Teacher Knowledge and Understanding
What knowledge is necessary or sufficient for teaching mathematics? Researchers have explored the distinctive characteristics of mathematical knowledge in and for teaching. A recognized challenge in teaching relates to the ability to draw upon appropriate mathematical knowledge in the moments of teaching and in response to unanticipated student interactions.
Knowledge at the Mathematical Horizon relates to a teacher's focus of attention and his or her ability to flexibly shift attention such that relevant properties, generalities, or connections, which embed particular mathematics in a greater structure, are accessed in teaching situations
This research explores the link between teachers' Knowledge at the Mathematical Horizon and their developing pedagogical sensitivities and their abilities to anticipate and respond to student learning. It examines how a more robust KMH may help teachers break away from familiar routines or strategies and broaden their expectations for what are important and helpful experiences for learners.
Where to learn more
Mamolo, A. & Pali, R. (2014). Factors influencing prospective teachers’ recommendations to students:
Horizons, hexagons, and heed. Mathematical Thinking and Learning, 16(1), 32-50.
Mamolo, A. & Zazkis, R. (2012). Stuck on convention: A story of derivative-relationships. Educational Studies
in Mathematics, 81(2), 161 – 177.
Zazkis, R. & Mamolo, A. (2012). Continuing conversations: Towards the horizon. For the Learning of
Mathematics, 32(1), 23 – 28.
Zazkis, R. & Mamolo, A. (2011). Reconceptualizing knowledge at the mathematical horizon. For the Learning
of Mathematics, 31(2), 8 – 13.
Wasserman, N., Mamolo, A., Ribeiro, C.M., Jakobsen, A. (2014). Exploring horizons of knowledge for teaching.
The 38th International conference for the Psychology of Mathematics Education, Vancouver, B.C.
Mamolo, A. (2014). An eye to the horizon: The case of Delia’s hexagon. Proceedings of the 17th SIGMAA on
RUME Conference. Denver, USA.
Mamolo, A. (2013). Pre-service teachers’ mathematical horizons: The case of the irregular hexagon. The
34th International conference for Psychology of Mathematics Education – NA Chapter. Chicago, USA.