Teaching Number in the Classroom with 4-8 Year Olds

Robert J Wright, Garry Stanger, Ann K. Stafford, James Martland

• Publisher: SAGE Publications Ltd
• Year: 2014
• ISBN:
  9781473908741
• Edition: 2
• Topic: Pedagogía
• Subtopic: Educación primaria

Bring the principles and practice of the acclaimed Mathematics Recovery Programme to whole-class teaching!

WHY INVEST IN THE NEW EDITION?

• In full-colour with a revised layout for clearer navigation
• More up-to-date tasks, activities and real classroom examples
• Learning trajectories for guiding instruction and tracking progress on key topics
• Extra resources online on the companion website

Part of the best-selling Maths Recovery series, thispractical, step-by-step guide to classroom instruction takes an inquiry-based approach to assess children?s knowledge and build on this to develop a firm foundation of understanding and confidence in mathematics. Topics covered range from beginning number and early counting strategies to multi-digit addition and subtraction right through to multiplication and division.

An invaluable resource for use on pre-service teacher training courses and for all primary classroom teachers and assistants, including experienced Mathematics Recovery instructors, as well as learning support personnel, primary mathematics advisors, numeracy consultants and educational psychologists. WHAT EXTRAS ARE ON THE COMPANION WEBSITE?

• Downloadableextra chapter resources like print-out grids, worksheets, cards and much more
• A Facilitator's Guide that can be used either individually or in group study to help you get the most out of the material
• In-class video demonstrations to clearly show how the instructional activities in the book are used in the classroom
• Webinar discussing the key points in the book and how it supports your teaching

"Research informs practice in this easy to access resource. Each chapter gives educators practical, bite-sized assessments, linked to a host of activities that helps them target teaching and develop the firm foundations which are so vital for confident and competent mathematicians." - Jill Piotrowski, Numeracy Consultant, Wigan Local Authority, UK "?The Classroom Instructional Framework in Early Number is research-based and provides a roadmap of not only the what, but the when and the how to teach all aspects of early number." - Vicki Nally, Mathematics Consultant at Catholic Education Office, Melbourne "The structured approach offers a wealth of rich and easily implemented classroom-based activities that work - thousands of teachers in Ireland attest to this!" - Noreen O?Loughlin, Director Maths Recovery and Maths Education Lecturer, Mary Immaculate College, Limerick, Ireland

PART I

1

Approaching, Designing and Organizing Instruction

Summary

This chapter consists of three sections. The first presents nine principles of classroom teaching which have been used extensively by the authors and others as a guide to classroom teaching. Also included in this section is the Classroom Instructional Framework for Early Number (CIFEN) which provides guidance for the development of learning trajectories, that is, sequences of interrelated instructional topics that progressively build an important aspect of children’s early number knowledge. The second section provides a description and illustration of the use of the Teaching and Learning Cycle for designing instruction. In the third section, models are presented which demonstrate different approaches to classroom organization for instruction. Block scheduling is also discussed.

Approaching Instruction

The purpose of this section is to set out key ideas in the general approach to teaching number in the classroom that is advocated in this book. These key ideas are presented in the following two topics: (a) Guiding Principles for Classroom Teaching (GPCT); and (b) the Classroom Instructional Framework for Early Number (CIFEN). This section draws on some of the ideas in our two earlier books: Early Numeracy: Assessment for Teaching & Intervention (2nd edn) (Wright et al., 2006a) and Teaching Number: Advancing Children’s Skills & Strategies (2nd edn) (Wright et al., 2006b).

Guiding Principles for Classroom Teaching

In the 1990s, we conducted several research and development projects in which we worked in collaboration with teachers and school systems. In these projects, we developed the following set of nine guiding principles of teaching. In more recent years, we have conducted additional research and development projects in which these principles have been applied extensively to guide the teaching of number in the early years of school:

1 The teaching approach is inquiry based, that is, problem based. Children routinely are engaged in thinking hard to solve numerical problems which for them are quite challenging.

2 Teaching is informed by an initial, comprehensive assessment and ongoing assessment through teaching. The latter refers to the teacher’s informed understanding of children’s current knowledge and problem-solving strategies, and continual revision of this understanding.

3 Teaching is focused just beyond the ‘cutting-edge’ of the child’s current knowledge.

4 Teachers exercise their professional judgement in selecting from a bank of teaching procedures each of which involves particular instructional settings and tasks, and varying this selection on the basis of ongoing observations.

5 The teacher understands children’s numerical strategies and deliberately engenders the development of more sophisticated strategies.

6 Teaching involves intensive, ongoing observation by the teacher and continual micro-adjusting or fine-tuning of teaching on the basis of her or his observation.

7 Teaching supports and builds on children’s intuitive, verbally based strategies and these are used as a basis for the development of written forms of arithmetic which accord with the child’s verbally based strategies.

8 The teacher provides the child with sufficient time to solve a given problem. Consequently the child is frequently engaged in episodes which involve sustained thinking, reflection on her or his thinking and reflecting on the results of her or his thinking.

9 Children gain intrinsic satisfaction from their problem-solving, their realization that they are making progress, and from the verification methods they develop.

Each of these principles is now discussed in more detail.

Principle 1

The teaching approach is inquiry based, that is, problem based. Children routinely are engaged in thinking hard to solve numerical problems which for them are quite challenging.

The inquiry-based approach to teaching number is sometimes referred to as learning through problem-solving or problem-based learning. In this approach, the central learning activity for children is to solve tasks that constitute genuine problems, that is, problems for which the children do not have a ready-made solution. What follows is that the issue of whether a particular task is appropriate as a genuine problem largely depends on the extent of the children’s current knowledge.

Principle 2

Teaching is informed by an initial, comprehensive assessment and ongoing assessment through teaching. The latter refers to the teacher’s informed understanding of children’s current knowledge and problem-solving strategies, and continual revision of this understanding.

Assessment for providing specific and detailed information to inform instruction is the critical ingredient in our approach to teaching early number. It is essential to conduct a detailed assessment of children’s current number knowledge, and to use the results of assessment in designing instruction. In each of Chapters 3 to 10, the second section of the chapter contains detailed descriptions of assessment tasks and notes on their use. These have the explicit purpose of informing the design of instruction. The second aspect of this principle, ongoing assessment through observation and reflection, is equally as important as initial assessment.

Principle 3

Teaching is focused just beyond the ‘cutting-edge’ of the child’s current knowledge.

This principle accords with Vygotsky’s notion of zone of proximal development, that is, instruction should be focused just beyond the child’s current levels of knowledge in the areas where the child is likely to learn successfully through sound teaching. This principle is very important in our focus on the teaching of early number. The principle highlights the importance of assessment to inform teaching. Assessment provides the teacher with a profile of children’s knowledge and the teacher focuses instruction so that children will be moved beyond their current levels of knowledge.

Principle 4

Teachers exercise their professional judgement in selecting from a bank of teaching procedures each of which involves particular instructional settings and tasks, and varying this selection on the basis of ongoing observations.

This principle highlights the need to develop a bank of instructional procedures and to understand the role of each procedure, in terms of its potential to bring about advancements in children’s current knowledge. In each of Chapters 3 to 10, the third section of the chapter includes up to 13 examples of learning activities which can be used to develop an appropriate bank of teaching procedures. Also, the second section of each chapter contains an extensive set of assessment tasks. These tasks constitute an additional source of instructional procedures because the tasks are easily adapted for instruction.

Principle 5

The teacher understands children’s numerical strategies and deliberately engenders the development of more sophisticated strategies.

This principle highlights the need for teachers to have a working model of children’s knowledge of early number and the ways in which children’s knowledge typically progresses. In each of Chapters 3 to 10, the first section of the chapter provides a detailed overview of the development of an aspect of early number knowledge. Our belief is that teachers can develop an appropriate working model through reading, reflecting and observing, in conjunction with their teaching practice.

Principle 6

Teaching involves intensive, ongoing observation by the teacher and continual micro-adjusting or fine-tuning of teaching on the basis of her or his observation.

This principle highlights the importance of observational assessment in determining children’s specific learning needs, and the need for this assessment to be ongoing and to lead to action, that is, the fine-tuning of instruction on the basis of ongoing assessment.

Principle 7

Teaching supports and builds on the child’s intuitive, verbally based strategies and these are used as a basis for the development of written forms of arithmetic which accord with the child’s verbally based strategies.

This principle highlights that children’s initial number knowledge is by and large verbally based rather than involving written forms. Thus we suppose that children’s initial counting and calculating strategies mainly involve mentally computing with sound images of number words and number word sequences. The further development of number knowledge involves a gradual process of incorporating wri...