17 Apr 2013
Problems students could face when calculating with fingers
Math teacher at Ho Math Chess Learning Centre, Vancouver, Canada
There are many ways to train children to calculate. Some teach abacus, some use special finger method. The design of Ho Math Chess worksheets encourages students to do calculations without using their fingers to do the counting forward or backwards. None of our A students and students participating in math competitions use their fingers to do basic calculations and their ability of mental math is strong than those who use fingers to count. The main reason is, without using fingers; students will develop strong number sense and are able to see steps ahead when working on math problems.
The following gives a list of potential problems students might encounter if continue to use fingers when going to higher grades:
- Difficult and slow to find answers which are related to work backwards such as subtractions or finding quotients. For example, it takes finger calculating students much longer than peers to find what is 12 - 9? When doing simple divisions such as 24 divided by 2, 36 divided by 3 finger calculating students cannot do them mentally without actually using pencil and paper.
- Have hard time to find product of primes of a number; slow to find an answer and have hard time to see if a number is divisible by certain number using divisibility rules; difficult to find GCF or LCM and later LCD; difficult and slow to reduce a fraction; have hard time to do the conversions between fractions, decimals, and % etc.
- Unable to see what is the trick to add certain type of questions such as 99 + 7 + 8 + 4 + 6 + 1 + 3 + 2 etc. Students who do not use fingers can scan this problem and then know the answer almost immediately.
- Because of the slow speed of doing basic calculations and the lack of mental math ability, the student has less chance to get in the enrichment math program due to competitiveness. By the same token, the student has less chance to do reasonably well in any math contests which stress calculations speed and the calculator is not allowed. Students will do poorly when oral math problems are presented in any math contests.
- Students will continue to experience difficulties when going to high schools with those problems requiring mental math quickly to recall four basic computation facts. Problems such as finding the square roots; adding like terms; factoring trinomials using cross-multiplication method; 30-60-90 special degree; graphing, 2x + 3y = 6 etc.
When we talk about calculation without using fingers, we are not saying the only benefit is so that students can recall arithmetic facts quickly. Form above observations, we can see that mental math or calculating without using fingers is not limited to the scope of being a human calculator of doing some calculations in lighting speed.
To acquire the mental math skills so it truly benefit students, the students must learn the skill of reversing calculating like how to get factors of a number, how to quickly find prime factors of a number, how to find if a number has perfect number as a factor, how to not only do calculation in linear fashion, but also know how to do calculations in cross or vertical way quickly and be able to see patterns. Mental math also helps student do trinomial factoring when they are in grade 9 or 10.
When in high school, students with math deficiencies often find it is difficult for them to go back to work on addition, subtraction, subtraction, or multiplication again since it is embarrassing for them to work on grade 3 math while they are already grade 10.
With the above in mind, we shall create an environment where students are encouraged to think more even when they are doing calculations. We also shall encourage students to do calculations without using their fingers so the calculations are totally done in their brains without relying on any manipulative. Calculating without using fingers can help students develop strong mental math ability. As a consequence, this helps students do well later in their SSAT, SAT and also increase the chance of getting into private schools if they want to. The chance of getting into enrichment math program in high schools is also higher.