Explanations in Mathematics Classrooms: A Discourse Analysis

Abstract

This article focuses on student explanations as a discourse practice central to mathematics teaching and learning. I discuss classrooms as hybrid discourse spaces and focus on how talk is used to accomplish social action. In doing so, I contrast several different social and sociomathematical norms for explanation and suggest that students’ choices of discourse practices position them within the classroom. Further, I caution educators against assuming that complete and detailed explanations are always best to support student learning. I discuss how explanations that are coconstructed by several students can actually support joint engagement in mathematical work and help peers stay “on the same page” while avoiding hierarchical positioning.     

Microstress in Reaction‐Bonded SiC from Crystallization Expansion of Silicon

Microstress in reaction‐bonded silicon carbide (RBSiC) has been measured using piezo‐Raman spectroscopy. Compressive microstresses as high as 2 GPa exist in the silicon phase and tensile microstresses as high as 2.3 GPa exist in the SiC phase of RBSiC. This is much larger than expected for thermoelastic microstress from coefficient of thermal expansion mismatch would provide. Instead the microstresses arise from the crystallization of liquid silicon. During the reaction bonding process, not all of the silicon reacts to form SiC and there is liquid free silicon. The phase transformation of the free silicon from liquid to solid has a large volume expansion, which results in large residual microstress within the silicon and SiC phases of RBSiC.     

Oscillatory squeeze film analysis of soft contact lenses

The complex modulus of a soft contact lens affects the optical performance, fitting, on-eye movement, wettability, physiological impact and overall comfort of the lens. However, despite acknowledgement that the mechanical behaviour of contact lenses is time-dependent, the rheological characteristics of contact lenses remain under-defined. While existing studies have focussed on elasticity to describe lens behaviour, this paper proposes using oscillatory squeeze film analysis to evaluate the complex modulus. The effects of excitation amplitude, repeatability and surface wetness are examined for four commercially available lenses. Slip at the lens/platen interface is considered along with bias introduced by pre-compressing the lens between platens. Test results when compared to results reported from other test methods indicate that a high degree of slip occurs at the lens platen interface suggesting that deformation is primarily due to biaxial extension.     

Sporadic Creutzfeldt-Jakob disease in the United Kingdom: analysis of epidemiological surveillance data for 1970-96

OBJECTIVE: To identify changes in the occurrence of Creutzfeldt-Jakob disease that might be related to the epidemic of bovine spongiform encephalopathy. DESIGN: Epidemiological surveillance of the United Kingdom population for Creutzfeldt-Jakob disease based on (a) referral of suspected cases by neurologists, neuropathologists, and neurophysiologists and (b) death certificates. SETTING: England and Wales during 1970-84, and whole of the United Kingdom during 1985-96. SUBJECTS: All 662 patients identified as sporadic cases of Creutzfeldt-Jakob disease. MAIN OUTCOME MEASURES: Age distribution of patients, age specific time trends of disease, occupational exposure to cattle, potential exposure to causative agent of bovine spongiform encephalopathy. RESULTS: During 1970-96 there was an increase in the number of sporadic cases of Creutzfeldt-Jakob disease recorded yearly in England and Wales. The greatest increase was among people aged over 70. There was a statistically significant excess of cases among dairy farm workers and their spouses and among people at increased risk of contact with live cattle infected with bovine spongiform encephalopathy. During 1994-6 there were six deaths from sporadic Creutzfeldt-Jakob disease in the United Kingdom in patients aged under 30. CONCLUSIONS: The increase in the incidence of sporadic Creutzfeldt-Jakob disease and the high incidence in dairy farmers in the United Kingdom may be unrelated to bovine spongiform encephalopathy. The most striking change in the pattern of Creutzfeldt-Jakob disease in the United Kingdom after the epidemic of bovine spongiform encephalopathy is provided by the incidence in a group of exceptionally young patients with a consistent and unusual neuropathological profile. The outcome of mouse transmission studies and the future incidence of the disease in the United Kingdom and elsewhere, will be important in judging whether the agent causing bovine spongiform encephalopathy has infected humans.     

Indigo Preal,靛蓝色的异域奇玑

拥有诸多光环照耀的Indigo Pearl,是一座充盈着传统泰式风情又张扬着现代艺术气息的新锐度假酒店。其泰国传统的建筑外观和后现代主义风格的室内设计,构成了一种强烈的视觉张力,吸引着人们欲到空间的深处一探究竟。