Analysis of students common errors in multiplying and factoring polynimials in high school mathematics

النوع : Mémoire

Mathematics, in today's world, is a prerequisite for more and more careers. Students’ errors in multiplying and factoring polynomials have a great impact on their performance, not only in algebra but also in other domains of mathematics. Several research studies have been done on students' common errors; however, this topic still requires further investigation for better opportunities to enhance the learning of algebra. This study identifies what errors students typically make, and explains how and why students make these errors. Quantitative and qualitative analyses of a test of 32 items administered to a sample of 200 secondary-level students are used to detect commonly observed students' errors in multiplying and factoring polynomials. A class of commonly recurring students’ errors is examined, and evidence is presented showing that such students' errors are fairly common. A group of common errors (occurrence percentage is 10% or more) is further analyzed, with the resulting data suggesting that certain misconceptions underlie these errors. In order for the researcher to get an insight of students’ ways of thinking and to collect evidence for error analysis, students that produced the most common errors were selected to take part in one-to-one interviews. Analysis of students’ interpretations indicates that such errors are due to overgeneralizations, interferences, or defective algorithms in computing with numbers and monomials, applying the basic multiplication and factoring identities, using methods, rules, properties, and operations. Moreover, review of international research shows that most of our student’s types and sources of errors are very similar to those of international research. Through interviews, it is observed that most students' errors are rational and meaningful efforts to cope with algebra. These errors are derivations from what they have been taught. Clearly, these derivations are objectively illogical and wrong, but from students’ perspective, as realized, make a lot of sense. The concluding discussion includes implications for teaching and avenues for further study.