The role of uncertainty in mathematical tasks for prospective elementary teachers

Mathematics teacher educators (MTEs) charged with the content preparation of prospective elementary teachers (PTs) receive widespread recommendations on a variety of issues, including which mathematical topics to include in their courses, the types of pedagogical strategies to use when working with PTs, and how to foster the development of particular mathematical practices. The nature of the mathematical tasks that MTEs can use to best support and extend PTs’ content knowledge is another area that deserves attention. This article considers uncertainty as a task feature and explains how it can be incorporated into mathematical tasks in order to support PTs’ specialized content knowledge. Using Zaslavsky’s (2005) three types of uncertainty – competing claims, unknown path or questionable conclusion, and non-readily verifiable outcomes – we provide three classroom examples of ways in which MTEs incorporated uncertainty into their mathematical tasks. Each example provides detail about the task design, background research on PTs’ knowledge of the underlying mathematical content, the type of uncertainty the task generated for PTs, and the ways in which that uncertainty may have contributed to PTs’ understandings of the content. Each example concludes with recommendations for MTEs on specific ways to incorporate that particular type of uncertainty into their own teaching

A rapid method for the isolation of peroxisomes from rat liver

A preparative method for the isolation of peroxisomes from the liver of normal, untreated rats is described. The peroxisome-enriched "light mitochondrial" fraction is layered on a 30% Nycodenz (5-[N-2,3-dihydroxypropylacetamido]-2,4,6-triiodo-N,N'-bis[2,3-dihydroxypropyl]isophthalamide) solution containing 1 m tetrasodium EDTA and then centrifuged in an angular rotor for 1 h at 130,000gavg. Peroxisomes are sedimented to the bottom leaving other organelles at the top of the tube. On the basis of morphological and biochemical studies, it is found that the peroxisomes (marker-enzymes catalase and urate oxidase) obtained in this method are not contaminated with lysosomes (marker-enzyme acid phosphatase) and contained very few mitochondria (marker-enzyme succinate-cytochrome c reductase) and microsomal vesicles (marker-enzyme glucose-6-phosphatase).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25978/1/0000044.pd

Environmental change and migration from Indian Sundarban : the need for an adaptation policy

PowerPoint presentationThe presentation focuses on climate change and forced migration patterns in vulnerable areas of Bangladesh, factoring in changes in sea surface temperature (SST), sea level rise, monsoon rainfall and events such as cyclones. Thousands of island residents have been displaced due to disappearance of land and coastal erosion. Environmental degradation has led to population migrations of 60,000 people - with women, infirm people and children often left behind

Spontaneous Blinks Activate the Precuneus: Characterizing Blink-Related Oscillations Using Magnetoencephalography

Spontaneous blinking occurs 15–20 times per minute. Although blinking has often been associated with its physiological role of corneal lubrication, there is now increasing behavioral evidence suggesting that blinks are also modulated by cognitive processes such as attention and information processing. Recent low-density electroencephalography (EEG) studies have reported so-called blink-related oscillations (BROs) associated with spontaneous blinking at rest. Delta-band (0.5–4 Hz) BROs are thought to originate from the precuneus region involved in environmental monitoring and awareness, with potential clinical utility in evaluation of disorders of consciousness. However, the neural mechanisms of BROs have not been elucidated. Using magnetoencephalography (MEG), we characterized delta-band BROs in 36 healthy individuals while controlling for background brain activity. Results showed that, compared to pre-blink baseline, delta-band BROs resulted in increased global field power (p < 0.001) and time-frequency spectral power (p < 0.05) at the sensor level, peaking at ∼250 ms post-blink maximum. Source localization showed that spontaneous blinks activated the bilateral precuneus (p < 0.05 FWE), and source activity within the precuneus was also consistent with sensor-space results. Crucially, these effects were only observed in the blink condition and were absent in the control condition, demonstrating that results were due to spontaneous blinks rather than as part of the inherent brain activity. The current study represents the first MEG examination of BROs. Our findings suggest that spontaneous blinks activate the precuneus regions consistent with environmental monitoring and awareness, and provide important neuroimaging support for the cognitive role of spontaneous blinks

Multimodal Characterization of the Semantic N400 Response within a Rapid Evaluation Brain Vital Sign Framework

Background: For nearly four decades, the N400 has been an important brainwave marker of semantic processing. It can be recorded non-invasively from the scalp using electrical and/or magnetic sensors, but largely within the restricted domain of research laboratories specialized to run specifc N400 experiments. However, there is increasing evidence of signifcant clinical utility for the N400 in neurological evaluation, particularly at the individual level. To enable clinical applications, we recently reported a rapid evaluation framework known as “brain vital signs” that successfully incorporated the N400 response as one of the core components for cognitive function evaluation. The current study characterized the rapidly evoked N400 response to demonstrate that it shares consistent features with traditional N400 responses acquired in research laboratory settings—thereby enabling its translation into brain vital signs applications. Methods: Data were collected from 17 healthy individuals using magnetoencephalography (MEG) and electroencephalography (EEG), with analysis of sensor-level efects as well as evaluation of brain sources. Individual-level N400 responses were classifed using machine learning to determine the percentage of participants in whom the response was successfully detected. Results: The N400 response was observed in both M/EEG modalities showing signifcant diferences to incongruent versus congruent condition in the expected time range (p<0.05). Also as expected, N400-related brain activity was observed in the temporal and inferior frontal cortical regions, with typical left-hemispheric asymmetry. Classifcation robustly confrmed the N400 efect at the individual level with high accuracy (89%), sensitivity (0.88) and specifcity (0.90). Conclusion: The brain vital sign N400 characteristics were highly consistent with features of the previously reported N400 responses acquired using traditional laboratory-based experiments. These results provide important evidence supporting clinical translation of the rapidly acquired N400 response as a potential tool for assessments of higher cognitive functions

Statistical Origin of Quantum Mechanics

The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an ontological support to the orthodox quantum mechanics. This approach to quantum mechanics, constitutes a deductive and direct method which, in a self-consistent scheme of a classical kinetics, allows us: i) to obtain the probabilistic nature of the quantum description and to interpret the wave function $\psi$ according to the Copenhagen school; ii) to derive the quantum potential and then the Schr\"odinger equation; iii) to calculate the values of the physical observables as mean values of the associated quantum operators; iv) to obtain the Heisenberg uncertainty principle.Comment: Accepted for publication in Physica

Developing Brain Vital Signs: Initial Framework for Monitoring Brain Function Changes over Time

Clinical assessment of brain function relies heavily on indirect behavior-based tests. Unfortunately, behavior-based assessments are subjective and therefore susceptible to several confounding factors. Event-related brain potentials (ERPs), derived from electroencephalography (EEG), are often used to provide objective, physiological measures of brain function. Historically, ERPs have been characterized extensively within research settings, with limited but growing clinical applications. Over the past 20 years, we have developed clinical ERP applications for the evaluation of functional status following serious injury and/or disease. This work has identified an important gap: the need for a clinically accessible framework to evaluate ERP measures. Crucially, this enables baseline measures before brain dysfunction occurs, and might enable the routine collection of brain function metrics in the future much like blood pressure measures today. Here, we propose such a framework for extracting specific ERPs as potential “brain vital signs.” This framework enabled the translation/transformation of complex ERP data into accessible metrics of brain function for wider clinical utilization. To formalize the framework, three essential ERPs were selected as initial indicators: (1) the auditory N100 (Auditory sensation); (2) the auditory oddball P300 (Basic attention); and (3) the auditory speech processing N400 (Cognitive processing). First step validation was conducted on healthy younger and older adults (age range: 22–82 years). Results confirmed specific ERPs at the individual level (86.81–98.96%), verified predictable age-related differences (P300 latency delays in older adults, p < 0.05), and demonstrated successful linear transformation into the proposed brain vital sign (BVS) framework (basic attention latency sub-component of BVS framework reflects delays in older adults, p < 0.05). The findings represent an initial critical step in developing, extracting, and characterizing ERPs as vital signs, critical for subsequent evaluation of dysfunction in conditions like concussion and/or dementia

Brain Vital Signs: Expanding From the Auditory to Visual Modality

The critical need for rapid objective, physiological evaluation of brain function at point-of-care has led to the emergence of brain vital signs—a framework encompassing a portable electroencephalography (EEG) and an automated, quick test protocol. This framework enables access to well-established event-related potential (ERP) markers, which are specific to sensory, attention, and cognitive functions in both healthy and patient populations. However, all our applications to-date have used auditory stimulation, which have highlighted application challenges in persons with hearing impairments (e.g., aging, seniors, dementia). Consequently, it has become important to translate brain vital signs into a visual sensory modality. Therefore, the objectives of this study were to: 1) demonstrate the feasibility of visual brain vital signs; and 2) compare and normalize results from visual and auditory brain vital signs. Data were collected from 34 healthy adults (33 ± 13 years) using a 64-channel EEG system. Visual and auditory sequences were kept as comparable as possible to elicit the N100, P300, and N400 responses. Visual brain vital signs were elicited successfully for all three responses across the group (N100: F = 29.8380, p < 0.001; P300: F = 138.8442, p < 0.0001; N400: F = 6.8476, p = 0.01). Initial auditory-visual comparisons across the three components showed attention processing (P300) was found to be the most transferrable across modalities, with no group-level differences and correlated peak amplitudes (rho = 0.7, p = 0.0001) across individuals. Auditory P300 latencies were shorter than visual (p < 0.0001) but normalization and correlation (r = 0.5, p = 0.0033) implied a potential systematic difference across modalities. Reduced auditory N400 amplitudes compared to visual (p = 0.0061) paired with normalization and correlation across individuals (r = 0.6, p = 0.0012), also revealed potential systematic modality differences between reading and listening language comprehension. This study provides an initial understanding of the relationship between the visual and auditory sequences, while importantly establishing a visual sequence within the brain vital signs framework. With both auditory and visual stimulation capabilities available, it is possible to broaden applications across the lifespan

Brain Vital Signs: Expanding From the Auditory to Visual Modality

The critical need for rapid objective, physiological evaluation of brain function at point-of-care has led to the emergence of brain vital signs—a framework encompassing a portable electroencephalography (EEG) and an automated, quick test protocol. This framework enables access to well-established event-related potential (ERP) markers, which are specific to sensory, attention, and cognitive functions in both healthy and patient populations. However, all our applications to-date have used auditory stimulation, which have highlighted application challenges in persons with hearing impairments (e.g., aging, seniors, dementia). Consequently, it has become important to translate brain vital signs into a visual sensory modality. Therefore, the objectives of this study were to: 1) demonstrate the feasibility of visual brain vital signs; and 2) compare and normalize results from visual and auditory brain vital signs. Data were collected from 34 healthy adults (33 ± 13 years) using a 64-channel EEG system. Visual and auditory sequences were kept as comparable as possible to elicit the N100, P300, and N400 responses. Visual brain vital signs were elicited successfully for all three responses across the group (N100: F = 29.8380, p < 0.001; P300: F = 138.8442, p < 0.0001; N400: F = 6.8476, p = 0.01). Initial auditory-visual comparisons across the three components showed attention processing (P300) was found to be the most transferrable across modalities, with no group-level differences and correlated peak amplitudes (rho = 0.7, p = 0.0001) across individuals. Auditory P300 latencies were shorter than visual (p < 0.0001) but normalization and correlation (r = 0.5, p = 0.0033) implied a potential systematic difference across modalities. Reduced auditory N400 amplitudes compared to visual (p = 0.0061) paired with normalization and correlation across individuals (r = 0.6, p = 0.0012), also revealed potential systematic modality differences between reading and listening language comprehension. This study provides an initial understanding of the relationship between the visual and auditory sequences, while importantly establishing a visual sequence within the brain vital signs framework. With both auditory and visual stimulation capabilities available, it is possible to broaden applications across the lifespan. The critical need for rapid objective, physiological evaluation of brain function at point-of-care has led to the emergence of brain vital signs—a framework encompassing a portable electroencephalography (EEG) and an automated, quick test protocol. This framework enables access to well-established event-related potential (ERP) markers, which are specific to sensory, attention, and cognitive functions in both healthy and patient populations. However, all our applications to-date have used auditory stimulation, which have highlighted application challenges in persons with hearing impairments (e.g., aging, seniors, dementia). Consequently, it has become important to translate brain vital signs into a visual sensory modality. Therefore, the objectives of this study were to: 1) demonstrate the feasibility of visual brain vital signs; and 2) compare and normalize results from visual and auditory brain vital signs. Data were collected from 34 healthy adults (33 ± 13 years) using a 64-channel EEG system. Visual and auditory sequences were kept as comparable as possible to elicit the N100, P300, and N400 responses. Visual brain vital signs were elicited successfully for all three responses across the group (N100: F = 29.8380, p < 0.001; P300: F = 138.8442, p < 0.0001; N400: F = 6.8476, p = 0.01). Initial auditory-visual comparisons across the three components showed attention processing (P300) was found to be the most transferrable across modalities, with no group-level differences and correlated peak amplitudes (rho = 0.7, p = 0.0001) across individuals. Auditory P300 latencies were shorter than visual (p < 0.0001) but normalization and correlation (r = 0.5, p = 0.0033) implied a potential systematic difference across modalities. Reduced auditory N400 amplitudes compared to visual (p = 0.0061) paired with normalization and correlation across individuals (r = 0.6, p = 0.0012), also revealed potential systematic modality differences between reading and listening language comprehension. This study provides an initial understanding of the relationship between the visual and auditory sequences, while importantly establishing a visual sequence within the brain vital signs framework. With both auditory and visual stimulation capabilities available, it is possible to broaden applications across the lifespan