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38536 results in Cambridge Textbooks

Page 1581 of 1927

  • Chapter 11 - Designing mathematical experiences for numeracy in the 21st century

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 252-269

  • Summary

    Overview

    In this chapter you will become familiar with:

  • the ways in which mathematical understandings support numeracy in the 21st century

  • the elements in the design cycle that can be used to create effective teaching and learning contexts for numeracy

  • using child-centred assessment to maximise individual learning potential.

    • The chapters in this book have considered the foundational concepts and processes of mathematics that are fundamental in establishing confidence and competence in the early years. The book has considered some of the ways in which these concepts and processes can be incorporated into learning activities designed by teachers and caregivers, and encountered and experienced in the early years of a child’s life. It has explored the concepts of number, measurement, space, chance and data, and patterns and algebra, since these form the basis of the mathematics curriculum in many countries, and shown how they might be incorporated into early childhood learning experiences. A critical link has been made between the acquisition of confidence and competence in mathematics and becoming numerate in the 21st century. That is, we need to be able to understand and use mathematical concepts and processes in order to function effectively in the 21st century. Throughout a child’s life, she will encounter problems, challenges and technologies that require the application and successful use of mathematical concepts and processes.

  • Chapter 7 - Measurement

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 159-191

  • Summary

    Overview

    In this chapter you will become familiar with:

  • the ways in which measurement can be an important part of children’s everyday lives and how measuring experiences can be personally relevant to them

  • the understanding that measuring is about the quantity of a particular unit of measurement

  • using different measures in order to teach children which measures are appropriate for a particular measuring context.

    • Measurement is part of a young child’s everyday life. Initially, children are exposed to measuring through interactions with adults. We measure children’s height and mass. We give children money to buy a drink. We tell children when it is time to go to play. But as children get older, they need first-hand experiences to develop their ability to measure many different attributes − length, area, volume, capacity, mass, time and money. Measuring is finding out ‘how much’ there is of a particular attribute. It involves an understanding of the attribute to be measured, and knowledge of an appropriate unit of measure and how to measure with this unit. It also requires good number understanding.

  • Chapter 10 - Contexts and connections

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 230-251

  • Summary

    Overview

    In this chapter you will become familiar with:

  • the ways in which mathematical understandings can be used in everyday life and in projects designed by teachers or instigated by young children

  • the importance of using mathematics in our everyday lives

  • the need to challenge, extend and build children’s capacities for posing and solving problems in realistic contexts.

    • Working with topics or on projects that derive from young children’s spontaneous interests is an excellent way to create contexts for learning that are meaningful and enable learners to connect mathematics to their personal, cultural and everyday lives. In this chapter three topics are illustrated. The first topic, Ourselves, focuses on the child. The second topic, Celebrations, considers traditional events in an integrated approach to the curriculum. It is a very useful topic for those living in multicultural communities, as it enables different cultures to understand some of the main ideas inherent in a particular culture or community group. The final topic, Out and About, explores mathematical ideas in everyday community life. The activities related to these topics are intended as starting points for investigations.

  • Chapter 2 - Early mathematical understandings

  • Nicola Yelland, Victoria University of Technology, Melbourne, Carmel Diezmann, Australian Catholic University, Deborah Butler, St Margaret's Anglican Girls School
  • Book:
    Early Mathematical Explorations
    Published online:
    06 August 2018
    Print publication:
    20 January 2014, pp 11-27

  • Summary

    Overview

    In this chapter you will become familiar with:

  • the beginning processes for early mathematical understandings – describing attributes, matching, comparing, ordering, sorting and patterning

  • the mathematical concepts of number, measurement, space, and chance and data, and the ways in which these relate to the everyday experiences of young children

  • the importance of language in exploring mathematics in the early years, as well as the use of children’s literature to support mathematical thinking

  • playful explorations as a pedagogical process to stimulate early mathematical learning.

    • Young children are curious from the moment they are born. They look around them, explore objects that they encounter and communicate with utterances in interactions with others. From birth to five years of age, which is generally when compulsory schooling begins, there are many different ways in which the foundations for mathematical understandings are established. The activities and experiences are usually informal and play-based, but there are also opportunities for teachable moments in which a teacher might consolidate particular language or highlight relationships that are fundamental to mathematical thinking and understandings. For example, when telling a child the story of The Very Hungry Caterpillar by Eric Carle, there are many opportunities for the adult to create contexts for understanding mathematical concepts and processes. These are shown in Table 2.1. As well as spanning the concepts of number, measurement, space, and chance and data, these opportunities provide a context for using language to communicate ideas and understandings about the various relationships that occur in the story.

  • 2 - Description of separation in open separators

  • Kamalesh K. Sirkar, New Jersey Institute of Technology
  • Book:
    Separation of Molecules, Macromolecules and Particles
    Published online:
    28 May 2018
    Print publication:
    16 January 2014, pp 39-75

  • Summary

    Separations for preparative or analytical purposes are often carried out batchwise in a closed vessel. On the other hand, industrial-scale separations are commonly achieved in a continuous manner with open vessels into which feed streams enter and from which product streams leave. In this chapter, we consider the available methods of describing separation in such open separators. The quantities, fluxes and mass balances necessary for such descriptions are presented first in Section 2.1. Section 2.2 describes the available indices of separation and their interrelationships for binary separation with a single feed stream entering the separator. In Section 2.3, we briefly introduce indices for binary separation with two feed streams entering a separator. The complications encountered in describing multicomponent separations with a single-entry or double-entry separator are presented in Section 2.4. This section provides also an introduction to the description of systems of continuous chemical mixtures and size-distributed population of particles. Separation by any of the separators considered in these sections presupposes that the output streams have different compositions. There are separation processes, e.g. chromatography, in which the separator has only one output stream, but that has a time-varying composition. The description of separation in such a separator with the help of various indices has been considered in Section 2.5. Triple-entry separators etc. have not been dealt with here. Further, except for Section 2.5, steady state operation is assumed throughout.

  • Preface

  • Kamalesh K. Sirkar, New Jersey Institute of Technology
  • Book:
    Separation of Molecules, Macromolecules and Particles
    Published online:
    28 May 2018
    Print publication:
    16 January 2014, pp xi-xii

  • Summary

    This is an introductory textbook for studying separation. Primarily, this book covers the separation of mixtures of molecules; in addition, it provides a significant treatment of particle separation methods. Separation of macromolecules has also received some attention. The treatment and coverage of topics are suitable for chemical engineering students at undergraduate and graduate levels. There is enough material here to cover a variety of introductory courses on separation processes at different levels.

    This book is focused on developing a basic understanding of how separation takes place, and of how the resulting separation phenomenon is utilized in a separation device. The role of various forces driving molecules or particles from a feed mixture into separate phases/fractions/regions is basic to such an approach to studying separation. The separation achieved is then amplified in an open separator via different patterns of bulk-phase velocities vis-à-vis the direction(s) of the force(s). The forces are generated by chemical potential gradient, electrical field, rotational motion, gravity, magnetic field, etc. The resulting separation is studied under three broad categories of separation processes.

  • 3 - Physicochemical basis for separation

  • Kamalesh K. Sirkar, New Jersey Institute of Technology
  • Book:
    Separation of Molecules, Macromolecules and Particles
    Published online:
    28 May 2018
    Print publication:
    16 January 2014, pp 76-204

  • Summary

    The preceding chapters introduced first the notion of separation and then a variety of indices to describe separation. These indices were used to characterize quantitatively the amount of separation achieved in a closed or an open separation vessel. The quantitative description included systems at steady or unsteady state involving chemical or particulate systems. Systems studied were either binary or multicomponent or a continuous mixture. Not considered in these two chapters was the fundamental physicochemical basis for these separations; appropriately, this is the focus of our attention in this chapter.

    In Section 3.1, we distinguish between bulk and relative displacements and describe the external and internal forces that cause separation-inducing displacements. This section then identifies species migration velocities and the resulting fluxes as a function of various potential gradients. Section 3.2 is devoted to a quantitative analysis of separation phenomena and multicomponent separation ability in a closed vessel as influenced by two basic types of forces. The criteria for equilibrium separation in a closed separator vessel and individual species equilibrium between immiscible phases are covered in Section 3.3. Section 3.4 treats flux expressions containing mass-transfer coefficients in multiphase systems. Flux expressions for transport through membranes are also introduced here.

  • 6 - Open separators: bulk flow parallel to force and continuous stirred tank separators

  • Kamalesh K. Sirkar, New Jersey Institute of Technology
  • Book:
    Separation of Molecules, Macromolecules and Particles
    Published online:
    28 May 2018
    Print publication:
    16 January 2014, pp 346-484

  • Summary

    Chapter 4 described the extent of separation that can be achieved in a closed vessel under three basic categories of separation: phase equilibrium based separations; external force based separations; membrane based separations. Beginning with Chapter 6, we focus on separation achieved in an open vessel: fluid streams and/or solid streams may flow into and/or out of the vessel. Thus, we have bulk flow/s in and/or out of this device. A broad variety of bulk flow patterns can exist in a separation vessel. We will, however, mostly study separations under three general categories of bulk flow configurations defined with respect to the direction of the force which is the source of the basic separation phenomenon. The three general categories of bulk flow–force combinations are:

  • (a) bulk flow of phase(s) parallel to the force direction;

  • (b) bulk flow of feed-containing fluid phase/region perpendicular to the force direction;

  • (c) bulk flow of two fluid phases/fractions/regions perpendicular to the force direction.

    • In the bulk flow–force combination of (c), there can be cases where, instead of two fluid phases, one can have one fluid phase and another solid phase. Categories (b) and (c) provide a broader and more useful framework than the category of bulk flow perpendicular to the force direction illustrated by Giddings (1991) using a few examples.

Page 1581 of 1927