Investigating practitioner self-efficacy in an era of mathematical reform

The purpose of this study is to explore teacher self-efficacy at a time of radical mathematical reform. Project Maths – the new initiative which was rolled out nationwide in 2010 differs from previous attempts at innovation in that it targets a much closer connection between curriculum and pedagogy. Gone are the days of well-rehearsed routines where the role of the mathematician was essentially that of demonstrator. Teaching for understanding is now the main ‘official’ pedagogical focus, with emphasis on the practitioner playing the part of mediator between subject-matter and student. Mathematical instruction is not merely concerned with the transmission of knowledge and skills which is a particular pedagogical position to take. It is also an emotional practice (Hargreaves, 1998) that colours and expresses the feelings and actions of practitioners. While emotion plays a key role in teachers’ commitment to curricular reform, it is also shaped by the social and cultural contexts of mathematical change, alongside with the attitudes and beliefs of the mathematical teaching community. Inspired by Bandura’s theory of learning (1986), this investigation aims to shed light on the complex interplay between so-called mastery and vicarious experiences, social persuasion and physiological states. Vygotsky’s view of learning (1978) as a socio-cultural process is also drawn upon, as it provides a useful structure against which teacher self-efficacy and professional development can be examined. Finally, Hiebert’s theory (1986) is used to examine mathematics teaching self-efficacy and mathematics self-efficacy.

THE EFFECT OF PURPOSEFUL MATHEMATICS DISCOURSE IN THE CLASSROOM ON STUDENTS’ MATHEMATICS LANGUAGE IN THE CONTEXT OF PROBLEM SOLVING

This study examines how one secondary school teacher’s use of purposeful oral mathematics language impacted her students’ language use and overall communication in written solutions while working with word problems in a grade nine academic mathematics class. Mathematics is often described as a distinct language. As with all languages, students must develop a sense for oral language before developing social practices such as listening, respecting others ideas, and writing. Effective writing is often seen by students that have strong oral language skills. Classroom observations, teacher and student interviews, and collected student work served as evidence to demonstrate the nature of both the teacher’s and the students’ use of oral mathematical language in the classroom, as well as the effect the discourse and language use had on students’ individual written solutions while working on word problems. Inductive coding for themes revealed that the teacher’s purposeful use of oral mathematical language had a positive impact on students’ written solutions. The teacher’s development of a mathematical discourse community created a space for the students to explore mathematical language and concepts that facilitated a deeper level of conceptual understanding of the learned material. The teacher’s oral language appeared to transfer into students written work albeit not with the same complexity of use of the teacher’s oral expression of the mathematical register. Students that learn mathematical language and concepts better appear to have a growth mindset, feel they have ownership over their learning, use reorganizational strategies, and help develop a discourse community.

Myanmar DIL WORKSHOP SERIES Unit 4: Working Online and Using Information

The Mobile Information Literacy curriculum is a growing collection of training materials designed to build literacies for the millions of people worldwide coming online every month via a mobile phone. Most information information and digital literacy curricula were designed for a PC age, and public and private organizations around the world have used these curricula to help newcomers use computers and the internet effectively and safely. The better curricula address not only skills, but also concepts and attitudes. The central question for this project is: what are the relevant skills, concepts, and attitudes for people using mobiles, not PCs, to access the internet? As part of the Information Strategies for Societies in Transition project, we developed a six-module curriculum for mobile-first users. The project is situated in Myanmar, a country undergoing massive political, economic, and social changes, and where mobile penetration is expected to reach 80% by the end of 2015 from just 4% in 2014. Combined with the country’s history of media censorship, Myanmar presents unique challenges for addressing the needs of people who need the ability to find and evaluate the quality and credibility of information obtained online, understand how to create and share online information effectively, and participate safely and securely.

Principles and Practice of Fire Modelling: A Collection of Lecture Notes for a Short Course

Once the preserve of university academics and research laboratories with high-powered and expensive computers, the power of sophisticated mathematical fire models has now arrived on the desk top of the fire safety engineer. It is a revolution made possible by parallel advances in PC technology and fire modelling software. But while the tools have proliferated, there has not been a corresponding transfer of knowledge and understanding of the discipline from expert to general user. It is a serious shortfall of which the lack of suitable engineering courses dealing with the subject is symptomatic, if not the cause. The computational vehicles to run the models and an understanding of fire dynamics are not enough to exploit these sophisticated tools. Too often, they become 'black boxes' producing magic answers in exciting three-dimensional colour graphics and client-satisfying 'virtual reality' imagery. As well as a fundamental understanding of the physics and chemistry of fire, the fire safety engineer must have at least a rudimentary understanding of the theoretical basis supporting fire models to appreciate their limitations and capabilities. The five day short course, "Principles and Practice of Fire Modelling" run by the University of Greenwich attempt to bridge the divide between the expert and the general user, providing them with the expertise they need to understand the results of mathematical fire modelling. The course and associated text book, "Mathematical Modelling of Fire Phenomena" are aimed at students and professionals with a wide and varied background, they offer a friendly guide through the unfamiliar terrain of mathematical modelling. These concepts and techniques are introduced and demonstrated in seminars. Those attending also gain experience in using the methods during "hands-on" tutorial and workshop sessions. On completion of this short course, those participating should: - be familiar with the concept of zone and field modelling; - be familiar with zone and field model assumptions; - have an understanding of the capabilities and limitations of modelling software packages for zone and field modelling; - be able to select and use the most appropriate mathematical software and demonstrate their use in compartment fire applications; and - be able to interpret model predictions. The result is that the fire safety engineer is empowered to realise the full value of mathematical models to help in the prediction of fire development, and to determine the consequences of fire under a variety of conditions. This in turn enables him or her to design and implement safety measures which can potentially control, or at the very least reduce the impact of fire.

The Voice of History and the Message of the National Curriculum: Recontextualising History to a Pedagogic Discourse for Upper Secondary VET

In the reform by the liberal-conservative government of Swedish upper secondary education in 2011, history was recognized as an important part of citizenship education and was introduced into the curriculum for vocational education and training (VET) tracks. Through the concepts of classification and framing, this article explores the process of constructing the history syllabus for VET. The data consist of archived material from the working group responsible for the history curriculum under the Swedish National Agency for Education. The analysis shows that there are competing discourses concerning the relative emphasis on competencies and skills and concerning the emphasis on contemporary and modern history. Although historians, history teachers and other agents are invited to respond to the content of the curriculum, the respondents have no influence on the knowledge structure of the curriculum, which is controlled by agents of the dominant educational ideology. From a critical perspective, this article suggests that the curriculum reflects the instrumental and neoconservative message of the reform through strong classification and framing and through the emphasis on general abilities and a contemporary history that has a more direct explanatory value to contemporary society.

A Haptic System for Depicting Mathematical Graphics for Students with Visual Impairments

When teaching students with visual impairments educators generally rely on tactile tools to depict visual mathematical topics. Tactile media, such as embossed paper and simple manipulable materials, are typically used to convey graphical information. Although these tools are easy to use and relatively inexpensive, they are solely tactile and are not modifiable. Dynamic and interactive technologies such as pin matrices and haptic pens are also commercially available, but tend to be more expensive and less intuitive. This study aims to bridge the gap between easy-to-use tactile tools and dynamic, interactive technologies in order to facilitate the haptic learning of mathematical concepts. We developed an haptic assistive device using a Tanvas electrostatic touchscreen that provides the user with multimodal (haptic, auditory, and visual) output. Three methodological steps comprise this research: 1) a systematic literature review of the state of the art in the design and testing of tactile and haptic assistive devices, 2) a user-centered system design, and 3) testing of the system’s effectiveness via a usability study. The electrostatic touchscreen exhibits promise as an assistive device for displaying visual mathematical elements via the haptic modality.

Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.

No right to sext? A critical examination of media and legal debates about teenage girls' sexual agency in the digital age

Advances in digital photography and distribution technologies enable many people to produce and distribute images of their sex acts. When teenagers do this, the photos and videos they create can be legally classified as child pornography since the law makes no exception for youth who create sexually explicit images of themselves. The dominant discussions about teenage girls producing sexually explicit media (including sexting) are profoundly unproductive: (1) they blame teenage girls for creating private images that another person later maliciously distributed and (2) they fail to respect—or even discuss—teenagers’ rights to freedom of expression. Cell phones and the internet make producing and distributing images extremely easy, which provide widely accessible venues for both consensual sexual expression between partners and for sexual harassment. Dominant understandings view sexting as a troubling teenage trend created through the combination of camera phones and adolescent hormones and impulsivity, but this view often conflates consensual sexting between partners with the malicious distribution of a person’s private image as essentially equivalent behaviors. In this project, I ask: What is the role of assumptions about teen girls’ sexual agency in these problematic understandings of sexting that blame victims and deny teenagers’ rights? In contrast to the popular media panic about online predators and the familiar accusation that youth are wasting their leisure time by using digital media, some people champion the internet as a democratic space that offers young people the opportunity to explore identities and develop social and communication skills. Yet, when teen girls’ sexuality enters this conversation, all this debate and discussion narrows to a problematic consensus. The optimists about adolescents and technology fall silent, and the argument that media production is inherently empowering for girls does not seem to apply to a girl who produces a sexually explicit image of herself. Instead, feminist, popular, and legal commentaries assert that she is necessarily a victim: of a “sexualized” mass media, pressure from her male peers, digital technology, her brain structures or hormones, or her own low self-esteem and misplaced desire for attention. Why and how are teenage girls’ sexual choices produced as evidence of their failure or success in achieving Western liberal ideals of self-esteem, resistance, and agency? Since mass media and policy reactions to sexting have so far been overwhelmingly sexist and counter-productive, it is crucial to interrogate the concepts and assumptions that characterize mainstream understandings of sexting. I argue that the common sense that is co-produced by law and mass media underlies the problematic legal and policy responses to sexting. Analyzing a range of nonfiction texts including newspaper articles, talk shows, press releases, public service announcements, websites, legislative debates, and legal documents, I investigate gendered, racialized, age-based, and technologically determinist common sense assumptions about teenage girls’ sexual agency. I examine the consensus and continuities that exist between news, nonfiction mass media, policy, institutions, and law, and describe the limits of their debates. I find that this early 21st century post-feminist girl-power moment not only demands that girls live up to gendered sexual ideals but also insists that actively choosing to follow these norms is the only way to exercise sexual agency. This is the first study to date examining the relationship of conventional wisdom about digital media and teenage girls’ sexuality to both policy and mass media.

Working with Student Teachers: A Mixed Methods Study to Examine the Roles and Self-Identified Dispositions of Cooperating Teachers

A critical component of teacher education is the field experience during which candidates practice under the supervision of experienced teachers. Programs use the InTASC Standards to define the requisite knowledge, skills, and dispositions for teaching. Practicing teachers are familiar with the concepts of knowledge and skills, but they are less familiar with dispositions. Practicing teachers who mentor prospective teachers are underrepresented in the literature, but they are critical to teacher preparation. The research goals were to describe the self-identified dispositions of cooperating teachers, identify what cooperating teachers consider their role in preparing prospective teachers, and explain challenges that cooperating teachers face. Using a mixed methods design, I conducted a quantitative survey followed by a qualitative case study. When I compared survey and case study data, cooperating teachers report possessing InTASC critical dispositions described in Standard 2: Learning Differences, Standard 3: Learning Environments, and Standard 9: Professional Learning and Ethical Practice, but not Standard 6: Assessment and Standard 10: Leadership and Collaboration. Cooperating teachers assume the roles of modeler, mentor and advisor, and informal evaluator. They explain student teachers often lack skills and dispositions to assume full teaching responsibilities and recommend that universities better prepare candidates for classrooms. Cooperating teachers felt university evaluations were not relevant to teaching reality. I recommend modifying field experiences to increase the quantity and duration of classroom placements. I suggest further research to detail cooperating teacher dispositions, compare cooperating teachers who work with different universities, and determine if cooperating teacher dispositions influence student teacher dispositions.

Preliminary assessment of the numerical competencies of children from a public preschool and kindergarten in Cuenca

Existe abundante evidencia de que los niños pequeños son capaces de desarrollar un conocimiento matemático y que las destrezas aritméticas de estos niños son predictores de su desempeño académico futuro. También existe un acuerdo común de que la calidad de la educación matemática inicial tiene una importante influencia en el aprendizaje posterior de los niños. En Ecuador hay escasos estudios sobre las competencias matemáticas tempranas de los niños y sobre su enseñanza. Por ello, se inició un estudio para (1) evaluar las competencias numéricas de los niños de pre-escolar y kindergarten (primero de básica) que asisten a una escuela pública de Cuenca, con el objetivo de analizar críticamente su pensamiento y razonamiento numérico; y (2) examinar las prácticas y creencias de los profesores con relación a la enseñanza de la matemática y a las competencias matemáticas de los niños. La aplicación del Test de Conocimiento Numérico (Griffin, 2005) demostró que la mayoría de los niños participantes no habían desarrollado habilidades numéricas básicas. Adicionalmente, los profesores expresaron una fuerte creencia de que los niños pequeños no son capaces de tener un pensamiento matemático. Como consecuencia, las actividades matemáticas que realizan los niños y profesores son desarrolladas de manera insuficiente. Las implicaciones científicas y prácticas de estos resultados son discutidas.

Zig-zagging in geometrical reasoning in technological collaborative environments: a Mathematical Working Space-framed study concerning cognition and affect

This study highlights the importance of cognition-affect interaction pathways in the construction of mathematical knowledge. Scientific output demands further research on the conceptual structure underlying such interaction aimed at coping with the high complexity of its interpretation. The paper discusses the effectiveness of using a dynamic model such as that outlined in the Mathematical Working Spaces (MWS) framework, in order to describe the interplay between cognition and affect in the transitions from instrumental to discursive geneses in geometrical reasoning. The results based on empirical data from a teaching experiment at a middle school show that the use of dynamic geometry software favours students’ attitudinal and volitional dimensions and helps them to maintain productive affective pathways, affording greater intellectual independence in mathematical work and interaction with the context that impact learning opportunities in geometric proofs. The reflective and heuristic dimensions of teacher mediation in students’ learning is crucial in the transition from instrumental to discursive genesis and working stability in the Instrumental-Discursive plane of MWS.

O contributo da intervenção psicomotora para a aprendizagem da matemática : estudo do seu impacto na aprendizagem das pré-aptidões matemáticas em crianças de cinco anos de idade

A presente dissertação tem como objetivo analisar a importância da intervenção psicomotora no desenvolvimento das pré-competências matemáticas. Para tal foram discutidos conceitos e noções sobre a utilização da psicomotricidade como contributo para a aprendizagem das pré-aptidões matemáticas no pré-escolar. Num primeiro momento, será feito um breve enquadramento teórico sobre a temática em estudo – o contributo da intervenção psicomotora na aprendizagem da matemática no pré-escolar. Num segundo momento, apresenta-se a metodologia desenvolvida para o caso de estudo (programa) e expõem-se os resultados obtidos nos diversos momentos de avaliação. Por fim, apresenta-se a conclusão onde se sugere que a intervenção psicomotora promoveu uma evolução positiva na aquisição e na consolidação das pré-aptidões da matemática.

Governing the water conservation in the Urmia Lake Basin: addressing macro systems’ fit and micro users’ behavior

To change unadapted water governing systems, and water users’ traditional conducts in line with climate change, understanding of systems’ structures and users’ behaviors is necessary. To this aim, comprehensive and pragmatic research was designed and implemented in the Urmia Lake Basin where due to the severe droughts, and human-made influences, especially through the agricultural development, the lake has been shrunken drastically. To analyze the water governance and conservation issues in the basin, an innovative framework was developed based on mathematical physics concepts and pro-environmental behavior theories. Accordingly, in system level (macro/meso), the problem of fit of the early-shaped water governing system associating with the function of “political-security” and “political-economic” factors in the basin was identified through mean-field models. Furthermore, the effect of a “political-environmental” factor, the Urmia Lake Restoration Program (ULRP), on reforming the system structure and hence its fit was assessed. The analysis results revealed that by revising the provincial boundaries (horizontal alternation) for the entity of Kurdistan province to permit that interact with the headquarter of West Azerbaijan province for its water demand-supply initiatives, the system fit can increase. Also, the constitution of the ULRP (vertical arrangement) not only could increase the structural fit of the water governing system to the basin, but also significantly could enhance the system fit through its water-saving policy. Besides, in individual level (micro), the governing factors of water conservation behavior of the major users/farmers were identified through rational and moral socio-psychological models. In rational approach, incorporating PMT and TPB, the SEM results demonstrated that “Perceived Vulnerability”, “Self-Efficacy”, “Response Efficacy”, “Response Cost”, “Subjective Norms” and “Institutional Trust” significantly affect the water-saving intention/behavior. Likewise, NAM based analysis as a moral approach, uncovered the significant effects of “Awareness of Consequences”, “Appraisal of Responsibility”, “Personal Norms” as well as “Place Attachment” and “Emotions” on water-saving intention.

Matrix Support And Institutional Support: Analyzing Their Construction.

This is an analysis of the theoretical and practical construction of the methodology of Matrix Support by means of studies on Paideia Support (Institutional and Matrix Support), which is an inter-professional work of joint care in recent literature and official documents of the Unified Health System (SUS). An attempt was made to describe methodological concepts and strategies. A comparative analysis of Institutional Support and Matrix Support was also conducted using the epistemological framework of Field and Core Knowledge and Practices.

Psicologia, diretrizes curriculares e processos educativos na Amazônia: um estudo da formação de psicólogos

Este estudo objetiva analisar a formação de psicólogos frente às Diretrizes Curriculares Nacionais para os Cursos de Psicologia no que tange aos processos educativos. Realizamos revisão da literatura pertinente ao tema, pesquisa documental e empírica com alunos, professores e coordenador de curso, utilizando questionário, entrevistas e adotando a estratégia de triangulação a partir das categorias: perfil sociocultural; nível de conhecimento acerca das mudanças oriundas das Diretrizes para o curso de Psicologia; percepção na qualidade da prática docente; nível de satisfação com relação à própria formação universitária, tomando como referência os conhecimentos, habilidades e competências adquiridas. Apresenta contribuições para a compreensão da formação de psicólogos no campo da educação na Amazônia no Ensino Superior, centrada na construção de um profissional de pensamento e prática críticos, capaz de analisar as transformações nos vários contextos educacionais e escolares, utilizando referenciais que permitam a compreensão do fenômeno educativo na sua complexidade.