The aim of this work is to introduce and assess the potential of using GeoGebra software on multiple levels of mathematical education process and to analyze the expectation of pupils and students using this program. A reader is introduced to GeoGebra program itself and to various researches and articles sharing this common topic - usage of dynamic geometry educational programs and GeoGebra in mathematical education. This work is supported by two field researches that were carried out at the second stage of an elementary school and by another reseach made with students of mathematical education at the Charles University, the Faculty of Education. Next part of this work presents and covers more possibilities of using this program in the educational process of the second stage of elementary schools, and it also shows various options the program offers not just for teaching of mathematics, but also for other fields.

Estudamos neste trabalho as equações polinomiais em sua abrangência: quadráticas, cúbicas e quárticas por diversos métodos clássicos, a limitação das raízes, resultados sobre equações polinomiais com coeficientes reais e inteiros, entre outros / We studied in this work polynomial equations in a wide reach: quadratic, cubic and quartic polynomials by several classical methods, the boundness of roots, results about polynomial equations with real and integer coefficients, among other results

O presente trabalho, fundamentado teoricamente na Epistemologia Genética, investigou as concepções sobre avaliação de professores de Matemática da Educação Básica. Para isso, realizou-se a coleta de dados, embasada no Método Clínico Piagetiano, com dezessete sujeitos que atuam em escolas públicas e privadas do município de Porto Alegre/RS. Foram utilizados dois instrumentos: uma carta solicitando a reflexão do sujeito diante de uma situação proposta e uma entrevista a partir da análise do conteúdo das cartas. A análise dos dados possibilitou a construção de três categorias gerais e oito subcategorias. Os resultados indicam que os professores de Matemática entrevistados, em sua maioria, não têm um objetivo em relação a sua prática avaliativa e, quando o têm, está relacionado apenas a um evento pontual, não pressupondo a compreensão da avaliação como um processo. Constatou-se, também, que as práticas avaliativas se apresentam como reflexo das Concepções Epistemológicas dos professores. / The present paper, theoretically grounded in Genetic Epistemology, investigated the conceptions on evaluation of Mathematics professors of Basic Education. For this, it was performed data collection, based on Piaget´s Clinic Method, with sixteen subjects who work in public and private schools in the city os Porto Alegre/RS. Two instruments were used: a letter requesting the subject´s reflection towards the proposed situation and an interview based on the content analysis of the letters. The data analysis allowed the construction of three general categories and eight subcategories. The results indicated that the interviewed Mathematics professors, in their majority, do not have un objective in relation to their evaluation practice and, when they do, it´s related only to an specific event, not predicating the comprehension of evaluation as a process. It was found, also, that the evaluation practices present themselves as a reflex of the Epistemologic Conceptions of the professors.

Darbe analizuojami įvairūs metodai, tinkami mokyti(s) matematikos nuotoliniu būdu. Išnagrinėjus ŠMM dokumentus ir pedagoginę literatūrą, daroma išvada, jog nuotoliniam matematikos dalyko mokymui yra tinkamas mišrusis dalyko mokymas,kuomet tarpusavyje derinami programuotas mokymas (įgūdžių įtvirtinimui, turinio diferencijavimui) bei tradiciniai metodai (naujos medžiagos aiškinimui, konsultavimui). / In teaching mathematics it is not enough to realize the only one method. The analysis of scientific literature has opened, that for distance learning of mathematics it would be effective to realize composite method there programmed learning would be combined with traditional methods.

This study investigates the ways in which parents' and teachers' experiences and representations mediate their child's mathematics learning as they make the transition between home and school to either a multiethnic or mainly white school. In particular, it examines if the forms of mediation they adopt can shed light on the academic success of the child in school mathematics. The focus on mathematics learning has been chosen for the study because of its relative neglect, until recent times, to be seen as a subject influenced by cultural representations. Furthermore, there are significant implications in the relative neglect of understanding the achievement of ethnic minority pupils in mathematics. The research was framed by Vygotskian sociocultural theory and Wenger's (1998) communities of practice to explore the construction of meaning, identity and representations of practice. The amalgam of Wenger's communities of practice with sociocultural theory provided three key theoretical facets: (i) multiple levels of understanding in the form of meaning, practice and identity, (ii) the scope to explore the social and cultural worlds of the learner and (iii) understanding the ways that past experiences impact on current practice. Three different forms of qualitative data collection were used within the context of an ethnographic approach: (i) investigations in the form of classroom observations, (ii) in-depth semi-structured interviews and (iii) a child identity task. Twenty-two parents, eight teachers and fifty-eight children took part in the interviews, which form the main part ofthe data analysis. Out ofthese fifty-eight children, twenty-seven undertook the child identity task. The research took place in three schools with different ethnic make-up: a multicultural school, a mainly white school and a predominantly South Asian school. Two year groups were chosen, year 2 (ages 6/7 years) and year 6 (10/11 years), balancing high and low achievers. This study has provided data, which suggests that the way parents and teachers mediate the child's learning involves more than representations of mathematics. In making meaning of the mathematical, they draw on wider representations of the educational world, which include aspects like child development, notions of achievement, past experiences and the child's projected futures. This complex picture emerged from studying the highly interwoven aspects ofthe construction of meaning, identity and representations of practice. Representations of learning can be borrowed from both communities, providing the ethnic minority pupil with the potential to create hybrid representations of learning as they make the transition between home and school, which may be attributed a cultural status within the home. Each social actor has the potential to borrow from the home or school community to a greater or lesser degree. lfthe gap between the shared representations of the home and school are large, then this increases the likelihood of difficulties for the child in transition. However, the data suggests that even if the cultural representations of the home are very different from the school, the identification of high achievement and the engagement in mathematical activity at home can still provide success in learning. From the school community perspective, classrooms were represented by the teacher informants as 'cultureless' in both the multi ethnic and mainly white school. For example, in the multicultural school the teachers felt that there were so many ethnicities that differences were not visible. In the mainly white school, there were so few ethnic minority children that teachers also struggled to identify issues of culture. In the predominantly South Asian school, issues surrounding culture were brought to the forefront of the teacher discourse. However, in many ethnic minority homes, parents described how culture was influential in mediating representations ofleaming. This has implications in the educational arena with respect to the teachers' understanding of the transitional process that ethnic minority children undergo and the levels of visibility that culture and ethnicity is given in the school community.

The purpose of the study was to investigate the high school students&#039 / beliefs about mathematics and the teaching of mathematics. The study was conducted in Ankara with 425 tenth-grade students enrolled to general, Anatolian, foreign language and vocational high schools. Two measuring instruments were utilized: 1.Beliefs about Mathematics Scale (BaMS) / 2.Beliefs about the Teaching of Mathematics Scale (BTMS). The validity and reliability of these scales were tested. The design of the present research is a casual-comparative study. The hypotheses of the present study were tested by using multivariate analysis of variance at the significance level 0.05. The results of the study indicated that:1. There are statistically significant differences among the mean scores of students enrolled to different kinds of high schools with respect to beliefs about mathematics and beliefs about the teaching of mathematics / 2. There are statistically significant mean differences among students who have different mathematics achievement levels in terms of beliefs about mathematics and beliefs about the teaching of mathematics / 3. There are statistically significant mean differences among students who are in different branches in terms of beliefs about mathematics and beliefs about the teaching of mathematics / 4.There is no statistically significant mean difference between the male and female students on beliefs about mathematics. On the other hand, there is statistically significant mean difference between the male and female students on beliefs about the teaching of mathematics in the favor of female students.

The nature of creative mathematical thinking undertaken by students in classroom settings was studied through analysis of the autonomy and spontaneity associated with these processes. The theoretical lens developed enabled simultaneous analysis of cognitive, social, and affective elements of the creative process, and student responses to successes and failures during their exploratory activity (resilience or optimism). Collective case study was employed, with each case progressively informing the analysis of subsequent cases. The classrooms of teachers who were seen by their school communities to display 'good teaching practice' were selected for study. It was anticipated that such classrooms would provide more opportunity to study creative thinking than classrooms chosen at random. During the research period, each student participated individually in post-lesson interviews that were stimulated by lesson video material. To generate data to study student thinking, and the social and personal influences upon it, students were asked to identify parts of the lesson that were important to them, and discuss what was happening, and what they were thinking and feeling. Through this process, students who explored mathematical complexities to generate new mathematical knowledge were identified. (For complete abstract open document)

The early years of schooling are a crucial part of a student’s education. Recent years have seen the implementation of new literacy and numeracy programs in primary school classrooms. The key area of mathematics (numeracy) has been closely monitored and funded by political and educational bodies (Clarke, Cheeseman, Gervasoni, Gronn, Horne, McDonough, Montgomery, Roche, Sullivan, Clarke, & Rowley, 2002; Association of Independent Schools of South Australia, 2004). The new numeracy programs have been introduced into the school curriculum to ensure that all students’ needs are catered for in the classroom program. However, standardised testing using pencil and paper is still being used as the accepted form of assessment. The Victorian State Government uses the Achievement Improvement Monitor (AIM) to assess students’ mathematical achievement levels. This pencil and paper test is conducted for students in years three, five, seven and nine and is used to sort the students into a percentile group. Other than the ‘Early Numeracy in the Classroom’ program (2002) used by Victorian schools as a prep. to three program, where a one-on-one interview is used as a form of assessment, there is currently no program that offers students the opportunity to choose how best to represent their own mathematical understanding. Although, the learning needs of students are being better catered for within the classroom, students are being disadvantaged by the way in which they are assessed.

The aim of this essay is to study how teachers in mathematics in upper-secondary school think about the concept of individualized teaching and their way of tutoring students in a classroom environment. The study focuses on the area of functions. To answer the aim of the study two different qualitative methods are used, namely interview and observation. Three teachers have been interviewed and one lesson per teacher has been observed. The data has been divided into three categories to systematically present, analyse and discuss examples relevant to the aim of the study. Theoretically important concepts are used to analyse the material, for example zone of potential construction, scaffolding and the knowledge quartet. All of the teachers use some kind of conversation to be aware of what kind of individualized teaching their students need. They claim that most of the individualized teaching happens when they tutor the students one-to-one and they have a lot of different methods to do this. All teachers describe time as a factor preventing them from individualizing their teaching as much as they would like. / Syftet med denna uppsats är att undersöka matematiklärares tankar om individanpassningar och deras handledning av elever i gymnasieskolan. Studien fokuserar på området funktioner, specifikt linjära- och andragradsfunktioner. För att besvara studiens syfte används två olika kvalitativa metoder, intervju och observation. Urvalet består av tre lärare som har intervjuats och observerats. Materialet kategoriseras för att systematiskt presentera, analysera och diskutera relevanta exempel utifrån studiens syfte. Teoretiska begrepp används för att analysera resultatet, exempelvis används den potentiella konstruktionszonen, stöttning och kunskapskvartetten. Samtliga informanter använder någon form av samtal för att bli medvetna om elevers behov av individanpassningar. Lärarna menar att majoriteten av individanpassningen sker vid enskild handledning av elever och lärarna beskriver olika metoder för detta. Alla intervjuade lärare beskriver tid som ett hinder för att individanpassa deras undervisning i den utsträckning de önskar.

The aim of this research was to investigate how I engaged in constructivist teaching (CT) when helping a group of low-performing Grade 7 students to develop new meanings of notation as they started to learn formal algebra. Data was collected over a period of one scholastic year, in which I explored the teacher-student dynamics during my mathematics lessons, where students learnt new representations and interpretations of notation with the help of the computer software Grid Algebra. Analysing video recordings of my lessons, I observed myself continuously changing my teaching purpose as I negotiated between the mathematics I intended to teach and the mathematics being constructed by my students. These shifts of focus and purpose were used to develop a conceptual framework called Mathematics-Negotiation-Learner (M-N-L). Besides serving as a CT model, the M-N-L framework was found useful to determine the extent to which I managed to engage in CT during the lessons and also to identify moments where I lost my sensitivity to students constructions of knowledge. The effectiveness of my CT was investigated by focusing on students learning, for which reason I developed the analytical framework called CAPS (Concept-Action-Picture-Symbol). The CAPS framework helped me to analyse how students developed notions about properties of operational notation, the structure and order of operations in numerical and algebraic expressions, and the relational property of the equals sign. Grid Algebra was found to be a useful tool in helping students to enrich their repertoire of representations and to develop new interpretations of notation through what I defined as informal- and formal-algebraic activities. All students managed to transfer these representations and interpretations of notation to pen-and-paper problems, where they successfully worked out traditionally set substitution-and-evaluation tasks.