… I have another book I am about to buy for Sophie…

      I think the younger girls will easily learn all that most children learn during their primary years.

      I read an article online that stated the opinion that most of the mathematical principles children need to know can actually be taught in a very short time, and it is better for them to learn these at an older rather than a younger age. That was interesting.

      I am confident that my children will learn all the maths they need for everyday life without any problems. As you say, they may need higher maths though, if they go on to tertiary education. Charlotte (15) has decided for herself that she wants to complete an advanced maths course. She likes maths (and chemistry) and asked me to find her a suitable course. She's working her way through it with no problems at all. At the same time I'm trying to find some real situations that use the maths she's learning.

      Imogen finished the same course a couple of years ago. At the time she was thinking about doing a science degree. She changed her mind and is now doing an Arts one instead, so the maths is no longer so important.

      Imogen and Charlotte are different to my older three children. They both want/ed to learn higher maths. It was their decision to do this when they saw a possible need of the subject. They are directing their own learning and are motivated to do what is necessary to achieve their goals.

      My first three children all started an advanced maths course and they all dropped out before finishing. It was quite clear they didn't want to pursue a career in maths or a related discipline. They were all able to cope with university with the level of maths they had attained, so not finishing the course didn't really matter. Duncan is doing his Masters degree at the moment, and his maths is more than adequate.

      I like the idea of exposing children to maths in a way that makes it relevant and interesting. If they really enjoy maths they might decide to study at a level higher than most of us need. Then I think a course is probably the most efficient way of learning. I think by the time my children get to this stage they can decide for themselves if they have a need for higher maths or not, and whether they want to keep studying it.

      I know we can't see the future and shouldn't we cover all possibilities and do higher maths 'just in case'? We don't know when they might find it useful. But it is never too late to learn anything. If one of my children suddenly changes direction and decides she needs more maths, then she can always learn it then. It is easy to do a maths bridging course at university if necessary.

      We as parents could insist our children learn certain things just in case. But children who are allowed to follow their own interests and use their talents will have a good idea of where they are headed. They will learn what they need to know to attain their goals. And if they change their minds, it's not a disaster because it is never too late to learn anything. At least this seems to be how it works in our family!

      Wendy, I have rambled on I know, repeating myself. I am typing quickly during a coffee break. I hope something of what I said makes a little sense. Please feel free to question what I've said!

      Thank you for your comment!

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