In our explorations of students' concepts in an inquiry science classroom with grade 6 students from urban schools in India, we uncovered a variety of problems in their understanding of biological cells as structural and functional units of living organisms. In particular, we found not only that they visualised the cell as a two-dimensional (2-D) structure, instead of a closed three-dimensional (3-D) functional unit, but that they had a strong resistance to changing their 2-D conception to a 3-D one. Based on analyses of students' oral as well as written descriptions of cells in the classroom, and of models they made of the cell, we were able to identify the causes of students' difficulties in correctly visualising the cell. These insights helped us design a pedagogy involving guided discussions and activities that challenges students' 2-D conceptions of the cell. The activities entail very simple, low-cost, easily doable techniques to help students visualise the cell and to understand that it would not be able to function if its structure were 2-D. We also present the results of our investigations of conceptions of grade 7 students and biology undergraduates, revealing that the incorrect 2-D mental model can persist right up to the college level if it is not explicitly addressed. The classroom interactions described in this study illustrate how students' ideas can be probed and addressed in the classroom using pedagogical action research.