Mathematics education poses the greatest challenge worldwide. Traditional teaching methods as well as curriculum development have proved ineffective for the majority of students – and this has been true for generations. Even without a good understanding of mathematical concepts and mathematics as a whole, students still learn mathematical methods and procedures and come to apply them correctly in order to do their homework and pass their tests. In other words, they do classroom mathematics with little to no understanding of the concepts they use – and almost always their teachers are pleased with such results. This is possible due just to the nature of mathematics. On the basis of such double sufficiency (student’s and teacher’s), the idea is strengthened in the student’s system of beliefs that mathematics is something merely instrumental and calculational.

In practice, the inclination toward the procedural approach is largely the result of policy making, which imposes with the curricula and methodology a “socially useful” mathematics to be taught in schools. This approach is somehow justified by the constraints of the school setup: the limited time frame of a class and the relationships of mathematics with other disciplines being taught, the pragmatic goal of passing tests and exams (which are based on problem solving), and the applicative nature of mathematics itself. The negative effect of the exclusively procedural approach is incontestable and visible: Losing the battle with the conceptual base of mathematics, students develop a "mathematical anxiety” and stop seeking mathematical understanding. They come to see mathematics as their "traditional enemy" from school. In high school, the more complex notions taught (especially in calculus, statistics, trigonometry, and higher algebra) deliver the ultimate blow to the self-confidence artificially acquired in earlier grades through procedural skills learned without an understanding of the mathematical concepts involved As a result, fewer and fewer students come to study mathematics in college or pursue a career in mathematics – including good problem solvers and even Olympiad participants. The lack of conceptual-mathematics understanding also affects learning in mathematics-based disciplines, especially physics.

Parents call private tutoring services to help improve their children’s mathematical performance, including in what concerns understanding; however, these services use the same traditional procedural patterns, even if time is not as limited as at school, and the student may pose any number of questions. Are there any adequate solutions for this state of affairs? YES, Interdisciplinary research has offered a positive answer; however, the theoretical results have not yet been implemented in educational systems (with small exceptions among some mathematics faculties). Until a revolution occurs in the official education system, the solutions are individual and can be applied only through certain external resources (tutoring sessions for conceptual understanding of mathematics, problem-solving with fully explained solutions).

 

 

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