**CME 2021 programme contains:**

- Plenary lectures
- Working seminars (on three educational levels)
- Research reports
- Panel discussion

**CME 2021 plenary speakers are:**

- João Pedro da Ponte – Portugal
- Ivona Grzegorczyk – USA

**Titles and abstracts of the plenary lectures**

**Professor João Pedro da Ponte** – Instituto de Educação, Universidade de Lisboa, Portugal

**Learning to reason mathematically with meaning**

The aim of mathematics teaching is to get students not only to learn mathematical concepts and procedures but also to develop the ability to think mathematically. Thinking mathematically involves being able to perform mathematical reasoning, that is, to make inferences in which, from a certain information given, new conclusions are reached. In mathematics, deductive reasoning assumes a fundamental role, allowing the validation of knowledge, but an equally important role assumes inductive and abductive reasoning, essential for the creation of new knowledge. Mathematical reasoning assumes particular characteristics given the nature of the objects of this science, as abstract entities constructed from real-world experiences or from experiences with previously known mathematical entities. It is the links among mathematical objects and among them and real-world objects that allow the attribution of meaning to concepts and reasoning. In this lecture, I present results of recent research work in mathematics education, seeking to highlight key reasoning processes used in mathematics as conjecturing, generalizing, justifying and formulating problem solving strategies, and show how these processes can develop within the framework of an exploratory approach to mathematics teaching.

**Professor Ivona Grzegorczyk** – California State University Channel Islands, USA

**Using Modern Mathematics to Change Learning into Magic**

We will show modern mathematics supporting magical tricks promoting interactive learning, experimentation and algebraic modeling. Even though the activities are designed for introductory algebra courses to generate engagement, complexity and advanced mathematical thinking, everyone will be involved and surprised by some of the tricks.