The Teaching and Learning Innovation Digest - May 2023

as well as teachers. When discussing math
concepts, students have the opportunity to
compare their ideas and teachers have the
chance to provide on-the-spot feedback
and check students’ understanding. In fact,
discourse and instant feedback from teachers
contribute to higher student achievement
(Ing et al., 2015, as cited in Stockero et al.,
2020). Furthermore, mathematical discourse
is so important that it has been incorporated
into three of the six Standards of the National
Council of Teachers of Mathematics (NCTM)
released in 1991.
What does this mean for teachers? How can
mathematical discourse be promoted in
current classrooms to re-engage students?
Mathematical discourse can be promoted
through open-ended tasks that are relevant to
the learning material. The educator implements
the task, facilitates the discussion environment,
freeing them to check for understanding and
provide feedback.
At the same time, there is a role for
students. They become responsible to
engage in the discourse to deepen their
own understanding and by doing so, they
re-engage with instructors less as recipients
of instruction and more as collaborators in
learning. Mathematical discourse is not led by
teachers, it’s led by students based on their
own needs (Hufferd-Ackles et al., 2004).
In an online learning platform, teachers
cannot interact with every student to check
for their understanding, resulting in the
advancement in technology to compensate
for this disadvantage. As an example, the
number of websites containing mathematical
problems is increasing. These websites
can generate questions for students to
solve as well as marking and showing the
correct solutions. In online learning, this
task is very much solitary. However when
implemented in an in-person setting where
students are encouraged to work with each
other, the task can be used to promote
discourse among students to support and
share ideas. Returning to campus does not
mean abandoning everything that is not inperson.
The advancements made in technology
can be used in class as an additional method
to support discourse.
In summary, as a way to re-engage
students when returning to campus,
mathematical discourse is a beneficial
tool that furthers student learning. It can
provide opportunities for students to deepen
their understanding, share in collaboration
with peers, and allow teachers to check
students’ understanding and provide timely
feedback. Mathematical discourse re-thinks
learning from a one-directional lecture
by the teacher to an environment that
encourages student participation through
purposeful discussion.
References
Gresham, G., and Shannon, T. (2017). Building mathematics discourse in students. Teaching Children
Mathematics, 23(6), 360–366. https://doi.org/10.5951/teacchilmath.23.6.0360
Hufferd-Ackles, K., Fuson, K. C., and Sherin, M. G. (2004). Describing levels and components of a
math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81–116.
https://doi.org/10.2307/30034933
Moschkovich, J. (2003). What counts as mathematical discourse, 325–332.
https://doi.org/https://eric.ed.gov/?id=ED501034
NCTM. (1991). Professional standards for teaching mathematics. National Council of Teachers of
Mathematics.
Stockero, S. L., Van Zoest, L. R., Freeburn, B., Peterson, B. E., and Leatham, K. R. (2020). Teachers’
responses to instances of student mathematical thinking with varied potential to support student
learning. Mathematics Education Research Journal, 34(1), 165–187.
https://doi.org/10.1007/s13394-020-00334-x
Dr. Richard Williamson
Lead Facilitator and Faculty
Tongyu Zhang
Student
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