Abstract:

Recent publications highlight concerns about the lack of mathematical competence of math teachers, mainly due to a limited extensive training in mathematics. This lack of mathematical competence leads, as pointed out by several recent publications, to negative beliefs or predisposition towards mathematics which results in a lack of motivation, bad attitude or fear, which ultimately end up in what is known as mathematical anxiety among not only pre-service math teachers, but also among in-service teachers. It is therefore necessary to provide them with tools that improve their mathematical competence and, consequently, their attitude towards them.

The appearance of CAS (Computer Algebra Systems), such as Mathematica, Maple, Matlab, etc., in the second half of the twentieth century was an important advance in the resolution of mathematical problems. However, in relation to the 4 classic phases in problem solving commonly accepted by experts in mathematics didactics -understanding, planning, executing and reviewing- the CAS contribution is limited to the mathematical manipulation of algebraic expressions, that is, to the execution phase, which is reached after understanding and planning a problem. In other words, they only provide calculation capacity (symbolic and numerical) and graphic representation. Since they do not have the capacity to model problems or reason about their solution, their didactic application is limited.

However, recent research indicates that many of the difficulties of math teachers appear in the understanding and planning phases. In recent years, the development of generative artificial intelligence has been providing at least a partial solution to this question. Indeed, generative artificial intelligence systems can contribute ideas to the rest of the phases (such as understanding the problem, planning or reviewing), becoming a very useful tool for teaching problem solving. In fact, not only are they capable of modeling (some) problems mathematically and reasoning about their solution, using properly human reasoning patterns, but they also allow them to do so from natural (non-symbolic) language. However, the algebraic manipulation and mathematical calculation related to execution sometimes present unexpected basic errors.

Artificial intelligences specialized in mathematics (WolframGPT, Matlab GPT, Matlab Copilot, Copilot Math, etc.) integrate the properties of artificial intelligences and CAS, thus providing an excellent tool for solving mathematical problems by showing step by step an explanation of each of the classical phases.

In this sense, the main objective of this work is to show how these specialized artificial intelligences can serve math teachers as asynchronous and permanent advisors, to improve not only their mathematical knowledge and skills, but also their attitude towards mathematics.

Keywords:

AI on Education, ICT Skills Development, Mathematical Competence, Attitude towards Mathematics, Professional Development of Math Teachers, Life-long Learning.