My Homeschool Maths Lessons – Things I Wish I’d Known
Homeschool maths was a subject where I often felt a little ‘lost at sea’. I wasn’t bad at maths in school but at 40 years old my maths knowledge was rusty.
I did what I thought would work but I relied heavily on textbooks and didn’t take the time to learn the best way of teaching homeschool math. Through trial and error, I found a system that worked. But it would have been a lot easier if I could have avoided some of the mistakes I made.
Let me share with you a few things I wish I’d known when I started teaching homeschool maths.
- Teach Concrete Before Abstract
When I started teaching formal homeschool maths to my first child I went straight to textbooks. I didn’t really understand the value of teaching math concepts in a concrete way before I taught them in an abstract way.
I should have used manipulatives more. What are they? Objects used to teach mathematical concepts such as counters, shape blocks, and base ten blocks are called manipulatives.
Charlotte Mason wrote this about teaching maths, “The next point is to demonstrate everything demonstrable. The child may learn the multiplication table and do a subtraction sum without any insight into the rationale of either. He may even become a good arithmetician, applying rules aptly, without seeing the reason of them; but arithmetic becomes elementary training only in so far as the reason why of every process is clear to the child. 2+2=4, is a self-evident fact, admitting of little demonstration; but 4X7=28 may be proved. He has a bag of beans; places four rows with seven beans in a row; adds the rows, thus: 7 and 7 are 14, and 7 are 21, and 7 are 28; how many sevens are in 28? 4. Therefore it is right to say 4X7=28; and the child sees that multiplication is only a short way of doing addition…” p. 255-256 Home Education
I hardly ever used counters to teach, I mostly used paper and the pictures that appeared on the paper. My first son survived the lack of manipulatives because he was very bright and went on to a very high level of maths, but I realised with subsequent children that those early homeschool maths lessons could have been less frustrating, and much quicker for him, if I used more counters and practical demonstrations.
- Teach Homeschool Maths In Daily Living
Some parents are natural teachers, they instinctively see a lesson in everything. However, some of us need to learn that habit. There are many opportunities in our day when we can have mini math moments without making it an official ‘homeschool math lesson’.
Real life teaching helps your child learn ideas. Charlotte Mason says:
“On the same principle, let him learn ‘weights and measures’ by measuring and weighing; let him have scales and weights, sand or rice, paper or twine, and weigh, and do up, in perfectly made parcels, ounces, pounds, etc. The parcels, though they are not arithmetic, are educative, and afford considerable exercise of judgment as well as of neatness, deftness, and quickness. In like manner, let him work with foot-rule and yard measure, and draw up tables for himself. Let him not only measure and weigh everything about him that admits of such treatment, but let him use his judgment on questions of measure and weight. How many yards long is the tablecloth? How many feet long and broad a map, or picture? What does he suppose a book weighs that is to go by parcel post? The sort of readiness to be gained thus is valuable in the affairs of life, and, if only for that reason, should be cultivated in the child. While engaged in measuring and weighing concrete quantities, the scholar is prepared to take in his first idea of a ‘fraction,’ half a pound, a quarter of a yard, etc.” Charlotte Mason, p. 259-260 Home Education
Here’s a lovely set of nature activities that incorporate homeschool maths.
Many of my friends and I used songs to teach the multiplication tables when driving the car.
- Choose Your Homeschool Maths Textbook Thoughtfully
With my four children I tried many math curriculums. My list included: Singapore Maths, Maths Online, Mathletics, Saxon Math, Life of Fred, Teaching Textbook, Miquon Math, Targeting Maths, Haese Maths, Signpost Math and I looked at a whole lot more than that.
I couldn’t settle on a maths curriculum because I was lured by the promise of the other curriculums. This chopping and changing was to my children’s detriment. Each time I swapped curriculums we had to repeat some concepts. But eventually I worked out that I needed to stop flipping all over the place, and stick with what I knew was good even though it was a little boring at times.
In the process of switching curriculums, I worked out some key components to finding a homeschool maths curriculum suitable for Australians.
Three things to be aware of when choosing a math curriculum:
- Do you want it to line up with your state syllabus or the Australian Curriculum?
If that is something that you need to do then watch out for the American Curriculums. Also American curriculums use imperial measurements instead of metric. Many of their money problems in the primary years include nickels, dimes and quarters.
- Choose a textbook you feel you can confidently teach.
Another issue I discovered in my quest for the best homeschool maths curriculum was usability. I discovered that school math textbooks were not homeschool maths friendly. They often had a thick complicated teacher’s manual that required a long lesson before allowing your child to go and do their maths exercises. The teacher’s manual also assumed you had maths teacher training.
For primary homeschool maths, Singapore Math was my favourite. Although not written for Australian schools, it followed the Australian Curriculum well. It was probably slightly more demanding than some Australian curriculums, but it still used metric measurements and their money system converted well. My children still joke about the word problems of which included shopping for 35 kg of rice and 30 durians.
Here are some tips on getting started with Singapore Math.
To buy this product in Australia look here. (Pr1me Math is an Australian version of this curriculum although more expensive and it can be hard to buy).
However, Singapore Math for high school is quite different in its layout to the primary program and it wasn’t set out in a way that was as easy to understand.
Saxon Math, although American was my pick for a high school math textbook. It did teach new concepts incrementally and had a good indexing system so you could look up something you were not sure about. It also had excellent revision each lesson. We did use this for quite a few years in high school. My main criticism of this was that each day’s maths lesson was easily an hour long (that was with my skipping some of the revision). It did use imperial measurements but it also included metric. It didn’t line up directly with the Australian Curriculum either, however if you were using it consistently you covered the same concepts eventually. Saxon also prepares children very well for university math.
For online math homeschool lessons, Maths Online was definitely the best program we used. I used it for all of my children. Pat Murray, the tutor of the lessons explained the high school math concepts very well. But for the most part my children managed this independently. And in high school we used it for many years as our main math program. I also loved it for record keeping. I was able to print off a summary of the work they had completed for the year. At My Homeschool we now offer a 50% Maths Online discount for our members.
I did try to use Teaching Textbooks, but the format was too silly and very American. I did try Mathletics, but the incentives ended up being distractions and my children wasted a lot of time without actually completing their maths lesson. I also occasionally used Khan Academy for the times my children got stuck on a concept. However, Khan was not a suitable curriculum as a stand alone.
- Learn To Teach Math or Find Someone Who Can
“Mathematics depends upon the teacher rather than upon the textbook and few subjects are worse taught; chiefly because teachers seldom have time to give the inspiring ideas.” Charlotte Mason, p. 233 Toward a Philosophy of Education
When my first child started learning difficult algebra, I spent one Friday night working on the lesson he had struggled with that day, after a couple of hours (and a few wrong answers) I gave up. I didn’t want to redo my whole high school maths course again. I had other ways I wanted to spend my time. So how could I serve my child well in math when I didn’t have the skills.
Three Things That Helped Me Be A Better Homeschool Maths Teacher
- Be observant. I had two children who found maths easy and two who didn’t. I discovered, if my children were complaining or refusing to do their lessons it may be that their lessons were too long, too hard or that they were bored. If this is the case for you, try to work out reasons your child is struggling.
- Find a good tutor. My husband is an engineer and he helped teach maths sometimes, but he wasn’t home during the day when I needed the help. So we used Maths Online because it had a built in tutor, and we left the occasional problems that couldn’t be solved for an after dinner lesson.
- Sit on your hands. In the early years when the math problems that the children had were simple to solve, on more than one occasion, I took their pencil away and just solved the problem for them. It was so much quicker. BUT even as I was doing this I knew I shouldn’t. I needed to let them solve it which involved me taking them through the steps slowly. This was hard to do. When I was tempted to grab the pencil, I began to sit on my hands. One of my friends said she knitted during homeschool maths lessons for the same reason—to keep her hands off the pencil.
As Charlotte Mason says, “…there is no subject in which the teacher has a more delightful consciousness of drawing out from day to day new power in the child. Do not offer him a crutch: it is in his own power he must go. Give him short sums, in words rather than in figures, and excite him in the enthusiasm which produces concentrated attention and rapid work. Let his arithmetic lesson be to the child a daily exercise in clear thinking and rapid, careful execution, and his mental growth will be as obvious as the sprouting of seedlings in the spring”. Home Education p261
Preparing For Their Future
So even if you feel a little ‘lost at sea’ teaching homeschool maths, with some planning and by wisely choosing your curriculum, you can offer your child a challenging math education.
Lastly, let me remind you that not all children will have the same aptitude for maths. Two of mine stopped their math studies at Year 10 level. Two went on to higher grades, all went to university but only one studied math at university level.
Charlotte Mason says, “Therefore perhaps the business of teachers is to open as many doors as possible in the belief that Mathematics is one out of many studies which make for education, a study by no means accessible to everyone. Therefore it should not monopolise undue time, nor should persons be hindered from useful careers by the fact that they show no great proficiency in studies which are in favour with examiners no doubt, because solutions are final, and work can be adjudged without the tiresome hesitancy and fear of being unjust which beset the examiner’s path in other studies. We would send forth children informed by ‘the reason firm, the temperate will, endurance, foresight, strength and skill,’ but we must add resolution to our good intentions and may not expect to produce a reasonable soul of fine polish from the steady friction, say, of mathematical studies only.” p 152-153 Toward a Philosophy of Education
For more recommendations on teaching homeschool maths in Australia see here.
My Homeschool Maths
My Homeschool offers a Charlotte Mason inspired homeschool maths curriculum from Kindergarten to Year 2.
In Year 7 and 8 we include a daily drill homeschool maths resource called Alboe which is A Little Bit Of Everything to supplement your chosen math curriculum.