Secondary School Students’ Construction and Use of Mathematical Models in Solving Word Problems

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15–16 years old). Four levels of the development of constructing and using mathematical models were identified using a constant-comparative methodology to analyse the student’s problem-solving processes. Identifying the general in the particular and using the particular to endow the general with meaning were the key elements employed by students in the processes of construction and use of models in the different situations. In addition, attention was paid to the difficulties that students had in using their mathematical knowledge to solve these situations. Finally, implications are provided for drawing upon student’s use of mathematical models as conceptual tools to support the development of mathematical competence from socio-cultural perspectives of learning.     

Students’ conception of infinite series

This is a report of a study of students’ understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be built so that we may uncover ways to help students improve their understanding. The theoretical framework consists of action–process–object–schema theory and the specific model of conceptions in Balacheff’s theory of conception, knowing, and concept. Approaching the problem from these two different theoretical perspectives allows us to provide different and at the same time complementary explanations of observed phenomena. The two different infinite series constructions are, briefly stated, series as an infinite unending process of addition and series as a sequence of partial sums. Students are found to have difficulty building an understanding of series as a sequence of partial sums and thus tend to have difficulty in problem situations that require this interpretation. The study uses semi-structured interviews with 10 graduate students. The interviews explore situations that might give insight into students’ notion of the sequence of partial sums.