Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

https://onlinelibrary.wiley.com/doi/pdf/10.1207/s15516709cog2601_2

Memory for goals: an activation-based model

The authors propose the idea of threaded cognition, an integrated theory of concurrent multitasking-that is, performing 2 or more tasks at once. Threaded cognition posits that streams of thought can be represented as threads of processing coordinated by a serial procedural resource and executed across other available resources (e.g., perceptual and motor resources). The theory specifies a parsimonious mechanism that allows for concurrent execution, resource acquisition, and resolution of resource conflicts, without the need for specialized executive processes. By instantiating this mechanism as a computational model, threaded cognition provides explicit predictions of how multitasking behavior can result in interference, or lack thereof, for a given set of tasks. The authors illustrate the theory in model simulations of several representative domains ranging from simple laboratory tasks such as dual-choice tasks to complex real-world domains such as driving and driver distraction.

/pdf/threaded-cognition-an-integrated-theory-of-concurrent-tdilfh7nmn.pdf

Threaded cognition: An integrated theory of concurrent multitasking

https://www.princeton.edu/~yael/Publications/BotvinickNivBarto2008.pdf

Hierarchically organized behavior and its neural foundations: A reinforcement learning perspective

In this article we describe production compilation, a mechanism for modeling skill acquisition. Production compilation has been developed within the ACT-Rational (ACT-R; J. R. Anderson, D. Bothell, M. D. Byrne, & C. Lebiere, 2002) cognitive architecture and consists of combining and specializing task-independent procedures into task-specific procedures. The benefit of production compilation for researchers in human factors is that it enables them to test the strengths and weaknesses of their task analyses and user models by allowing them to model the learning trajectory from the main task level and the unit task level down to the key-stroke level. We provide an example of this process by developing and describing a model learning a simulated air traffic controller task. Actual or potential applications of this research include the evaluation of user interfaces, the design of systems that support learning, and the building of user models.

/pdf/production-compilation-a-simple-mechanism-to-model-complex-3plraorkky.pdf

Production compilation: a simple mechanism to model complex skill acquisition.

http://act-r.psy.cmu.edu/wordpress/wp-content/uploads/2012/12/245fjl_jra_2001_a.pdf

Does learning a complex task have to be complex? A study in learning decomposition.

Cognitive modeling has evolved into a powerful tool for understanding and predicting user behavior. Higher-level modeling frameworks such as GOMS and its variants facilitate fast and easy model development but are sometimes limited in their ability to model detailed user behavior. Lower-level cognitive architectures such as EPIC, ACT-R, and Soar allow for greater precision and direct interaction with real-world systems but require significant modeling training and expertise. In this paper we present a modeling framework, ACT-Simple, that aims to combine the advantages of both approaches to cognitive modeling. ACT-Simple embodies a "compilation" approach in which a simple description language is compiled down to a core lower-level architecture (namely ACT-R). We present theoretical justification and empirical validation of the usefulness of the approach and framework.

/pdf/simple-cognitive-modeling-in-a-complex-cognitive-2agne40fsr.pdf

Simple cognitive modeling in a complex cognitive architecture

Increased preference for immediate over delayed and for risky over certain rewards has been associated with unhealthy behavioral choices. Motivated by evidence that enhanced cognitive control can shift choice behavior away from immediate and risky rewards, we tested whether training executive cognitive function could influence choice behavior and brain responses. In this randomized controlled trial, 128 young adults (71 male, 57 female) participated in 10 weeks of training with either a commercial web-based cognitive training program or web-based video games that do not specifically target executive function or adapt the level of difficulty throughout training. Pre- and post-training, participants completed cognitive assessments and functional magnetic resonance imaging (fMRI) during performance of validated decision-making tasks: delay discounting (choices between smaller rewards now vs. larger rewards in the future) and risk sensitivity (choices between larger riskier rewards vs. smaller certain rewards). Contrary to our hypothesis, we found no evidence that cognitive training influences neural activity during decision-making, nor did we find effects of cognitive training on measures of delay discounting or risk sensitivity. Participants in the commercial training condition improved with practice on the specific tasks they performed during training, but participants in both conditions showed similar improvement on standardized cognitive measures over time. Moreover, the degree of improvement was comparable to that observed in individuals who were reassessed without any training whatsoever. Commercial adaptive cognitive training appears to have no benefits in healthy young adults above those of standard video games for measures of brain activity, choice behavior, or cognitive performance. Registry: NCT01252966, www.clinicaltrials.gov SIGNIFICANCE STATEMENT Engagement of neural regions and circuits important in executive cognitive function can bias behavioral choices away from immediate rewards. Activity in these regions may be enhanced through adaptive cognitive training. Commercial brain training programs claim to improve a broad range of mental processes; however, evidence for transfer beyond trained tasks is mixed. We undertook the first randomized controlled trial of the effects of commercial adaptive cognitive training (Lumosity®) on neural activity and decision-making in young adults (N = 128), compared to an active control (playing online video games). We found no evidence for relative benefits of cognitive training with respect to changes in decision-making behavior or brain response, or for cognitive task performance beyond those specifically trained.

https://www.jneurosci.org/content/jneuro/early/2017/07/10/JNEUROSCI.2832-16.2017.full.pdf

No Effect of Commercial Cognitive Training on Brain Activity, Choice Behavior, or Cognitive Performance.

Multitasking allows people to cope with the ever changing and complex world that we live in However, as much as cognitive scientists have learned about the details of human cognition, the question of how people acquire multitasking ability remains a mystery In this paper, we argue that multitasking can be best understood as a product of skill acquisition In particular, we describe production composition, a computational theory of procedural skill acquisition, which can account for the acquisition of multitasking skill We explore this idea in this paper as part of our effort to develop a cognitive model of a simulated air-traffic controller Task

/pdf/multitasking-as-skill-acquisition-2vtfsns8h6.pdf

Frank J. Lee

Papers

Production compilation: a simple mechanism to model complex skill acquisition.

Does learning a complex task have to be complex? A study in learning decomposition.

Simple cognitive modeling in a complex cognitive architecture

No Effect of Commercial Cognitive Training on Brain Activity, Choice Behavior, or Cognitive Performance.

Multitasking as Skill Acquisition