Abstract:

Students need to acquire procedural knowledge, both for their progress in school and for their lives. However, it is important to emphasize that the teacher's role is not only to teach procedural knowledge, but also to explain why the procedures work. A teacher should explore conceptual knowledge, and if this is not happening in school, something is going wrong. In terms of mathematics, which contains a robust body of procedures and algorithms, this dual responsibility for the learning process is paramount.

Attracting students to mathematics is only possible with a good understanding. If the student is not captivated, the learning process becomes more difficult. Since understanding is the first building block for learning mathematics, the teacher is required to use a didactic approach that includes the important conceptual knowledge.

A main idea of the Great Math teaching method is to propose exactly a constructivist didactic approach to meet this challenge. Already with 10 years of experience, Great Math has produced a complete series of elementary school books - Viva a matemática! (Princípia editor).

In this post we give a brief overview of Great Math's approach. As an example, we have chosen the topic "Multiplying Decimals", where it is often observed that the teacher focuses strongly on procedural knowledge without paying special attention to conceptual knowledge. There is a good reason for this: procedural knowledge is relatively easy to teach, unlike the concepts behind it. Teachers often take the easiest route, which makes sense. But paying little attention to the fundamental concepts comes at a high price, not only for the subject being taught, but also for everyone involved.

The models proposed by Great Math attempt to provide a deeper understanding of the traditional multiplication algorithm. These models are described and analyzed, as are the real-word problems used to do them.

Keywords:

Elementary math teaching, multiplication, decimals, Great Math, procedural knowledge, conceptual knowledge.