PRESERVICE TEACHERS’ LEARNING TO TEACH
MATHEMATICS: THE IMPORTANCE OF THE INTERCONNECTION AMONG MANIPULATIVES, TALK,
AND SYMBOLS
Florence
Glanfield
University
of Saskatchewan
Joyce
Mgombelo
University
of Alberta
What does it mean for preservice teachers to
learn to teach children mathematics through the interaction between actions and
manipulatives, the talk describing these actions, and mathematical symbols
describing the talk and actions?
During interviews to
assess a preservice teacher education course, students demonstrated how they
would use manipulatives to teach concepts in mathematics, selecting from those use
in the course (e.g., base 10 blocks, pattern blocks, algebra tiles, etc.). They were to demonstrate how manipulatives
could model a particular mathematical concept, the language associated with
using manipulatives, and how mathematical symbols described the actions with
the manipulative.
Some preservice teachers ‘took for granted’ the
multiple meanings of mathematical expressions, thereby failing to demonstrate
their meanings with manipulatives. One,
for example, trying to demonstrate 8÷2 did it within the concept of sharing,
both in terms of her actions and language.
However, she could not demonstrate division as repeated subtraction with
the manipulatives, repeatedly returning to the idea of division as sharing. Yet she was able to calculate 8 ÷2 using
repeated subtraction.
Using interviews for assessment reveals both
understandings and misunderstandings to the interviewer and provides an
occasion for the preservice teachers to reflect on their teaching. The interviews showed that preservice teachers
need more help to develop awareness of multiple meanings of mathematical
expressions.
Bibliography
Pirie, S. E. B.
(1998). Crossing the gulf between
thought and symbol: language as (slippery) stepping-stones. In H. Steinbring, M. G. Barolini Bussi,
& A. Sierpinska (Eds.), Language and
Communication in the Mathematics Classroom (pp. 7-29). Reston, VA: National Council of Teachers of
Mathematics.