Exposing the mathematical differences between enactments of the same written lesson

In this paper we respond to Huntley and Heck’s 2014 call for new conceptual frameworks that recognize mathematical differences between enactments of the same written lessons that stick “closely” to the textbook. We use a mathematical story framework to describe differences in the mathematical development of three enactments of the same algebra 1 lesson by three different experienced teachers. We find and document differences in how the lessons raise questions, sustain inquiry (or not), and progress toward resolution of the questions. These differences influence the overall mathematical and temporal structure of the enactments, which, in turn, affect the student experience and potentially affect student opportunities to learn

Patterns Within Nine Preattack Phases That Emerged in Israel Suicide Bombing Cases

From 2000 to 2013, Israel had the second highest number of deaths from suicide attacks and was on the list of countries that may experience increases in terrorism due to ongoing conflicts. Suicide bombings present highly complex situations for counterterrorism and counterinsurgency professionals. Using Freeman, Tucker, and Merton\u27s framework of 9 preattack phases as the primary theoretical constuct, the purpose of this multiple case study was to explore specific patterns that consistently emerged in the adversary planning process for 6 successful or failed suicide bombing cases in Israel. Secondary, archival data were acquired through a data use agreement with a private security organization in Israel and a maximum variation sampling procedure was used to identify cases. These data were subjected to Straus and Corbin\u27s open and axial coding procedures. Coded data were analyzed using Merriam\u27s cross case analysis procedure. Findings indicated that although the nine preattack phases emerged in both the successful and unsuccessful attacks, they were more consistently present in the successful bombing cases. For the successful attacks, general planning, financing, and operational preparation received the most occurrences. The implications for positive social change are directed at counterterrorist decision makers and operators as focusing on the early planning phases of a terrorist attack will help them to better identify essential opportunities to prevent suicide attacks from occurring

Woo! Aesthetic variations of the "same" lesson

Efforts to enhance the aesthetic impact of mathematics lessons must account for the role of teachers in shaping the unfolding mathematical content of their enacted lessons. In this paper, we draw from Dietiker (2015) to describe differences in the mathematical stories of the enacted lessons of two veteran teachers teaching the same lesson. We identify connections between these differences and the variations in student experiences as illustrated by visible student reactions

Opportunities created by misdirection in mathematics education

This study provides evidence that enacted lessons based on written curriculum do not need to follow a direct curricular path from beginning to end. Deviations in this path, which we refer to as misdirection, can create opportunities for enhanced student interest in mathematical questions. We present three examples of misdirection from two enacted lessons and describe how they intensified student investment in the mathematics by creating contradictions that inspired students to ask their own mathematical questions. These examples can serve as models to teachers and curriculum writers who seek ways to motivate students to pursue mathematical understanding

Hyperlexia in a 4-year-old boy with Autistic Spectrum Disorder

This paper presents a case study of a 4-year-old boy with Autistic Spectrum Disorder and a mental age of approximately 1:5 who demonstrates precocious oral-reading behaviour in the absence of spontaneous speech. Tests of reading regular and irregular words, pseudowords, homographic heterophones, single sentences and texts were carried out. Performance on a variety of reading tasks suggests the ability to use grapheme–phoneme correspondences and whole word reading for decoding single words. In addition, successful reading of some homographic heterophones and semantic paraphrasing of texts suggests a level of lexical, syntactic, semantic and pragmatic development far beyond his mental or chronological age. The realisation of highly developed reading ability is paradoxical in the context of profound impairment in cognitive development and an absence of spoken language

Hyperactivity, impulsivity, and inattention in boys with cleft lip and palate: relationship to ventromedial prefrontal cortex morphology

The purpose of this study is to evaluate quantitative structural measures of the ventromedial prefrontal cortex (vmPFC) in boys with isolated clefts of the lip and/or palate (ICLP) relative to a comparison group and to associate measures of brain structure with quantitative measures of hyperactivity, impulsivity, and inattentiveness. A total of 50 boys with ICLP were compared to 60 healthy boys without clefts. Magnetic resonance imaging brain scans were used to evaluate vmPFC structure. Parents and teachers provided quantitative measures of hyperactivity, impulsivity, and inattentiveness using the Pediatric Behavior Scale. Boys with ICLP had significantly higher ratings of hyperactivity/impulsivity/inattention (HII) and significantly increased volume of the right vmPFC relative to the comparison group. There was a direct relationship between HII score and vmPFC volume in both the ICLP group and control group, but the relationship was in the opposite direction: in ICLP, the higher the vmPFC volume, the higher the HII score; for the comparison group, the lower the vmPFC volume, the greater the HII score. The vmPFC is a region of the brain that governs behaviors of hyperactivity, impulsivity and inattention (HII). In boys with ICLP, there are higher levels of HII compared to the controls and this is directly related to a significantly enlarged volume of the right vmPFC. Enlargement of this region of the brain is therefore considered to be pathological in the ICLP group and supports the notion that abnormal brain structure (from abnormal brain development) is the underlying etiology for the abnormal behaviors seen in this population

Expression and trans-specific polymorphism of self-incompatibility RNases in Coffea (Rubiaceae)

Self-incompatibility (SI) is widespread in the angiosperms, but identifying the biochemical components of SI mechanisms has proven to be difficult in most lineages. Coffea (coffee; Rubiaceae) is a genus of old-world tropical understory trees in which the vast majority of diploid species utilize a mechanism of gametophytic self-incompatibility (GSI). The S-RNase GSI system was one of the first SI mechanisms to be biochemically characterized, and likely represents the ancestral Eudicot condition as evidenced by its functional characterization in both asterid (Solanaceae, Plantaginaceae) and rosid (Rosaceae) lineages. The S-RNase GSI mechanism employs the activity of class III RNase T2 proteins to terminate the growth of "self" pollen tubes. Here, we investigate the mechanism of Coffea GSI and specifically examine the potential for homology to S-RNase GSI by sequencing class III RNase T2 genes in populations of 14 African and Madagascan Coffea species and the closely related self-compatible species Psilanthus ebracteolatus. Phylogenetic analyses of these sequences aligned to a diverse sample of plant RNase T2 genes show that the Coffea genome contains at least three class III RNase T2 genes. Patterns of tissue-specific gene expression identify one of these RNase T2 genes as the putative Coffea S-RNase gene. We show that populations of SI Coffea are remarkably polymorphic for putative S-RNase alleles, and exhibit a persistent pattern of trans-specific polymorphism characteristic of all S-RNase genes previously isolated from GSI Eudicot lineages. We thus conclude that Coffea GSI is most likely homologous to the classic Eudicot S-RNase system, which was retained since the divergence of the Rubiaceae lineage from an ancient SI Eudicot ancestor, nearly 90 million years ago.United States National Science Foundation [0849186]; Society of Systematic Biologists; American Society of Plant Taxonomists; Duke University Graduate Schoolinfo:eu-repo/semantics/publishedVersio

Catching Element Formation In The Act

Gamma-ray astronomy explores the most energetic photons in nature to address some of the most pressing puzzles in contemporary astrophysics. It encompasses a wide range of objects and phenomena: stars, supernovae, novae, neutron stars, stellar-mass black holes, nucleosynthesis, the interstellar medium, cosmic rays and relativistic-particle acceleration, and the evolution of galaxies. MeV gamma-rays provide a unique probe of nuclear processes in astronomy, directly measuring radioactive decay, nuclear de-excitation, and positron annihilation. The substantial information carried by gamma-ray photons allows us to see deeper into these objects, the bulk of the power is often emitted at gamma-ray energies, and radioactivity provides a natural physical clock that adds unique information. New science will be driven by time-domain population studies at gamma-ray energies. This science is enabled by next-generation gamma-ray instruments with one to two orders of magnitude better sensitivity, larger sky coverage, and faster cadence than all previous gamma-ray instruments. This transformative capability permits: (a) the accurate identification of the gamma-ray emitting objects and correlations with observations taken at other wavelengths and with other messengers; (b) construction of new gamma-ray maps of the Milky Way and other nearby galaxies where extended regions are distinguished from point sources; and (c) considerable serendipitous science of scarce events -- nearby neutron star mergers, for example. Advances in technology push the performance of new gamma-ray instruments to address a wide set of astrophysical questions.Comment: 14 pages including 3 figure