This paper addresses the design of teaching to promote engineering students' conceptual understanding of mathematics, and its outcomes for mathematical meaning-making. Within a developmental research approach, inquiry-based tasks have been designed and evaluated, through the use of competencies proposed for their potential to promote conceptual learning. A sociocultural frame draws attention to interactions between different cultural elements to address challenges to teaching related to student perspectives and the mathematical meanings they develop. The paper recognizes tensions between design of inquiry-based practice and the outcomes of that practice, and demonstrates the need for new research to address mathematical meanings of a student community within a sociocultural frame.