Common Sense About the Common Core

Is the Common Core the best thing since sliced bread, or the work of the devil? Is it brand new, or a rehash of old ideas? Is it anything more than a brand name, or is there substance? Can it work, given the implementation challenges in our political and school systems? Opinions about the Common Core are everywhere, but the op-eds I’ve seen are often short on facts, and equally short on common sense. A mathematician by training, I’ve worked for nearly 40 years as an education researcher, curriculum materials developer, test developer, standards writer, and teacher. What follows is a Q&A based on that experience. I focus on the Common Core State Standards for Mathematics, known as CCSSM, but the issues apply to all standards (descriptions of what students should know and be able to do)

If you really want to get ahead, get a bunch of theories… and data to test them

This paper addresses questions of mathematics teachers’ professional development. My goal is not to provide “answers,” although I have worked for some years to enhance teachers’ capacity to create rich learning environments for their students. Rather, my goal is to problematize the issue, to ask: How do we frame questions of professional development in ways that are theoretically grounded? What theories do you need to know, in order do a good job of professional development? In the light of this kind of theoretical framing, I will discuss two related attempts at supporting teachers in their work

Reflections on Problem Solving Theory and Practice

In this article, the author reflects on the current state of mathematical problem solving, both in theory and in instruction. The impact of the book Mathematical Problem solving (Schoenfeld, 1985) is also discussed, along with implications of problem solving today with the advent of 21st century technologies

Scholastic Standards in the United States – The Discussion concerning the ‘Common Core’

Preface: This article has been developed based on a personal discussion between the German author Günter Törner and Alan Schoenfeld, who is an expert in the field of mathematical didactics. Basically there are three reasons for us to share our insights with the public: (1) Readers, having subscribed to Jerry Becker’s e-mail information network, have received numerous messages over the past few months; what do we need to know about this fact in Germany? (2) Scholastic standards – a keyword that sounds very familiar to us in terms of educational policy… But it is also a hot topic in other countries. What can we conclude from these discussions? (3) Scholastic standards – if they are developed, people will be eager to test their implementation. A very complex problem in the United States and maybe even in Germany!

Audiovisual temporal correspondence modulates human multisensory superior temporal sulcus plus primary sensory cortices

The brain should integrate related but not unrelated information from different senses. Temporal patterning of inputs to different modalities may provide critical information about whether those inputs are related or not. We studied effects of temporal correspondence between auditory and visual streams on human brain activity with functional magnetic resonance imaging ( fMRI). Streams of visual flashes with irregularly jittered, arrhythmic timing could appear on right or left, with or without a stream of auditory tones that coincided perfectly when present ( highly unlikely by chance), were noncoincident with vision ( different erratic, arrhythmic pattern with same temporal statistics), or an auditory stream appeared alone. fMRI revealed blood oxygenation level-dependent ( BOLD) increases in multisensory superior temporal sulcus (mSTS), contralateral to a visual stream when coincident with an auditory stream, and BOLD decreases for noncoincidence relative to unisensory baselines. Contralateral primary visual cortex and auditory cortex were also affected by audiovisual temporal correspondence or noncorrespondence, as confirmed in individuals. Connectivity analyses indicated enhanced influence from mSTS on primary sensory areas, rather than vice versa, during audiovisual correspondence. Temporal correspondence between auditory and visual streams affects a network of both multisensory ( mSTS) and sensory-specific areas in humans, including even primary visual and auditory cortex, with stronger responses for corresponding and thus related audiovisual inputs

Beyond deficit-based models of learners' cognition: Interpreting engineering students' difficulties with sense-making in terms of fine-grained epistemological and conceptual dynamics

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: He does see common-sense as connected to formalism (though not always tractably so) and in some circumstances this connection is both salient and valued.Comment: Submitted to the Journal of Engineering Educatio

High-field fMRI reveals brain activation patterns underlying saccade execution in the human superior colliculus

Background The superior colliculus (SC) has been shown to play a crucial role in the initiation and coordination of eye- and head-movements. The knowledge about the function of this structure is mainly based on single-unit recordings in animals with relatively few neuroimaging studies investigating eye-movement related brain activity in humans. Methodology/Principal Findings The present study employed high-field (7 Tesla) functional magnetic resonance imaging (fMRI) to investigate SC responses during endogenously cued saccades in humans. In response to centrally presented instructional cues, subjects either performed saccades away from (centrifugal) or towards (centripetal) the center of straight gaze or maintained fixation at the center position. Compared to central fixation, the execution of saccades elicited hemodynamic activity within a network of cortical and subcortical areas that included the SC, lateral geniculate nucleus (LGN), occipital cortex, striatum, and the pulvinar. Conclusions/Significance Activity in the SC was enhanced contralateral to the direction of the saccade (i.e., greater activity in the right as compared to left SC during leftward saccades and vice versa) during both centrifugal and centripetal saccades, thereby demonstrating that the contralateral predominance for saccade execution that has been shown to exist in animals is also present in the human SC. In addition, centrifugal saccades elicited greater activity in the SC than did centripetal saccades, while also being accompanied by an enhanced deactivation within the prefrontal default-mode network. This pattern of brain activity might reflect the reduced processing effort required to move the eyes toward as compared to away from the center of straight gaze, a position that might serve as a spatial baseline in which the retinotopic and craniotopic reference frames are aligned

Single photon Mach-Zehnder interferometer for quantum networks based on the Single Photon Faraday Effect: principle and applications

Combining the recent progress in semiconductor nanostructures along with the versatility of photonic crystals in confining and manipulating light, quantum networks allow for the prospect of an integrated and low power quantum technology. Within quantum networks, which consist of a system of waveguides and nanocavities with embedded quantum dots, it has been demonstrated in theory that many-qubit states stored in electron spins could be teleported from one quantum dot to another via a single photon using the Single Photon Faraday Effect. However, in addition to being able to transfer quantum information from one location to another, quantum networks need added functionality such as (1) controlling the flow of the quantum information and (2) performing specific operations on qubits that can be easily integrated. In this paper, we show how in principle a single photon Mach-Zehnder interferometer, which uses the concept of the single photon Faraday Effect to manipulate the geometrical phase of a single photon, can be operated both as a switch to control the flow of quantum information inside the quantum network and as various single qubit quantum gates to perform operations on a single photon. Our proposed Mach-Zehnder interferometer can be fully integrated as part of a quantum network on a chip. Given that the X gate, the Z gate, and the XZ gate are essential for the implementation of quantum teleportation, we show explicitly their implementation by means of our proposed single photon Mach-Zehnder interferometer. We also show explicitly the implementation of the Hadamard gate and the single-qubit phase gate, which are needed to complete the universal set of quantum gates for integrated quantum computing in a quantum network.Comment: 25 pages, 16 figure

Late onset of Huntington's disease

Twenty-five patients with late-onset Huntington's disease were studied; motor impairment appeared at age 50 years or later. The average age at onset of chorea was 57.5 years, with an average age at diagnosis of 63.1 years. Approximately 25% of persons affected by Huntington's disease exhibit late onset. A preponderance of maternal transmission was noted in late-onset Huntington's disease. The clinical features resembled those of mid-life onset Huntington's disease but progressed more slowly. Neuropathological evaluation of two cases reveal less severe neuronal atrophy than for mid-life onset disease