Rubric Assessment of Mathematical Processes in Homework

In this action research study of my classroom of 11th grade geometry, I investigated the use of rubrics to help me assess my students during homework presentations. I wanted to know more about the processes students went through as they did their homework problems, so homework presentations were implemented with the rubrics being the main form of assessment. I discovered that students are willing to speak about mathematics and can gain more understanding of mathematical processes as a result of homework presentations. The scores of the class improved after they talked about the homework assignments with each other. As a result of this research, I plan to keep on using homework presentations in my classroom to talk about homework, but discontinue the use of rubrics in assessment of students in mathematics. I also found students going to the board to solve problems in small groups are another helpful way to use presentations prior to assessment to help me understand where the students are with a new concept prior to assigning homework or giving an assessment.

Motivating Middle School Mathematics Students

In this action research study I examined the relationship between the teacher, the students and the types of motivation used in mathematics. I specifically studied the mathematic teachers at my school and my seventh grade mathematics students. Motivating middle school students is difficult and the types of motivation can be as numerous as the number of students studied. I discovered that the teachers used multiple motivating tactics from praise, to extra time spent with a student, to extra fun activities for the class. I also discovered that in many instances, the students’ perception of mathematics was predetermined or predetermined by parental perceptions of mathematics. The social environment of the student and a sense of belonging also plays a role in how motivated a student stays. As a result of this research, I plan to notify the mathematics teachers at my school of the most effective types of motivation so we can become a more effective mathematics department.

Risikomaße in der Finanzmathematik

„Risikomaße in der Finanzmathematik“ Der Value-at -Risk (VaR) ist ein Risikomaß, dessen Verwendung von der Bankenaufsicht gefordert wird. Der Vorteil des VaR liegt – als Quantil der Ertrags- oder Verlustverteilung - vor allem in seiner einfachen Interpretierbarkeit. Nachteilig ist, dass der linke Rand der Wahrscheinlichkeitsverteilung nicht beachtet wird. Darüber hinaus ist die Berechnung des VaR schwierig, da Quantile nicht additiv sind. Der größte Nachteil des VaR ist in der fehlenden Subadditivität zu sehen. Deswegen werden Alternativen wie Expected Shortfall untersucht. In dieser Arbeit werden zunächst finanzielle Risikomaße eingeführt und einige ihre grundlegenden Eigenschaften festgehalten. Wir beschäftigen uns mit verschiedenen parametrischen und nichtparametrischen Methoden zur Ermittlung des VaR, unter anderen mit ihren Vorteilen und Nachteilen. Des Weiteren beschäftigen wir uns mit parametrischen und nichtparametrischen Schätzern vom VaR in diskreter Zeit. Wir stellen Portfoliooptimierungsprobleme im Black Scholes Modell mit beschränktem VaR und mit beschränkter Varianz vor. Der Vorteil des erstens Ansatzes gegenüber dem zweiten wird hier erläutert. Wir lösen Nutzenoptimierungsprobleme in Bezug auf das Endvermögen mit beschränktem VaR und mit beschränkter Varianz. VaR sagt nichts über den darüber hinausgehenden Verlust aus, während dieser von Expected Shortfall berücksichtigt wird. Deswegen verwenden wir hier den Expected Shortfall anstelle des von Emmer, Korn und Klüppelberg (2001) betrachteten Risikomaßes VaR für die Optimierung des Portfolios im Black Scholes Modell.

Intuizione e visualizzazione in matematica con particolare riferimento a Felix Klein

Questo lavoro trae spunto da un rinnovato interesse per l’«intuizione» e il «pensiero visivo» in matematica, e intende offrire un contributo alla discussione contemporanea su tali questioni attraverso lo studio del caso storico di Felix Klein. Dopo una breve ricognizione di alcuni dei saggi più significativi al riguardo, provenienti sia dalla filosofia della matematica, sia dalla pedagogia, dalle neuroscienze e dalle scienze cognitive, l’attenzione si concentra sulla concezione epistemologia di Klein, con particolare riferimento al suo uso del concetto di ‘intuizione’. Dai suoi lavori e dalla sua riflessione critica si ricavano non solo considerazioni illuminanti sulla fecondità di un approccio «visivo», ma argomenti convincenti a sostegno del ruolo cruciale dell’intuizione in matematica.

INVESTIGATION OF STRATEGIES TO PROMOTE EFFECTIVE TEACHER PROFESSIONAL DEVELOPMENT EXPERIENCES IN EARTH SCIENCE

This dissertation serves as a call to geoscientists to share responsibility with K-12 educators for increasing Earth science literacy. When partnerships are created among K-12 educators and geoscientists, the synergy created can promote Earth science literacy in students, teachers, and the broader community. The research described here resulted in development of tools that can support effective professional development for teachers. One tool is used during the planning stages to structure a professional development program, another set of tools supports measurement of the effectiveness of a development program, and the third tool supports sustainability of professional development programs. The Michigan Teacher Excellence Program (MiTEP), a Math/Science Partnership project funded by the National Science Foundation, served as the test bed for developing and testing these tools. The first tool, the planning tool, is the Earth Science Literacy Principles (ESLP). The ESLP served as a planning tool for the two-week summer field courses as part of the MiTEP program. The ESLP, published in 2009, clearly describe what an Earth science literate person should know. The ESLP consists of nine big ideas and their supporting fundamental concepts. Using the ESLP for planning a professional development program assisted both instructors and teacher-participants focus on important concepts throughout the professional development activity. The measurement tools were developed to measure change in teachers’ Earth science content-area knowledge and perceptions related to teaching and learning that result from participating in a professional development program. The first measurement tool, the Earth System Concept Inventory (ESCI), directly measures content-area knowledge through a succession of multiple-choice questions that are aligned with the content of the professional development experience. The second measurement, an exit survey, collects qualitative data from teachers regarding their impression of the professional development. Both the ESCI and the exit survey were tested for validity and reliability. Lesson study is discussed here as a strategy for sustaining professional development in a school or a district after the end of a professional development activity. Lesson study, as described here, was offered as a formal course. Teachers engaged in lesson study worked collaboratively to design and test lessons that improve the teachers’ classroom practices. Data regarding the impact of the lesson study activity were acquired through surveys, written documents, and group interviews. The data are interpreted to indicate that the lesson study process improved teacher quality and classroom practices. In the case described here, the lesson study process was adopted by the teachers’ district and currently serves as part of the district’s work in Professional Learning Communities, resulting in ongoing professional development throughout the district.

A Simple Computer Game for Learning Mathematics

It is sometimes unquantifiable how hard it is for most people to deal with game addiction. Several articles have equally been published to address this subject, some suggesting the concept of Educational and serious games. Similarly, researchers have revealed that it does not come easy learning a subject like math. This is where the illusive world of computer games comes in. It is amazing how much people learn from games. In this paper, we have designed and programmed a simple PC math game that teaches rudimentary topics in mathematics.

Schul-, Praxis- und habituelles Herrschaftswissen. Bildung ländlicher Eliten mit Blick auf die korporative Selbstverwaltung in der frühmodernen Schweiz (18. und 19. Jahrhundert)

Knowledge taught at schools, everyday skills and practical know-how. The relevancy of formation for local elites and the corporative self-government of Early Modern Switzerland Daniel Schläppi, Bern There were different kinds of rural elites in Early Modern Switzerland. The diverse parts of the country developed in very dissimilar ways politically and economically. Some regions were dominated by traditional types of agriculture. Some territories were ruled by major cities. In some of the rural Cantons like Uri, Schwyz, Unterwalden, Glarus and Zug a political elite took control over generations and practiced a cultural lifestyle comparable to the famous aristocracies in cities like Bern, Basel, Freiburg, Luzern, Solothurn and Zurich. Intense proto-industrialization formed a completely different sort of elite with strong affinities to industry and trade in other regions. Meanwhile the habitants of the valley close-by stayed farmers like their ancestors (like in Appenzell). In the most conservative parts of the country mercenary business played an important role till the very end of the Ancien Regime and even furthermore. In summery the variety of historical circumstances caused heterogeneous elites all over. Such socio-political diversity provoked a variety of educational backgrounds. I an academic understanding of the term we know only little about literacy in local rural elites. But there is strong evidence that a lively culture of reading and story-telling existed. This means that even simple countrymen seem to have been in possession of some books. The organisation and capacity of the school system is subject of controversial discussions among up to date researchers. The state of research makes us suppose that the people designed to political careers learned their essential skills not only in school but also in everyday life or on the job. Based on the fact that every community and countless public corporations managed their affairs by their own it’s evident that the local elite’s key-players had a large repertoire of techniques and skills like writing, calculating, strategic thinking or knowledge of oral tradition, old usage or important rituals. Unfortunately the historical actors left not that many sources that would tell us precisely how knowledge and know-how were transferred in former times. Hardly any private account books or common correspondence have been conserved. But a huge bunch of sources that originate from corporative self-administration shows us that most local elites were well-educated and had the necessary skills anyway. Above all other sources like for instance the «Topographische Beschreibungen» (topographic descriptions) that were initiated by the «Ökonomische Gesellschaft» of Berne since the sixties of the 18th century provide an insight into pre-modern classrooms. More important information on the historical formation-reality can be gained by the autobiography of the famous poor peasant Ulrich Bräker (1735‒1798) or some of the novels by Albert Bitzius (1797‒1854, better known as Jeremias Gotthelf). The pedagogic writings by Johann Heinrich Pestalozzi (1746‒1827) and the influences by his mentors Johann Rudolf Tschiffeli (1716‒1780) or Philipp Emanuel von Fellenberg (1771‒1884) are quite illustrative as well.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

An example of Learning based on competences: Use of Maxima in Linear Algebra for Engineers

This paper analyzes the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is defined as an indicator of the generic ompetence: Use of Technology. Additionally, we show that using CAS could help to enhance the following generic competences: Self Learning, Planning and Organization, Communication and Writing, Mathematical and Technical Writing, Information Management and Critical Thinking.

Therapeutic metaphors in engineering: how to cure a building structure

Cognitive linguistics have conscientiously pointed out the pervasiveness of conceptual mappings, particularly as conceptual blending and integration, that underlie language and that are unconsciously used in everyday speech (Fauconnier 1997, Fauconnier & Turner 2002; Rohrer 2007; Grady, Oakley & Coulson 1999). Moreover, as a further development of this work, there is a growing interest in research devoted to the conceptual mappings that make up specialized technical disciplines. Lakoff & Núñez 2000, for example, have produced a major breakthrough on the understanding of concepts in mathematics, through conceptual metaphor and as a result not of purely abstract concepts but rather of embodiment. On the engineering and architecture front, analyses on the use of metaphor, blending and categorization in English and Spanish have likewise appeared in recent times (Úbeda 2001, Roldán 1999, Caballero 2003a, 2003b, Roldán & Ubeda 2006, Roldán & Protasenia 2007). The present paper seeks to show a number of significant conceptual mappings underlying the language of architecture and civil engineering that seem to shape the way engineers and architects communicate. In order to work with a significant segment of linguistic expressions in this field, a corpus taken from a widely used technical Spanish engineering journal article was collected and analysed. The examination of the data obtained indicates that many tokens make a direct reference to therapeutic conceptual mappings, highlighting medical domains such as diagnosing,treating and curing. Hence, the paper illustrates how this notion is instantiated by the corresponding bodily conceptual integration. In addition, we wish to underline the function of visual metaphors in the world of modern architecture by evoking parts of human or animal anatomy, and how this is visibly noticeable in contemporary buildings and public works structures.

Categorical Structures in Non-Commutative Measure Theory.

In this paper, we investigate effect algebras and base normed spaces from the categorical point of view. We prove that the category of effect algebras is complete and cocomplete as well as the category of base normed spaces is complete, and discuss the contravariant functor from the category of effect algebras to the category of base normed spaces.

New Literacy for Reading Using ICT

This article will analyse the key strategies in the relationship between reading and writing in the area of ICT and the resulting importance in supporting literacy in this area so that the education system as a whole (primary and secondary schools and universities) can be guided to make full use of the opportunities ICT can provide. ICTs are able to help improve overall comprehension, evaluate general perspectives and raise awareness of the value of cooperation and, as a result, the essential quality of individuals and their contributions. These contributions are far-reaching and strategic. The benefits of applying ICT in reading and writing are also felt in oral expression and can result in education based more on dialogue which, in turn, leads to social change.

Relationship between sociometric types and academic achievement in a sample of compulsory secondary education students

The aim of this study was to analyse the relationship between sociometric types, behavioural categories and academic achievement in a sample of 1,349 compulsory secondary education students (51.7% boys), ranging in age from 12 to 16 years. The students’ sociometric identification was performed by using the Programa Socio and academic performance was measured by school marks provided by teachers in the subjects of Spanish language, mathematics and average academic performance. The results show that sociometric types were significant predictors of academic achievement, as students who were rated positively by their peers (popular, leaders, collaborators and good students) were more likely to have high academic achievement (in mathematics, Spanish language and average academic achievement) than students rated negatively by peers (rejected-aggressive, rejected-shy, neglected and bullies).

Dificuldades de aprendizagem em alunos do 3º ano duma escola pública do Estado de Alagoas, Brasil : uma visão da psicoeducação.

Enquadramento: A par da não alfabetização e do abandono escolar, as taxas de insucesso no ensino fundamental no Brasil atingem indicadores preocupantes. A aprendizagem é um processo complexo e são múltiplos os fatores que contribuem tanto positivamente quanto negativamente na aprendizagem dos alunos e os seus efeitos irão refletir-se no futuro dos educandos. Se há crianças com distúrbios fisiopatológicos que prejudicam a sua aprendizagem, noutras, porém, as dificuldades surgem por influência da escola/professores e da relação destes com a família Objetivos: Identificar as áreas de dificuldades de aprendizagem na componente curricular de português e matemática; identificar as dificuldades nos domínios de aprendizagem de cada área e analisar a relação das variáveis sociodemográficas e escolares com as dificuldades de aprendizagem. Material e métodos: Estudo exploratório-descritivo, quantitativo e correlacional numa amostra de 178 alunos, do 3º ano, numa escola pública de Taquarana, Alagoas, Brasil. Utilizamos um questionário para a caraterização socio demográfica e escolar dos alunos e uma escala utilizada na escola para a avaliação formal da aprendizagem. Resultados: Os participantes são na maioria do sexo masculino (55,6%) com uma média de idades de 8,53 anos, distribuídos em 6 turmas (3 manhã e 3 tarde) em que a menor tem 25 alunos e a maior tem 35. Demoram em média 20 minutos na deslocação para a escola. Verificamos que 34,3% vivem com pais solteiros, separados divorciados ou viúvos. 31,5% dos alunos referem ter muito mau, ou mau ambiente familiar e há turmas onde isso é mais evidente. Os pais dos alunos em 37,1% não têm instrução e em 53,4% não ajudam nos estudos ou trabalhos de casa. Os alunos que já reprovaram são 26,4% e destes, 36,2% já reprovaram 3 ou mais vezes. As dificuldades de aprendizagem em língua portuguesa e matemática são maiores nos alunos mais velhos, do sexo masculino e que já reprovaram mais de uma vez. Um ambiente familiar mau/muito mau e a situação familiar dos pais a falta de instrução dos pais e o não ajudarem nas tarefas de casa contribui com as dificuldades. Na língua portuguesa há maior dificuldade no respeitar o momento de escuta e fala, na leitura e interpretação, produção textos e uso das regras ortográficas. Em matemática globalmente têm maiores dificuldades sobressaindo os parâmetros de identificação das operações nas situações-problemas e elaboração de tabelas e gráficos. Conclusões: Encontramos no nosso estudo alunos com grandes taxas de reprovações e com dificuldades evidentes tanto na língua portuguesa como em matemática. Constatamos que diversos são os fatores que contribuem para o aparecimento das dificuldades na aprendizagem de alguns alunos mas não podemos deixar de refletir sobre a influência da família. A destruturação familiar, mau ambiente e o fato de não terem instrução e não ajudarem os filhos nos estudos mostraram-se influenciadores no insucesso dos alunos PALAVRAS-CHAVE – Aprendizagem, Dificuldades de aprendizagem, Família, Educação.