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.

Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Thai students' engagement with cooperative learning in mathematics classrooms

Over the past decade, Thai schools have been encouraged by the Thai Ministry of Education to introduce more student-centred pedagogies such as cooperative learning into their classrooms (Carter, 2006). However, prior research has indicated that the implementation of cooperative learning into Thai schools has been confounded by cultural traditions endemic within Thai schools (Deveney, 2005). The purpose of the study was to investigate how 32 Grade 3 and 32 Grade 4 students enrolled in a Thai school engaged with cooperative learning in mathematics classrooms after they had been taught cooperative learning strategies and skills. These strategies and skills were derived from a conceptual framework that was the outcome of an analysis and synthesis of social learning, behaviourist and socio-cognitive theories found in the research literature. The intervention began with a two week program during which the students were introduced to and engaged in practicing a set of cooperative learning strategies and skills (3 times a week). Then during the next four weeks (3 times a week), these cooperative learning strategies and skills were applied in the contexts of two units of mathematics lessons. A survey of student attitudes with respect to their engagement in cooperative learning was conducted at the conclusion of the six-week intervention. The results from the analysis of the survey data were triangulated with the results derived from the analysis of data from classroom observations and teacher interviews. The analysis of data identified four complementary processes that need to be considered by Thai teachers attempting to implement cooperative learning into their mathematics classrooms. The paper concludes with a set of criteria derived from the results of the study to guide Thai teachers intending to implement cooperative learning strategies and skills in their classrooms.

Teaching and learning mathematics with robotics in middle-years of schooling

Engaging and motivating students in mathematics lessons can be challenging. The traditional approach of chalk and talk can sometimes be problematic. The new generation of educational robotics has the potential to not only motivate students but also enable teachers to demonstrate concepts in mathematics by connecting concepts with the real world. Robotics hardware and the software are becoming increasing more user-friendly and as a consequence they can be blended in with classroom activities with greater ease. Using robotics in suitably designed activities promotes a constructivist learning environment and enables students to engage in higher order thinking through hands-on problem solving. Teamwork and collaborative learning are also enhanced through the use of this technology. This paper discusses a model for teaching concepts in mathematics in middle year classrooms. It will also highlight some of the benefits and challenges of using robotics in the learning environment.

Teacher aides and their pedagogical contributions in the underachieving Indigenous mathematics classroom

This study examines the pedagogical contributions made by teacher aides in underperforming Indigenous mathematics secondary classrooms. Three teaching teams, each consisting of a teacher and their teacher aide, responded to semi-structured interviews. Their mathematics classrooms were observed for details of pedagogical contributions to the mathematics lessons. It was found that the pedagogical contributions of the teacher aides varied from co-teaching contributions, to the provision of menial support and behaviour management. The techniques used by the teacher aides to provide student feedback, to support behaviour management and to undertake questioning vary greatly, and this variance is also evident in the classroom atmosphere. Teacher aides are providing pedagogical contributions, and are engaged in instructional interactions, and are in a sense “teaching”.

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.

Opettajan uskomukset opetustyön lähtökohtana : näkökulmia pedagogiseen ajatteluun

The purpose of this research was to examine teacher’s pedagogical thinking based on beliefs. It aimed to investigate and identify beliefs from teachers’ speech when they were reflecting their own teaching. Placement of beliefs in levels of pedagogical thinking was also examined. The second starting point for a study was the Instrumental Enrichment -intervention, which aims to enhance learning potential and cognitive functioning of students. The goal of this research was to investigate how five main principles of the intervention come forward in teachers’ thinking. Specifying research question was: how similar teachers’ beliefs are to the main principles of intervention. The teacher-thinking paradigm provided the framework for this study. The essential concepts of this study are determined exactly in the theoretical framework. Model of pedagogical thinking was important in the examination of teachers’ thinking. Beliefs were approached through the referencing of varied different theories. Feuerstein theory of Structural cognitive modifiability and Mediated learning experience completed the theory of teacher thinking. The research material was gathered in two parts. In the first part two mathematics lessons of three class teachers were videotaped. In second part the teachers were interviewed by using a stimulated recall method. Interviews were recorded and analysed by qualitative content analysis. Teachers’ beliefs were divided in themes and contents of these themes were described. This part of analysis was inductive. Second part was deductive and it was based on theories of pedagogical thinking levels and Instrumental Enrichment -intervention. According to the research results, three subcategories of teachers’ beliefs were found: beliefs about learning, beliefs about teaching and beliefs about students. When the teachers discussed learning, they emphasized the importance of understanding. In teaching related beliefs student-centrality was highlighted. The teachers also brought out some demands for good education. They were: clarity, diversity and planning. Beliefs about students were divided into two groups. The teachers believed that there are learning differences between students and that students have improved over the years. Because most of the beliefs were close to practice and related to concrete classroom situation, they were situated in Action level of pedagogical thinking. Some teaching and learning related beliefs of individual teachers were situated in Object theory level. Metatheory level beliefs were not found. Occurrence of main principles of intervention differed between teachers. They were much more consistent and transparent in the beliefs of one teacher than of the other two teachers. Differences also occurred between principles. For example reciprocity came up in every teacher’s beliefs, but modifiability was only found in the beliefs of one teacher. Results of this research were consistent with other research made in the field. Teachers’ beliefs about teaching were individual. Even though shared themes were found, the teachers emphasized different aspects of their work. Occurrence of beliefs that were in accordance with the intervention were teacher-specific. Inconsistencies were also found within teachers and their individual beliefs.

Tekstiilityötä ja matematiikkaa yhdistävän oppimateriaalin käyttökelpoisuus perusopetuksen yläluokilla

In this study the researcher wanted to show the observed connection of mathematics and textile work. To carry this out the researcher designed a textbook by herself for the upper secondary school in Tietoteollisuuden Naiset TiNA project at Helsinki University of Technology (URL:http://tina.tkk.fi/). The assignments were designed as additional teaching material to enhance and reinforce female students confidence in mathematics and in the management of their textile work. The research strategy applied action research, out of which two cycles two have been carried out. The first cycle consists of establishing the textbook and in the second cycle its usability is investigated. The third cycle is not included in this report. In the second cycle of the action research the data was collected from 15 teachers, five textile teachers, four mathematics teachers and six teachers of both subjects. They all got familiar with the textbook assignments and answered a questionnaire on the basis of their own teaching experience. The questionnaire was established by applying the theories of usability and teaching material assessment study. The data consisted of qualitative and quantitative information, which was analysed by content analysis with computer assisted table program to either qualitative or statistical description. According to the research results, the textbook assignments seamed to be applied better to mathematics lessons than textile work. The assignments pointed out, however, the clear interconnectedness of textile work and mathematics. Most of the assignments could be applied as such or as applications in the upper secondary school textile work and mathematics lessons. The textbook assignments were also applicable in different stages of the teaching process, e.g. as introduction, repetition or to support individual work or as group projects. In principle the textbook assignments were in well placed and designed in the correct level of difficulty. Negative findings concerned some too difficult assignments, lack of pupil motivation and unfamiliar form of task for the teacher. More clarity for some assignments was wished for and there was especially expressed a need for easy tasks and assignments in geometry. Assignments leading to the independent thinking of the pupil were additionally asked for. Two important improvements concerning the textbook attainability would be to get the assignments in html format over the Internet and to add a handicraft reference book.

A Pilot Study of Reciprocal Peer Tutoring in Irish Medium Schools

A pilot study to investigate the effects of mathematics peer tutoring in Irish medium primary schools was undertaken. Five schools and 90 students took part in the pilot. Materials and resources that had previously been shown to work in English medium Scottish schools were translated into Irish by CCEA. Irish medium teachers attended three professional development days. Teachers implemented the peer tutoring techniques during mathematics lessons during a period of 16 weeks. Changes in attainment were measures with an Irish translation of the Scottish Survey of Achievement Mathematics Test. Results were positive. Student attainment was significantly raised during the 16-week implementation period by over one standard deviation. This equated to one-year’s worth of mathematics development during this time period. Results must be treated with caution. No control group was used in the pilot study. However, results are very promising and indicate that reciprocal role peer tutoring may be a useful pedagogy in Irish medium education. Further work would be required to establish this definitively.

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.