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Wittgenstein On Miscalculation And The Foundations Of Mathematics, Samuel J. Wheeler
Wittgenstein On Miscalculation And The Foundations Of Mathematics, Samuel J. Wheeler
Philosophy Faculty Publications
In Remarks on the Foundations of Mathematics, Wittgenstein notes that he has 'not yet made the role of miscalculating clear' and that 'the role of the proposition: "I must have miscalculated"...is really the key to an understanding of the "foundations" of mathematics.' In this paper, I hope to get clear on how this is the case. First, I will explain Wittgenstein's understanding of a 'foundation' for mathematics. Then, by showing how the proposition 'I must have miscalculated' differentiates mathematics from the physical sciences, we will see how this proposition is the key to understanding the foundations of mathematics.
Multivariate Distributions Of Correlated Binary Variables Generated By Pair-Copulas, Huihui Lin, N. Rao Chaganty
Multivariate Distributions Of Correlated Binary Variables Generated By Pair-Copulas, Huihui Lin, N. Rao Chaganty
Mathematics & Statistics Faculty Publications
Correlated binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. The generalized estimating equations (GEEs) and the multivariate probit (MP) model are two of the popular methods for analyzing such data. However, both methods have some significant drawbacks. The GEEs may not have an underlying likelihood and the MP model may fail to generate a multivariate binary distribution with specified marginals and bivariate correlations. In this paper, we study multivariate binary distributions that are based on D-vine pair-copula models as a superior alternative to these methods. We elucidate the construction of these binary distributions …
Teacher Support Of Co- And Socially-Shared Regulation Of Learning In Middle School Mathematics Classrooms, Melissa Quackenbush, Linda Bol
Teacher Support Of Co- And Socially-Shared Regulation Of Learning In Middle School Mathematics Classrooms, Melissa Quackenbush, Linda Bol
Educational Leadership & Workforce Development Faculty Publications
Social influences on classroom learning have a long research tradition and are critical components of self-regulated learning theories. More recently, researchers have explored the social influences of self-regulated learning in cooperative learning contexts. In these settings, co-regulation of learning and socially-shared regulation of learning strategies have been aligned with self-regulated learning theory. However, without specific training or structure, teachers are not likely to explicitly integrate SRL strategies into their teaching. We use case studies to better understand how Zimmerman's theory of self-regulated learning (2008) and Hadwin's conceptual framework of socially-shared regulation of learning (2018) emerge from teachers' support of student-centered …
Number Knowledge And Error Types Of Elementary Portuguese Students: Implications For Instruction, Silvana Watson, Sharon Judge, João Lopes, Célia Oliveira, Ana Catarina Jesus
Number Knowledge And Error Types Of Elementary Portuguese Students: Implications For Instruction, Silvana Watson, Sharon Judge, João Lopes, Célia Oliveira, Ana Catarina Jesus
Communication Disorders & Special Education Faculty Publications
In the present study, we examined number knowledge skills of 697 Portuguese elementary students from first to fourth grade. Students completed three number knowledge tasks: 1) translating numbers into words, 2) symbolic magnitude (i.e., number comparison), and 3) decomposing numbers. We evaluated students’ answers by means of error analysis using a three-category coding system adopted from specific error types were computed by grade level. Results showed that there were significant differences among grades and that the prerequisite linguistic error type (i.e., pre linguistic rules or principles of the cardinal number system), particularly in the magnitude tasks, significantly contributed to students’ …
Mathematics In The Age Of Technology: There Is A Place For Technology In The Mathematics Classroom, Helen Crompton
Mathematics In The Age Of Technology: There Is A Place For Technology In The Mathematics Classroom, Helen Crompton
Teaching & Learning Faculty Publications
In today’s world of ubiquitous computing there are a number of technologies available to K-12 educators for teaching and learning mathematics. However, Koehler and Mishra (2008) have described how teaching and learning with such technologies presents a “wicked problem,” as it can involve a number of variables, independent of each other and contextually bound, that need to be brought together. This article highlights the advantages technology offers for mathematics education and looks at some of the reasons behind the poor uptake, such as teacher beliefs and lack of training. A number of solutions are offered to address these issues, including …
Addressing The Principles For School Mathematics: A Case Study Of Elementary Teachers Pedagogy And Practices In An Urban High-Poverty School, Robert Q. Berry, Linda Bol, Sueanne E. Mckinney
Addressing The Principles For School Mathematics: A Case Study Of Elementary Teachers Pedagogy And Practices In An Urban High-Poverty School, Robert Q. Berry, Linda Bol, Sueanne E. Mckinney
Educational Leadership & Workforce Development Faculty Publications
The extent to which four novice teachers assigned to an urban high-poverty school implemented the Principles of School Mathematics during their mathematics instruction program was investigated using a case study design. The research team conducted 36 unannounced observations of the participating teachers and utilized a developed assessment to guide their observations. Results indicated that only one teacher was judged proficient for all the principles. The remaining three teachers fell short in the implementation and direction of the principles. Detailed descriptions of the pedagogical practices of the teachers are provided.
Flowers Of Ice- Beauty, Symmetry, And Complexity: A Review Of The Snowflake: Winter's Secret Beauty, John A. Adam
Flowers Of Ice- Beauty, Symmetry, And Complexity: A Review Of The Snowflake: Winter's Secret Beauty, John A. Adam
Mathematics & Statistics Faculty Publications
(First paragraph) Growing up as a child in southern England, my early memories of snow include trudging home from school with my father, gazing at the seemingly enormous snowdrifts that smoothed the hedgerows, fields and bushes, while listening to the soft “scrunch” of the snow under my Wellington boots. In the country, snow stretching as far as I could see was not a particularly uncommon sight. The quietness of the land under a foot of snow seemed eerie. I cannot remember the first time I looked at snowflakes per se; my interests as a small child were primarily in their …