The Teaching of Quadratic Equations in Mathematics is Improperly Introduced
Over the years when I meet my new students in first year mathematics at university, I notice something very unusual about their understanding of quadratic equations. It seems they always want to use the quadratic formula all the time and very few use the factorization method.
It seems that when they are introduced to quadratic equations they treat the quadratic formula and completing the square as two very different methods. Due to this problem many students do not know why the quadratic formula is used and there do not appreciate its use. This situation carries on until students are third year mathematics class resulting in them failing to solve more advanced quadratic equations.
To clarify the issue, I suggest that in the teaching of quadratic equations it is important to explain to students that the quadratic formula is obtained by completing the square. This means that completing the square on any quadratic equation is deriving the quadratic formula. Another method that many students fail to use is the method of factorization. This is usually caused by early introduction of calculator use in the mathematics curriculum. Given the general quadratic equation of the form; ax2+bx+c=0
, the method demands that one needs to think of two numbers such that when they are multiplied ac
is obtained and when they are added b
is obtained. Since calculators cannot perform this operation, the method of factorization is hardly used. I suggest that students learn about factors and multiples of numbers at an stage.
Details of how to complete the square on the general quadratic equation is shown on the site http://www.purplemath.com/modules/sqrquad2.htm If there are others who would like to comment on this please to not hesitate.