Explain this
Teaching and Learning Algebra
How the publisher describes it:
“Continuum has repackaged some of its key academic backlist titles to make them available at a more affordable price. These reissues will have new ISBNs, distinctive jackets and strong branding. They cover a range of subject areas that have a continuing student sale and make great supplementary reading more accessible. A comprehensive, authoritative and constructive guide to teaching algebra”
Review by Richard Knottenbelt
In brief:
If you are not satisfied with the book there is an extensive Bibliography referring to other books , reports and journal articles. And finally the choices we make in the classrooms are our own. This book will widen the range from which we choose and can be recommended to every teacher of school level mathematics.
“Understanding comes from engagement in meaningful activity”
Algebra is certainly an essential part of mathematics, both intrinsically and as a tool applicable in almost every other branch of the subject. Missing out on the basic package of skills reflected in all school and examination syllabuses is a serious handicap, and author Doug French has put much thought into offering an approach which will lessen the traumas and increase the joy of encounters in Mathematics.
While mathematicians all agree that algebra is both interesting and useful, the vast majority of school pupils would disagree with the first and rather reluctantly agree with the second. Obviously this leads to major problems with motivation in tackling this part of the subject.
It could be said that the theme of Teaching and Learning Algebra is that algebra can be taught so that it is at once meaningful and useful. That phrase occurs at least once in every chapter and is an excellent reminder of the need to connect with pupils experience at their level. The suggested activities all are plausible starting points.
In each chapter the author highlights elements of the basic theory and structures which appear in the school syllabuses and makes explicit many of the common errors and misconceptions, starting with the standard notation. These focus on O or GCSE levels but include a few of the elementary A-level topics. His approaches are designed to begin at the level and within the experience of the pupils and use activities that make concrete the key ideas. And while the structure encourages the formation of concepts efficiently he is clear that there is no substitute for listening to pupils explain their processes as they recount what they have done. There are several short class dialogues which indicate some of the smoother sortings out which can arise naturally in such discussion.
It is interesting that the section on directed numbers contains the admission that the author has not found his final answer to teaching the - x - = + concept and is thrown back on the multiplication table ‘patterns’ which seems an unfortunate climb down. Perhaps ATM teachers could have a new look at their favourite methods of dealing with this and publish in ‘Mathematics Teaching’?
Understanding comes from engagement in meaningful activity which contains conceptual seeds. There are plenty of ideas on all the standard topics and even if one does not use them considering their relevance will probably focus teachers on why they choose their particular approaches.
Doug French insists that the initial stages should always be with simple, often numerical situations which are then generalised. Those kind of situation also provide much of the monitored practice which is needed to develop fluency. He suggests the use of ‘mental algebra’ tests as a way of getting immediate feedback so that errors are dealt with on the spot, listening to pupils explanations, rather than encouraging the practice of errors as often arises when work set as consolidation homework is imperfectly understood. There are many references to relevant research on concept formation and achievement of competence.
Much is made of the potential for understanding arising from cognitive dissonance in which contradictions arise, perhaps from applying obvious methods and obtaining two or more different answers. Some of these situations contain the reminder to look at the situation with common sense.
That is a universal starting point but requires considerable skill to get pupils to see the surprises as such. The suggested approaches in the book do not relieve the teacher from the task and duty of careful planning but will certainly widen the choice of methods as well as preparing for possible errors and stumbling blocks. The mini- dialogues which appear are very suggestive and should encourage teachers not to weigh in with immediate ‘explanations’ but let pupils make what is in their minds clear and allow them to interact between themselves.
The considerable potential of technology in the form of graphic and programmable calculators on the one hand and computers on the other is explored with these being used to provide patterns as well as check conjectures. The TI -92 gets special mention, and there are several spreadsheets and graph-plotter printouts.
The book ends with chapters on Geometry, Trigonometry, Sequences and Series and Calculus. There are many stimulating ideas in these chapters but the links to mainstream algebra sometimes seem rather forced. All contain applications of the author’s ‘meaningful and useful’ guideline and include unusual approaches.
If you are not satisfied with the book there is an extensive Bibliography referring to other books , reports and journal articles. And finally the choices we make in the classrooms are our own. This book will widen the range from which we choose and can be recommended to every teacher of school level mathematics.
Richard Knottenbelt • Victoria High School, Masvingo, Zimbabwe
Paperback: 199 pages
Publisher: Continuum International Publishing Group Ltd.; New Ed edition (9 Jun 2005)
Language English
ISBN-10: 0826477496
ISBN-13: 978-0826477491
Product Dimensions: 24 x 16.8 x 1.2 cm
