The use of some historical mathematical textbooks from the Teachers’ Institute in Spišská Kapitula in the 19th century and first half of 20th century

We would like to present some excerpts of historical mathematical textbooks from the Teachers’ Institute in Spišská Kapitula, because this institute is at the roots of primary education in Central Europe. The methodological approaches used in these textbooks contain suitable motivation and models for explaining basic mathematical notions in primary education and the training of future primary teachers. There are some projects in Europe which use educational software and modern modes of interpretation to present sections from historical mathematical textbooks in contemporary teaching. In our article we would like to do the same for the Slovakian situatio

Some methods of problem solving in historical mathematical textbooks

This paper makes an excursion into the history of mathematics as presented in mathematics textbooks. We describe some components of mathematical notions in textbooks by Jakub Kresa (1648-1715) as well as some approaches to the problem solving in textbooks by Franz Mo?nik (1814-1892). These historical approaches are connected to modern mathematics education because many international studies, such as The Programme for International Student Assessment (PISA) support the use of problem solving and real-life problems in mathematics education. Word tasks have an important place in school mathematics. There are three important stages for solving these tasks: mathematization, calculation and interpretation of the tasks’ results. We also highlight divergent thinking in problem solving during the educational process.Este artículo hace un recorrido por la historia de las matemáticas presentada en los libros de matemáticas. Describimos algunos componentes de las nociones matemáticas en los libros didácticos escritos por Jakub Kresa (1648-1715), así como algunos enfoques para la resolución de problemas en los libros didácticos escritos por Franz Mo?nik (1814-1892). Estos enfoques históricos se conectan con la educación matemática moderna porque muchos estudios internacionales, como el Programa Internacional de Evaluación de Estudiantes (PISA), apoyan el uso de la resolución de problemas y los problemas de la vida real en la educación matemática. Las tareas con palabras tienen un lugar importante en las matemáticas escolares. Hay tres pasos importantes para resolver estas tareas: matematización, cálculo e interpretación de los resultados de las tareas. También destacamos el pensamiento divergente en la resolución de problemas durante el proceso educativo.Este artigo faz um percurso na história da matemática apresentada em livros de matemática. Descrevemos alguns componentes de noções matemáticas em livros didáticos de autoria de Jakub Kresa (1648-1715), bem como algumas abordagens para a resolução de problemas em livros didáticos de autoria de Franz Mo?nik (1814- 1892). Essas abordagens históricas se conectam à educação matemática moderna porque muitos estudos internacionais, como o Programa de Avaliação Internacional de Estudantes (PISA), apoiam o uso de resolução de problemas e de problemas da vida real na educação matemática. Tarefas com palavras têm um lugar importante na matemática escolar. Existem três etapas importantes para resolver essas tarefas: matematização, cálculo e interpretação dos resultados das tarefas. Também destacamos o pensamento divergente na resolução de problemas durante o processo educacional

Theorien des Erkenntnisprozesses im Mathematikunterricht an der Grundschule

Wir zeigen in diesem Beitrag einige Theorien des Erkenntnisprozesses im Mathematikunterricht an der Grundschule. Wir präsentieren Ziele des Mathematikunterrichts in Bereichen Allgemeine Haltungen und Fähigkeiten, Geistige Grundtechniken. Theorien des Erkenntnisprozesses demonstrieren wir am Beispiel Algorithmus der Division. Wir benutzen passenden universalen und separierten Modellen für die Grundschule.In this article we describe some theories of the process of gaining knowledge in mathematics education for primary level. We show some aims and goals for different topics of mathematics education. For demonstration of using theories of the process of gaining knowledge we use the algorithm of division. We show some teaching methods and models suitable for primary level.Wir zeigen in diesem Beitrag einige Theorien des Erkenntnisprozesses im Mathematikunterricht an der Grundschule. Wir präsentieren Ziele des Mathematikunterrichts in Bereichen Allgemeine Haltungen und Fähigkeiten, Geistige Grundtechniken. Theorien des Erkenntnisprozesses demonstrieren wir am Beispiel Algorithmus der Division. Wir benutzen passenden universalen und separierten Modellen für die Grundschule

Supporting mathematical and digital competences useful for STEM education

Acronym STEM (Science, Technology, Engineering, and Mathematics) has become very frequently word among many stakeholders in the school policy. Mathematical and computational thinking are important for STEM Education. There are common thinking skills, but computational thinking focuses more on automation. Mathematical thinking focuses more on proofing. We present n our contribution the theoretical requirements that are needed for students in mathematical and digital competences. Practical examples represent, how it is possible to develop mentioned competences in educational practice

Development of geometrical thinking via educational software by pupils of elementary school

The study is aimed to describe the using of geometrical educational software oriented to develop geometrical spatial thinking. This software is available on the webpage www.delmat.info. We would like to show his functions, propose concrete thematic areas in Slovak and Polish curriculum in the elementary level useful for this software. Future research in Polish elementary school in the 1-3 grades will be discussed

Regulated functions and integrability

Properties of functions defined on a bounded closed interval, weaker than continuity, have been considered by many mathematicians. Functions having both sides limits at each point are called regulated and were considered by J. Dieudonné [2], D. Fraňková [3] and others (see for example S. Banach [1], S. Saks [8]). The main class of functions we deal with consists of piece-wise constant ones. These functions play a fundamental role in the integration theory which had been developed by Igor Kluvanek (see Š. Tkacik [9]). We present an outline of this theory

Some aspects of thinking of Jakub Kresa for development of school mathematics

This article makes an excursion into the history of mathematics, which is used in school mathematics. We would like to describe some components of mathematical notions developed by Jakub Kresa (1648-1715). We would like to compare his work with another two big mathematicians Isaac Newton (1643 -1727) and René Descartes (1596-1650), because it is possible to see some similarities in topics of their works. Isaac Newton wrote separately arithmetic and algebra in Arithmetica universalis, but in his work Philosophiae naturalis principia mathematica he used only geometry. René Descartes integrates the knowledge from algebra, arithmetic and geometry in his work La Geometrie and in a similar way, Jakub Kresa described the mathematical theory in his work Analysis speciose trigonometriae sphaericae

Motivation for the use of Content and Language Integrated Learning (CLIL) at the Slovak minority school in Hungary

Content and Language Integrated Learning (CLIL) can support the use of a minority language in different subjects. In our paper we present this method in the case of school mathematics. First, we describe the process of gaining knowledge in teaching mathematics. We will then present some students’ work who will be future Slovak minority teachers