Mathematical Modeling of Grade 10 Students in Solving Derivative-Application Problems in Cambridge International AS & A Level

Abstract

ABSTRACT

This study examined the mathematical modeling of 32 Grade 10 students, working in 16 pairs, in two Cambridge International AS & A Level Mathematics classes. Each pair solved derivative-application problems using an Observe–Model–Differentiate–Verify–Conclude (OMDVC) worksheet and later presented its solution. Written and oral evidence were analyzed separately through directed content analysis across six aspects: understanding the context, formulating the model, applying differentiation, verifying, interpreting, and communicating. Differentiation was the most consistently complete aspect, but a correct calculation did not always rest on a complete model or adequate verification. Written and oral evidence closely matched in only five pairs (31.3%). Among the other 11 pairs, five supplied details during the presentation before any guiding question, four had correct written solutions but could explain only part of their reasoning orally, and two clarified or revised their reasoning only after a guiding question. Looking at both sources revealed reasoning that had not been written down, as well as written evidence that students could not fully explain during the presentation. A correct differentiation procedure, by itself, was not sufficient evidence of a complete modeling process.