This paper presents an inquiry into teaching and learning practices in a Year 11 mathematics class at a private college for girls in Western Australia, studying a topic on vectors. The focus is on learning through problem-solving, where students used graphics calculators as a matter of routine. Constructivist and sociocultural theories were referents for the inquiry, and purposive selection of data led to consideration of a range of theoretical issues. The following five key classroom actions are considered from both constructivist and sociocultural perspectives: (1) answering questions in whole-class work; (2) drawing diagrams; (3) answering friends' questions; (4) trying things out on a graphics calculator and explaining to the class; and (5) listening to the teacher in whole-class work. The sometimes inconsistent assumptions of the two perspectives allowed complementary insights into teaching and learning, thus enriching the analysis. The critical and inquiring stance raises questions for mathematics teachers looking to achieve a sensitive and inclusive learning environment characterized by reflective mathematical thinking and rich mathematical conversations. Appendices include a copy of a student questionnaire and a graphics calculator activity worksheet. Contains 44 references. (MES)