9 Aug 2009
Students Need to Have Basic Mental Math Ability
Frank Ho, Amanda Ho
Ho Math and Chess Learning Centre
Canada certified math teacher
Vancouver, BC, Canada
In our over fifteen years of teaching math experience, we have witnessed how important it is for students to have basic mental math ability. What is basic mental math ability? We are not talking about how fast a student can do 15 times 16 in a few seconds or if a students can remember the ratio of a circumference to its diameter to 10^{th} decimal place. We are referring to a condition that if students do not possess this kind of math mental ability then they will not have adequate “number sense” and thus it hampers them from developing good math ability. One area seems to stand out to strike a major difference is student’s factoring ability (reverse of time table). We would like to give some examples to illustrate how important it is for students to develop the mental math ability in factoring.
To reduce 9/15, students are not able to quickly see its greatest common factor is 3 then they will have trouble to simplify its fraction. It is very important for students to know how to simplify a fraction. For example, it will be difficult for students to do this fraction if they do not know how to simplify 3/5 times 25/9 times 18/50. All these problems require students to have very basic factoring ability and if students have not mastered times table this could be the time they get frustrated with math.
Factoring not only affects simplifying fractions, it also affects equation solving. For example, 4x = 2 is a very simple equation and yet so many students are not able to solving it without visually doing a division like 4x/4 = 2/4. This is partly the problem for some math teachers who have always taught students to physically and visually carry out the computation and do not encourage mental math computation. It is a good idea to promote mental math computation whenever it is possible.
When going to high school, students will continue to lack behind in doing trinomial factoring since they will not remember the formulas of the square of x + y or what are factors of x squared minus y squared etc. Because of these reasons, they will have difficulty in seeing how to rationalize 1 /(square root of 3 plus 2).
They seem to have difficulty in doing completing the square method for coming up with a standard form of a parabola.
When working on rational expression, students have difficulties in finding the GCF of x square + 2x + 1 and (x + 1) square because they do not know that (x square + 2x + 1) = (x + 1) squared.
When working on square root and cubed roots, students have trouble to see the root of 4 is 2 and the root of 27 is 3 and have some difficulties in coming up answers for some numbers because they could not come up with perfect square numbers and cubed numbers quickly.
For a bit more complicated factoring problems, then students basically are lost. For example, to factor x cubed + 3 x squared – 16 x – 48, students have no clue in how to factor this expression if they do not have mental math ability since the coefficient gives clues but they can not see the relationship between numbers.
Many times, students can not prove trigonometry identities because they do not know which identity formulas to use. Without any idea of which identity formula to use, they do not have any instinct on how to prove an equation.
Frank Ho, Amanda Ho
