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Tuesday, November 10, 2009

An Evolution of Math Drill

Learning basic math facts has been a bittersweet experience in our family. I'm sure many people can sympathize! While one of my kids really enjoys math, another does not. I have come to realize that much of their individual success or failure with math has had to do with how well they know their basic math facts. I never knew just how important this is! I'll explain why it is indeed so important, and how drilling math facts can be of help in this area.

photo by rolve
IF you know your addition facts, then subtraction is WAY easier and vice versa. Having the facts on the tip of your tongue cuts down on time spent on math considerably.
Imagine if as an adult you need to do the problem 876-284, and you have to get out your base 10 blocks for each simple operation. 6-4=2, find the six block, the four block - good. Now, 7-8... oh, get the blocks out again...7 is less than 8, so I'll have to borrow from the 8 hundreds space, which makes that 8-8=0, okay, get the blocks out then 7-2=5...Yes. This must be frustrating even for the kids! Knowledge is power!
IF you have your multiplication tables down, not only will you spend less time doing bigger multiplication problems, but division will be much less intimidating as well. The better you have the facts down, the more you can do in your head, the quicker the whole thing goes! Sometimes it's not really that math is hard, but that it takes too much time... more time than we want to spend on it!

photo by januszek
SO... Realizing how important it is to learn these facts, we could see no other option but to put other things aside and just concentrate for some time on mastering those necessary evils. Thankfully, my husband took charge of this area spending time with the kids and their flashcards! I recommend using fun math games throughout that reinforce the math concepts being memorized/mastered. If your child has memorized the facts without drill, way to GO! The following advice is for those having some trouble with memorizing basic math facts.

Here's how the use of math drill might evolve over a longer period of time:

Step one: Let the kids have some time for the facts to set in naturally, through experience and play. Don't drill. Though, for certain kids who WANT to drill at this age... by all means, drill!
When our kids were first learning their math facts, we didn't drill at all. We just kept it light hearted. Counting objects, adding some, taking some away, etc. We let them be entirely dependent on their math blocks and visual aids. This lasted at least until the boys were about 8 years old, around 2nd grade or so.
Step two: When they have had ample exposure to the natural method, and you are ready to have them start buckling down and memorizing, start with short and simple. Go through the facts orally, or use addition flashcards here, here, or make your own. Find multiplication flashcards here, here, or again, make your own. Start by letting them build the problem with their blocks if they don't know the answer right off. Or, if they don't answer it within 5-10 seconds, before their face falls, quickly tell them the answer. Have them repeat it after you. "Five and five makes ten." Don't use the timer at this point (unless you have a very competitive child who likes to compete with their own time - I have one of these). Spend 10min on this 2-3 times a week.
By the time our kids had gone over all the facts, when they knew a good number of them if they had all the time in the world to think, we started drilling with flashcards. We kept it short and simple. For 5 minutes, or 2-3x through the +3s for example and that's it for the day. We did this while continuing on with our math curriculum. When I felt they had a pretty good handle on the facts I took a break from this.

photo by iprole
Step three: If in the course of time, the kids still are not fluid with their basic math fact recall (mine were not), you might choose to spend some time really cementing the facts before moving on. This might include separating time a week or more where the only math you do is drills. Print off some drill sheets and start timing them. Perhaps you won't tell them you are timing them if they would be intimidated by that. In that case, you'd just keep the information for yourself in order to see their problem areas and progress. Use the information (repeated trouble with the +7s for instance) to know which facts to work on. Go back to the flashcards or find a fun game to play to reinforce those missing facts. See my links below for drill sheet links and a downloadable record sheet.
We had finished Beta (Multiple-digit addition and subtraction and other topics) and recently started on Gamma (Single and multiple-digit multiplication and other topics ) when I realized, the boys were slow with their +6, +7 and +8 facts. They were having to count on fingers or get out their math blocks for these simple operations. It was taking too much time, and they were getting frustrated. I realized that it was essential that they master these facts before moving a step further in their curriculum. So, we stopped everything and decided to drill.
Here's how we did it:

We made reusable drill sheets: I found drill sheets online at (in those days she didn't have so many level options available!) I made the sheets reusable by printing Drill Sheet A on one side and Drill Sheet B on the other side of a sheet of card stock, then had it laminated. The boys used overhead markers (less smeary than dry erase). When they were finished, I just rinsed the sheets off under the faucet (no paper towel mess).

We started out having the boys fill in the sheets taking as much time as they needed. After a week of this, I started timing them secretly, but I didn't tell them their times, and just kept the records for myself. I also kept track of the date, drill sheet used and number of problems missed. Download a copy of my record sheet here. They started catching on, and wanted to know their times and soon it became a great game. I intentionally never pitted them against each other, that would have been disheartening for the one boy. I would correct their sheets (or better yet, have them correct their own work) and they would make corrections. Often they would do this later in the day as they were about done after the drill itself.

After a couple weeks of this, they had their math facts down! Because we were doing this as remedial work, we actually did addition, subtraction and the x0, x1, x2, x5 at the same time but on a separate laminated drill sheets. In retrospect, I would advise doing a little bit of drill all along the way from earlier on through maintenence long after the facts are mastered. I would definitely recommend the use of LOTS of supplemental math games reinforcing the same concepts. We didn't. We just left it with that.
Step four: Once the kids have gained proficiency with their facts, decide on a day of the week or once every other week to pull out the drill sheets just for fun. Have them try to beat their old record. Keep it light and fun. This takes about 5-10 min.

Step five: Use online games throughout the whole process for timed drill practice to increase speed and accuracy... if they are anything like my boys, they'll have so much fun playing, they'll forget they are even doing math!

So, while it may be possible that lots of math can be learned using only fun and games, I believe there are some parts that require discipline and serious study. Basic math facts are so important that I think it worthwhile spending the extra time and effort to get them down.

**Please let me know if this information has been helpful by leaving a comment. :)

1 comment:

Richele said...

Oh, glad this post came up under "You might also like:" as I so needed this info. Thanks, Amy, once again for your resourcefulness.

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