Texas Mathematics Teacher Spring/Summer 2018 - 6

Community-Building
Discourse Practices in Math Workshop

"

What is Math Workshop?

Implementing math workshop
is complex and begins with the
understanding that every student
has the potential to understand
mathematics conceptually.

"

Have you ever wondered what a mathematical
community would look like in an elementary classroom?
What if the majority of interactions within this
mathematical community encompassed rich, mathematical
discourse practices that promote deep learning?
According to Hattie, Fisher, and Frey (2017), mathematical
discourse extends beyond discussion and encompasses
the different ways that students agree, disagree,
represent, talk, and think about mathematics. Specifically,
mathematical discourse "includes not only ways of
talking, acting, interacting, thinking, believing, reading,
writing but also mathematical values, beliefs, and points
of view" (Moschkovich, 2003, p. 326). The fundamental
goal of mathematical discourse is to transcend traditional
procedure- and rule-driven approaches to mathematics
instruction and develop conceptual understandings about
mathematics among all students (Griffin, League, Griffin,
& Bae, 2013). Furthermore, mathematical discourse
transforms classrooms into communities where "students
hear one another's ideas and have opportunities to
articulate and refine or revise their own," while also
developing "confidence in themselves as mathematical
knowers" (Ball, 1993, p. 394).
In 2014, the National Council of Teachers in Mathematics
[NCTM] called for teaching practices that "facilitate
discourse among students to build shared understanding
of mathematical ideas" (p. 29). However, the concepts
of 'community' and 'discourse' are not novel within
the realm of mathematics instruction. For over 25 years,
much literature has provided evidence supporting the
notion that establishing a mathematical community to
facilitate discourse practices develops mathematical
understandings among elementary-aged students (e.g.,
Ball, 1993; Hiebert & Wearne, 1993; Prawat, 1989; Wood,
Williams, McNeal, 2006). While there are many effective
teaching practices that support this type of mathematical
community, we propose the use of math workshop.
We believe that teachers could utilize math workshop
as an effective strategy for supporting rich discourse to
build community. In this article, we provide a description
of math workshop and how its structure establishes a
mathematical community to facilitate discourse practices
among all students. Next, we present three classroom
vignettes of elementary teachers who implement math
workshop at the 2nd, 3rd, and 4th grade levels in varied
ways. We conclude by offering recommendations and
resources for teachers who are interested in learning more
about math workshop.

6

| Spring/Summer 2018

Math workshop is a promising approach that transforms
a class of students into "a community of mathematicians"
(Hoffer, 2012, p. 5) and addresses all levels of learning
(Hattie et al., 2017). According to Hoffer (2012), the
structure of math workshop consists of four components:
1. Opening: Students engage with a problem
connected to the lesson objective that unlocks prior
knowledge.
2. Mini-lesson: The teacher develops student
understandings with the lesson objective through
the use of verbal explanations, or talk-alouds
(Wright, 2014). During the mini-lesson, the teacher
may introduce new information, revisit previous
information, model thinking, or review strategies
for work time (Hoffer, 2012).
3. Work Time: Students engage with a challenging,
collaborative task in small groups that extends
their thinking with the lesson objective. The teacher
moves among small groups and confers with
students.
4. Reflection: At the end of the lesson, students reflect
upon their metacognitive understandings with the
lesson objective.
The math workshop structure supports a paradigm shift
in how mathematics is taught and learned (Hoffer, 2012).
In math workshop, the teacher is no longer a presenter of
information, but rather a facilitator of learning. Students
are no longer passive recipients of information. Instead
they "devote the majority of their time to thinking and
talking about important mathematical ideas" (p. 3). As
students engage with mathematical discourse practices
individually and collaboratively, they utilize language,
perspectives, and cognitive functions that are rooted in
unique cultural and social identities (Moschkovich, 2007).
In other words, understandings and contributions towards
the co-construction of knowledge in math workshop are
influenced and shaped by each student's unique "ways
of behaving, interacting, valuing, thinking, believing,
speaking, and often reading and writing" (Gee, 2012, p. 3).
Implementing math workshop is complex and begins with
the understanding that every student has the potential
to understand mathematics conceptually (Hoffer, 2012).
Therefore, the most critical aspect of designing a math
workshop lesson is the third component, Work Time task.
While planning for this task, the teacher must consider
the learning levels of each student and incorporate
differentiated tasks based upon learning needs. Work
Time tasks must align with the lesson objective and
promote exploration, sense-making, and the application
of mathematical procedures (Hattie et al., 2017). The
primary goal of the Work Time task is to present students
with challenging and rigorous problems that promote
engagement and persistence through the use of productive
discourse practices in a supportive mathematical
community (Boaler, 2016).

Texas Mathematics Teacher



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