The Ministry of Education (MoE)/Ghana Education Service (GES) require all mathematics teachers to use manipulative materials to teach mathematics in Junior High Schools (JHSs) because they have the potential to demystify learning of the subject. The study was designed to examine the use of manipulative materials in teaching mathematics among junior high school teachers in the Seikwa Central Circuit of the Tain District of the Bono Region. The questionnaire was used to collect data from 15 teachers and 9 headteachers sampled from JHSs in the Seikwa Central Circuit of the Tain district. Descriptive statistical analysis was applied to the quantitative data obtained from the questionnaire. The study showed those teachers use manipulative materials in teaching mathematics in the classroom. Teachers knew the benefits of manipulative materials in learning; two factors challenged their use in the classroom: non-availability and inadequate supply of manipulative materials, and the high cost of preparing some manipulative materials. The study concluded that most JHS teachers in the circuit improvise most of the manipulative materials they use in the classroom since they are not supplied by MOE/GES, NGOs/Philanthropists, Tain district assembly, and PTA/SMC. The study recommended that stakeholders in education in the Seikwa Circuit should boost the supply of manipulative materials and organize periodic in-service training for JHS teachers on the use and development of manipulative materials for teaching mathematics. Lastly, MOE/GES should organize in-service training on the use of problem-solving in teaching mathematics.

In the case of an unexpected occurrence, disruption management is a method of rescheduling activities and it has been used in a variety of fields, including organized carrier scheduling and project management. The purpose of this review is to examine Ant Colony Optimization (ACO), the problems of Heuristics for Delivery Waste Collection (VRP), ARC Routing, Node Routing, and Container/skip. Other issues and problems examined in the paper were Non-Skip, Algorithms for the VRP, Improvement Algorithms, Simulated Annealing, and ACO for Capacitated Vehicle Routing, Clustering Analysis, and Probabilistic-D Cluster Analysis. It covers the fundamental characteristics of disruption management as well as the related goals and kinds of disruption that may occur in this setting. The various formulations and solution techniques are discussed in facets. A collection of relevant articles has been summarized and categorized according to the kind of disruption problem being addressed, the relevant goals, and the solution method used to resolve the problem. Vehicles must be emptied at a trash disposal facility before they may be used to collect garbage from further clients. The growing amount of solid waste generated as a result of p

This review article visualizes the use of manipulative materials in teaching mathematics among junior high school teachers. The review correlated to the study in the following areas: The concept of manipulative materials, types of manipulative materials teachers use in teaching mathematics, How teachers obtain manipulative materials for teaching mathematics, teaching methods teachers use for teaching mathematics with the use of manipulative materials, teachers’ perceived benefits of using manipulative materials in teaching mathematics, and challenges of using manipulative materials in teaching mathematics among teachers. In order to develop every student’s mathematical proficiency, leaders and teachers must systematically integrate the use of concrete and virtual manipulative materials into classroom instruction at all grades. Manipulative materials not only allow students to construct their own cognitive models for abstract mathematical ideas and processes, but they also provide a common language with which to communicate these models to the teacher and other students.