A Avaliação na sala de aula de matemática: práticas e concepções

This research aims to understand the assessment practices used by teachers at a public state school in the city of Cunha, Sao Paulo. To this end, we interviewed five mathematics teachers, who answered a questionnaire with five questions. The responses were analyzed according to the rigor of phenomenological research. To understand the investigation region, that is to say, the meaning of evaluation, we proceeded to a review of studies on the subject in authors like Buriasco (2002), Pavanello (2006), Hoffmann (1994), expressive in Mathematics Education that allows us to explain the concept of prevailing interpretation in the area. The phenomenological analysis enabled the development of three categories open revealing the concept of evaluation of teachers investigated. The first shows the review As a way to measure the knowledge acquired by the student. His interpretation leads us to understand that for some teachers, the research subjects, the assessment becomes a method to ' measure ' the knowledge acquired by the student. The second category, expressed by As a way of understanding the student's behavior in class, shows that some of the interviewees understand the evaluation as a medium that reveals and appreciates the ways of the student behave in class. Finally, the third category refers to the evaluation by means of said instruments. On this subject the claim that the assessment is through instruments such that: evidence, exercise lists, among others. In summary, interviews and categories analyzed explain the ways in which the assessment reveals the concept of implicit learning the instruments used in the evaluation practices of teachers interviewed. However, the authors read, evaluation is a necessary and permanent teaching job in teaching, which must follow step by step the process of teaching and learning. It follows, ... (Complete abstract click electronic access below)

A Resolução de problemas no ensino de matemática

The Troubleshooting is a methodology that stands out in mathematics teaching, it provides a meaningful learning, favoring the intellectual development of the student and the autonomous and critical thinking. In this work an exploratory study on the use of Problem Solving as a teaching strategy. Along it is discussed the importance of problem solving, which is a problem and their differences for years, the types of problems, how to solve a problem and as a teacher should apply problem solving in the classroom choosing problems and exercises adequate and properly questioning the student

GEDI: a user-friendly toolbox for analysis of large-scale gene expression data

Abstract Background Several mathematical and statistical methods have been proposed in the last few years to analyze microarray data. Most of those methods involve complicated formulas, and software implementations that require advanced computer programming skills. Researchers from other areas may experience difficulties when they attempting to use those methods in their research. Here we present an user-friendly toolbox which allows large-scale gene expression analysis to be carried out by biomedical researchers with limited programming skills. Results Here, we introduce an user-friendly toolbox called GEDI (Gene Expression Data Interpreter), an extensible, open-source, and freely-available tool that we believe will be useful to a wide range of laboratories, and to researchers with no background in Mathematics and Computer Science, allowing them to analyze their own data by applying both classical and advanced approaches developed and recently published by Fujita et al. Conclusion GEDI is an integrated user-friendly viewer that combines the state of the art SVR, DVAR and SVAR algorithms, previously developed by us. It facilitates the application of SVR, DVAR and SVAR, further than the mathematical formulas present in the corresponding publications, and allows one to better understand the results by means of available visualizations. Both running the statistical methods and visualizing the results are carried out within the graphical user interface, rendering these algorithms accessible to the broad community of researchers in Molecular Biology.

Rigidity for piecewise smooth homeomorphisms on the circle

We find conditions for two piecewise 'C POT.2+V' homeomorphisms f and g of the circle to be 'C POT.1' conjugate. Besides the restrictions on the combinatorics of the maps (we assume that the maps have bounded combinatorics), and necessary conditions on the one-side derivatives of points where f and g are not differentiable, we also assume zero mean-nonlinearity for f and g.

Lê–Greuel type formula for the Euler obstruction and applications

The Euler obstruction of a function f can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we establish several Lê–Greuel type formulas for germs f:(X,0)→(C,0) and g:(X,0)→(C,0). We give applications when g is a generic linear form and when f and g have isolated singularities.

Learning for well being : Studies using the International Adult Literacy Survey

This thesis is a collection of five independent but closely related studies. The overall purpose is to approach the analysis of learning outcomes from a perspective that combines three major elements, namely lifelonglifewide learning, human capital, and the benefits of learning. The approach is based on an interdisciplinary perspective of the human capital paradigm. It considers the multiple learning contexts that are responsible for the development of embodied potential – including formal, nonformal and informal learning – and the multiple outcomes – including knowledge, skills, economic, social and others– that result from learning. The studies also seek to examine the extent and relative influence of learning in different contexts on the formation of embodied potential and how in turn that affects economic and social well being. The first study combines the three major elements, lifelonglifewide learning, human capital, and the benefits of learning into one common conceptual framework. This study forms a common basis for the four empirical studies that follow. All four empirical studies use data from the International Adult Literacy Survey (IALS) to investigate the relationships among the major elements of the conceptual framework presented in the first study. Study I. A conceptual framework for the analysis of learning outcomes This study brings together some key concepts and theories that are relevant for the analysis of learning outcomes. Many of the concepts and theories have emerged from varied disciplines including economics, educational psychology, cognitive science and sociology, to name only a few. Accordingly, some of the research questions inherent in the framework relate to different disciplinary perspectives. The primary purpose is to create a common basis for formulating and testing hypotheses as well as to interpret the findings in the empirical studies that follow. In particular, the framework facilitates the process of theorizing and hypothesizing on the relationships and processes concerning lifelong learning as well as their antecedents and consequences. Study II. Determinants of literacy proficiency: A lifelong-lifewide learning perspective This study investigates lifelong and lifewide processes of skill formation. In particular, it seeks to estimate the substitutability and complementarity effects of learning in multiple settings over the lifespan on literacy skill formation. This is done by investigating the predictive capacity of major determinants of literacy proficiency that are associated with a variety of learning contexts including school, home, work, community and leisure. An identical structural model based on previous research is fitted to the IALS data for 18 countries. The results show that even after accounting for all factors, education remains the most important predictor of literacy proficiency. In all countries, however, the total effect of education is significantly mediated through further learning occurring at work, at home and in the community. Therefore, the job and other literacy related factors complement education in predicting literacy proficiency. This result points to a virtual cycle of lifelong learning, particularly to how educational attainment influences other learning behaviours throughout life. In addition, results show that home background as measured by parents’ education is also a strong predictor of literacy proficiency, but in many countries this occurs only if a favourable home background is complemented with some post-secondary education. Study III. The effect of literacy proficiency on earnings: An aggregated occupational approach using the Canadian IALS data This study uses data from the Canadian Adult Literacy Survey to estimate the earnings return to literacy skills. The approach adapts a labour segmented view of the labour market by aggregating occupations into seven types, enabling the estimation of the variable impact of literacy proficiency on earnings, both within and between different types of occupations. This is done using Hierarchical Linear Modeling (HLM). The method used to construct the aggregated occupational classification is based on analysis that considers the role of cognitive and other skills in relation to the nature of occupational tasks. Substantial premiums are found to be associated with some occupational types even after adjusting for within occupational differences in individual characteristics such as schooling, literacy proficiency, labour force experience and gender. Average years of schooling and average levels of literacy proficiency at the between level account for over two-thirds of the premiums. Within occupations, there are significant returns to schooling but they vary depending on the type of occupations. In contrast, the within occupational return of literacy proficiency is not necessarily significant. The latter depends on the type of occupation. Study IV: Determinants of economic and social outcomes from a lifewide learning perspective in Canada In this study the relationship between learning in different contexts, which span the lifewide learning dimension, and individual earnings on the one hand and community participation on the other are examined in separate but comparable models. Data from the Canadian Adult Literacy Survey are used to estimate structural models, which correspond closely to the common conceptual framework outlined in Study I. The findings suggest that the relationship between formal education and economic and social outcomes is complex with confounding effects. The results indicate that learning occurring in different contexts and for different reasons leads to different kinds of benefits. The latter finding suggests a potential trade-off between realizing economic and social benefits through learning that are taken for either job-related or personal-interest related reasons. Study V: The effects of learning on economic and social well being: A comparative analysis Using the same structural model as in Study IV, hypotheses are comparatively examined using the International Adult Literacy Survey data for Canada, Denmark, the Netherlands, Norway, the United Kingdom, and the United States. The main finding from Study IV is confirmed for an additional five countries, namely that the effect of initial schooling on well being is more complex than a direct one and it is significantly mediated by subsequent learning. Additionally, findings suggest that people who devote more time to learning for job-related reasons than learning for personal-interest related reasons experience higher levels of economic well being. Moreover, devoting too much time to learning for personal-interest related reasons has a negative effect on earnings except in Denmark. But the more time people devote to learning for personal-interest related reasons tends to contribute to higher levels of social well being. These results again suggest a trade-off in learning for different reasons and in different contexts.

Decomposing Blaschke Products And Polynomials

The goal of this paper is to contribute to the understanding of complex polynomials and Blaschke products, two very important function classes in mathematics. For a polynomial, $f,$ of degree $n,$ we study when it is possible to write $f$ as a composition $f=g\circ h$, where $g$ and $h$ are polynomials, each of degree less than $n.$ A polynomial is defined to be \emph{decomposable }if such an $h$ and $g$ exist, and a polynomial is said to be \emph{indecomposable} if no such $h$ and $g$ exist. We apply the results of Rickards in \cite{key-2}. We show that $$C_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,(z-z_{1})(z-z_{2})...(z-z_{n})\,\mbox{is decomposable}\},$$ has measure $0$ when considered a subset of $\mathbb{R}^{2n}.$ Using this we prove the stronger result that $$D_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,\mbox{There exists\,}a\in\mathbb{C}\,\,\mbox{with}\,\,(z-z_{1})(z-z_{2})...(z-z_{n})(z-a)\,\mbox{decomposable}\},$$ also has measure zero when considered a subset of $\mathbb{R}^{2n}.$ We show that for any polynomial $p$, there exists an $a\in\mathbb{C}$ such that $p(z)(z-a)$ is indecomposable, and we also examine the case of $D_{5}$ in detail. The main work of this paper studies finite Blaschke products, analytic functions on $\overline{\mathbb{D}}$ that map $\partial\mathbb{D}$ to $\partial\mathbb{D}.$ In analogy with polynomials, we discuss when a degree $n$ Blaschke product, $B,$ can be written as a composition $C\circ D$, where $C$ and $D$ are finite Blaschke products, each of degree less than $n.$ Decomposable and indecomposable are defined analogously. Our main results are divided into two sections. First, we equate a condition on the zeros of the Blaschke product with the existence of a decomposition where the right-hand factor, $D,$ has degree $2.$ We also equate decomposability of a Blaschke product, $B,$ with the existence of a Poncelet curve, whose foci are a subset of the zeros of $B,$ such that the Poncelet curve satisfies certain tangency conditions. This result is hard to apply in general, but has a very nice geometric interpretation when we desire a composition where the right-hand factor is degree 2 or 3. Our second section of finite Blaschke product results builds off of the work of Cowen in \cite{key-3}. For a finite Blaschke product $B,$ Cowen defines the so-called monodromy group, $G_{B},$ of the finite Blaschke product. He then equates the decomposability of a finite Blaschke product, $B,$ with the existence of a nontrivial partition, $\mathcal{P},$ of the branches of $B^{-1}(z),$ such that $G_{B}$ respects $\mathcal{P}$. We present an in-depth analysis of how to calculate $G_{B}$, extending Cowen's description. These methods allow us to equate the existence of a decomposition where the left-hand factor has degree 2, with a simple condition on the critical points of the Blaschke product. In addition we are able to put a condition of the structure of $G_{B}$ for any decomposable Blaschke product satisfying certain normalization conditions. The final section of this paper discusses how one can put the results of the paper into practice to determine, if a particular Blaschke product is decomposable. We compare three major algorithms. The first is a brute force technique where one searches through the zero set of $B$ for subsets which could be the zero set of $D$, exhaustively searching for a successful decomposition $B(z)=C(D(z)).$ The second algorithm involves simply examining the cardinality of the image, under $B,$ of the set of critical points of $B.$ For a degree $n$ Blaschke product, $B,$ if this cardinality is greater than $\frac{n}{2}$, the Blaschke product is indecomposable. The final algorithm attempts to apply the geometric interpretation of decomposability given by our theorem concerning the existence of a particular Poncelet curve. The final two algorithms can be implemented easily with the use of an HTML

Attempting to improve standardized test results using Study Islands' web-based mastery program

State standardized testing has always been a tool to measure a school’s performance and to help evaluate school curriculum. However, with the school of choice legislation in 1992, the MEAP test became a measuring stick to grade schools by and a major tool in attracting school of choice students. Now, declining enrollment and a state budget struggling to stay out of the red have made school of choice students more important than ever before. MEAP scores have become the deciding factor in some cases. For the past five years, the Hancock Middle School staff has been working hard to improve their students’ MEAP scores in accordance with President Bush's “No Child Left Behind” legislation. In 2005, the school was awarded a grant that enabled staff to work for two years on writing and working towards school goals that were based on the improvement of MEAP scores in writing and math. As part of this effort, the school purchased an internet-based program geared at giving students practice on state content standards. This study examined the results of efforts by Hancock Middle School to help improve student scores in mathematics on the MEAP test through the use of an online program called “Study Island.” In the past, the program was used to remediate students, and as a review with an incentive at the end of the year for students completing a certain number of objectives. It had also been used as a review before upcoming MEAP testing in the fall. All of these methods may have helped a few students perform at an increased level on their standardized test, but the question remained of whether a sustained use of the program in a classroom setting would increase an understanding of concepts and performance on the MEAP for the masses. This study addressed this question. Student MEAP scores and Study Island data from experimental and comparison groups of students were compared to understand how a sustained use of Study Island in the classroom would impact student test scores on the MEAP. In addition, these data were analyzed to determine whether Study Island results provide a good indicator of students’ MEAP performance. The results of the study suggest that there were limited benefits related to sustained use of Study Island and gave some indications about the effectiveness of the mathematics curriculum at Hancock Middle School. These results and implications for instruction are discussed.

SUPPORTING LEARNING FOR NAVAJO STUDENTS THROUGH ETHNOMATHEMATICS

The purpose of this research was to address how culturally informed ethnomathematical methods of teaching can be utilized to support the learning of Navajo students in mathematics. The study was conducted over the course of four years on the Navajo Reservations at Tohatchi Middle School in Tohatchi New Mexico. The students involved in the study were all in 8th grade and were enrolled either in Algebra 1 or a Response to Intervention, RTI, class. The data collected came in the form of a student survey, student observation and student assessment. The teacher written survey, a math textbook word problem, and two original math textbook problems along with their rewritten version were the sources of these three studies. The first year of the study consisted of a math attitude survey and how Navajo students perceived math as a subject of interest. The students answered four questions pertaining to their thoughts about mathematics. The students’ responses were positive according to their written answers. The second year of the study involved the observation of how students worked through a math word problem as a group. This method tested how the students culturally interacted in order to solve a math problem. Their questions and reasoning to solve the problem were shared with peers and the teacher. The teacher supported the students in understanding and solving the problem by asking questions that kept the students focused on the goal of solving the problem. The students worked collaboratively and openly in order to complete the activity. During the iv study, the teacher was more able to notice the students’ deficiencies individually or as a group, therefore was able to support them in a more specific manner. The last study was conducted over a period of two different years. This study was used to determine how textbook bias in the form of its sentence structure or word choice affects the performance of students who are not culturally familiar with one or both. It was found that the students performed better and took less time on the rewritten problem than on the original problem. The data suggests that focusing on the culture, language and education of Navajo students can affect how the students learn and understand math.

Interactive Curriculum Based on Models of Mind & Brain

What does it mean for curriculum to be interactive? It encourages student engagement and active participation in both individual and group work. It offers teachers a coherent set of materials to choose from that can enhance their classes. It is the product of on-going development and continuous improvement based on research and feedback from the field. This paper will introduce work in progress from the Center for Excellence in Education, Science, and Technology (CELEST), an NSF Science of Learning Center. Among its many goals, CELEST is developing a unique educational curriculum, an interactive curriculum based upon models of mind and brain. Teachers, administrators, and governments are naturally concerned with how students learn. Students are greatly concerned about how minds work, including how to learn. CELEST aims to introduce curricula that not only meet current U.S. standards in mathematics, science, and psychology but also influence plans to improve those standards. Software and support materials are in development and available at http://cns.bu.edu/celest/private/. Interested parties are invited to contact the author for access.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Gender Stereotypes and Gendered Vocational Aspirations among Secondary School Students

Research Topic/Aim: Horizontal gender inequalities appear to be rather stable, with girls more often choosing ‘female' service professions, and boys choosing career paths related to science, technology, engineering or mathematics, since measures to bring more women into typical ‘male' jobs and more men into typical ‘female' jobs did not turn out to be sustainable. This paper focuses on gender stereotypes, namely non-egalitarian patriarchal gender-role orientations and gender associations of the school subjects German and mathematics. Dealing with and abolishing such gender stereotypes may be key strategy to reach sustainability regarding more equal vocational choices. Thus, gender stereotypes will be theorised and empirically analysed as a major predictor of gender-typical vocational perspectives considering interest in these school subjects as a mediating factor. Furthermore, we focus on structural patriarchy as a root of gender-role orientations, and teacher gender regarding its impact on gendered images of subjects. Theoretical and methodology framework: Our analyses of gender segregation in vocational aspirations and vocational choice center on Gottfredson's (2002; Gottfredson and Becker, 1981) Theory of Circumscription, Compromise and Self-Creation. One of the main assumptions of this theory is that people associate jobs with particular sexes and those jobs that do not fit particular gender roles are not considered. Empirical analyses are based on survey data of eighth-graders in the Swiss canton of Bern (N = 672). Structural Equation Models (SEM) for male and female students are estimated. Conclusions/Findings: Results reveal different patterns for boys and girls; for boys, gender-typical (male) vocational perspective could be explained via gender role orientations, interest in mathematics and gender associations of the school subjects, for girls, the factors under consideration could be empirically linked to ‘atypical vocational perspective'. Relevance to Nordic educational research: The study focuses on gender relations in society and how they are reproduced. Gender segregation in vocational choice and at the labour market is a universal issue - affecting both egalitarian and non-egalitarian gender regimes in similar ways. Although in general Northern countries appear to be more equal regarding gender inequality, gender segregation is rather persistent (Jarman, Blackburn and Brooks, 2012) and therefore remains a relevant topic.