Mathematical Challenges: Developing Problem Solving Skills
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(Photocopiable pages – CD-ROM included) 105 pages
Author: Professor Valsa Koshy
This pack has been written in response to requests from teachers for resources to enhance mathematical problem solving and, particularly, for making provision for mathematically very able learners. It provides a set of problem solving activities which should enable children to appreciate the beauty and creativity of mathematics, whilst also appreciating that problem solving can enhance confidence and develop more positive attitudes to the learning of mathematics. Large numbers of teachers have found them to be very effective and enjoyable with children of all abilities.
Problem Solving Skills
The role of Problem Solving, as an integral part of the learning and teaching of mathematics, has been cited in all official documents for decades. National and standardised tests that schools use to assess children’s mathematical learning require children to solve problems, both to test mathematical content and the skills of thinking mathematically.
This pack of problems emphasises that problem solving is an intellectual activity, involving the pursuit of solutions to problems, which is highly satisfying and stimulating requires logic, reasoning and systematic working provides a strong framework in which some key skills, learnt in the context of mathematics, transfer to other learning provides a natural context for training children to apply mathematics can help to develop children’s tenacity and confidence in doing mathematics and is often described by brain function researchers as a helpful strategy to enhance children’s general capacity for learning.
The pack includes:
An introduction which explains the process of problem solving with examples of the types of problems and how to use the pack. The contents of this section may be useful for leading an in-service session on problem solving. A list of helpful problem solving strategies is provided for children to use. (See explanatory list on page 3).
Sets of Problems are marked A, B and C to indicate the level of complexity – problems in section A being simpler, B more challenging and those under C being much more complex, requiring longer time and greater content knowledge and skills. Two sets of Multiple Choice questions are also included.
Solutions to all the problems are given at the back of the book. A certificate template is also provided.
Teachers have used the pack in the following ways:
Working with the whole class at a specific time, selecting the most appropriate problems for different groups of children. Problems may be cut up, mounted on cards and laminated for use at appropriate times as Challenge cards.
Use a selection of problems from sections A, B and C, or use the Multiple Choice questions for a ‘mathematics day’ for children or for a ‘parents’ mathematics day’.
The problems, under Sections B and C in particular, can be used for enrichment groups or in ‘set’ groups for more able/promising mathematicians as sets of challenges.
The problems may be used for homework.
They are suitable for individual or group work.
Helpful steps in Problem Solving for Children:
Read the question carefully.
What is the problem asking you to find out?
Read it again and a third time if you are not sure.
What do you know? Make a list and notes, then organise them.
What will help you? Draw a picture. Make a model. Draw a table. Talk it through with someone.
Work on the problem, keeping a record of what you are doing. What steps are you listing? Don’t worry about scribbles and crossings out as all really good mathematicians make mistakes. Your scribbles will help you to keep track of your progress and show the teacher what you are thinking.
Got an answer?
Ask yourself – have I solved the problem? Is this what I was asked to do?
Does the answer make sense? Is it realistic?
Can I check the answer, using the given clues? Perhaps working backwards.
Are there other solutions?
It is OK to be stuck, it shows you are learning.