Pupils' Misconceptions in Mathematics

This paper, on mathematical misconceptions among secondary school pupils (i.e. pupils aged 11 to 16), was written in 2004 during studies at Sheffield Hallam University towards my PGCE (teaching qualification) in secondary mathematics.


Misconceptions discussed include problems in with the collection of like terms in algebraic expressions, a variety of difficulties with the equality sign and with mathematical operators, struggles with the addition of fractions and some peculiarities around the reflection of shapes. The origins of these misconceptions and some strategies for dealing with them are also considered.


An attempt is made to locate these misconceptions, and the strategies for combating them, relative to the theories of learning of Jean Piaget and Lev Vygotsky. In so doing, I draw out some common themes in the remedies which could be usefully applied to other misconceptions in mathematics and perhaps other areas.


The assignment was graded an "Excellent Pass".