Over the last few decades I've noticed a very worrying trend amongst math educators that downplays the importance of knowing math facts well enough that you don't have to think when asked one. I've seen arguments that suggest that calculators take the place of knowing math facts.
For a while, when I lived in South Africa, I tutored underprivileged high school junior and seniors in math. These were all strong students who wanted to go onto do something that required math in university. They were hamstrung by the poor math teaching they received in their schools.
I generally tutored algebra and trig and discovered pretty quickly that they were also hamstrung by the fact that they couldn't easily find factors and common denominators.
My first action became going back to basics. I become a tyrant about math fact drills. I expected all my students to be able to give me the answers to the 1-12 times tables (and the divisions), squares of 1-20 and square roots of a long list of numbers within seconds of my asking them. I wanted these things to be automatic. I didn't want anyone having to think what 17+22 was, I wanted them to immediately know it was 39.
Without a single exception, all my students started excelling at their higher level math once they had their math facts down pat and we'd done some basic tutoring on methodology.
I had almost forgotten about all this until I started homeschooling my own kids. I have twins who love math and who want to scream ahead in the syllabus. I have no doubt in my mind at all that they could cope with the concepts of beginning algebra right now. The problem is that they'd be frustrated by their slowness in math facts.
I've spent the last year looking for tools to drill math facts.
We've done pages upon pages of written problems. There are a host of different free worksheet webpages, but the one I used most often was Math-Drills.com.
Whenever I added a timer to them, Shira fell apart. I struggled to keep Ben focused. Shira would complete her worksheets in record time, as long as there was no timer, Ben could do it, but became bored.
We tried games at Multiplication.com, Timez Attack, the river crossing game at AHA Math, flash cards and mom asking questions while we drive.
Flash cards and mom asking worked well but it took up too much of my time. I tried having each child quiz the other but it ended up in too many tears.
We discovered that the computer games helped the children learn new math facts but didn't do much for speed. Both my kids hated Timez Attack. I was surprised at that because I had only read great reviews. I realized that since we're not a video gaming family, my kids were becoming too frustrated learning how to play the game. They just wanted to focus on the facts and the extraneous activities were driving them crazy.
Before I forget, we also had a subscription to Big Math Time. This worked really well for addition and subtraction of small numbers but it fell apart for us on multiplication, division and addition and subtraction of large numbers because of the strange way they had the kids show the carrying.
About a month ago a fellow homeschooler reminded me about FlashMaster. She'd used it with her children and was convinced that it would solve my issues.
I am so glad I listened to her and bought two for my kids.
My only complaint is that I didn't buy them sooner.
Our goal is for the children to do the "timed flash cards" so fast that it takes them less than 1.5 seconds per problem.
Every morning, my kids know to do 20-30 min on the FlashMaster while I make breakfast and feed the dogs. Each child competes against his/her self. This is a BIG deal in our overly competitive household. I love anything that takes the focus off competing with a sibling and onto competing with one's self.
I love how I can go into each unit and see how the children are doing on their problems. It's also useful that besides the standard, 1+3=?, 4-3=?. 3x4=? etc, you can also do things like, 32/?=4 or 3+?=12.
Last week I sat down and quickly taught the kids the basics of the next few things we are going to learn in math; long division, factorization, lowest common denominators, factor reduction, improper fractions and mixed numbers. I have two children who are champing at the bit. They are desperate to sink their teeth into meatier math. I can see that they understand the concepts but I know that if I let them loose on this math without automaticity of their math facts they'll become disheartened because everything will take too long to do.
it's wonderful, now they have incentive to work on their math drill. They know what exciting math is just around the corner but that they are not going to be let loose on it until they can do anything, in 1.5 seconds, that the FlashMaster throws at them.
The FlashMaster has made my life so easy. The children can practice math drill while we're driving, waiting on a sibling at an extramural activity or anytime I so wish.
3 days ago