Perspectives of Teachers Regarding the Integration of Mathematics and Science at the Secondary School Level

The integration of mathematics and science in secondary schools in the 21st century continues to be an important topic of practice and research. The purpose of my research study, which builds on studies by Frykholm and Glasson (2005) and Berlin and White (2010), is to explore the potential constraints and benefits of integrating mathematics and science in Ontario secondary schools based on the perspectives of in-service and pre-service teachers with various math and/or science backgrounds. A qualitative and quantitative research design with an exploratory approach was used. The qualitative data was collected from a sample of 12 in-service teachers with various math and/or science backgrounds recruited from two school boards in Eastern Ontario. The quantitative and some qualitative data was collected from a sample of 81 pre-service teachers from the Queen’s University Bachelor of Education (B.Ed) program. Semi-structured interviews were conducted with the in-service teachers while a survey and a focus group was conducted with the pre-service teachers. Once the data was collected, the qualitative data were abductively analyzed. For the quantitative data, descriptive and inferential statistics (one-way ANOVAs and Pearson Chi Square analyses) were calculated to examine perspectives of teachers regardless of teaching background and to compare groups of teachers based on teaching background. The findings of this study suggest that in-service and pre-service teachers have a positive attitude towards the integration of math and science and view it as valuable to student learning and success. The pre-service teachers viewed the integration as easy and did not express concerns to this integration. On the other hand, the in-service teachers highlighted concerns and challenges such as resources, scheduling, and time constraints. My results illustrate when teachers perceive it is valuable to integrate math and science and which aspects of the classroom benefit best from the integration. Furthermore, the results highlight barriers and possible solutions to better the integration of math and science. In addition to the benefits and constraints of integration, my results illustrate why some teachers may opt out of integrating math and science and the different strategies teachers have incorporated to integrate math and science in their classroom.

Knowledges and practices of successful literacy teachers (Brazil, 1950-1980)

Significant changes have marked Brazilian education in the period focused on by this research. Aiming to understand the configurations of the teaching profession in that period, this work focuses on the issue of the school success in the area of literacy by means of an analysis of the practices of literacy teachers who were at work between the 1950s and 1980s. The research is based on life-history accounts. The study aimed at describing the various experiences of these teachers identifying the knowledges and practices that sustained their successful literacy work as well as the various factors of a social, religious, political, familiar or other nature that, in the history of each of these teachers, favoured the development of a pedagogical style of literacy particular to each one of them. Despite the peculiarities and originality of each history, the success in the literacy process, as the defining feature of the profile of the four teachers, results from two main aspects: first, the autonomy that each one managed to keep in the development of his/her teaching work, particularly in the organisation of the teaching practices that indicated greater chances of a pupil`s learning to read and write; second, their trust in the capacity of every child for learning, independently of his/her social, economic and cultural conditions. Based on this evidence it is argued that the success of the pedagogical work, particularly during the early years of schooling, lies in an ethics of the teaching work with a double implication: first, it requires the teachers` dedication to their pupils, and second, it requires respect for the work of the teacher, so that she/he can maintain her/his autonomy and inventiveness. These aspects indicate the need for reflection on teaching work and a review of current teacher education policies, particularly the policies targeted at teachers working with literacy practices.

Changing representations and practices in school mathematics: the case of Modern Math in Portugal

The curricular movement known as Modern Mathematics aimed at the transformation of representations and practices in school mathematics. Its study provides us with ways of understanding how these changes came about. The purpose of this paper is to contribute to the understanding of the ways in which representations of school mathematics gradually were influenced by ideas from the Modern Mathematics movement, how these new ideas merged into local educational traditions, and how they were transformed into meaningful practice. This work is centred on the Portuguese context from the middle 1950s to the middle 1960s, and builds on Chervel’s notion of school culture and Gruzinski’s discussion of connected histories.

Estudio de los modos de vida e historia biológica de las poblaciones humanas de la región central de argentina desde el registro bioarqueológico. Lifestyles and biological history of human populations of the central region of argentina from bioarchaeological record.

Se pretende aportar al estudio de la estructura, historia biológica y estilos de vida de las poblaciones que habitaron la región central de Argentina durante el Holoceno, desde una perspectiva que combina los aportes teóricos y metodológicos de la Genética del paisaje y la Bioarqueología. Interesa a) identificar barreras de diferenciación morfológica entre poblaciones, b) poner a prueba modelos poblacionales para explicar la variación observada e identificar las variables que contribuyan a dicha diferenciación, c) evaluar la congruencia de los resultados obtenidos, d) reconstruir los patrones de movilidad residencial de las poblaciones, e) estudiar sus patrones dietarios considerando diferencias temporales y espaciales, f) identificar indicadores de diversos tipos de estrés (nutricional, funcional), así como traumas, g) estudiar las historias tafonómicas del registro bioarqueológico regional, y h) proponer un modelo para explicar el poblamiento y la evolución local de las poblaciones que habitaron esta región, a partir de la información arqueológica y bioantropológica. Para el análisis de los patrones espaciales de variación biológica se trabajará a partir del registro de rasgos epigenéticos craneales, medidas lineales y datos obtenidos a partir de morfometría geométrica sobre fotografías en 2D sobre muestras arqueológicas procedentes de esta región y de otras regiones geográficas de la Argentina. Para el análisis de la estructura de la población se trabajará a partir del cálculo de la matriz R para datos morfológicos y sus estimaciones derivadas (distancia D², Fst, coordenadas principales) y la aplicación del modelo de Harpending y Ward. Desde la genética del paisaje, se realizarán análisis de autocorrelación espacial, barreras genéticas y análisis geoestadísticos (kriging). Para el estudio de los modos de vida a partir del registro bioarqueológico se relevarán patologías dento-alveolares y alteraciones vinculadas con la salud bucal tales como desgaste dental –a nivel micro y macroscópico- caries, abscesos, pérdidas dentales antemortem, cálculos, hipoplasias, marcadores esqueletales de salud y lesiones traumáticas. Se analizarán isótopos estables (δ13C, δ15N, 86Sr y 87Sr) en restos óseos humanos de diversos sitios arqueológicos con el objetivo de reconstruir patrones dietarios y analizar la movilidad residencial y migración de las poblaciones. Paralelamente, se establecerán procedimientos de control tafonómico de los restos óseos, y se harán análisis específicos para estudiar las historias tafonómicas y evaluar el grado de integridad de los contextos de depositación y de las colecciones en general. Estimamos que el análisis de los patrones espaciales y temporales de variabilidad morfológica craneofacial, así como el estudio de las dietas a partir de información isotópica y bioarqueológica, de las migraciones y la movilidad residencial de las poblaciones a partir de isótopos de estroncio, la reconstrucción de comportamientos y actividades cotidianas a partir de marcadores de estrés músculo-esqueletal, en un marco cronológico y espacial constituye un aporte novedoso y eficaz que permitirá incrementar de manera substancial la información sobre la evolución de las poblaciones originarias del centro del territorio argentino. The aim of this project is to study the structure, biological history and lifestyles of the people that inhabitated the central region of Argentina during the Holocene, from a perspective that combines theoretical and methodological contributions of Landscape Genetics and Bioarchaeology. To analyze the spatial patterns of biological variation we consider epigenetic cranial traits, linear measurements and data obtained from geometric morphometric on 2D photographs. Morphological variation will be focused on landscape genetics (autocorrelation, genetic barriers and geostatistical analysis –kriging-) and population structure (matrix R, D², Fst, principal coordinates, Harpendig and Ward model). For the study of lifestyles from bioarchaeological record we consider alveolar pathologies and disorders related to oral health such as tooth wear, micro and macroscopic level, caries, abscesses, antemortem tooth loss, hypoplasia, markers skeletal health and traumatic injuries, as well as taphonomic processes. Stable isotopes will be analyzed (δ13C, d15N, 86Sr and 87Sr) in human skeletal remains from various archaeological sites in order to reconstruct and analyze dietary patterns of residential mobility and migration of populations. It will be established procedures of taphonomic control on skeletal remains, analysis to study taphonomic histories and assess the degree of completeness of depositional context and collection, in general terms. We consider that analysis of spatial and temporal patterns of variability in craniofacial morphology and the study of health and diets from isotopic and bioarchaeological data, migration and residential mobility patterns from strontium isotopes, as well as activity patterns from stress markers is a novel and effective contribution that will substantially increase the information about the local evolution of populations that inhabitated the center of Argentina.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

History of England from the peace of Utrecht to the peace of Aix-la-Chapelle. Edition 3,Volume 2 / by lord Mahon

Collection : Collection of ancient and modern british authors ; 325-326

History of England from the peace of Utrecht to the peace of Aix-la-Chapelle. Volume 1,Edition 3 / by lord Mahon

Collection : Collection of ancient and modern british authors ; 325-326

Investigating Formative Assessment: Exploring the Impact on the Self-Efficacy and Motivation of Mathematics Students

This is a study of the implementation and impact of formative assessment strategies on the motivation and self-efficacy of secondary school mathematics students. An explanatory sequential mixed methods design was implemented where quantitative and qualitative data were collected and analyzed sequentially in 2 different phases. The first phase involved quantitative data from student questionnaires and the second phase involved qualitative data from individual student and teacher interviews. The findings of the study suggest that formative assessment is implemented in practice in diverse ways and is a process where the strategies are interconnected. Teachers experience difficulty in incorporating peer and self-assessment and perceive a need for exemplars. Key factors described as influencing implementation include teaching philosophies, interpretation of ministry documents, teachers’ experiences, leadership in administration and department, teacher collaboration, misconceptions of teachers, and student understanding of formative assessment. Findings suggest that overall, formative assessment positively impacts student motivation and self-efficacy, because feedback is provided which offers encouragement and recognition by highlighting the progress that has been made and what steps need to be taken to improve. However, students are impacted differently with some considerations including how students perceive mistakes and if they fear judgement. Additionally, the impact of formative assessment is influenced by the connection between self-efficacy and motivation, namely how well a student is doing is a source of both concepts.

Settlement history of a mountain oasis in Northern Oman

To unravel the settlement history of oases in northern Oman, data on topography, the agricultural setting, water and soil parameters and archaeological findings were collected in the Wadi Bani Awf with its head oasis Balad Seet. Data collection lasted from April 2000 to April 2003 and was based on the establishment of a 3D-georeferenced map of the oasis comprising all its major infrastructural and agronomic features. At today's Balad Seet, a total of 8.8 ha are planted to 2,800 date palms and 4.6 ha are divided into 385 small fields dedicated to wheat, barley, sorghum, oats, alfalfa, garlic, onion, lime and banana. Radiocarbon dating of charcoal in the lower part of the main terrace system determined its age to 911 ± 43 years. Monthly flow measurements of four major aflaj systems showed a total maximum flow of 32 m^3 h^-1 with the largest falaj contributing 78% of the total flow. During drought periods, average water flow decreased by 3% per month, however, with significant differences between the spring systems. The analysis of the tritium/^3helium ratio in the water led to an estimated water age of up to 10 years. In combination with the flow data, this provided insights into the elasticity of the spring flow over time. The use of the natural resources of the Wadi Bani Awf by a pastoral population started probably in the early 3rd millennium BC. The first permanent settlement might have been established at Balad Seet during the first part of the 1st millennium BC. Presumably it was initiated by settlers from al-Hamra, a village at the southern foot of the Hajar mountains. Given an abundant und stable flow of springs, even in periods of drought, the construction of Balad Seet's first irrigation systems may have occurred at this early time. The combination of topographic, agricultural, hydro-pedological and archaeological data allowed assessment of the carrying capacity of this oasis over the three millennia of its likely existence. The changing scarcity of land and water and the eventual optimisation of their use by different aflaj constructions have been major driving forces for the development and apparent relativeley stable existence of this oasis.

Science learning and graphic symbols: an exploration of early years teachers’ views and use of graphic symbols when teaching science

The study investigated early years teachers’ understanding and use of graphic symbols, defined as the visual representation(s) used to communicate one or more “linguistic” concepts, which can be used to facilitate science learning. The study was conducted in Cyprus where six early years teachers were observed and interviewed. The results indicate that the teachers had a good understanding of the role of symbols, but demonstrated a lack of understanding in regards to graphic symbols specifically. None of the teachers employed them in their observed science lesson, although some of them claimed that they did so. Findings suggest a gap in participants’ acquaintance with the terminology regarding different types of symbols and a lack of awareness about the use and availability of graphic symbols for the support of learning. There is a need to inform and train early years teachers about graphic symbols and their potential applications in supporting children’s learning.

Performance of the Quantitative Food Frequency Questionnaire Used in the Brazilian Center of the Prospective Study Natural History of Human Papillomavirus Infection in Men: The HIM Study

The Natural History of Human Papillomavirus (HPV) Infection in Men: The HIM Study is a prospective multi-center cohort study that, among other factors, analyzes participants` diet. A parallel cross-sectional study was designed to evaluate the validity and reproducibility of the quantitative food frequency questionnaire (QFFQ) used in the Brazilian center from the HIM Study. For this, a convenience subsample of 98 men aged 18 to 70 years from the HIM Study in Brazil answered three 54-item QFFQ and three 24-hour recall interviews, with 6-month intervals between them (data collection January to September 2007). A Bland-Altman analysis indicated that the difference between instruments was dependent on the magnitude of the intake for energy and most nutrients included in the validity analysis, with the exception of carbohydrates, fiber, polyunsaturated fat, vitamin C, and vitamin E. The correlation between the QFFQ and the 24-hour recall for the deattenuated and energy-adjusted data ranged from 0.05 (total fat) to 0.57 (calcium). For the energy and nutrients consumption included in the validity analysis, 33.5% of participants on average were correctly classified into quartiles, and the average value of 0.26 for weighted kappa shows a reasonable agreement. The intraclass correlation coefficients for all nutrients were greater than 0.40 in the reproducibility analysis. The QFFQ demonstrated good reproducibility and acceptable validity. The results support the use of this instrument in the HIM Study. J Am Diet Assoc. 2011;111:1045-1051.

The Development of Dalton`s Atomic Theory as a Case Study in the History of Science: Reflections for Educators in Chemistry

The inclusion of the history of science in science curricula-and specially, in the curricula of science teachers-is a trend that has been followed in several countries. The reasons advanced for the study of the history of science are manifold. This paper presents a case study in the history of chemistry, on the early developments of John Dalton`s atomic theory. Based on the case study, several questions that are worth discussing in educational contexts are pointed out. It is argued that the kind of history of science that was made in the first decades of the twentieth century (encyclopaedic, continuist, essentially anachronistic) is not appropriate for the development of the competences that are expected from the students of sciences in the present. Science teaching for current days will benefit from the approach that may be termed the ""new historiography of science"".

Teaching Mathematics in English to Swedish Speaking Students : The Use of Second Language Teaching Practices in the Teaching of Mathematics in English to Swedish Speaking Students in Lower Secondary School

Over 20,000 Swedish lower high school students are currently learning mathematics in English but little research has been conducted in this area. This study looks into the question of how much second language learner training teachers teaching mathematics in English to Swedish speaking students have acquired and how many of those teachers are using effective teaching practices for second language learners. The study confirms earlier findings that report few teachers receive training in second language learning but indicates that some of the teaching practices shown to be effective with second language learners are being used in some Swedish schools

Um estudo sobre a apreciação do raciocínio matemático na formação inicial de professores

The present work focused on developing teaching activities that would provide to the student in initial teacher training, improving the ability of mathematical reasoning and hence a greater appreciation of the concepts related to the golden section, the irrational numbers, and the incommensurability the demonstration from the reduction to the nonsensical. This survey is classified itself as a field one which data collection were inserted within a quantitative and qualitative approach. Acted in this research, two classes in initial teacher training. These were teachers and employees of public schools and local governments, living in the capital, in Natal Metropolitan Region - and within the country. The empirical part of the research took place in Pedagogy and Mathematics courses, IFESP in Natal - RN. The theoretical and methodological way construction aimed to present a teaching situation, based on history, involving mathematics and architecture, derived from a concrete context - Andrea Palladio s Villa Emo. Focused discussions on current studies of Rachel Fletcher stating that the architect used the golden section in this village construction. As a result, it was observed that the proposal to conduct a study on the mathematical reasoning assessment provided, in teaching and activity sequences, several theoretical and practical reflections. These applications, together with four sessions of study in the classroom, turned on to a mathematical thinking organization capable to develop in academic students, the investigative and logical reasoning and mathematical proof. By bringing ancient Greece and Andrea Palladio s aspects of the mathematics, in teaching activities for teachers and future teachers of basic education, it was promoted on them, an improvement in mathematical reasoning ability. Therefore, this work came from concerns as opportunity to the surveyed students, thinking mathematically. In fact, one of the most famous irrational, the golden section, was defined by a certain geometric construction, which is reflected by the Greek phrase (the name "golden section" becomes quite later) used to describe the same: division of a segment - on average and extreme right. Later, the golden section was once considered a standard of beauty in the arts. This is reflected in how to treat the statement questioning by current Palladio s scholars, regarding the use of the golden section in their architectural designs, in our case, in Villa Emo