How to Teach Math Facts
For our purposes, math facts are the basic number combinations for the different operators. from 0 + 0 to 10 + 10, from 0 - 0 up to 20 - 10, 0 x 0 up to 10 x 10 or 12 x 12, and 0 ÷ 0 up to 100 ÷ 10 or 144 ÷ 12.
Why is it important to memorize, to become fluent, or to achieve automaticity in the basic math facts? Let’s make an analogy to reading. In reading, phonics are the basics, and knowing what sounds the phonemes, or basic letter combinations make, is key. A student who is weak in them takes so long to get to the end of a sentence, that by the time they do, they’ve forgotten what the sentence was about in the first place. The same thing holds for math facts. If a student is not fluent in them, when a teacher is explaining a “math sentence,” if the student has to figure out the answer to each basic math fact, they will get so far behind that they will forget the purpose and steps of what they are doing. Math facts are the “phonics of math.” Except instead of only 44 phonemes from 26 letters, there are 121 facts for addition, another 121 for subtraction, etc. A total of 580 facts if you go up to 144 ÷ 12! No wonder it takes so much practice!
The most important thing when starting to memorize the basic math facts is that the student must fully understand the operator they are studying. Research shows that fluency practice will actually be harmful if they don’t understand the operator concept. For example, they should be able to show you addition and subtraction with blocks, and explain what is being represented.
Now some advice:
- Don’t overload. Students’ brains can only hold 3 or 4 things in short term memory at a time, maximum. Adding more things will just cause others to “leak out.” So introducing and beginning to work on the 3’s all at one time, for example, is introducing 15 new facts. If you only consider fact families, it’s still 8 fact families. Just adding 1 or 2 facts at a time is much more effective. Select the most connected facts with the quickest too slow time. (Computers time to the millisecond, and are really good here.) Try to make the list of not-fluent facts shorter by pointing out the symmetric property of equality; if 2 x 3 = 6, then 3 x 2 = 6. Also when the difficulty level is getting too high, mix in enough fluent facts to reduce the strain. The zone of proximal development is 90 - 95% accurate.
- The process of becoming fluent starts with being able to get the answer. This could be counting on fingers, remembering a story, using dots, etc. Now the answer is known. It becomes fluent through repetition of retrieval. The more the answer is retrieved, the more likely it is to move into fluency. However, at some point, the crutch, such as counting on fingers, should go away. As good software moves toward fluency, it won’t give students time to count on their fingers
- The more connections there are in the brain to a fact, the easier it is to retrieve, or find the way back to the answer. If the related facts around it are all known, a story is constructed, and something is done to make the fact more concrete, whether it be having 3 marbles in the left pocket and 2 marbles in the right, or having a piece of paper in a pocket with 2 + 3 = 5 on it, the fact will be easier to memorize. Be creative
- No pain, no gain. Memorizing is hard work. The brain has to do the work of retrieving the answer on its own. If someone blurts out the answer before the brain gets to it, no learning has taken place. Multiple choice answers are not as good, because the brain doesn’t have to work as hard to get the answer.
- Mnemonics have been shown to help learning disabled students, however, they help with getting the right answer more than they help with understanding why. There are websites and books to help with this. Math Facts Pro has some mnemonic videos on the site.
- Practice needs to be good practice. Often when a student practices flashcards on their own, the practice readily degrades until it is not helpful. When students check their own work, seeing a wrong answer can be remembered and cause confusion later. It’s been said that the way to Carnegie Hall is to practice, practice, practice. But in reality, only perfect practice will get you there. Computers can be helpful here.
- The results are directly related to the quantity of practice. Students are wired to resist boring things. If we can make it fun, we will increase engagement, learning, and thus fluency. Games and competition are good for this.
- Timed paper/pencil tests aren’t very good math fact assessment tools. Doing a group of facts correctly in a certain time limit is helpful. But a student can go super fast on the fluent, easy facts, to make up for how slow they go on their non-fluent facts. So the tests don’t reveal to the teacher which facts still need practice.
Yes, Math Facts Pro was designed with these concepts in mind. (I’ll bet you didn’t see that one coming.)
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