RIC-0563 Developing algebraic thinking
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DEVELOPING ALGEBRAIC THINKING<br />
Foreword<br />
Over the past few years, many mathematics educators have directed<br />
their interests towards the development of <strong>algebraic</strong> <strong>thinking</strong> in students.<br />
As more and more schools move towards algebra for all, teachers<br />
need to be able to provide their students with the knowledge and skills<br />
necessary for success in a mathematics class where the focus on algebra<br />
is considerably different from the traditional course of study.<br />
What is <strong>algebraic</strong> <strong>thinking</strong>? Although there does not appear to be one<br />
agreed-upon definition, several common threads appear in the related<br />
literature.<br />
• Exploring and conjecturing about patterns<br />
• Formalising patterns<br />
• Verbalising relationships<br />
• Making generalisations<br />
• Symbolising relationships<br />
• Working with functions<br />
• Making connections between real-world situations and <strong>algebraic</strong><br />
statements<br />
Together, all of these interrelated components form a framework for<br />
<strong>algebraic</strong> <strong>thinking</strong>. This type of <strong>thinking</strong> ‘embodies the construction and<br />
representation of patterns and regularities, deliberate generalisation,<br />
and most important, active exploration and conjecture (Chambers,<br />
1994, 85).’ Problem-solving and problem-solving strategies permeate<br />
the activities.<br />
Contents<br />
Teachers notes ............................................................. 2–8<br />
Place value picks ........................................................ 9–22<br />
Same sums ............................................................... 23–34<br />
Primes and composites ........................................... 35–44<br />
Divisibility rules ....................................................... 45–58<br />
Locker numbers ....................................................... 59–66<br />
Exciting components ............................................... 67–74<br />
Plus and times .......................................................... 75–82<br />
Shapes ...................................................................... 83–92<br />
Pentomino puzzles ................................................. 93–100<br />
Alphabet algebra ................................................. 101–132<br />
Numbered tiles ............................................................ 133<br />
R.I.C. Publications ® www.ricgroup.com.au DEVELOPING ALGEBRAIC THINKING 3<br />
ISBN 978-1-74126-088-5
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