People's ability to transfer what they have learned depends upon a number of factors:
— “People must achieve a threshold of initial learning that is sufficient to support transfer.” (p. 235)
— “Spending a lot of time (“time on task”) in and of itself is not sufficient to ensure effective learning.” (p. 235)
— “Learning with understanding is more likely to promote transfer than simply memorizing information from a text or a lecture.” (p. 236)
— “Knowledge that is taught in a variety of contexts is more likely to support flexible transfer than knowledge that is taught in a single context.” (p. 236)
— “Students develop flexible understanding of when, where, why, and how to use their knowledge to solve new problems if they learn how to extract underlying themes and principles from their learning exercises.” (p. 236)
— “All learning involves transfer from previous experiences.” (p. 236)
— “Sometimes the knowledge that people bring to a new situation impedes subsequent learning because it guides thinking in the wrong direction.” (p. 236)
Teachers need expertise in both subject-matter content and in teaching; need to develop an understanding of the theories of knowledge that guide the subject-matter disciplines in which they work; need to develop an understanding of pedagogy as an intellectual discipline that reflects theories of learning, including knowledge of how cultural beliefs and the personal characteristics of learners influence learning; and need to develop models of their own professional development that are based on lifelong learning, rather than on an “updating” model of learning (p. 242).
“Computer-based technologies hold great promise both for increasing access to knowledge and as a means of promoting learning” (p. 243).
As comprehensive summaries of what we currently know about learning in general, about learning mathematics in particular, and about the implications of this knowledge for teaching and creating school environments conducive to learning, Adding It Up and How People Learn can serve as resources for professional discussions, for course and seminar content, and for guiding future research. What we know about how students learn suggests that educators, researchers, and policy makers can do the following:
Draw from the extensive findings in these reports to educate parents and the community at large about, and build support for, changes in school mathematics programs.