Visualisation and paper folding in problem-solving tasks -

Isabel Vale - Instituto Politécnico de Viana do Castelo – Portugal and Centro de Investigação em Estudos da Criança, Universidade do Minho – Portugal

Ana Barbosa - Instituto Politécnico de Viana do Castelo, Portugal, Centro de Investigação em Estudos da Criança, Universidade do Minho, Portugal and Centro de Investigação e Inovação em Educação, Instituto Politécnico do Porto, Portugal

Isabel Cabrita - Research Centre on Didactics and Technology in the Education of Trainers, University of Aveiro, Portugal.

Abstract

Middle primary years (8 to 11 years)

School mathematics requires effective teaching that engages students in meaningful learning through individual and collaborative experiences, giving opportunities to communicate, reason, be creative, think critically, solve problems, make decisions, and make sense of mathematics. Students are active individuals involved in their learning process which emerges from experiences and interactions between intellectual, social and physical dimensions.

However, not all students learn in the same way, they often show individual preferences regarding how they communicate, receive and synthesize information, which presupposes that teachers must consider the existence of a diversity of ways of understanding, reasoning and solving problems:

• Analytic: use of logical-verbal methods involving algebraic, numeric and verbal representations;
• Visual/geometric: use of visual-pictorial schemes, involving graphic representation
• Harmonic/integrated: no specific preference.

In particular, we highlight the potential of visual/geometric as a powerful support for understanding and explaining mathematical concepts and solving problems. Teachers should implement practices that lead students to use different representations, particularly visual ones, to communicate and reason mathematically. Some students think predominantly visually and for them, a visual approach is appropriate, but not everyone has this ability. However, visual abilities can be learned, as long as the right opportunities are used. In active learning, challenging hands-on tasks provide learning experiences that promote curiosity and interest, facilitating the introduction of formal concepts or the resolution of a problem where students are engaged and become good mathematics thinkers.

In this workshop, after a brief theoretical contextualisation, we will propose some tasks to solve, with which we intend to highlight the potential of visual communication involving the use of a sheet of paper, to facilitate the emergence of communication and reasoning in different ways.