Differences in Teaching between Six Primary and Five Intermediate Teachers in One School

This study examined differences between primary and intermediate teachers concerning teacher behaviors, teacher communications, grouping, control, and materials. 6 primary classrooms (grades 1 and 2) and 5 intermediate classrooms ( grades 4 and 5) were each observed for 4 45-minute periods. In addition, observers, teachers, and 5 students from each classroom responded to 2 vignettes depicting classroom situations and 1 vignette asking respondents to describe a lesson on nutrition. Responses were coded for teacher behaviors, goals, and instructional methods. Analyses of observational data showed that in comparison with teachers in intermediate grades, primary teachers used significantly more sanctions, procedural communications and total teacher communications. Primary teachers also used a greater proportion of small-group instruction and manipulative materials than did intermediate teachers. Analysis of subjects\u27 responses to vignettes clarified these findings and added further detail

A Tutorial on the Structure of Distributed Optimization Algorithms

We consider the distributed optimization problem for a multi-agent system. Here, multiple agents cooperatively optimize an objective by sharing information through a communication network and performing computations. In this tutorial, we provide an overview of the problem, describe the structure of its algorithms, and use simulations to illustrate some algorithmic properties based on this structure.Comment: 6 pages, 14 figures, to appear at IEEE Conference on Decision and Control 202

A Tutorial on a Lyapunov-Based Approach to the Analysis of Iterative Optimization Algorithms

Iterative gradient-based optimization algorithms are widely used to solve difficult or large-scale optimization problems. There are many algorithms to choose from, such as gradient descent and its accelerated variants such as Polyak's Heavy Ball method or Nesterov's Fast Gradient method. It has long been observed that iterative algorithms can be viewed as dynamical systems, and more recently, as robust controllers. Here, the "uncertainty" in the dynamics is the gradient of the function being optimized. Therefore, worst-case or average-case performance can be analyzed using tools from robust control theory, such as integral quadratic constraints (IQCs). In this tutorial paper, we show how such an analysis can be carried out using an alternative Lyapunov-based approach. This approach recovers the same performance bounds as with IQCs, but with the added benefit of constructing a Lyapunov function.Comment: 6 pages, 3 figures, to appear at IEEE Conference on Decision and Control 202