Algeburble

We've started a new blog, Algeburble. It is aimed at younger students, in particular pupils in Key Stage 2.

The ATM

In June 2019, the Association of Teachers of Mathematics (ATM) published the Algebradabra! blog as an A5, spiral-bound book. It can be purchased from the ATM website and costs £12 for members of ATM, £16 for non-members. The book comes with a high-definition pdf file of SLIDES showing all the tasks from the book, along with a link for downloading a set of QuickTime movies that support some of the tasks. 

The ATM was established in the UK in 1952 to encourage the teaching and learning of mathematics.
It is a registered charity and has a membership of approximately 3000 individual teachers and other maths educators, as well as schools and other institutions.

The Association offers a number of CDP opportunities that include the annual conference, local branch meetings and regional one-day events. Its journal, Mathematics Teaching, is published five times a year, with articles which reflect on the practice of teaching mathematics from the Foundation Stage to Higher and Further Education. Contributors are encouraged to express their personal views on the teaching and learning of mathematics.

ATM also produces many other resources and publications, including now the Algebradabra book!

The BOOK

In June 2019, an edited version of the Algebradabra! blog was published in the UK as an A5, spiral-bound, 129-page book by the Association of Teachers of Mathematics (ATM). It can be purchased from the ATM website and costs £12 for members of ATM, £16 for non-members. The book comes with a high-definition pdf file of SLIDES showing all the tasks (and other images) from the book, along with a link for downloading a set of 17 QuickTime movies that support some of the tasks. 

This is the INTRODUCTION to the book:

This book is based on a blog, Algebradabra! The blog’s aim was to provide tasks that would help lower secondary school students get a better feel for algebra - and to give teachers a fresh perspective on familiar areas of the school algebra curriculum.

The format of the blog was to post a new task at the beginning of each week, followed by a variant of the task on each of the next four weekdays, together with comments and guidance. This was a device aimed at maintaining readers’ interest in the blog which also imposed a discipline to keep writing on the author - me! The result was 20 sets of tasks, making 100 tasks in all, which were released one at a time on the blog between February and June 2018.

Each of these 100 tasks appears in this book, and we have adopted the same format as the blog, of having a ‘weekly’ set of 5 ‘daily’ tasks. However, this format should not be interpreted too literally. Not every class will have a maths lesson every day, and even if it did, it is unlikely that a teacher would want to devote at least part of each maths lesson to algebra. And many of the tasks in this book could easily be developed into a whole lesson, and many of the sets of tasks into a sequence of lessons. It is therefore up to you to determine which tasks you wish to use in the classroom (and adapt to your liking) and how much lesson time to devote to any one of them.

However, whether or not you eventually use a task or set of tasks in the classroom, we hope you will work through them yourself and that some at least will give you the pleasure and the satisfaction that can come from being challenged - and of gaining insights and a wider understanding of the nature and demands of school algebra.

Some of the ideas that have gone into this book can be traced back to my experience on the CSMS project in the 1970s, where we looked at students’ responses to a range of carefully designed written tests. The Algebra test looked at the uses of letters in generalised arithmetic, which we placed into these six categories: Letter evaluated, Letter ignored, Letter as object, Letter as specific unknown, as generalised number, as variable. 

These categories have proved useful for devising the current tasks. I have also hugely benefited from my work since 2008 on the ICCAMS project directed by Jeremy Hodgen, though I have tried hard not to duplicate activities that I helped develop there. 

The current tasks are wide-ranging, but there is perhaps a particular emphasis on the notion of variable (as opposed to specific unknown) and on generalising. This should come as no surprise in an algebra book, though these ideas are often poorly represented in school textbooks. Thus many of the tasks involve dynamic contexts and make use of graphs or focus on general structure by, for example, analysing generic patterns. I have also tried to devise tasks that can help students see the purpose and utility of algebra (to use a phrase of Janet Ainley and Dave Pratt), though this can be notoriously difficult to achieve! However, I make no claims that the content covered by the book is comprehensive. [If you sense any glaring ommissions, please let me know - if we can get to 20, there might be scope for another book!]  

The tasks vary in cognitive demand, though most should be accessible (or could be made accessible) to students at Key Stages 3 and 4. Most, it is hoped, will also engage the teacher.

Note 1: Each of the tasks in this book is also available as a slide in a pdf file (so that it can be displayed on a screen), along with a small number of QuickTime movies that have been created for some of the tasks.

Note 2: Many tasks are in several parts which, because of the nature of the original blog, appear on the same slide. On the principle that less is more (or more haste, less speed), we recommend that where practicable, these parts are displayed in the classroom one at a time, so that sufficient time is devoted to each and to avoid students wanting to rush through the parts in order to ‘complete’ the task.

Dietmar Küchemann

And here is the CONTENTS page: