ABSTRACT

This study sought to examine the various errors and misconception committed by students in algebra with the view to exposing the nature and origin of the errors and misconceptions in secondary schools in Machakos district. Teachers‟ knowledge of students‟ errors was investigated together with strategies for dealing with them. The various teaching methods and how they contribute to the alleviation of the errors were also investigated. The underlying theoretical view of learning was constructivist, namely that students commit errors in the course of their efforts to construct meaning within mathematical situations. According to Merriam & Ceffarella (1999) “Meaning is made by the individual and dependent upon the individuals‟ previous and current knowledge structure”. Therefore to make sense of a new material the individual will have to use the existing knowledge. Descriptive survey design  was adopted and carried out in fifteen out of one hundred and forty two schools in Machakos district. The study used a sample of four hundred and thirty form two students and fifteen mathematics teachers of the respective classes at the time of the study. Data comprised of the results from mathematics students tests (MST), student interview schedule (SIS) and mathematics teachers‟ questionnaire (MTQ). The validation of the instruments was done in one randomly selected secondary school which was not included in the main study. The data collected was coded and analyzed using descriptive statistics. This involved organization of statistical data in form of frequency distribution tables, whose explanation was mainly descriptive. The findings indicated that the students make errors and that they have misconceptions in algebra. The findings of the study indicated that most (63%) students experienced difficulties with the word problem while equations had the least percentage (22.3%) of errors. Variables and expressions had percentage errors of 39.6% and 40.9% respectively. The results also revealed that mathematics teachers were aware of the errors that the students make. The prediction of the errors in this study was a manifestation of how well aware teachers are of students errors and misconception in algebra. As a result the teachers  did make attempts to counteract such errors in algebraic class. However only38% of the teachers diagnosed difficulties and misconceptions involved while 62% of the teachers were interested in assessing manipulations. This shows that though the main purpose of this study was to identify errors that would inform classroom instruction the error/misconception identification did not necessarily lead to instructional strategies that address students‟ difficulties. The major difficulty seems to lie with the teachers‟ ability to make use of the knowledge they have on student error, rather than their awareness of the errors. This reveals that there are deficiencies in the teaching of algebra. Teachers will need assistance not only in error identification but also how the error would be built in the whole process of learning. More emphasis should be put on students‟ understanding of the algebraic concepts in order to eliminate rot learning and cramming which contribute to most of these errors. To enhance teachers‟ use of student‟s experiences, teacher education will need to focus on encouraging a variety of ways of teacher-student interaction during which students‟ mathematical ideas should be considered exhaustively.