¿Para qué sirven los problemas en la clase de matemáticas? = What is the use of problems in Mathematics lessons?

The results obtained in several yield tests, at an international level (mainly the famous PISA 2003 report, by the OCDE), have raised a multiplicity of performances in order to improve the students' yield regarding problem solving. In this article we set a clear guideline on how problems should be used in Mathematics lessons, not for obtaining better scores in the yield tests but for improving the development of Mathematical thinking in students. From this perspective, the author analyses, through eight reflections, how the concept of problem, transmitted both in the school and from society, influences the students

50 mathematics lessons : rich and engaging ideas for secondary Mathematics.

Es una colección de cincuenta lecciones de matemáticas que requieren poco tiempo de preparación y que resultan idóneas para profesores de secundaria muy ocupados y con varias clases en el mismo día.

Towards New Teaching in Mathematics How to Realize Inquiry Based and Problem Oriented Mathematics Lessons?

Дагмар Рааб Математиката е вълнуваща и забавна. Можем ли да убедим учениците, че това може да стане действителност. Задачите са най-важните инструменти за учителите по математика, когато планират уроците си. Планът трябва да съдържа идеи как да се очертае и как да се жалонира пътят, по който учениците ще стигнат до решението на дадена задача. Учителите не трябва да очакват от учениците си просто да кажат кой е отговорът на задачата, а да ги увлекат в процеса на решаване с подходящи въпроси. Ролята на учителя е да помогне на учениците • да бъдат активни и резултатни при решаването на задачи; • самите те да поставят задачи; • да модифицират задачи; • да откриват закономерности; • да изготвят стратегии за решаване на задачи; • да откриват и изследват различни начини за решаване на задачи; • да намират смислена връзка между математическите си знания и проблеми от ежедневието. В доклада са представени избрани и вече експериментирани примери за това как учители и ученици могат да намерят подходящ път към нов тип преживявания в преподаването и изучаването на училищната математика.

Creating Meaningful Homework and Implementing Homework Presentations to Aid in Mathematics Instruction

In this action research study of sixth grade mathematics, I investigated the use of meaningful homework and the implementation of presentations and its effect on students’ comprehension of mathematical concepts. I collected data to determine whether the creating of meaningful homework and the implementation of homework presentations would have a positive impact on the students’ understanding of the concepts being taught in class and the reasoning behind assigning homework. The homework was based on the lesson taught during class time. It was grade-level appropriate and contained problems similar to those students completed in class. A pre-research and post-research survey based on homework perceptions and my teaching practices was given, student interviews were conducted throughout the research period, weekly teacher journals were kept that pertained to my teaching practices and the involvement of the students that particular week, and homework assignments were collected to gauge the students’ understanding of the mathematics lessons. Most students’ perceptions on homework were positive and most understood the reasoning for homework assignments.

Matematikläxans fördelar och nackdelar : En intervjustudie av lärares syn på matematikläxor i grundskolans tidigare år

Syftet med denna studie är att få kunskap om lärares syn på matematikläxor i grundskolans tidigare år. Förhoppningen var att få förståelse för lärares syfte med matematikläxor och vilka förmågor eleverna förväntas utveckla med matematikläxors hjälp samt att jämföra vilka för- och nackdelar matematikläxan har. För att undersöka detta har sju intervjuer gjorts med lärare från olika skolor och olika årskurser från 1-6. Samtliga lärare som intervjuats undervisar i matematik. Lärares erfarenheter av läxornas betydelse för matematikundervisningen är ett viktigt område att få kunskap om. De lärare som deltog i intervjuerna uttryckte olika synpunkter på matematikläxan. Något lärarna var överens om var att läxa är en skoluppgift som eleven tar med hem efter skolans slut och arbetar med hemma. Lärarna uttryckte samstämmigt att eleverna inte utvecklar några förmågor med matematikläxans hjälp utan förmågorna utvecklar eleverna i skolan med hjälp av lärarna. Det framgick att samtliga lärare upplevde att matematikläxan var tidskrävande och för att matematikläxan ska nå syftet på bästa möjliga sätt behövs mer tid. Att läxan kopplas till undervisning och uppföljning är centralt för att syftet med matematikläxan ska uppnås enligt de intervjuade lärarna. Av resultaten framgår att några lärare är negativt inställda till matematikläxor för att uppföljning och koppling till undervisningen inte finns med och därför förlorar matematikläxan sitt syfte. Föräldrarnas förutsättningar är väldigt olika som exempelvis att de har svårigheter med det svenska språket eller inte är engagerade i barnets skolgång. Andra lärare är positivt inställda till matematikläxor för att färdighetsträningen och repetitionen är viktig och tiden som behövs för det inte räcker till i skolan.

Um estudo de práticas matemáticas históricas e sugestões de uso na matemática escolar

This dissertation aims to contribute on teaching of mathematics for enabling learning connected to the relationship among science, society, culture and cognition. To this end, we propose the involvement of our students with social practices found in history, since. Our intention is to create opportunities for school practices that these mathematical arising from professional practice historical, provide strategies for mathematical thinking and reasoning in the search for solutions to problematizations found today. We believe that the propose of producing Basic Problematization Units, or simply UBPs, in math teacher formation, points to an alternative that allows better utilization of the teaching and learning process of mathematics. The proposal has the aim of primary education to be, really forming the citizen, making it critical and society transformative agent. In this sense, we present some recommendations for exploration and use of these units for teachers to use the material investigated by us, in order to complement their teaching work in mathematics lessons. Our teaching recommendations materialized as a product of exploration on the book, Instrumentos nuevos de geometria muy necessários para medir distancia y alturas sem que interuengan numeros como se demuestra em la practica , written by Andrés de Cespedes, published in Madrid, Spain, in 1606. From these problematizations and the mathematics involved in their solutions, some guidelines for didactic use of the book are presented, so that the teacher can rework such problematizations supported on current issues, and thus use them in the classroom

A aprendizagem matemática em uma posição de fronteira: Foregrounds e intencionalidade de estudantes de uma favela brasileira

In a large metropolis, students from different neighbourhoods can experience very different life opportunities. This can influence their attitude towards schooling and learning, including the learning of mathematics. We interviewed a group of six students from a favela in a large city in the interior of the state of São Paulo in Brazil. We invited the students to look into their future and explore whether or not there could be learning motives that linked mathematics in school to possible out-of-school practices, either in terms of possible future jobs or further studies. We identified some themes in the students' descriptions of their experiences. The first theme is discrimination. The students feel discriminated against due to the fact that they come from a poor neighbourhood. They fear being trapped in some stereotypes. The second theme is escape. There is a strong motivation to begin a new life away from the favela. A third theme concerns the obscurity of mathematics. It seems clear to everybody that education is relevant to ensure a change in life. However, the mathematics lessons do not provide any clues regarding how mathematics might function is this respect. The fourth theme is uncertainty with respect to the future. The students could easily formulate almost unattainable aspirations, while reality might impose some very heavy limitations. In this article we introduce a theoretical framework for discussing the relation between favela students' life conditions in relation to their educational experiences and opportunities. Students' intentions for learning are related to their foregrounds, that is, how they perceive their future possibilities, as made evident to them by their social environment. Students in a favela could experience what we call a borderland position, a relational space where individuals meet their social environment and come to terms with the multiple choices that cultural and economic diversity make available to them.

O uso das TIC nas aulas de matemática na perspectiva do professor

The objective of this research is to understand whether the mathematics lessons teachers use ICT and how they see their use. For this, we prepared a questionnaire with four questions for the subjects of our research, which are ex - students of Bachelor in Mathematics FEG / UNESP, in exercise of the profession. The questionnaire data were analyzed following the procedures of phenomenological research. This approach enabled us to draw up three open categories. The first Recourse to boost student learning and school, leads us to interpret that for the interviewees, ICT resources are leading students to do research making them responsible for their learning and providing them with conditions respond the issues raised by the teacher, which generates greater interactivity. The second, Possibility to use software related to mathematical content shows that the subject sees ICT as resources that allow the study of mathematical content, especially geometry and functions, so that student learning is leverage. The third, Obstacles to the use of technology in the classroom shows that even if the subjects recognize the importance of ICT use, they do not use it as often as they would like because of the difficulties that are related to infrastructure and didactic and pedagogical conditions

Модел за изследване на креативното мислене и действие на ученици

Veselina Valkanova, Stanimir Stoyanov, Hussein Zedan, Ivan Popchev - In the paper a theoretical model for investigation of creative thinking and action of student is presented. The model extends the formal system called Creativity Map. Furthermore, an experiment for applying this model in the secondary school is explained. Although the experiment will be implemented during the mathematics lessons, the theoretical model can be applied in different subjects.

Dokumentation der Befragungsinstrumente der Interventionsstudie im Projekt “Conditions and Consequences of Classroom Assessment” (Co²CA)

Das im Rahmen des DFG-Schwerpunktprogramms „Kompetenzmodelle“ durchgeführte Projekt „Conditions and Consequences of Classroom Assessment“ (Co²CA) geht in vier Teilstudien der Frage nach, wie formatives Assessment im Unterricht gestaltet werden kann, um sowohl eine präzise Leistungsmessung zu ermöglichen als auch positive Wirkungen auf den Lehr-Lernprozess zu erreichen. Das Project Co²CA leistet damit einen wichtigen Beitrag zur Erforschung zweier Kernelemente formativen Assessments – der detaillierten Diagnose von Schülerleistungen und der Nutzung der gewonnenen Informationen in Form lernförderlichen Feedbacks. Zentrale Idee von formativem Assessment (Lernbegleitende Leistungsbeurteilung und –rückmeldung) ist es mit Hilfe von Leistungsmessungen Informationen über den Lernstand der Schülerinnen und Schüler zu gewinnen und diese Informationen für die Gestaltung des weiteren Lehr- und Lernprozess zu nutzen. Den Lernenden kann auf Basis der Leistungsbeurteilung lernförderliches Feedback gegeben werden, um so die Diskrepanz zwischen Lernstand und Lernziel zu verringern. Die Kernelemente formativem Assessments bestehen also aus einer detaillierten Diagnose des Lernstandes und der Nutzung der gewonnen Informationen – z.B. in Form von Feedback. [...] Das vorliegende Skalenhandbuch dokumentiert die in der Unterrichtsstudie eingesetzten Befragungsinstrumente für Schülerinnen und Schüler sowie für Lehrkräfte. (DIPF/Autor)

O desenvolvimento e integração de estratégias de cálculo mental no 5.º ano de escolaridade

Relatório de estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e 2.º Ciclo do Ensino Básico

Beiträge zum Mathematikunterricht 2015. Vorträge auf der 49. Tagung für Didaktik der Mathematik vom 09.02.2015 bis 13.02.2015 in Basel [Band 2]

Die Jahrestagung der Gesellschaft für Didaktik der Mathematik fand im Jahr 2015 zum dritten Mal in der Schweiz statt. [...] Mit rund 300 Vorträgen, 16 moderierten Sektionen, 15 Arbeitskreistreffen und 21 Posterpräsentationen eröffnete sich ein breites Spektrum an Themen und unterschiedlichen Zugangsweisen zur Erforschung von Fragen rund um das Lernen und Lehren von Mathematik. (DIPF/Orig.)

Beiträge zum Mathematikunterricht 2015. Vorträge auf der 49. Tagung für Didaktik der Mathematik vom 09.02.2015 bis 13.02.2015 in Basel [Band 1]

Die Jahrestagung der Gesellschaft für Didaktik der Mathematik fand im Jahr 2015 zum dritten Mal in der Schweiz statt. [...] Mit rund 300 Vorträgen, 16 moderierten Sektionen, 15 Arbeitskreistreffen und 21 Posterpräsentationen eröffnete sich ein breites Spektrum an Themen und unterschiedlichen Zugangsweisen zur Erforschung von Fragen rund um das Lernen und Lehren von Mathematik. (DIPF/Orig.)

A short course in college mathematics, comprising thirty-six lessons on algebra, coordinate methods, and plane trigonometry,

Mode of access: Internet.

Mathematics for the practical engineer. Engineers' study course from Power; a mathematical manual for the power plant engineer. Contains simplified lessons for home-study in fractions, ratio and proportion, percentage, involution and evolution, square root, cube root, formulas, logarithms, mensuration and plane trigonometry,

Mode of access: Internet.