Friday, March 03, 2006

Math Facts

When we first began our home school journey, we got our first set of flash cards along with the Saxon Homeschool Math curriculum. Then, I didn't realize that math facts and flash cards would rule our existence for so long (Four years so far. I'm glad I have only two children). I will be so happy when I can finally toss all the flash cards in the fire and watch them go up in flames. I am sick and tired of being the drill sergeant, nagging mother, flash card manager, and Princess of Torture.

At first I was not obsessive compulsive about my children mastering the facts. I thought that the knowledge would sort of spontaneously fill the void with enough manipulative use and problem solving in early learning. Now, I panic because I was a product of the "children master addition/subtraction facts in first and second grade and multiplication/division in third grade" educational philosophy. And I never loved math, though I was not horrible at it. My 9 year old is not a multiplication and division fact master, nor is he a speed demon with subtraction. I still feel torn. Is it too early for this child? Yet, teaching new concepts in math is much more difficult when the child has to grapple with the basic facts, so now math lessons are a struggle and take so much longer than they should. My six year old is taking her cues from her older brother and believes the math and math facts are difficult. These same children can memorize long poems, Shakespearean soliloquies, and obscure passages in books in minutes, so why are they taking so long to master these few math sentences?

Feeling, always, that learning is developmentally sensitive, I have always put things aside if they seem too difficult and bring them back in a few months. I have done this with the math facts to a certain extent, but I've never been able to leave them alone for more than a week. I feel that they must, at some point, buckle down and do it even if it is unpleasant. Here are some resources we have used on our journey. Scroll down and down and down if you don't see the table. I cannot figure out why this table wants to sink to the bottom. I promise the information is worth it.

Flash cards SaxonThese are utilitarian and are already included in the kit. Having the answer on the back in the form of the subtraction fact saves them money on paper but is sometimes difficult for the younger learners. Of course, this helps show the relationship between the facts. The card stock is a bit too light if you use the cards for more than one student. I do like that they are color coded. This helps when you have to find the facts in one set quickly.

Three corner Flash Cards These are supposed to be the intuitive way to learn math facts, but I found that without the addition, subtraction, multiplication or division symbol that the child doesn't "get" how intuitive they are. You never visualize the number sentence because you never see it.

The Perfect Card The perfect card would be laminated, color coded and present the facts with the answer on one side and without on the other side. I haven't seen this card commercially.
Computer Games/Practice Math Blaster: In Search of Spot I really like this old program. Speed is rewarded in the meteor blasting and banana peel toss. The energy refueling is more logic based fact practice. Levels are adjustable and you may also input your own problems. You can check your child's progress. The negative is that your child must learn the numbers keyboard before he can play effectively and quickly. Also, this only plays on older Windows and Mac systems (9.2 and below for Mac(classic mode is not good enough) and 98 and below for windows). There are new Math Blaster programs for Windows XP, but I don't find they are as good as the original.

Racing Math This is a speed only program for Mac OSX. There is no real teaching because the cues for correct and incorrect answers go by so quickly there is no real immediate positive reinforcement. You do get to race either sheep or cars with classical music in the background. The graphics are pretty corny for the money you spend on the program. Yet if speed practice is what you need this straightforward, nothing to interfere with the facts, program is good. Facts are presented in sentence format and reports on progress are available. There is a full demo version available for testing at, the child must learn to use the keyboard before he/she has any success.

Online facts We don't do much online practice even though there are hundreds and hundreds of sites because we have no DSL or satellite, only a exceptionally slow dial up. With phone lines what they are I always feel lucky to get on-line at all. Doc has compiled a great list of online resources. Go to her homeschool links page and look for Math.
BooksTimes Tables the Fun Way! by Judy Liautaud

I wanted this book to solve all my problems instantly. It didn't. There are some cute stories and activities here, but nothing life changing. The little stories did little to weave the facts into the memory. The book came, of course, with it's own set of flash card cut-outs.

The Best of Times by Greg Tang

I really like this book and even more importantly my children do. No, this book is not an instant cure, but certainly shares the tricks of the trade. An example is:

Four Eyes

"Four is very fast to do, when you multiply by 2. Here's a little good advice - please just always double twice."

There are practice tables in the back, but, thank goodness, no flash cards.

CDs and TapesAddition and Subtraction Country My children affectionately call this "The cowboy." This CD or tape is not bad. I have, at least, not hurled it from the car while going 70 mph on the interstate. The facts are not presented in any sections. You have up to 10 facts, up to 18 facts, then mixed facts. If you or your child has problem areas they are difficult to isolate on this CD. The voices are not annoying and in the genre of fact practice music this is a real plus.

Multiplication Songs by Audio Memory Publishing This is about the most annoying tape I have ever heard. How can a child be expected to listen to this more than once without accusing you of torture. The squeaky pitch and sing song recitation is far from musical. But the facts are organized by number so you only have to listen to the songs with the problem facts.
ManipulativesCuisenaire rods I love these things! They are visual, tactile, and fun. They do help to visualize the facts. The caveats are: Your children have to work with these a lot before they can pick up the blue rod and think 9, the yellow is 5, and the red is 2. Also the introductory set is not enough. You must have lots and lots of rods, especially if you have more than one child. The wooden rods feel nicer. Don't scrimp here.

Number lines Once the child can visualize quantity represented by numbers, number lines can help illustrate the less two and plus three concepts.

CountersCounters are available these days in as many forms as can be imagined. Some people use M & M's, beans, and other household items. I find that you can't use M & M's because they are gone by the time you need them.
We use plastic fish, bugs, and snakes as counters because they are fun and are not eaten before used like the candy.

Hundred Number Boards I like these because you can practice skip counting by covering the numbers with the clear colored tiles and you can visualize the relationships between distances of numbers - like adding 10.
TablesMultiplication Table Charlotte Mason felt that children should create a multiplication table for themselves before they began to memorize the facts. Once the child creates one with manipulatives or whatever, then create one in excel with
color coded lines and laminate it. Have the children use it while they are memorizing.
GamesMulti function Snap and Times Tables Snap Fun, yet child must know most of the facts before it becomes fun. I find that I must wait an embarrassing amount of time before moving on to the next card. The child then knows it is a snap because you pause to wait for them to call it.

DominoesDominoes is a wonderful math facts practice game. Be careful, though, it is altogether too easy to help too much.
Things I have learned:
  • Use a hole punch and punch holes in your flash cards. Then, put them onto one of those metal book rings. This saves you picking up and sorting time.
  • Save the daily Saxon 100 facts timed exercises for special occasions. A little of this goes a long way in the lives of small people.
  • Exercise and chant the facts with your children. i.e. jumping jack fives
  • If there is just one fact in a group with which your child is struggling, use Sculpty to create the fact in clay along with a visual of the actual groups. Then bake and paint the fact.
  • Don't get as serious as I did.


Maria Miller said...

Would it help to study the addition facts in groups with same sum like shown in this lesson?

I've written an ebook with that approach.

Also I wonder if it helps to first get addition facts, emphasizing the missing addend form, and only then go onto subtraction. You really don't need to learn separate "subtraction facts" then.

Say for example you study addition facts with sum 6:
make pics to go with these, then make kids to make the pics:
0 + 6
6 + 0

5 + 1
1 + 5

4 + 2
2 + 4

3 + 3

So you study that those make 6, then practice it with the missing number idea:

2 + __ = 6
5 + __ = 6
1 + __ = 6

That makes them associate 2,4,6 as a 'family', 1,5,6 and 3,3,6.

Or maybe you've already tried all that, who knows.

MonicaR said...

We loved the 'Times Tables the Fun Way' book and workbook! It's not instant - we still have to work with them but the oldest knows her facts quite well.

Creating the multiplication table was GREAT! Not only did she enjoy it but it has helped immensely.

I have horrible memories of flash cards. I still get a terrible feeling in the pit of my stomach when I think of it...

Wonderful ideas - thanks!

JoVE said...

It would be okay if you let go. Really. And it would be important to do so before they learn to hate math. Because it is SOOO hard to change that attitude.

If some of the stuff takes longer because they are counting on their fingers or using a number line, so be it. Do fewer problems.

The key question to ask yourself is "Do they understand the concept?" If so, move on. The facts will come once they've used them enough. Keep a number line handy so they can quickly refer to it to figure things out. Encourage them to use their fingers. Ask them how they figure out harder ones (some kids are doing complicated things particularly when subtracting 9s). Don't rush them.

The point of math is NOT to be able to do it quickly. Really. It's not a race.

Susan said...

hey, Wisteria. Thank you for this post! You list some great-sounding resources that I am going to check out. Junior, a p.s. 2nd grader, has a good understanding of concepts, but the facts are a different matter. And I so like JoVE's comment that math is not a race. I am going to remind myself of that!

I bought an Addition Bingo game, and my son thinks it's grand. It's a good way to practice the facts (without his realizing that he's even doing that).