Discuss Various Theories of Management

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Portraits of the Case Studies
The Case Study problems are teaching units, each of which supports 3 to 5 lessons on a topic from outside mathematics. They develop thinking, reasoning and problem solving skills and put substance into the Key Concepts and Processes of the new Programme of Study (PoS) for Key Stage 3 – aspects of the National Curriculum that are less familiar to many teachers. Between them, the Case Studies cover most of the PoS. The Case Studies are very different from each other and have been developed by a wide range of developers. Each one is rich in mathematical possibilities and provides pupils and their teachers with interesting and exciting problems on topics that pupils find fun and engaging. The topics range from the real world to pure fantasy. The problems make extensive use of ‘open’ questions, to which there is often no one right answer. most require a number of steps and can be explored at various levels of depth by pupils of differing abilities. Each Case Study contains materials for pupils to use in the classroom as well as teachers’ notes and lesson plans. Most of the Case Studies, but not all of them, require access to some form of ICT. Each Case Study took about 18 months to develop. In addition to fieldwork tests by its developer, each one was subjected to ‘action’ tests in two ‘cold trial’ schools by independent evaluators; the feedback from the trials was used for further development. Over 100 schools were involved in the development of the Case Studies. Choosing a case study The case studies are very diverse - over time it would be good to try them all. To help teachers decide where to start this document provides the following summary information: Examples of mathematical activity provide a few lines that sketch the problem that each case study presents and the mathematics that it involves. Comparison charts summarise the case studies from various perspectives: • Type of problem: The case studies cover six broad types of problem – planning and organizing; designing and making; modelling and explaining; exploring and discovering relationships; interpreting and explaining; solving logic puzzles. A case study may have more than one of these aspects. • Time required in terms of the number of (typically) 1 hour lessons suggested • Suitability for age and ability groups • Resources needed: particularly computers and interactive whiteboards – a few case studies require other resources • Links to the Key Stage 3 Programme of Study: This table indicates the potential contribution of each case study to developing: key concepts; key processes; content areas; curriculum opportunities, that comprise the KS3 Programme of Study Outline descriptions provide a short explanation of what each case study is about. This document serves as a quick reference and comparison guide, but is no substitute for exploring the case studies themselves. Each case study itself includes a more extensive description of its content, pedagogical aims and practicalities. These descriptions can be accessed from the Case Studies section of the Bowland Player on the DVD or website.


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Examples of mathematical activities
Alien invasion Locate spaceships using clues to estimate and calculate distances and directions. Interpret graphs and maps to plan an escape; crack a code to escape from a cell. General problem solving. Control variables systematically (e.g. speeds, design of cars, barrier types). Make hypotheses and test them by observing the effects in crash test experiments. Present findings to the class. Plan a route in space, bearing in mind fuel, food reserves and distance. Trade between planets using fantasy units of currency. Use algebraic functions to decide where explosive charges should be placed to destroy asteroids. Propose the location of a by-pass, using data tables and graphs from the Highways Agency. Find ways to satisfy constraints (minimum radii of curvature,...
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