20,365 research outputs found
In Search of Professional Dispositions that Yield Cultural Relevance in Primary Grade Pedagogy: A Cautionary Tale of One Kindergarten Teacher
Primary grade teachers are challenged to establish firm learning foundations for all children, yet for many teachers cultural diversity makes this a complex pedagogical challenge. It is widely assumed that the success with which teachers meet this challenge is reflected in their dispositions toward diversity, and ultimately toward culturally relevant pedagogy as a professional orientation. This article describes a multi-year study of cultural relevance in early mathematics teaching. Using the case of one kindergarten teacher who exhibited positive dispositions toward cultural relevance, the authors examine factors that seemed to work against its adoption in her pedagogy
Lacunarity of Fractal Superlattices: a Remote Estimation using Wavelets
The lacunarity provides a useful parameter for describing the distribution of gap sizes in discrete self-similar (fractal) superlattices and is used in addition to the similarity dimension to describe fractals. We show here that lacunarity, as well as the similarity dimension, can be remotely estimated from the wavelet analysis of superlattices impulse response. As a matter of fact, the skeletonâthe set of wavelet-transform modulus-maximaâof the reflected signal overlaps two hierarchical structures in the time-scale domain: such that one allows the direct remote extraction of the similarity dimension, while the other may provide an accurate estimation of the lacunarity of the interrogated superlattice. Criteria for the choice of the mother wavelet are established for impulse response corrupted by additive Gaussian white noise
Building Middle-Level Mathematics Teachers\u27 Capacities as Teachers and Leaders: The Math in the Middle Institute Partnership
This article describes professional development for middle-level mathematics teachers offered through the Math in the Middle Institute Partnership, a National Science Foundation-funded project to build teachersâ capacities to improve mathematics learning for all students. An overview of the project, including descriptions of its goals and curriculum are provided. Detailed descriptions of two mathematics courses and one pedagogy course are offered. The mathematics courses included here are the introductory course to the Math in the Middle Institute, as well as one of the ïŹnal math courses of the Institute in which participants apply mathematical knowledge and processes to real-world problems. The pedagogy course features curriculum that enables teachers to acquire an understanding of the nature and purpose of action research, and launches teachers into planning and implementing systematic inquiry in their own mathematics classrooms around topics of their choosing. The varied abilities of teachers, as well as growth in teachersâ mathematical and pedagogical capacities, are represented by several samples of student work provided within the article. In addition, mathematical and pedagogical products of student work are also provided through the projectâs URL links. Improving teacher quality is identiïŹed as a national need in mathematics education and one many universities and schools across the country are working in partnership to try to address. This article describes a professional development project aimed at improving mathematics teaching and learning in the middle grades. An overview of the project, along with a close look at several of its course offerings, are presented highlighting mathematical and pedagogical goals, challenges, and accomplishments
If Archimedes would have known functions
These are notes and slides from a Pecha-Kucha talk given on March 6, 2013.
The presentation tinkered with the question whether calculus on graphs could
have emerged by the time of Archimedes, if the concept of a function would have
been available 2300 years ago. The text first attempts to boil down discrete
single and multivariable calculus to one page each, then presents the slides
with additional remarks and finally includes 40 "calculus problems" in a
discrete or so-called 'quantum calculus' setting. We also added some sample
Mathematica code, gave a short overview over the emergence of the function
concept in calculus and included comments on the development of calculus
textbooks over time.Comment: 31 pages, 36 figure
Householder triangularization of a quasimatrix
A standard algorithm for computing the QR factorization of a matrix A is Householder triangularization. Here this idea is generalized to the situation in which A is a quasimatrix, that is, a âmatrixâ whose âcolumnsâ are functions defined on an interval [a,b]. Applications are mentioned to quasimatrix leastsquares fitting, singular value decomposition, and determination of ranks, norms, and condition numbers, and numerical illustrations are presented using the chebfun system
Preparing Secondary Mathematics Teachers: Focus on Modeling in Algebra
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities. We also interviewed a group of three to four PSTs at each of the universities. We coded the interview transcripts using an analytic framework developed based on related literature and policy documents. We report the similarities and differences in perspectives among instructors and PSTs related to modeling at each university, along with comparisons of OTL across universities
âWalking in a Foreign and Unknown Landscapeâ : studying the history of mathematics in initial teacher education
This article develops the argument that students in initial teacher education benefit in terms of who they are becoming from developing awareness of and engagement in the history of mathematics. Initially, current school mathematics practices in the UK are considered and challenged. Then the role of teachersâ relationship to mathematical subject knowledge and of teachersâ engagement in critical thinking are considered. Connections are made between these concerns and studying the history of mathematics in initial teacher education classrooms. I then draw on the perspectives and practices of the mathematics teacher educators at one institution to understand these connections better and to exemplify them. Issues of equity are threaded throughout
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