Glosarium Matematika

273 p.; 24 cm

A Comparative Analysis of the Singapore Math Curriculum and the Everyday Mathematics Curriculum on Fifth Grade Achievement in a Large Northeastern Urban Public School District

This study examined the differences between the achievement effects of one proposed Common Core State Standards-aligned mathematics program, Math in Focus: Singapore Math, and one NCTM-aligned mathematics program, Everyday Mathematics, on Grade 5 mathematics performance. An explanatory non-experimental research design was employed using post hoc pre- and post-treatment data from 2010 NJ ASK3 and 2012 NJ ASK5 administrations, respectively. The study examined the achievement outcomes of 205 Grade 5 general education students across several independent variables (race/ethnicity, gender, SES, attendance). Statistical analyses revealed fairly consistent results regarding differences in student performance on the 2012 NJ ASK5 in schools implementing Singapore Math and in schools implementing Everyday Mathematics. Generally, across all analyses, there were no substantial differences in performance based upon treatment status. Similarly, there were no patterns of differential treatment effects across the dimensions of race/ethnicity, gender, and SES. Overall, treatment was found to be the weakest predictor of student performance, whereas student background characteristics (race/ethnicity and SES), and attendance accounted for the greatest proportion of variation in the performance of certain subgroups

Number Sense Mediated by Mathematics Self-Concept in Impacting Middle School Mathematics Achievement

The purpose of the current study was to extend the research on number sense to the middle school level and to simultaneously consider socioemotional elements related to the construct at this developmental stage. Its genesis was initially rooted in an ongoing and dramatic emphasis by U.S. policymakers, researchers, and educators on improving mathematics achievement in order to compete globally in technology and innovation. Despite debates about optimal curriculum and instruction, tremendous support exists for the construct of number sense. However, middle school research examining the phenomena has been limited to intervention protocols targeting specific skillsets and better measurement of its domains. Concomitantly, educational research has produced ample evidence of the decline in student mathematics motivation over time, and the corresponding literature establishes a link between mathematics self-concept and mathematics achievement, particularly during adolescence. The Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 provides a sample of 4,425 U.S. eighth graders for the present study, assessed directly and indirectly in cognitive, demographic, and affective domains. Multiple regression analyses confirmed the hypotheses that number sense predicts both mathematics self-concept and mathematics achievement at the middle school level, when controlling for gender, race, socioeconomic status, and special education services. Additionally, a path analysis with Statistical Analysis Software (SAS) and the Sobel test revealed that mathematics self-concept mediates the relationship between number sense and mathematics achievement. This indirect effect, when combined with the direct effect of number sense, results in a significant, medium total effect value of .35 for the model. By incorporating this knowledge regarding the interconnection of these three constructs into mathematics curriculum and instruction, as well as teacher education, the United States can move closer to bringing about equity of opportunity and motivating students to pursue more complex mathematics coursework and subsequently professions

Delineamento regressional múltiplo para um factorial de base prima estritamente associado a uma álgebra de Jordan comutativa

Quando para cada tratamento de um modelo base está definida uma regressão linear múltipla nas mesmas variáveis (dependente e explicativas) obtém-se um delineamento regressional múltiplo. O objectivo desta tese é desenvolver os delineamentos regressionais múltiplos associados a factoriais de base prima de efeitos fixos (factorial completo, confundimento e fraccionamento). A estrutura associada ao factorial de base prima assenta nos espaços lineares sobre corpos de Galois e na relação entre os modelos e álgebras de Jordan comutativas. Combinando esta abordagem com o Modelo-L é possível alargar o estudo, tanto do factorial, como do delineamento regressional múltiplo associado a um factorial, ao caso não equilibrado

Methods for efficient, exact combinatorial computation in machine learning

Combinatorial problems are common in machine learning, but they are often large-scale, exponential or factorial complexity optimization problems, for which exhaustive methods are impractical. Heuristics are typically used instead but these are not provably optimal, although they may produce a workable compromise solution in a reasonable time. On the other hand, dynamic programming (DP) is an efficient and broadly applicable tool that finds exact solutions to combinatorial problems. However, DP lacks systematicity as most algorithms are derived in an ad-hoc, problem-specific manner. In the literature, there are attempts to standardize DP algorithms, but they are either unnecessarily general (constructive algorithmics) or have limited applications to different problems (Emoto’s GTA). In this thesis, we propose a rigorous algebraic approach that systematically solves DP problems either by deriving algorithms from existing ones, or by deriving them from simple functional recurrences. The main contribution is providing novel, exact solutions for combinatorial optimization problems in machine learning and artificial intelligence. Our novel formalism largely bypasses the need to invoke the often quite high level of abstraction present in classical constructive algorithmics, as well as providing algorithms that are provably correct and polymorphic over any semiring. These algorithms can be applied to any combinatorial problem expressible in terms of semirings as a consequence of polymorphism. This approach also contributes to systematicity in embedding combinatorial constraints applying tupling to avoid the need for ad-hoc backtracking

Learning Disentangled Representations

Artificial intelligence systems are seeking to learn better representations. One of the most desirable properties in these representations is disentanglement. Disentangled representations show merits of interpretability and generalizability. Through these representations, the world around us can be decomposed into explanatory factors of variation, and can thus be more easily understood by not only machines but humans. Disentanglement is akin to the reverse engineering process of a video game, where based on exploring the beautiful open world we need to figure out what underlying controllable factors that actually render/generate these fantastic dynamics. This thesis mainly discusses the problem of how such "reverse engineering" can be achieved using deep learning techniques in the computer vision domain. Although there have been plenty of works tackling this challenging problem, this thesis shows that an important ingredient that is highly effective but largely neglected by existing works is the modeling of visual variation. We show from various perspectives that by integrating the modeling of visual variation in generative models, we can achieve superior unsupervised disentanglement performance that has never been seen before. Specifically, this thesis will cover various novel methods based on technical insights such as variation consistency, variation predictability, perceptual simplicity, spatial constriction, Lie group decomposition, and contrastive nature in semantic changes. Besides the proposed methods, this thesis also touches on topics such as variational autoencoders, generative adversarial networks, latent space examination, unsupervised disentanglement metrics, and neural network architectures. We hope the observations, analysis, and methods presented in this thesis can inspire and contribute to future works in disentanglement learning and related machine learning fields

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 04. bis 06.07. 2012, Bauhaus-Universität Weimar

The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference