Scientists widely believe that mathematics is the language of the nature. Research in language acquisition suggests that children, even if exposed to a foreign language, learn through practice. Elementary language skills (basic words of communication e.g., boy, girl, man, he, I..) are learned mainly by observation and mimicking. The logistics of organizing words into sentences, the grammar, and other necessities for creating meaningful writing are learned at advanced stages of acquisition. Imagine writing an essay, when you have no knowledge of the words needed to describe a character. It is very hard. Nobody would disagree with that.
Now consider how mathematics, especially in the light of NCTM guidelines, is taught. NCTM, and indeed politicians, media, etc in our society, stress the acquisition of math skills through problem solving. Problem solving, generally, is associated with ability to discern information in a short writing and involves modeling of the problem, followed by adopting a skill or technique to get the correct answer. Students are asked to solve problems as part of learning math. In direct contrast to language acquisition, they are asked to learn and utilize the grammar of mathematics ( a set of logical steps) even before they have understood the basic techniques. As a result, mathematical skill acquisition is sacrificed in the name of problem solving.
However, there is one big disconnect in NCTM’s philosophy. People, especially kids at young age, don’t learn language for no reason. They desire to communicate. This breeds desire to learn new words, sentences and so on. Placing a real world problem, no matter how captivating, can’t make a person learn math, if his/her life did not depend on it in some sense. If the child does not feel the need to know the solution, asking him to solve is quiet quiet frivolous.
Education researchers should focus on ways to promote thinking about mathematics, instead of hypothetical problem solving. This thinking should naturally evolve into learning about math skills. Once skills are mastered, problem solving should be encouraged. Once problem solving is accomplished, problem construction should be encouraged.