Building reflective practices in a pre-service math and science teacher education course that focuses on qualitative video analysis

The use of video for in-service and pre-service teacher development has been gaining acceptance, and yet video remains a challenging and understudied tool. Many projects have used video to help pre-service and in-service teachers reflect on their own teaching processes, examine teacher–student interactions, and develop their professional vision. But rarely has video been used in ways more akin to qualitative education research that is focused on student learning. Even more rarely has this focus occurred at the earliest stages of pre-service teaching when students have not yet decided to pursue teaching careers. Yet here we argue that there are benefits to our approach. We examine a course for prospective pre-service math and science teachers at the University of California, Berkeley, that engages participants in qualitative video analysis to foster their reflective practice. This course is unique in that the prospective pre-service teachers engage in qualitative video analysis at a level characteristic of professional educational research, in that their analysis focuses on student learning of math and science content. We describe classroom activities that provide opportunities for the preservice teacher participants to better observe, notice, and interpret their students’ sociocognitive activity. The course culmination project involves participants developing and teaching lessons in a high school classroom. The participants then videotape the lessons and conduct qualitative video analysis. Results include detailed examples of two selected prospective pre-service teachers demonstrating coherent and effective approaches to conceptualizing the learning and teaching of mathematical and science content along with some potential design principles for building reflective practices through qualitative video projects. © 2018 Association for Science Teacher Education

Superstatistics

We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the statistical properties of the fluctuations, we obtain different effective statistical mechanics descriptions. Tsallis statistics is one, but other classes of generalized statistics are obtained as well. We show that for small variance of the fluctuations all these different statistics behave in a universal way.Comment: 12 pages /a few more references and comments added in revised versio

The maximum number of minimal codewords in an [n,k]−[n,k]-code

Upper and lower bounds are derived for the quantity in the title, which is tabulated for modest values of $n$ and $k.$ An application to graphs with many cycles is given.Comment: 6 pp. Submitte

Synchronization in Scale Free networks: The role of finite size effects

Synchronization problems in complex networks are very often studied by researchers due to its many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, Scale Free networks with degree distribution $P(k)\sim k^{-\lambda}$, are widely used in research since they are ubiquitous in nature and other real systems. In this paper we focus on the surface relaxation growth model in Scale Free networks with $2.5< \lambda <3$, and study the scaling behavior of the fluctuations, in the steady state, with the system size $N$. We find a novel behavior of the fluctuations characterized by a crossover between two regimes at a value of $N=N^*$ that depends on $\lambda$: a logarithmic regime, found in previous research, and a constant regime. We propose a function that describes this crossover, which is in very good agreement with the simulations. We also find that, for a system size above $N^{*}$, the fluctuations decrease with $\lambda$, which means that the synchronization of the system improves as $\lambda$ increases. We explain this crossover analyzing the role of the network's heterogeneity produced by the system size $N$ and the exponent of the degree distribution.Comment: 9 pages and 5 figures. Accepted in Europhysics Letter

Patient-Reported Disability Measures Do Not Correlate with Electrodiagnostic Severity in Carpal Tunnel Syndrome.

BACKGROUND: Electrophysiologic studies including electromyography and nerve conduction studies play a role in the evaluation of carpal tunnel syndrome (CTS), despite evidence that these studies do not correlate with CTS-specific symptom scores. There is a lack of evidence comparing electrophysiologic data with general measures of function. METHODS: Fifty patients presenting for CTS treatment over an 8-month period were analyzed retrospectively. All patients completed surveys including the Quick Disabilities of the Arm, Shoulder, and Hand questionnaire (DASH) and the Medical Outcomes Study 12-Item Short-Form Survey [(physical component summary 12, mental component summary (MCS-12)]. Electromyography and nerve conduction studies were performed on all patients and compared with outcome scores. RESULTS: Analysis demonstrated no relationship between DASH or MCS-12 and electrodiagnostic severity. No significant correlations were noted between DASH or MCS-12 and median motor or sensory latency. There was a moderate-weak correlation (rho = 0.34) between more severe electrophysiologic grade and better function based on physical component summary 12. CONCLUSIONS: Electrodiagnostic severity grades do not correlate with patient-reported disability, including the DASH and MCS-12 surveys. There is a counterintuitive correlation between more-severe electrodiagnostic findings and decreased physical disability. These findings indicate that disability may not correlate with electrodiagnostic severity of median neuropathy in CTS

Sequentializing Parameterized Programs

We exhibit assertion-preserving (reachability preserving) transformations from parameterized concurrent shared-memory programs, under a k-round scheduling of processes, to sequential programs. The salient feature of the sequential program is that it tracks the local variables of only one thread at any point, and uses only O(k) copies of shared variables (it does not use extra counters, not even one counter to keep track of the number of threads). Sequentialization is achieved using the concept of a linear interface that captures the effect an unbounded block of processes have on the shared state in a k-round schedule. Our transformation utilizes linear interfaces to sequentialize the program, and to ensure the sequential program explores only reachable states and preserves local invariants.Comment: In Proceedings FIT 2012, arXiv:1207.348

Fuzzy hh-ideals of hemirings

A characterization of an $h$-hemiregular hemiring in terms of a fuzzy $h$-ideal is provided. Some properties of prime fuzzy $h$-ideals of $h$-hemiregular hemirings are investigated. It is proved that a fuzzy subset $\zeta$ of a hemiring $S$ is a prime fuzzy left (right) $h$-ideal of $S$ if and only if $\zeta$ is two-valued, $\zeta(0) = 1$, and the set of all $x$ in $S$ such that $\zeta(x) = 1$ is a prime (left) right $h$-ideal of $S$. Finally, the similar properties for maximal fuzzy left (right) $h$-ideals of hemirings are considered

The role of the rigged Hilbert space in Quantum Mechanics

There is compelling evidence that, when continuous spectrum is present, the natural mathematical setting for Quantum Mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in Quantum Mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space.Comment: 29 pages, 2 figures; a pedestrian introduction to the rigged Hilbert spac

What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement

The question of what makes a data distribution suitable for deep learning is a fundamental open problem. Focusing on locally connected neural networks (a prevalent family of architectures that includes convolutional and recurrent neural networks as well as local self-attention models), we address this problem by adopting theoretical tools from quantum physics. Our main theoretical result states that a certain locally connected neural network is capable of accurate prediction over a data distribution if and only if the data distribution admits low quantum entanglement under certain canonical partitions of features. As a practical application of this result, we derive a preprocessing method for enhancing the suitability of a data distribution to locally connected neural networks. Experiments with widespread models over various datasets demonstrate our findings. We hope that our use of quantum entanglement will encourage further adoption of tools from physics for formally reasoning about the relation between deep learning and real-world data.Comment: Accepted to NeurIPS 202