A language of thought for the mental representation of geometric shapes

Why do geometric shapes such as lines, circles, zig-zags or spirals appear in all human cultures, but are never produced by other animals? Here, we formalize and test the hypothesis that all humans possess a compositional language of thought that can produce line drawings as recursive combinations of a minimal set of geometric primitives. We present a programming language, similar to Logo, that combines discrete numbers and continuous integration in higher-level structures based on repetition, concatenation and embedding, and show that the simplest programs in this language generate the fundamental geometric shapes observed in human cultures. On the perceptual side, we propose that shape perception in humans involves searching for the shortest program that correctly draws the image (program induction). A consequence of this framework is that the mental difficulty of remembering a shape should depend on its minimum description length (MDL) in the proposed language. In two experiments, we show that encoding and processing of geometric shapes is well predicted by MDL. Furthermore, our hypotheses predict additive laws for the psychological complexity of repeated, concatenated or embedded shapes, which are experimentally validated.

Eksplorasi Etnomatematika Pada Benteng Belgica Di Neira Maluku Tengah

Ethnomathematics is the study of mathematics learning. One of the cultural assets in Indonesia is Belgica Fort which is located on Neira Island, Central Maluku, which has a pentagon shape on the outside. The purpose of this research is to know the history of Belgica Fort and to know the construction of Belgica Fort building which is associated with mathematics in geometric shapes. The research method is a document analysis by analyzing and reducing data from several articles that become references, with the conclusion that the Belgica Fort building is composed of various forms of flat and spatial shapes. The results of his research that learning mathematics on geometry material associated with Belgica Fort can be used as teaching materials and encourage students to be active in exploring their knowledge through observations made in this ethnomathematics-based learning. Keywords: Fort Belgica, Ethnomathematics, Geometry

Desenvolvimento e aplicação de um objeto de aprendizagem m-learning para crianças da educação infantil

Este trabalho visa inferir se a utilização de tecnologia da informação como instrumento de apoio ao ensino-aprendizagem pode influenciar e ajudar na identificação de formas geométricas básicas e ligeira indicação das cores primárias na educação infantil. Foi proposto e desenvolvido um jogo para tablet (objeto de aprendizagem), aplicado e observado em turmas do maternal e jardim de infância. Neste artigo são descritas as etapas da implementação, a descrição das interfaces a fim de identificar a adequação desta proposta, que como resultado considerou-se adequado para as crianças da turma do jardim de infância, mostrando verbalmente que fixaram o conteúdo proposto. This work aims to infer whether the use of information technology as a support tool for teaching-learning can influence and help in the identification of basic geometric shapes and slight indication of primary colors in early childhood education. A tablet game (learning object) was proposed and developed, applied and observed in kindergarten and nursery classes. This article describes the stages of implementation, the description of the interfaces in order to identify the suitability of this proposal, which as a result was considered appropriate for the children of the kindergarten class, showing verbally that they fixed the proposed content.

Developing Property-Based Geometric Reasoning

Recognizing the complex nature of students’ geometric reasoning, we present guidelines and suggestions for implementing a Guess My Shape minilesson that focuses students’ attention on properties and attributes of geometric shapes.

Examination of 4th Grade Students' Definitions for Square, Rectangle and Triangle Geometric Shapes

The aim of this study is to obtain information about students' definitions, mistakes, misconceptions, and van Hiele geometry thinking levels by using the definitions of 4th grade students for geometric shapes of rectangle, square, isosceles triangle, equilateral triangle, and scalene triangle. The study was carried out with 156 primary school 4th grade students. In the study, the case design, one of the qualitative methods, was used. Students were asked to describe geometric shapes. It was observed that most of the 4th grade students participating in the study were in the visualization stage of van Hiele. There are very few definitions of the hierarchical structure in the study. Most correct definitions are in the partitional form. In the study, misconceptions were detected in some of the students.