Math Basic Facts
As teachers of all grade levels know very well, it is extremely difficult to teach students higher order math algorithms when they are not fluent with their basic facts (addition, subtraction, multiplication anddivision). If students are not automatic in responding to math facts, their attention is necessarily taken away from the multiple steps necessary to solve more complex problems.
Think about long division. Students must be able to come up with the answers to multiplication, subtraction and division facts all in the context of the higher order algorithm. Less than automatic facility with math facts often results in either errors in the algorithm or fact errors. Both kinds of errors appear to be the result of carelessness when in fact it is the result of being distracted by having to figure out the answers to facts. Below are 12 principles necessary to successfully teaching math facts.
Teach a Limited Number of Math Facts at a Time
There is a big difference between figuring out the answer and memorizing facts. If students have too many facts to learn at one time, they necessarily fall back on figuring out the answer. Instead, we want students to REMEMBER the answers without having to figure them out.
Only add more facts to learn as the previous set has been mastered
Once students have learned a set a set of facts to mastery, it is now possible to add two or three more facts to be learned. Student success is greatest when they have only two or three things to learn in a sea of material they have already mastered.
Practice should be cumulative
Practice must be structured in a way that facts which have been previously deemed mastered continue to appear along with the two or three new facts that are being learned.
Students should memorize facts in a way that forms a verbal chain
Students should always practice by saying the whole problem and the answer aloud. In this way, students memorize a verbal chain. As a result of this kind of practice, students hear/see 8x7 and can’t stop from saying/writing 56.
Mastery = automaticity
Automaticity is the ability to say the answer to a problem immediately after reading the fact. There should be no hesitation.
Students should have realistic, individual fluency goals
Students write at different speeds. The speed at which students can write the answer to facts is limited by their writing skill. Automaticity means that students should write answers to math facts exactly as fast they can write.
A routine for daily practice sessions should be in place
Practice is most effective when it is distributed throughout the year. Learning math facts is just one part of a math program therefore efficient use of limited time is critical. A standard daily routine is necessary in order to accomplish this goal.
A routine for corrective feedback during practice should be in place
Whenever students hesitate or give an incorrect answer, a corrective procedure should give them the answer, ensure they know it and provide them with a delayed test. It is very important that the delayed test occur before the student has a chance to forget the correct response.
Practice sessions should be short
Students cannot maintain focus on drill for more than 2-4 minutes at a time. Practice sessions may occur more than one time during the day, but should remain short.
A process for progress monitoring should be in place
If students are really learning math facts, the number of facts they can answer within a set time period should gradually increase. Periodically, students should be given a timed test of all the facts in the operations they are learning to see if their fluency is improving.
If students are to keep up with their grade level math program, they must begin memorizing multiplication facts in Grade 4 at the latest
Because fractions demand instantaneous recognition of multiplication facts, these must be mastered before fractions can be successfully learned. Even those students who need their fingers to add and subtract in Grade 4 and above, should learn multiplication facts to mastery or their continued progress in math is in jeopardy.
Celebrate success!
Students will be motivated to learn math facts if teachers act like it is important. Finding ways to celebrate students’ success is the best way to demonstrate the importance of learning math facts.