University of Southampton
Title: Critical thinking and geometry education
Geometry education is generally seen as a key component of the mathematics curriculum in which learners can encounter, and be involved in, argumentation and proof. Yet critical thinking, the analysis and evaluation of an issue in order to form a judgement, does not necessarily emerge straightforwardly from teaching the geometry curriculum. Indeed, if geometry education is primarily seen as a vehicle for enculturating learners into dispassionate reasoning, then this might not entail them experiencing the taking into account of ethical and social dimensions of situations. This talk examines some of the challenges facing the teaching and learning of geometry and reviews some possible ways to re-imagine geometry education to encompass more aspects of critical thinking.
Pavel Wlodkowic University College at Plock
Title: Discipline and critical thinking as one of the basic types of creative mathematical activity
The first part of the lecture contain a short description of the conception of shaping and developing creative mathematical activity (CMA) of high school students. This conception is based on an analysis of mathematical activity of a creative nature leading to the identification and characterization of selected basic types of CMA as some complex procedures that exist in the creative work of professional mathematicians. The characteristics and description of particular types of CMA activity are based on appropriately selected examples.
The concept of shaping and developing creative mathematical activity presented in the lecture is based on two elements. The first of them, (A), are the identified basic types of creative mathematical activity that I conventionally call in this article as follows:
The (B) second important element of the presented conception are so-called multi-stage tasks based on problem situations that bind different types of creative mathematical activities in complex mathematical and didactic situations. They constitute a complex structure of tasks, problems and didactic situations, and help create a laboratory for conducting creative mathematical activity by students, thus making it possible to place students (when content and problems are properly selected) in situations similar to those in which creative mathematicians work on their own mathematical problems.
The second part of the lecture contain, based on appropriate selection of examples, short description of discipline and critical thinking in the mentioned above three aspects.
Esther S. Levenson
Tel Aviv University
Title: Mathematical creativity in the classroom: Teachers’ beliefs and values
Along with promoting critical thinking, fostering mathematical creativity is one of the major aims of mathematics education. One of the challenges to promoting creativity in the classroom is that educators do not agree on how to define, promote, or evaluate mathematics creativity. The first part of this talk will present researchers’ views regarding these issues. A second challenge is that teachers may hold various beliefs related to creativity that may or may not coincide with educational goals. For example, do teachers believe that we can foster mathematical creativity among all students or do they believe that creativity is it an inborn trait? A third challenge is that teachers’ values may also interact with their intention to foster creativity. For example, if a teacher values originality, he may promote individual creativity as opposed to collective creativity. This talk will present results from studies which investigated teachers’ beliefs and values related to mathematical creativity, and discuss how beliefs and values may impact on the ways teachers foster mathematical creativity in their classrooms.
Maria Alessandra Mariotti
Università di Siena
Title: Educating to rationality: from argumentation to mathematical proof
Mathematicians know what proof is. Such a knowledge assures their participation to the scientific community: to them it involves rigorous reasoning that establishes the validity of a mathematical statement based on clearly formulated assumptions, and referring to well defined theories. That means that Mathematics constitutes a very peculiar context where creative, imaginative and productive thinking has to be accompanied by justification, and eventually by arguments according to specific rules of acceptance. The educational problem rises whether is it necessary, and or appropriate, to introduce students to such a proving practice. I will discuss the role of proof in mathematics education and its possible more general value in educating to rational thinking, beyond the specific area of Mathematics.