Research in mathematics education has shown significant changes in the
last 25 years. The presence of qualitative methods has helped researc
hers to investigate in detail aspects related to the process used by s
tudents to understand mathematical ideas. The development of the cogni
tive sciences has played an important role in the acceptance of the qu
alitative paradigm in the field of mathematics education. The aim of t
his paper is to discuss criteria that are important to enhance the use
of qualitative methodology in the study of the learning of mathematic
s. For example, the presentation of the research context, rationale of
the method, and the illustration and discussion of limitations of the
analysis are important components addressed throughout the paper. The
discussion of these components helps to understand the value of this
research and also provides basis for the transfer of these methods to
other similar studies. In addition, some results from studies in mathe
matical problem solving are presented as an example of this type of qu
alitative research.