Graphical Approach to Teaching Compound Interest in High School Math Classes

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

A qualitative study of selected fourth -grade teachers' perceptions of the Sunshine State Standards

Despite a history of grappling with educational standards, never before has the federal government attempted to establish explicit national standards for what American children should learn in school. Recently, U.S. educators have developed voluntary national content standards, or explicit expectations of what students should know and be able to do. Not surprisingly, this major curriculum reform has provoked considerable debate. Today, teachers face difficult challenges working towards the implementation of standards. The objective of this study was to describe and explain the perceptions of a selected team of fourth-grade teachers regarding the language arts component of their state's Sunshine State Standards (SSS). The exploratory questions that guided this qualitative study were: (a) How are the SSS perceived by these fourth-grade teachers? (b) In what ways do the SSS affect teachers' self-perceptions? and, (c) To what extent and how do the SSS affect the participants' professional classroom behavior? ^ Direct observations, interviews, analysis of relevant documents and the researcher's critical reflective journal served as the methods of inquiry employed in this qualitative study. Bandura's Teacher Self-Efficacy Scale was used as a tool to help categorize the data specifically related to self-perception. ^ Analysis of the data suggests that participants perceived the SSS as a useful guideline as they taught. The SSS were a decisive factor in teachers' planning. They were the actual guide lines used by teachers to plan their lessons. However, participants did not believe the SSS were attainable by all students or were fair to students with special needs. They also believed there was not sufficient time allocated for the effective implementation of the SSS. This lack of time created pressure among some of the participants and others even felt disempowered regarding the curriculum and the instructional focus implemented during the test preparation time. The SSS negatively affected the participants when they felt constraints during this time, which led to their inability to carry out important activities in their classrooms. Thus, the SSS directly affected the participants' behavior in their classrooms. ^

Investigating high-achieving sixth grade students' erroneous answers on the angle concept in Yozgat

The angle concept is a multifaceted concept having static and dynamic definitions. The static definition of the angle refers to “the space between two rays” or “the intersection of two rays at the same end point” (Mitchelmore & White, 1998), whereas the dynamic definition of the angle concept highlights that the size of angle is the amount of rotation in direction (Fyhn, 2006). Since both definitions represent two diverse situations and have unique limitations (Henderson & Taimina, 2005), students may hold misconceptions about the angle concept. In this regard, the aim of this research was to explore high achievers’ knowledge regarding the definition of the angle concept as well as to investigate their erroneous answers on the angle concept.

104 grade 6 students drawn from four well-established elementary schools of Yozgat, Turkey were participated in this research. All participants were selected via a purposive sampling method and their mathematics grades were 4 or 5 out of 5, and. Data were collected through four questions prepared by considering the learning competencies set out in the grade 6 curriculum in Turkey and the findings of previous studies whose purposes were to identify students’ misconceptions of the angle concept. The findings were analyzed by two researchers, and their inter-rater agreement was calculated as 0.91, or almost perfect. Thereafter, coding discrepancies were resolved, and consensus was established.

The angle concept is a multifaceted concept having static and dynamic definitions.The static definition of the angle refers to “the space between two rays” or“the intersection of two rays at the same end point” (Mitchelmore & White, 1998), whereas the dynamicdefinition of the angle concept highlights that the size of angle is the amountof rotation in direction (Fyhn, 2006). Since both definitionsrepresent two diverse situations and have unique limitations (Henderson & Taimina, 2005), students may holdmisconceptions about the angle concept. In this regard, the aim of thisresearch was to explore high achievers’ knowledge regarding the definition ofthe angle concept as well as to investigate their erroneous answers on theangle concept.

A operacionalização do programa de matemática em vigor no 1.º Ciclo do Ensino Básico pelos professores do concelho de Machico

Trabalho de projeto apresentado à Escola Superior de Educação de Paula Frassinetti para obtenção do grau de Mestre em Ciências da Educação Especialização em Supervisão Pedagógica

O currículo de matemática do 1º ciclo doensino secundário de Cabo Verde na perspectiva de professores

Este estudo tem por objetivo compreender a perspetiva de professores sobre o currículo de Matemática do 1º ciclo do Ensino Secundário cabo-verdiano e conhecer necessidades de formação que identificam, para um melhor desempenho na sua catividade profissional. As questões de estudo são: 1) Como se reveem os professores de Matemática no currículo do 1º ciclo do Ensino Secundário, enquanto agentes que interpretam e implementam esse currículo? 2) Que potencialidades e dificuldades reconhecem nesse currículo? 3) Que áreas consideram haver necessidade de formação, para a melhoria da sua prática docente, nesse nível de ensino? O desenvolvimento do referencial teórico integra duas áreas temáticas como eixos centrais: o currículo, o professor e o professor de Matemática. Foi feita uma análise de normativos cabo-verdianos para a educação, entre os quais se destacam a Lei de Bases do Sistema Educativo, o Plano de estudos para o ensino secundário e o Programa de Matemática do 1o ciclo do Ensino Secundário. A metodologia adotada na investigação segue uma abordagem interpretativa e descritiva, suportada por um design de estudo de caso. São estudados três casos, relativos a professores de Matemática cabo-verdianos do 1º ciclo do Ensino Secundário. A recolha de dados recorre a urna entrevista semiestruturada a cada professor, à observação de três aulas por professor participante e à recolha documental. A análise de dados foi feita utilizando principalmente a técnica de análise de conteúdos. Os professores revêem-se como executores de um currículo uniforme, de cumprimento obrigatório, normativo, emanado centralmente e do qual procuram interpretar as intenções. A sua visão de currículo é centrada nos conteúdos do programa, um dos motivos para que o enquadramento ao nível dos meios institucionais e as competências esperadas ao nível do saber fazer e ao nível do saber ser nem sempre serem conhecidas e/ou cumpridas. Em Acão, revêem-se como figuras centrais do currículo. Todos se reveem com mais competência na implementação curricular à medida que vão adquirindo experiência profissional. Concordam com os temas do programa e um deles sugere a inclusão de um tema. Consideram que os conteúdos nem sempre estão bem organizados e mostram a necessidade de a metodologia do programa ser mais detalhada, evidenciando claramente os seus propósitos. Eventualmente, podem não concordar com a estrutura de currículo em espiral do programa. Os professores identificam mais formação com melhor desempenho. As necessidades de formação são: Metodologia do Ensino da Matemática, Resolução de Problemas, Avaliação e a Geometria ligada à utilização de materiais pedagógicos. O estudo parece indicar que os professores não desenvolvem práticas diferentes por não terem essa vivência e aponta os professores mais jovens como mais abertos à mudança. ABSTRACT: The aim of this study is to understand the perspective of the teacher in relation to the Mathematics curriculum of the 1st cycle of Secondary School of Cape Verde (grades 7-8) and to learn about his/her training needs to develop better skills and performance in their professional activity. The key questions in this study are: 1) how do Mathematics teachers, acting in the capacity of agents who interpret and implement the 1st cycle of Secondary School curriculum, see themselves in this curriculum? 2) What potentialities and difficulties can they recognize in the curriculum? 3) What areas do they consider in need of training to improve teaching capacity within such education grade? The theoretical framework of this investigation integrates two main areas: the curriculum and the teacher. An analysis of Cape-Verdian normative texts for education has been made, including the Lei de Bases do Sistema Educativo (Basis Law of the Educational System), the Study plan for secondary school and the Mathematics program of the 1st cycle of secondary school. ln terms of methodology, we opted for an interpretative approach to our investigation, namely the case study. We looked at three case studies concerning the Cape-Verdian mathematics teacher of the 1st cycle of secondary school. The data collection uses a semi­structured interview for each teacher, the observation of three classes per participating teacher and the documental collection. Content analysis is the main technique used for analyzing the data. Teachers see themselves as practitioners of a uniform curriculum with mandatory compliance and delineated guidelines set by the administration, and they follow their own understanding of its intended purpose. Their vision of the curriculum is focused on program contents, one of the reasons why the expected skills at the level of "how to do" and "how to be" are not always known and/or done. ln their professional setting they see themselves with professional skills growing in tandem with professional experience. They all agree with the program contents but one of them suggests one content to add. ln their opinion the program is not always well organized and they suggest the need for a more comprehensive and detailed methodology of program contents. ln addition, they might not agree with the spiral structure of the program curriculum. They also identified the need for more elaborate professional training including: A Methodology for Mathematics Education, solving problems, Evaluation and the Geometry related to the utilization of pedagogical materials. The study seems to indicate that teachers refrain from developing different practices because of lack of experience but also demonstrates that younger teachers are more open to change.

Estado actual de los planes de mejora en los Centros de Desarrollo Infantil Privados

Dentro de la presente investigación, se realiza un análisis de la situación actual de los centros de desarrollo infantil privados en donde se detalla el plan de mejora. El desarrollo de este trabajo de titulación pretende demostrar la viabilidad del Plan de Mejora en cuanto a fortalecer las debilidades encontradas en cada institución para ofrecerles cuidados y educación de calidad, una infraestructura adecuada, espacios lúdicos con seguridad, involucramiento de los padres en el proceso educativo y resolución de los conflictos con los niños. Esta idea surge de la necesidad de concientizar a las instituciones para un adecuado manejo de las actividades en el desarrollo del aprendizaje, encaminadas alcanzar una enseñanza de excelencia no solo a nivel académico sino en todos los aspectos que rodean al niño; a partir de la matriz del plan de mejora y de encuestas ejecutadas a directoras y docentes de cada centro, como propósito de este trabajo, se hace un análisis con los problemas más sobresalientes y con las acciones que toman para obtener resultados favorables, la factibilidad de la investigación se determinó mediante un enfoque cualitativo por medio del cual se pudo evidenciar la falta de resultados frente a las acciones tomadas dentro de los CDI, con tablas de frecuencia que demuestran claramente esto y a su vez que tanto las directoras como docentes difieren en los tipos de problemas que fueron tratados en cada establecimiento. El plan de mejora de los centros de desarrollo infantil privados consolida a una educación de calidad, siempre y cuando se trabaje conjuntamente entre directivos, docentes y padres de familia para alcanzar un nivel de educación de primera y desarrollar en el niño un rendimiento escolar de acuerdo a la reforma curricular actual.

Primary teachers notice the impact of language on children’s mathematical reasoning

Mathematical reasoning is now featured in the mathematics curriculum documents of many nations, but this necessitates changes to teaching practice and hence a need for professional learning. The development of children’s mathematical reasoning requires appropriate encouragement and feedback from their teacher who can only do this if they recognise mathematical reasoning in children’s actions and words. As part of a larger study, we explored whether observation of educators conducting mathematics lessons can develop teachers’ sensitivity in noticing children’s reasoning and consideration of how to support reasoning. In the Mathematical Reasoning Professional Learning Research Program, demonstration lessons were conducted in Australian and Canadian primary classrooms. Data sources included post-lesson group discussions. Observation of demonstration lessons and engagement in post-lesson discussions proved to be effective vehicles for developing a professional eye for noticing children’s individual and whole-class reasoning. In particular, the teachers noticed that children struggled to employ mathematical language to communicate their reasoning and viewed limitations in language as a major barrier to increasing the use of mathematical reasoning in their classrooms. Given the focus of teachers’ noticing of the limitations in some types of mathematical language, it seems that targeted support is required for teachers to facilitate classroom discourse for reasoning.

Teacher educators mediating curricular reform : anticipating the Australian curriculum

Many education systems are experiencing a re-scaling and consolidation of governance through rolling national agendas of standardisation and centralisation. This paper considers the case of Australia as it moves towards implementing its first national curriculum, to explore how teacher educators plan to retain pedagogical space for debate, diversity and contestation of such systemic curricular reform. This paper reports on an interview study conducted with nine teacher educators across the four curriculum areas included in the first wave of the Australian Curriculum: English, Science, Mathematics and History. The analysis reveals how teacher educators reported professional dilemmas around curricular design, and planned to resolve such dilemmas between the anticipated changes and their preferences for what might have been. While different curricular areas displayed different patterns of professional dilemma, the teacher educators are shown to construe their role as one of active curriculum mediators, who, in recontextualising curricular reforms, will use the opportunity to reinsert both residualised and emergent alternatives in their students’ professional value sets. The study also identifies a new set of dilemmas emerging around the politicisation and standardisation of curriculum, and its impact on the teaching profession and teacher educators.

High quality/high equity systems of education: Curriculum, teachers and reform in the search for equitable outcomes for all students

The issue of what an effective high quality / high equity education system might look like remains contested. Indeed there is more educational commentary on those systems that do not achieve this goal (see for example Luke & Woods, 2009 for a detailed review of the No Child Left Behind policy initiatives put forward in the United States under the Bush Administration) than there is detailed consideration of what such a system might enact and represent. A long held critique of socio cultural and critical perspectives in education has been their focus on deconstruction to the supposed detriment of reconstructive work. This critique is less warranted in recent times based on work in the field, especially the plethora of qualitative research focusing on case studies of ‘best practice’. However it certainly remains the case that there is more work to be done in investigating the characteristics of a socially just system. This issue of Point and Counterpoint aims to progress such a discussion. Several of the authors call for a reconfiguration of the use of large scale comparative assessment measures and all suggest new ways of thinking about quality and equity for school systems. Each of the papers tackles different aspects of the problematic of how to achieve high equity without compromising quality within a large education system. They each take a reconstructive focus, highlighting ways forward for education systems in Australia and beyond. While each paper investigates different aspects of the issue, the clearly stated objective of seeking to delineate and articulate characteristics of socially just education is consistent throughout the issue.

Politicizing mathematics education : has politics gone too far? Or not far enough?

In this chapter we tackle increasingly sensitive questions in mathematics education, those that have polarized the community into distinct schools of thought as well as impacted reform efforts.

Standards, teacher judgement and moderation in contexts of national curriculum and assessment reform

This paper puts forward a proposal for reviewing the role and purpose of standards in the context of national curriculum and assessment reform more generally. It seeks to commence the much-needed conversation about standards in the work of teachers as distinct from large-scale testing companies and the policy personnel responsible for reporting. Four key conditions that relate to the effective use of standards to measure improvement and support learning are analysed: clarity about purpose and function; understanding of the representation of standards; moderation practice; and the assessment community. The Queensland experience of the use of standards, teacher judgement and moderation is offered to identify what is educationally preferable in terms of their use and their relationships to curriculum, improvement and accountability. The article illustrates how these practices have recently been challenged by emerging political constraints related to the Australian Government’s implementation of national testing and national partnership funding arrangements tied to the performance of students at or below minimum standards.

Role and purpose of standards in the context of national curriculum and assessment reform for accountability, improvement and equity in student learning

In this article our starting point is the current context of national curriculum change and intense speculation about the assessment, standards and reporting. It is written against a background of accountability measures and improvement imperatives, and focuses attention on standards as offering representations of quality. We understand standards to be constructs that aim to achieve public credibility and utility. Further, they can be examined for the purposes they seek to serve and also their expected functions. Fitness for purpose is therefore a useful notion in considering the nature of standards. Our interest in the discussion is the ‘fit’ between how standards are formulated and how they are used in practice, by whom and for what purposes. A related interest is in the matter of how standards can be harnessed to realise improvement.

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.

Stepping Stones A world-Class Mathematics program for the Australian Curriculum Year 1 (Student Journal)

ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals. This uniquely interactive program allows students to participate in exciting learning activites whilst still allowing the teacher to maintain control of learning outcomes. It is the first program in Australia to give teachers activities to differentiate instruction within each lesson and across school years. Written by a team of Australia's leading mathematics educators, this program integrates key research findings in a practical sequence of modules and lessons providing schools with a step-by-step approach to the new curriculum. Click links on the right to explore the program.