The purpose of this research is to

The purpose of this research is to try to determine, through individual interview sessions, the reasoning behind the adoption of certain strategies by several pupils as they are engaged in simplifying a complex algebraic term.The simplification of expressions was chosen as an area of study for two reasons. First, this researcher has witnessed many instances of errors in the cancelling of terms. Second, he has found much less literature on the simplification of complex algebraic terms than on the solution of equations.
Mathematically, complex algebraic terms differ from equations in many ways. But they also differ in several psychological ways as well; perhaps even at the metacognitive level of thought associated with choosing a strategy. For instance, equations have a solution as a goal. When the line beginning "variable =" is reached even the beginning algebra pupil will know that this signifies the end of the problem. In other words, there is a definite indication that the end is reached, albeit produced by the pupil himself. On the other hand, expressions may have no such a trigger to signal an ending. Indeed, depending on
the particular expression, there may be several mathematically satisfactory places to stop the simplifying process e.g. is it more useful to leave a term in factorised or unfactorised form. As will be seen from the interview transcripts in this investigation, there is significant thought by several pupils on devising a plan and evaluating the answer, albeit with mal-rules of algebra. Hence pupils' metacognition may come into play while determining the number of steps in the problem (i.e. planning and deciding when to stop)
when following the instruction “simplify”. One of the main aims of this investigation will be to show that some pupils overshoot an acceptable correct answer (and get the final answer wrong) in an attempt to simplify. A psychological effect, namely fear of lack of closure, may be experienced by pupils as
they attempt to simplify expressions: pupils may be unwilling to stop before reaching an answer with which they are comfortable e.g. a numerical answer. In other words, if there are few clues as to when an acceptable answer is reached, the pupil may continue simplifying until she arrives at one acceptable to her. At the point of oversimplification, certain errors may be identified which might have remained undetected had the pupil simply stopped earlier. Such errors will be analysed with reference to the cognitive and
metacognitive domains. Research into pupils’ thoughts while simplifying expressions gains in significance when it is appreciated that algebraic simplification can be viewed in several ways: as being a skill in its own right and as a skill useful in the solution of equations.2 Further, pupils’ thoughts on the subject can provide a window into other areas such as how variables are perceived and the level of meaning algebraic expressions may have for pupils. Indeed, according to recent research by Tirosh et. al. (1998), there has been evidence of success in making teachers knowledgeable about research findings regarding
specific student conceptions and developing new ways to teach that take such knowledge into account.