Pupils Errors and Misconceptions in Key Stage 3 Algebra.
Errors and misconceptions are common place in the classroom especially in mathematics. “It is important to establish a distinction between an error and a misconception” (Spooner, 2002, p3). An error can be due to a number of different factors, such as lack of concentration, carelessness and misreading a question. On the other hand, a misconception is generally when a student misinterprets the correct procedure or method. “Students often misunderstand or develop their own rules for deciding how something should be done. This is part of normal development.” (Overall et al. 2003. p127). Whilst many of these invented rules are correct, they may only work under certain circumstances.
It is important, when teaching, that error patterns and misconceptions are eradicated and corrected when pupils are learning and that they use procedures and algorithms correctly to obtain the right answer.
In this report I am going to focus on the basic errors and misconceptions made by pupils studying algebra, specifically within key stage 3. Algebra is the generalisation of arithmetic, containing a wealth of symbolic notation, in which students have not previously met. It is not surprising that students find the basic concepts hard to grasp, resulting in many errors and misconceptions.
I am going to cover ‘what does the equal sign mean?’ and students’ understanding of algebraic letters. These are the two fundamental concepts in which pupils need to be fully competent in, in order to be successful in working with algebra.
Pupils Understanding of Letters in Algebraic Expressions
In order for students to be confident in working with algebra they first need to be able to understand algebraic expressions and variables. In a study by Küchemann (1981), he found less than half the children, in his study, seemed able to use a letter as a numerical entity in its own right, instead the letter was ‘evaluated’ or regarded as an ‘object’. Children can interpret letters in a number of
It is important, when teaching, that error patterns and misconceptions are eradicated and corrected when pupils are learning and that they use procedures and algorithms correctly to obtain the right answer.
In this report I am going to focus on the basic errors and misconceptions made by pupils studying algebra, specifically within key stage 3. Algebra is the generalisation of arithmetic, containing a wealth of symbolic notation, in which students have not previously met. It is not surprising that students find the basic concepts hard to grasp, resulting in many errors and misconceptions.
I am going to cover ‘what does the equal sign mean?’ and students’ understanding of algebraic letters. These are the two fundamental concepts in which pupils need to be fully competent in, in order to be successful in working with algebra.
Pupils Understanding of Letters in Algebraic Expressions
In order for students to be confident in working with algebra they first need to be able to understand algebraic expressions and variables. In a study by Küchemann (1981), he found less than half the children, in his study, seemed able to use a letter as a numerical entity in its own right, instead the letter was ‘evaluated’ or regarded as an ‘object’. Children can interpret letters in a number of