Understanding Mathematical Equation: Does Practice Make You Perfect?
There’s no doubt that rote learning stifles the creativity of students in classrooms. Traditional teaching methods in American high schools have long focused on memorization and despite the radically different demands of mathematics, it’s still subject to old-school teaching methods.
This is why many students have trouble understanding and applying mathematical concepts outside of context. Changes in values, numbers and problem statements can completely render all practice useless, despite it being practiced multiple times.
So, if you’re a student who’s having a hard time in your math class, what do you do? If not practice, what can make your math perfect to pass the grade easily? Let’s break it down!
Learn the Concepts
Before you start filling pages with the same equation over and over again, make sense of it.
If you write a2-b2 = (a-b).(a+b) multiple times, you may be able to answer a2-b2 = ? in multiple choice questions but you definitely won’t be able to use it to solve an elaborate problem.
So, what do you do? You break it down! First, look at the equation numerically. Start by assigning values to ‘a’ and ‘b’ and solve the equation. This is just to help you verify the equation.
You can then graph the equation and use it by factoring a2-b2. Factoring a2-b2=0 will help you understand what the difference between two squares really means and how it may be solved.
When you understand the process, you can use it to practice with varying values. After you have successfully understood the concept, its solution and the process, repetition can be crucial for heightened and long-term retention.
Does Practice Stop You from Thinking?
Practice has always been encouraged in academic learning and is encouraged in classrooms from as early as kindergarten level. It can be both detrimental and extremely beneficial for our learning ability, depending on the approach you use.
Figure 2: Math Practice
In objective subjects, such as math, practice is important but only if it’s followed by conceptual and relational understanding. Instrumental understanding, on the other hand, is useful for short-term tasks but contributes little to extended learning.
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