More graphics and fewer operations to teach math
The war of the "mates", also known internationally (math wars), exploded at the end of the 1980s, confronting teachers with respect to the teaching of mathematics with traditional or modern methods such as metacognition, which is the protagonist of the last one published by the OECD. Critical mathematics for innovative societies. The role of cognitive pedagogies.
The great novelty of this book is that it departs from the theory and lands in practice. Thus, it shows the excellent results of the Singapore method for teaching and learning mathematics, whose effectiveness is already recognized by the PISA tests.
It also details the approach that should be adopted by the new education systems of countries that want their new generations to be up to date and innovative. The book points out that to adapt mathematics to the real world, it may be more important to prioritize graphics and make operations less necessary.
Metacognition: the last thing to teach mathematics
This concept looks for different ways to arrive at solutions of problems. To understand it in an easier way, we talk about metacognition when we use rules, that is, if we want to remember a certain telephone number, we use memory, a cognitive activity, but if we create a rule or a method that allows us to remember this number, we are talking about a metacognitive activity. Metacognition is the knowledge of one's knowledge, it is learning to learn.
The OECD book also explains that metacognitive learning must consist of a training that the teacher must carry out and that the student must incorporate based on questions that the student must ask himself. According to the book, this is a process that talented people often perform.
Five mathematicians, George Pólya, Alan Schoenfeld, Lieven Verschaffel, Mevarech and Kramarski, have developed different models to teach mathematics to their students starting from the metacognitive method, but it is better known is the Pólya model, which is already known as the Singapore method, because to that the textbooks of this Asian country integrate this model and their students get the best positions in mathematical competence in the PISA exam.
The Singapore method
It includes five parts for mathematics that are represented in a pentagon: concepts (numerical, algebraic, geometric), processes (reasoning), attitudes (beliefs, interests), abilities (calculation, special visualization) and metacognition.
In practice, for the resolution of problems the following scheme is applied: understanding the problem, designing a plan, developing the plan, needing a new plan and review (the answer is reasonable?).
Marisol Nuevo Espín
