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The purpose of this paper is to examine how teachers improve core instructional practices in teaching mathematics for problem solving through lesson study (LS). The core practices included launching a task, implementing a task, and orchestrating students’ solutions.

This study adopted multiple case study and survey methodologies. Each of three LS groups developed a research lesson on problem solving in algebra through Chinese LS, which includes collaborative planning and repeated teachings/debriefings of the research lesson with support from experts. The data collected included lesson plans, videotaped research lessons and debriefing meetings, and an end-of-project survey. Case studies supported by survey data were utilized to describe how research lessons were improved and what teachers learned from LS.

A fine-grained analysis of the data revealed that the participants improved their strategies for teaching for problem solving, which included effectively launching tasks, strategically implementing tasks, and productively orchestrating students’ solutions to the tasks. Further, analyses revealed that the feedback from experts during debriefing meetings played crucial roles in making these changes. Moreover, participants learned how to implement these core instructional practices and changed their views about students’ learning.

The study uncovers the mechanisms about how teachers improve teaching and their expertise in teaching through Chinese LS. The importance of the dynamic between repeated teaching and immediate feedback from knowledgeable others is highlighted.

This paper aims to describe colonial competitive algorithm (CCA), a novel socio‐politically inspired optimization strategy, and how it is used to solve real world engineering problems by applying it to the problem of designing a multivariable proportional‐integral‐derivative (PID) controller. Unlike other evolutionary optimization algorithms, CCA is inspired from a socio‐political process – the competition among imperialists and colonies. In this paper, CCA is used to tune the parameters of a multivariable PID controller for a typical distillation column process.

The controller design objective was to tune the PID controller parameters so that the integral of absolute errors, overshoots and undershoots be minimized. This multi‐objective optimization problem is converted to a mono‐objective one by adding up all the objective functions in which the absolute integral of errors is emphasized to be reduced as long as the overshoots and undershoots remain acceptable.

Simulation results show that the controller tuning approach, proposed in this paper, can be easily and successfully applied to the problem of designing MIMO controller for control processes. As a result not only was the controlled process able to significantly reduce the coupling effect, but also the response speed was significantly increased. Also a genetic algorithm (GA) and an analytical method are used to design the controller parameters and are compared with CCA. The results showed that CCA had a higher convergence rate than GA, reaching to a better solution.

The proposed PID controller tuning approach is interesting for the design of controllers for industrial and chemical processes, e.g. MIMO evaporator plant. Also the proposed evolutionary algorithm, CCA, can be used in diverse areas of optimization problems including, industrial planning, resource allocation, scheduling, decision making, pattern recognition and machine learning.