A Compendium Of Mathematical Methods: A handbook for school teachers

by Joanne Morgan

How many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence? A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered. If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. Woven throughout this compendium are extracts from antiquated maths textbooks. We glimpse into the past to see what has changed, and we marvel at the curiosities we encounter. The following topics are Subtraction; Multiplication; Decimal multiplication; Division; Fraction division; Highest common factor and lowest common multiple; Reverse percentages; Two-step linear equations; Linear simultaneous equations; Expanding double brackets; Factorizing non-monic quadratics; Linear sequences; Quadratic sequences; Equations of linear graphs; Quadratic inequalities; Vertex of a quadratic; Simplifying surds; Angles in polygons; Polynomial division

Genres: Teaching, Education, Nonfiction, Mathematics

344 pages, Paperback

Published December 14, 2019

Reviews

[Jason · Rating 3 out of 5]

This is an interesting read for math educators. This book takes twenty concepts studied in elementary and high school mathematics, and demonstrates different ways the concept could be approached. Many of them are familiar approaches that most educators will have seen before; some are obscure and work only in specific situations. While I have my preferred ways, I found the alternate pathways helped me gain a deeper understanding of the concept and to see the pros and cons of my preferred methods. I appreciated the commentary that the author provides after demonstrating each method.

I've been trying to get my students to also understand there is no single 'correct' way to approach a problem. While it would be overwhelming for students to learn seven different ways to subtract, the alternate methods presented in the book would be helpful in two ways. If a student is having trouble understanding a more conventional approach, perhaps one of the alternates (e.g., something more visual) would be helpful. Secondly, for students who have caught onto a conventional approach quickly, presenting an alternate approach helps them gain a multi-dimensional and deeper understanding of the concept.

[John Chatterjee-Woolman · Rating 5 out of 5]

I've been looking forward to reading this book ever since Jo Morgan announced she'd released it. I suppose as somebody relatively new to teaching, I love to discover different ways to help others understand a concept. I hope that I maintain this fascination the longer I am in this field, rather than getting stuck in a rut. There's nothing wrong with sticking things if you know they're effective, but sometimes we end up doing these things because we used to it, and feel uncomfortable with moving outside of that zone. Well, this book just writes with this in mind. Jo Morgan delves into mathematics methods commonly taught today, and those that have now fallen out of favour. Is it time to dust off those textbooks? There are some proper treasures to be found here - it's well worth a look. Maybe you'll find a more effective way of teaching something. I definitely have, I'm going to try it out.

[Ruth Williams · Rating 4 out of 5]

In this book Jo takes common maths problems (eg multiplication, division, nth term, simultaneous equations, straight line graphs) and talks us through different methods of solving them. She also lists the pros and cons for each method, explains why they work and gives examples from old text books.
Some nice alternatives to the ones I usually use. Will definitely dip into it again. A useful book to keep in the classroom.

[Colin · Rating 4 out of 5]

A very clear exposition of some of the methods used to tackle mainly arithmetic and algebraic problems at GCSE. There is a little geometry and a little A-level.

I think this would be a useful book for anyone teaching GCSE maths and wondering “is the way I learnt it the best/only way?”, or “why does this method work?”

[Olly Colluphid · Rating 5 out of 5]

For maths teachers: five stars.
For popular maths fans probably only 4.

Interesting collection of methods that challenges you to ponder your own approaches. Some are clearly just curiosities but even they are glorious rabbit holes.