algebra

The topic of ‘Equations’ can be approached in several ways. The choice of approach has a strong impact on the conceptual image which a student builds about a given concept. Hence, the choice is crucial in helping a student in understanding the concept as well as in developing the procedure for solving the problems. However, every approach has its limitations and can be used only for solving certain types of problems. Its use is limited and it may become necessary to expose students to other approaches when the type or complexity of the problems alters.

A square dot sheet has equally spaced dots aligned vertically and horizontally. Many interesting investigations can be devised with this simple learning material.

For the middle school student, the transition from arithmetic to algebra is often quite daunting. In grade VI, the concept of a ‘variable’ is encountered for the first time. This is the stage where either a child embraces the newly introduced ‘Algebra’ or gets overwhelmed with the idea of numbers being replaced by letters of the alphabet. This is also the stage where the students learn to solve equations and find the value(s) of the unknown(s).

This article is Part II of the series ‘Algebra – a language of patterns and designs.’ The approach is based on the perception of algebra as a generalisation of relationships.

In Part I, we introduced the ideas of variable, constant, term and expression via numerical patterns. Various operations (addition, subtraction, multiplication) involving terms and expressions were also studied.

The late Shri P. K. Srinivasan had developed an approach to the teaching of algebra titled ‘Algebra – a language of patterns and designs’. I have used it for several years at the Class 6 level and found it to be very useful in making a smooth introduction to algebra, to the idea and usage of concepts such as variable and constant, to performing operations involving terms and expressions. This approach steadily progresses from studying numerical patterns to line and 2-D designs, finally leading to indices and identities.

Algebraic expressions are mathematical sentences such as 3x + 4. They do not have an equals sign (=), which makes them different from algebraic equations. Algebraic expressions play an important role in the mathematics curriculum and in mathematics in general. In order to progress and do well in mathematics, students need to be able to read and write expressions, and to be skilled in computations and manipulations of algebraic expressions.
 
The difference-of-two-squares formula a2 − b2 = (a − b)(a + b) is so basic that it would seem a difficult task to say anything new about it! But Agnipratim Nag of Frank Anthony Public School, Bangalore (Class 8) has done just this. In this short note we describe his interesting and innovative approach to prove the identity. It has particular relevance for those who teach at the middle school level.

This book is about developing such an open mindset about mathematics, through positive messages and creative teaching. Boaler sees the immense potential of the positive messages that teachers can convey to their students – about the brain and its learning potential as well as about maths.

An investigation can have a seemingly simple looking problem as its starting point but can lead to lines of inquiry which provide rich insight into a particular area of mathematics. It is important to let children develop their own lines of inquiry, and to have the experience of encountering ‘dead ends.’ In particular, one must not lead their inquiry but provide broad pointers for developing further lines of inquiry.
 
 

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