This study aimed to gain knowledge of students' beliefs and difficulties in understanding p-values, and to use this knowledge to develop improved teaching programs. This study took place over four consecutive teaching semesters of a one-semester tertiary statistics unit. The study was cyclical, in that the results of each semester were used to inform the instructional design for the following semester. Over the semesters, the following instructional techniques were introduced: computer simulation, the introduction of hypothetical probabilistic reasoning using a familiar context, and the use of alternative representations. The students were also encouraged to write about their work. As the interventions progressed, a higher proportion of students successfully defined and used p-values in Null Hypothesis Testing procedures.