Yes, there was a time not long ago, when a premium was placed on just getting the right answer. Clearly, not everyone thinks or analyzes problems in the same way. It might even seem acceptable to encourage students to adopt individualized approaches to learning. Creativity, after all, is a trait that we reward most of the time.
In certain subject areas, particularly science and technical subjects, basic knowledge is needed to be cultivated before effective creativity can take root. Basic knowledge in these subject areas has a cumulative effect. There are certain properties or characteristics that exist even at elementary stages upon which later knowledge rests.
Let us add another complication: Mathematics is not just a science; it is also a language. Reflect on this a bit. As a science, it possesses certain properties and characteristics. But it is also a language that permits one person to communicate to another in terms of problems, analysis and solutions. And as a language it relies on feedback and understanding. Mathematic is all about proof, i.e. demonstrating that it is understood and agreed by others.
Taken together, Science and Language, it is not surprising that math is a subject area that trips up a fair number of students. In today’s ultra fast paced world, many of us, parents and student alike, want and expect knowledge on demand. We have grown accustomed to the Google search bar as a gateway to knowledge. But we encourage you to alter your expectations a bit. Think of it as a gateway to information, not knowledge.
What education demands today is not just that the student gets the right answer. After all, he or she can get that today simply by entering a search term in a browser. Education standards today expect the student to demonstrate knowledge as to how the correct answer is derived. He is expected to demonstrate his understanding by providing work, which reflects his thought processes.
So, maybe there are two answers to the question “Why getting the right answer isn’t good enough.” The first quite simply is that math is cumulative. Getting the right answer, for the wrong reason will not provide a good foundation for later learning.
What does cumulative mean? It means that unless a student has a sound understanding of math concepts taught yesterday, she will struggle with today’s concept. Many subject areas build on concepts taught in earlier grades or terms, but perhaps none more so than math.
Think of math as a picture puzzle. If puzzle pieces are missing, the final product is defective. One’s eyes are drawn not to the picture as a whole, but rather to those one or two pieces that are missing and wondering just what was contained on those pieces.
Or think of a brick wall. Imagine if one or two rows of bricks are mortared in place poorly. As the bricklayer tries to build the wall higher, the entire wall is at risk of failing. Math is like that.
The second answer is that math is a language. It is a form of communicating from one person to another; or, from person to computer. The recipient of the communication has to be able to grasp the problem, analyze it and arrive at an answer that is consistent with the sender, otherwise communication did not take place. An individual that can’t fulfill the language element is essentially saying, “trust me on this.” Math doesn’t work that way.
When parents ask us to help them and their children, we begin by administering an assessment test. Why? Because we suspect that poor grades this term are probably an indication of poor learning some time ago, and it is our job to identify this learning gap. Once identified, we are able to create a custom Learning Path for your child that aims to rectify this gap. Once rectified, cumulative learning can recommence.