Reflection is increasingly used to support mathematics teacher education. Emerging from
Dewey’s (1933) work, reflection is widely accepted as an important tool to facilitate
prospective teachers’ learning during their education programs. It can allow prospective
teachers to make explicit and examine their initial conceptions and beliefs about teaching
and mathematics that provide a basis of their sense making and learning. It also allows
them to articulate, examine, question, and monitor their knowledge, beliefs, and goals
embodied in their practicum teaching to develop a deeper sense of teaching and themselves
as teachers (Freese, 2006). These uses of reflection are evident in instructional approaches
that have been investigated in studies on prospective mathematics teacher education (e.g.,
Artzt, 1999; Chapman, 2007; Ebby, 2000; Lee, 2005). In the case of Artzt (1999), she
provided a detailed model to guide prospective teachers’ reflection as a basis of their
learning during student teaching that consisted of pre- and post-lesson reflective activities
involving analysis of their cognition and instructional practice before, during, and after
their lessons. Such studies provide support for the importance of reflection as a tool in
mathematics teacher education. For example, Artzt (1999) explained that when prospective
teachers are made more aware of the monitoring they do of their students, they become
more conscious of the need to change their instruction accordingly. Lee (2005) also
suggested that an iterative planning–experience–reflection cycle allows prospective
teachers to reflect critically upon and improve their practice. In Chapman (2007), a
reflection–inquiry–reflection cycle was effective in allowing prospective teachers to
become aware of their thinking and improve their understanding of arithmetic operations.
Reflection, then, has been used to allow prospective mathematics teachers to inquire
about their thinking, learning, and instructional practices. But, based on the literature, the
trend has been to conceive of reflection as a looking back in the context of the past and
present and thus, with little attention to the future. Extending reflection into the future
could add another important dimension to its role in teacher education. The intent of this
editorial is to promote ‘‘imagination’’ as a tool with the potential of allowing this to be
accomplished. As Conway (2001) suggests, anticipatory or prospective reflection, or