Proceed with a spirit of enquiry

6th June 2003 at 01:00
John Dabell looks at key stage 2 problem-solving textbooks

Creativity and problem-solving are valued abilities in the modern world and primary teachers have the opportunity to make a real contribution. The importance of integrating a wide range of challenging tasks into the teaching day means that practical investigations and extended problem-solving have never been more popular.

The National Numeracy Strategy advocates problem-solving as an integral part of standard lessons. The main objectives are to identify the nature of problems and the key skills required to solve them, and to explore the particular problem-solving strategies of sorting, listing, analysis and reasoning.

Problem-solving provides the opportunity for teachers and children to enter into a spirit of enquiry. The key is to make the procedures overt by drawing attention to them when they are useful and recalling their use when appropriate. Mathematical skills, both written and mental, can be taught and applied when solving a problem. Pupils should be exposed to many different types of problem to build up a bank of experience which will inform future problem-solving tasks.

Problem-solving textbooks have proliferated in the past four years and the differences in their quality and approaches are great. Some are carefully crafted, well thought out resources that will impact positively on children's learning, whereas others are crafty re-workings of pre-numeracy strategy puzzle books that have been re-marketed as "problem solving" texts. When making decisions about purchasing, you should think about the following:

Teacher support

Does the resource help to teach effective problem-solving strategies? Is it constructive, supportive and sympathetic to the needs of teachers?

Design

Is the resource comprehensive, conscientious and co-ordinated? Is it practical, efficient and stylish? Are there graphics and other features which children will find motivating?

Coverage

Is the subject matter broad, balanced and meaningful? Does it include pertinent links to the national curriculum and the National Numeracy Strategy?

Learning strategies

Are the activities well thought out, heterogeneous and assiduous? Are there considered differentiated tasks to reflect a spread of ability levels?

TITLE

Badger publishing Badger Maths Problem Solving Book 1 (Years 4 to 5) pound;19.50 Book 2 (Year 6) pound;19.50 By Sharon Shapiro Tel: 01438 356907 www.badger-publishing.co.uk

STRUCTURE

These two photocopiable books cover teaching and learning skills and strategies for practical problem-solving. The books are divided into six sections, each containing teaching notes on how the strategy works, three teaching examples to work through with the whole class, a copy-master of prompt questions and five or six problem-solving task cards.

COVERAGE

Each book has a chart showing where the problems fit into the numeracy strategy framework. The material also addresses the "using and applyingproblem-solving" strands of each attainment target in the key stage 2 national curriculum.

LEARNING STRATEGIES

Differentiation is an explicit feature of the series. The problems are presented at three broad levels for pupils working below, at and above national expectations. The activities are extremely well thought out and provide superb practice.

TEACHER SUPPORT

Teachers will not find a better resource for helping them get to grips with the problem-solving process. Each strategy is supported by practical teaching notes that offer clear guidance and direction. The teaching examples are excellent and provide meaningful and intelligent starting points of entry into each strategy. Answers are included.

DESIGN

Children will enjoy the feel and look of this resource. The copiable task cards are attractive and eye-catching and the activities are original, lively and challenging throughout. The design is clear and helpful.

VERDICT

This series stands well above the others reviewed. It will equip teachers and pupils with the knowledge, understanding and confidence to approach a range of real-life problems. *****

TITLE

CUP Apex Maths series Pupil's Textbooks (Years 1 to 6) pound;4.95 Teacher's Handbook (Years 1 to 6) pound;29.95 By Paul Harrison and Ann Montague-Smith Tel: 01223 325588 www.cambridge.orguk

STRUCTURE

Apex is a new resource for the extension and enrichment of mathematical understanding. Pupil textbooks are packed with a variety of real-life problems designed to develop thinking skills. The teacher's handbook contains comprehensive background maths support materials.

COVERAGE

The handbook's scope and sequence chart lists all the problems and objectives addressed (from the numeracy strategy framework), the outcomes for each ability group for attainment target 1 in the national curriculum, and the framework topics for each problem.

LEARNING STRATEGIES

These resources use problem-solving to address the needs of more able pupils and they also have extension and enrichment activities for children of all abilities. The handbook has 30 lesson plans covering all problem-solving objectives. Each focuses on a core problem or investigation that is differentiated so children of all abilities can work at their own level on the same problem.

TEACHER SUPPORT

The level of teacher support is excellent. Each lesson plan includes: guidance on children's prior experience, resources needed, essential vocabulary, a description of the problem and the maths involved, problem-solving objectives, activities for ability groups, ideas for introducing the problem, suggestions for facilitating the problem-solving process, plenaries and solutions to problems.

DESIGN

Pupil textbooks are simple, colourful and appealing. Each is clearly laid out so children will have little trouble using them. Photocopiable pupil sheets are less impressive but are clear and purposeful.

VERDICT

This well organised, well written resource has clearly differentiated and accessible activities. The teacher notes are supportive and detailed. The solid and reliable materials will be a joy to use. ****

TITLE

Hopscotch Educational Publishing Problem Solving Years 3-4, Years 5-6 pound;14.99 each By Pete Hall Tel: 01249 701701 www.hopscotchbooks.com

STRUCTURE

These two photocopiable books contain 18 problem-solving lessons that aim to make learning challenging and fun. These contain many photocopiable activity and record sheets. Each lesson follows the same format: learning objectives, oral and mental starters, resources needed, teaching points for the main activity, vocabulary list, plenary notes, support and extension suggestions and questions to guide assessment.

COVERAGE

Each lesson combines teaching objectives from the "Solving Problems" section of the framework for teaching maths with objectives from the general sections. The "Solving Problems" objectives are linked to at least one other objective.

LEARNING STRATEGIES

All lessons contain ideas for support and extension, although these could have been expanded and increased in scope. Some of the activities are differentiated for three ability levels.

TEACHER SUPPORT

The teacher's notes are highly prescriptive, offering a safe and secure route through a lesson, from start to finish. They don't go far enough, however, as they omit assistance and advice about how to teach possible problem-solving processes.

DESIGN

The activities are measured, efficient and useful, although the activity sheets are far from inspiring or motivating for children to engage with.

VERDICT

This simple, unattractive series has a clear teaching programme that will help some but constrain others. Activities in the teaching format sections are scant but worthy. ***

TITLE

LDA Real Life Maths series Pupil Book (Years 3 to 6) pound;7.95 By Jillayne Prince Wallaker Tel: 01223 357788 www.LDAlearning.com

STRUCTURE

A series of teacher-led activity books designed to develop problem-solving skills at KS2. Each 32-page book contains open-ended fun maths investigations that begin with a scenario containing the basic facts needed to complete the task.

COVERAGE

There are no specific links made, although the activities could easily be dovetailed to particular objectives, enabling teachers to fulfil national curriculum and numeracy strategy requirements.

LEARNING STRATEGIES

Each investigation has hints and tips that pupils may find useful as a prompt to get started and to help make the most of the exercises, as well as an extension exercise for children who work faster or need more of a challenge. Differentiation is left to the teacher to suit the needs of the class.

TEACHER SUPPORT

Pupils will gain from these activities but only if they are equipped with strategies. The activities also need more input. Teachers would appreciate a plan of attack for teaching the process of problem-solving and a list of skills and procedures to help them structure and assess the processes gained in the activities against children's own methods.

DESIGN

The activity sheets are uncomplicated, lucid and manageable but would need to be teacher-directed to make them accessible to children with low reading skills.

VERDICT

This simple but effective resource encourages pupils to find their own way and will improve thinking skills, but won't add to their problem-solving repertoire. ***

TITLE

Network Educational press KS2 Maths Resource File series Numeracy Activities - Plenary, Practical and Problem Solving pound;18.95 By Afzal Ahmed and Honor Williams Tel: 01785 225515 www.networkpress.co.uk

STRUCTURE

A photocopiable resource pack of 40 activities in 14 independent units to help children improve their fluency with number and measures. The pack concentrates on teaching skills and pupils' learning experiences. Each unit begins by outlining the main focus, content, notes for teachers, further activities, learning outcomes, evaluation and resources.

COVERAGE

The resource is rich in mental activities, real-life problems, reasoning and problem-solving activities. Each unit is clearly referenced to the objectives from the framework for teaching maths, Years 4 to 6.

LEARNING STRATEGIES

Differentiation is left in the hands of the teacher. Activities can easily be modified to suit individual aptitudes and circumstances. The materials, which use pupils' own experiences as a source of learning activities, will develop the use of spoken and written language.

TEACHER SUPPORT

Teaching and learning assumptions prefix the numeracy activities and provide a sound background to understanding what makes effective maths.

Between activities are helpful tips and techniques to reflect and act on.

The notes for teachers are helpful, informed and detailed enough to translate into classroom success.

DESIGN

The activities are interesting, enjoyable and challenging, and have a mix of child-friendly pictures and mostly business-like graphics. The book is clear and accessible throughout.

VERDICT

A flexible well-structured resource that will help teachers supplement their existing schemes of work. This is a sound resource by respected authors. ***

TITLE

Prim-Ed Publishing Problem Solving with Mathematics series Series 1: Lower, Middle, Upper pound;13.95 each Series 2: Lower, Middle, Upper pound;13.95 each Tel: 0870 0131 208 www.prim-ed.com

STRUCTURE

These two series look at developing specific maths problem-solving strategies and identify these as exploring patterns, organising data, finding all answers, and concrete manipulation. Each problem-solving strategy has six related activities.

COVERAGE

Reference is made to the "Solving Problems" section of the numeracy strategy framework through a grid, but none of the activities is directly referenced.

LEARNING STRATEGIES

Each activity is presented as an entity without any differentiation alternatives so teachers will have to remodel and customise to suit individuals and groups. The activities are full of possibilities but a fair degree of teacher input will be needed to bring them to life.

TEACHER SUPPORT

A small section of teacher notes provides some support but doesn't offer the background, detail and reassurance teachers will need to make the most of these relevant activities.

DESIGN

The book is uncluttered and well co-ordinated with clear text. The activity sheets are basic and easy to use.

VERDICT

These resources are useful for supplementing the skills-based problem-solving resources that are rich in teacher support. The problems offer a chance to observe the quality of pupils' maths thinking. ***

TITLE

Scholastic Ten-Minute Maths Mind-Stretchers pound;14 By Laurie Steding Tel: 01926 887799 www.scholastic.co.uk

STRUCTURE

This resource is packed with 11 chapters of snappy maths problems and activities that help to reinforce essential numeracy skills in real-life contexts. Each problem is designed to encourage thinking skills and can be easily integrated into daily maths lessons.

COVERAGE

The problems correspond to the numeracy strategy and are designed to supplement a well-rounded curriculum. Each chapter includes "across the curriculum" sections describing activities to help pupils realise that maths is all around them.

LEARNING STRATEGIES

The problems and activities are varied in their level of difficulty. Some are easy, allowing pupils to display their strengths, while others are more challenging, encouraging children to explore and practise skills that need strengthening. Many of the problems are designed to be tackled with a partner or in small groups.

TEACHER SUPPORT

The only teacher guidance given is with reference to possible groupings. A chapter discussing problem-solving processes and strategies would add considerably to this resource. Solutions are given but with little or no explanation in some cases.

DESIGN

The problems are not presented in an easily photocopiable format. Teachers will either choose to copy the problems on the board or cut and paste and adapt them to their own design.

VERDICT

There are excellent ideas here, useful for focus groups, homework assignments and individuals. However, it doesn't support the teaching of problem-solving. ***

TITLE

BEAM Mad About Maths series Number Magic, Shape and Space, Mathematical Games pound;4.99 each By Adrian and Jeni Pinel Tel: 020 7684 3323 www.beam.co.uk

STRUCTURE

A series of three colourful children's books packed with imaginative theme-based interactive topics designed to stimulate children. Each resource aims to develop children's mathematical abilities and to help increase their confidence in using numbers. The books include six pages of games and puzzles to use at home. Each of the 14 double-page spreads contains "Info" boxes, handy hints and clues.

COVERAGE

The books contain games, puzzles and creative ideas to enable and encourage children to explore the skills and knowledge gained from the national curriculum KS2 and the numeracy strategy. However, no explicit links are made.

LEARNING STRATEGIES

Differentiation by outcome would characterise the use of these materials.

The activities could be adapted and modified as appropriate. The handy hints and "Info" sections are quirky but do not address the ability spectrum.

TEACHER SUPPORT

There is no teacher guidance in the books. The resources are a varied collection of fun mathematical games and investigations but children and teachers are left to fend for themselves.

DESIGN

The bright, colourful artwork will make this resource a big hit with visual learners and the puzzles pieces will benefit kinaesthetic learners. A jazzy and snazzy resource children will enjoy using.

VERDICT

Each book has practical and novelty maths material suitable for home learning. These books would also be useful for a maths library or for teachers to dip into for ideas. **

TITLE

David Fulton Publishers Using and Applying Mathematics at Key Stage 2 pound;13 By Elaine Sellars and Sue Lowndes Tel: 020 8996 3610

STRUCTURE

This book presents a series of activities that can be used with whole classes to provide a curriculum for the teaching of problem-solving and the development of thinking skills. Eleven investigations are included, each explained with ideas on how to introduce the task, as well as full solutions and resource sheets.

COVERAGE

The activities provide a basis for a structured curriculum for the teaching of problem-solving, but no direct attachments are tied to the numeracy strategy.

LEARNING STRATEGIES

Some pupils will find these classic investigation problems exciting and rewarding. The book aims to meet the needs of able pupils, and teachers will have to plan the activities methodically for this to happen. These aren't add-on activities for above-average students but lesson ideas for including able children. Less able pupils will struggle if not helped.

TEACHER SUPPORT

Teachers are given some basic ideas about how to introduce each task to a class but this information is scant. A section on writing up the investigation would be more helpful in terms of explanation. Resolutions and extension notes are thorough and detailed.

DESIGN

Black and white photos of children in classrooms performing the tasks is a feature of this book. The space may have been better spent explaining problem-solving strategies and skills.

VERDICT

This book is of limited value for classroom use, but OK for class-based research into problem-solving. The activities are designed for whole-class participation, but many will find them inaccessible. **

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