Using mental imagery processes for teaching and research in mathematics and computer science

Abstract

The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We give two detailed examples.

How to explain modern security concepts to your children

“…In [Forišek and Steinová, 2012], some metaphors and analogies for teaching some computer science algorithms are proposed. As it has been shown by A. Finkel in [Arnoux and Finkel, 2010], proposing mental representations helps students to learn abstract notions. One of our aims is to propose mental representations to help people understand modern security notions.…”

An Examination of Abstraction in K-12 Computer Science Education

“…Applying universal design for learning and global immersion therapy, Israel et al (2015) found that elementary, middle school and college students could be successful in learning computer science. Recognizing that computer science requires visual intelligence, using visualization and encouraging students to draw or writing code using human language, called pseudo code, has been shown to facilitate visualization capabilities (Baloukas, 2009;Shane & Sherman, 2014;Arnoux & Finkel, 2010;Fouh, Akbar, & Shafer, 2012;Ozurt, 2015). Csernoch et al (2015) indicated that using dance, music, and theater to teach introductory computer science to college students improved test scores, grades, and retention.…”

Learning Potential in Mathematics through Imagination and Manipulation of Building Blocks

“…Despite this, the usefulness of building representations is often downplayed as an aside or ignored entirely. Two possible explanations are that good representation is not easy to obtain and that many teachers and researchers underestimate the importance of the classroom environment (Arnoux, 2009). However, this type of implicit stimulation activity, especially in kindergarten and the early elementary grades, was highlighted by Varol and Farran (2006); Klibanoff, Levine, Huttenlocher, Vasilyeva, and Hedges (2006);and Clements and Sarama (2007), who stressed the importance of internal and external sound environments and the importance of activities with concrete materials, such as building-block games.…”

“…It follows that a large part of understanding consists of constructing representations of various types. These representations are often both external (e.g., a picture) and mental (e.g., a feeling), such as the geometric image of complex numbers forming the complex plane or the kinetic model for elementary calculus (Arnoux, 2009). The first specific study on the relationship between imagination and mathematics dates back to Bishop (1973Bishop ( , 1989, who studied the crucial relationship between spatial ability and visualisation.…”

“…Understanding a mathematical definition, proof, or concept, is strongly related to the ability to build and handle a mental object (Arnoux & Finkel, 2009). Through the manipulation of blocks, children provide continuous reminders to the imagination, which allows them to give a concrete shape to their multitude of images and to simultaneously consolidate the principles of mathematics and geometry that are gradually acquired at school.…”