Reflections on Teaching with a Standards-Based Curriculum: A Conversation Among Mathematics Educators

Many teachers and researchers have written about the challenges inherent in adopting new teaching practices in mathematics classrooms (e.g., Chazan, 2000; Clarke, 1997; Heaton, 2000). The authors of this article, all with secondary mathematics teaching experience, are convinced by research suggesting that Standards-based mathematics curricula are beneficial for student learning.1 However, the first three authors had not used such curriculum materials in their own classrooms, and we desired experience using a Standards-based mathematics curriculum with secondary students. To this end, we taught a week-long summer course with a focus on linear functions to high school students who had previously struggled with algebra and volunteered to participate

Absence of DNA Polymerase η Reveals Targeting of C Mutations on the Nontranscribed Strand in Immunoglobulin Switch Regions

Activation-induced cytosine deaminase preferentially deaminates C in DNA on the nontranscribed strand in vitro, which theoretically should produce a large increase in mutations of C during hypermutation of immunoglobulin genes. However, a bias for C mutations has not been observed among the mutations in variable genes. Therefore, we examined mutations in the μ and γ switch regions, which can form stable secondary structures, to look for C mutations. To further simplify the pattern, mutations were studied in the absence of DNA polymerase (pol) η, which may produce substitutions of nucleotides downstream of C. DNA from lymphocytes of patients with xeroderma pigmentosum variant (XP-V) disease, whose polymerase η is defective, had the same frequency of switching to all four γ isotypes and hypermutation in μ-γ switch sites (0.5% mutations per basepair) as control subjects. There were fewer mutations of A and T bases in the XP-V clones, similar to variable gene mutations from these patients, which confirms that polymerase η produces substitutions opposite A and T. Most importantly, the absence of polymerase η revealed an increase in C mutations on the nontranscribed strand. This data shows for the first time that C is preferentially mutated in vivo and pol η generates hypermutation in the μ and γ switch regions

Intended Mathematics Curriculum as Represented in State-Level Curriculum Standards: Consensus or Confusion?

Full Report published by: Information Age Publishers. http://www.infoagepub.comThis report represents the first detailed analysis of the grade placement of particular learning goals across all state-level curriculum documents published and current as of May 2005. The report documents the current situation regarding grade-level mathematics curriculum specification in the U.S. and highlights a general lack of consensus across states. As states continue to work to improve learning opportunities for all students, we hope this report will serve as a useful summary to inform future curriculum decisions.This report is based on the work of the Center for the Study of Mathematics Curriculum, supported by the National Science Foundation under Grant No. ESI-0333879. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation

A general framework for coupled hydro-mechanical modelling of rainfall-induced instability in unsaturated slopes with multivariate random fields

An accurate estimation of rainfall-induced instability of slopes for extremely nonhomogeneous materials such as lignite mine spoils is a major challenge. This paper investigates the stability of nonhomogeneous soil slopes with respect to slip surface development, size of sliding volume, and determination of safety factor. Specified dependent random variables are cross-correlated using a multivariate Gaussian copula, the use of which provides a faster and more accurate representation of the inter-dependent properties of randomly-distributed soil. A Monte-Carlo simulation is used to generate a series of multivariate random fields for slopes. These are then implemented in Abaqus and analysed under constant rainfall conditions using a fully coupled hydro-elasto-plastic model. The resulting stress, strain, pore pressure, and displacement data are further processed in MATLAB to evaluate critical slip surfaces and safety factors. Results indicate that the factor of safety in a homogenous case is overestimated compared to the nonhomogeneous condition, while the sliding volume is underestimated. Moreover, the factor of safety decreases as the rainfall simulation continues and the probability of failure increases to nearly 100% after 10 days of rainfall. The framework developed in this paper can provide guidance for conducting relatively inexpensive probabilistic analyses

The quest for hope and healing : a history of the residential school apology from St. Andrew's United Church in Port Alberni, B.C. : May 6, 1997

This history is an attempt to chronicle the historic “Apology From St. Andrew’s United Church [Port Alberni, BC] to First Nations Peoples for Harm Caused by “Indian” Residential Schools,” and the political and theological fall-out experienced during that journey towards rededication by the congregation and the United Church of Canada.Non UBCUnreviewedGraduat

Twig abscission in trembling aspen: Ecological causes and responses to shading and pruning.

Many shade-intolerant tree species abscise twigs and branches, but no study to date has directly examined the causes of abscission or evaluated the adaptive value of the behavior I hypothesize that unproductive twigs are selectively abscised and that this helps trees to maintain high growth rates: by annually abscising unproductive twigs, whole-tree growth rates are maximized because resources are allocated only to productive twigs. I tested whether light availability, the condition of the terminal bud and several factors affecting the relative sink strength of twigs are used as cues for abscission. I also tested the prediction that twig abscission has a positive effect on the growth of the remaining twigs. I studied nine natural clones of trembling aspen (Populus tremuloides Michx.) in southeastern lower Michigan. In a 2-year study of twigs on branches in 3 clones, I followed the initiation, growth, light environments, bud conditions and fates of twigs to identify likely cues for abscission. Logistic regression analyses showed that twigs were significantly more likely to abscise if they experienced lower light environments, were initially smaller, experienced lower growth rates, or had stunted or damaged terminal buds. These results support the hypothesis that twigs with low productivity are being abscised. Twigs with stunted buds were also from lower light environments, indicating that abscission of twigs in shaded positions is mediated in part by the effects of light on bud development. I tested directly the roles of light quantity and quality in causing twig abscission in a 1-year shading experiment, in which I shaded branches in 10 clones and observed the growth, buds, and fates of twigs. Treatments included no-shade, clear plastic, neutral shade, and green plastic (to simulate the shade of vegetation). Neutral and green shade allowed 5% transmission of incident light; in addition, the green shade reduced the red:far-red ratio to 0.1. The quantity, but not the quality, of light was important in determining twig fate: abscission rates were doubled under shade, but were similar under the neutral and green shade treatments. However, by affecting the development of buds, light quality may indirectly lead to abscission: stunted buds were 50% more frequent under green shade than under the other treatments, and twigs with stunted buds are more likely to be abscised. Finally, I tested the hypothesis that removal of some twigs benefits remaining twigs by reducing intrabranch competition for resources. Pruning half of the twigs from branches before bud-expansion began in the spring significantly increased the growth of remaining twigs by the end of the growing season. Pruning in mid-season improved the water status of the remaining twigs in the year of pruning, but did not increase their growth. Thus, natural seasonal abscission has the potential to increase whole-tree growth rates, whereas abscising twigs during periods of stress primarily minimizes losses by maintaining, rather than improving, the growing conditions of the remaining twigs.Ph.D.BiologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104963/1/9624643.pdfDescription of 9624643.pdf : Restricted to UM users only