A orquestração instrumental de uma situação matemática para o EFIIOrchestration instrumental of a mathematical situation for EFII

Este artigo apresenta uma pesquisa destinada à formação de professores do EFII. Essa formação foi concebida para tratar da relação professores, estudantes e tecnologia sob a lente teórica da orquestração instrumental. Para isso foram elaborados uma situação matemática envolvendo a problemática do teorema de Euler para poliedros e recursos construídos com o software GeoGebra. Foram também propostas orquestrações instrumentais para orientar o desenvolvimento da situação matemática. Os procedimentos metodológicos foram levantamento bibliográfico, leituras e análises, internos a uma pesquisa teórica. O objetivo da pesquisa foi apresentar uma proposta de ensino, contendo recursos digitais para abordar um conteúdo de geometria espacial para o ensino fundamental II e com um modo de exploração desses recursos suportado em uma teoria da educação matemática. Consideramos que o resultado atende esse objetivo, pois a situação possibilita a exploração de vários conceitos matemáticos e a formação de atitudes frente a esses conhecimentos, os recursos são suficientemente ricos para auxiliar a condução da situação matemática e as propostas de orquestração complementam as ideias dos autores para a formação pretendida. Além disso possibilita a divulgação da orquestração instrumental entre formadores de professores de matemática da educação básica, comunidades de prática de professores e entre professores em formação, pois será disponibilizado no espaço digital ensinodematematica.com.

ANALISIS KEMAMPUAN MEMECAHKAN MASALAH DAN KOMUNIKASI MATEMATIS SISWA SD DI KABUPATEN MANGGARAI NTT

This research aims to describe the ability in problem solving and the communication skills of the Manggarai Elementary school students; furthermore, investigate the particular aspects needed to pay attention more. This is a descriptive research which was conducted in elementary schools in Manggarai District in April 2014. The subjects of this research are 39 students from 13 elementary schools in Manggarai. The instruments which are utilized are test items, assessment sheets, the ability in problem solving, mathematical communication and interview guideline. The result of the research presents 39 students who become the subjects of the research, did not give the perfect answers towards the test items. Concerning the problem solving ability, the research result shows that not all aspects of problem solving are performed by the students. Concerning the mathematical communication, the research results show that the students’ ability in stating the mathematical situation into mathematical points of idea has been performed well; nevertheless, the elaboration of the problem solving stages are still poor. Based on the research results, it can be summed up that the ability of problem solving and mathematical communication of the students in Manggarai District elementary schools are poor.

Activities for Students: The Archaeological Dig Site: Using Geometry to Reconstruct the Past

In secondary mathematics, students often see little connection between geometry and the real-life mathematical situations around them. When asked to describe geometric figures, their descriptions are sometimes no more than an identification of sides and angles. They have not had experience in using more than one property in a mathematical situation or in describing how two geometric properties are related. The van Hiele model of how students learn geometry proposes that students' understandings of geometry move from recognition to description to analysis (Fuys, Geddes, and Tischler 1988). For students to make this transition to analytic thinking, teachers need to create problem situations that enhance development of students' intuitive understandings. These investigations allow students to explore relationships among geometric shapes and to make conjectures about properties. The conjectures can then be stated formally as theorems.

Explorations in Geometry: The “Art” of Mathematics

We often pose a mathematical situation, concept, or theorem and do not proceed to explore it fully. We do not experience the thrill of chasing our intuitions, the excitement of meeting the unexpected, the uplift of clarifying ideas, the feeling of enlightenment and pride upon discovering something new to us, and the rush of succinctly capturing the essence of complexity. In short, we miss the artistic experience in one of our great arts—mathematics.

A Technique for Assessing Mathematical Problem-Solving Ability

This report sets out the procedures followed in developing, administering, and scoring a set of mathematical problem-solving superitems and examining their construct validity through a recently developed technique of evaluation associated with a taxonomy of the structure of learned outcomes. Each superitem includes a mathematical situation and a structured set of questions about that situation. To judge whether the response patterns of students to the superitems were interpretable, two questions were raised about the response patterns. For each question, the data strongly support the validity of the underlying theoretical constructs.

Mathematics Recreations

Many teachers of mathematics believe that a mathematical recreation is a species of its own. In other words, not all mathematical situations may be turned into mathematical recreations. This department proposes to explode this misconception once and for all. Any mathematical situation, if appropriately treated, may become a mathematical recreation. While “exploding” the above misconception, this department will reveal some of the “secrets of the trade” so that any mathematics teacher may become a creator of mathematical recreations.

Looking Again at the Mathematical Situation

For nearly six decades there have been almost continuous efforts to reform mathematical instruction. A comprehensive account of these efforts will serve to bring out a number of significant facts.1 For example, from the very beginning this movement has had an international character. Moreover, in the world's leading countries it was sponsored by outstanding mathematicians and scientists. That is, the original impetus toward mathematical reform came from distinguished scholars connected with higher institutons of learning. And the issues which engaged their attention are as vital today as they were at the turn of the century. Among them may be mentioned the development of a continuous program extending from the kindergarten to the university; a persistent emphasis on such central themes as functional thinking or the study of relationships; the elimination of “inert ideas” and useless details; a genuine acquaintance with certain key concepts and methods of modern mathematics; a closer correlation of mathematics and science; the abandonment of purely mechanical drill in favor of real understanding and purposeful application; and, above all, a keen appreciation of the role of mathematics in the modern world.

The Introduction of Negative Numbers

It Is one of the most difficult tasks in teaching elementary mathematics in high schools to be both, understandable and correct. Most textbook authors know how to write simply and so to speak popularly, but, on the other hand, there is no doubt that many of them fall short of perfect scientific correctness. It would be ridiculous to try putting in school classes such modern scientific methods as, for example, the formal introduction of real fractions as couples of integral numbers, negative numbers as couples of positive numbers, imaginary numbers as couples of real numbers. However, we are often forced as teachers to meet a mathematical situation where we have to pay attention to two points: first, no conclusion must be gained surreptitously or by tricks, and secondly, when some of the steps within a statement are too difficult to be understood by young people the gaps must not be concealed but, on the contrary, pointed out to the students with the explanation that it is possible to accomplish the proof although we may not do so for the moment.

Enrichment Materials for First-Year Algebra

The place of mathematics in the secondary school curriculum has been a subject of very much discussion the last few years. Just what are the aims of a mathematical education? Let us paraphrase such aims as suggested by J. H. Minnick. We should give each individual such a knowledge of the subject as will enable him to understand the exactness and force with which mathematics works and the parts which it plays in solving the problems of nature and which makes it possible for man to turn the elements of nature to his own use; we should develop such fundamental concepts as will enable the student to express his thoughts more clearly and to understand written and spoken language more readily; we should give to each student such a knowledge of mathematics as will enable him to carry on the work of his future occupation as it is now conducted, as will serve as a basis for future preparation if progress in his work should demand it, as will enable him to find new and better ways of doing his work and to recognize a mathematical situation when be sees it; we should require of each student sufficient mathematics to determine whether he will profit by further study of the subject and to select those who will probably be leaders in mathematical thought; and of the select group we should give enough mathematics to keep open the door of specialization in mathematics and in fields dependent upon mathematics.1