Gymnasieelevers og Lærerstuderendes Viden Om Rationale Tal
Specialerapport. IND's studenterserie nr. 49. Matematik.
Maria Hørlyk Møller Kongshavn, juli 2016.
"Gymnasieelevers og Lærerstuderendes Viden Om Rationale Tal" [3Mb]
Vejleder: Cars Winsløw
Abstract
Many mathematic teachers see it as a limitation for learning in high school that students do not master basic knowledge of rational numbers.
The Thesis examines high school students practical knowledge of rational numbers. The
theoretical background is the anthropological theory of didactics (ATD). A praxeological reference model is constructed and it identifies which techniques high school students are expected to know about. Based on the reference model an empirical study is made which is a written test given to two comparable high school classes (1.year and 3.year) with maths at A level. The high school students had problems with several different techniques, especially multiplication and division of rational numbers. This indicates that they normally use calculators to do such operations. They answered correctly on only three-fourth parts of the tasks. Surprisingly the 1.year students performed best, however, there was no significant difference.
It suggests that students’ knowledge of rational numbers do not improve in high school,
which can be a problem for higher education. The thesis has examined teacher students technical knowledge of rational numbers through group interviews of 1.year students studying mathematics. It turned out as expected that their performance did not differ significantly from the high school students.
It is surprising that the basic knowledge of rational numbers do not improve through the work with more advanced mathematics in high school. If secondary schools must prepare students for higher education, you may have to rethink high school mathematics or explore what it takes to give students the basic knowledge of rational numbers with them from ground school.