T3 –
Tasks, Tools and Talk
The
Common Core State Mathematics Standards (CCSS-M, 2010) challenge traditional
beliefs regarding what it means to learn and teach mathematics. The Seneca Valley Middle School has embarked
on a professional development campaign, begun in the Seneca Valley Elementary
Schools four years ago, to help teachers meet the Mathematical Practice
standards defined by the CCSS-M (CCSS-M, 2010). Although the standards dictate neither curriculum
nor pedagogy, the emphasis on student reasoning and communication challenges
the traditional method of delivery, wherein teachers model procedures and
students use the procedures in repetitive fashion (Lampert,1990; Ball, Goffney,
& Bass, 2005). Supporting students
in a way that encourages a belief in their own efficacy and a positive disposition
toward mathematics, demands teacher reflection regarding the vision of good
instruction and the related classroom culture that supports it (Hill, Rowan,
& Ball, 2005).
Seneca
Valley teachers are taking a close look at the classroom culture created during
math instruction. With the help of professional development experts associated
with the National Council of Teachers of Mathematics and faculty from the
University of Pittsburgh, teachers work toward creating a discussion- rich
community. When one considers classroom
culture, teaching mathematics in a way that is consistent with the Common Core State
Standards includes more than teaching mathematical content. The first
three practices: make sense of problems and persevere in solving them; reason
abstractly and quantitatively; and construct viable arguments and critique the
reasoning of others, focus on making sense of problems and solutions through
the process of logical explanation as well as through probing the understanding
of others as students construct arguments, identify correspondences among
approaches, and explore the truth of conjectures.
It is through talk that mathematical ideas are aired, revised,
connected to prior knowledge and to one another, examined, and challenged.
Exchanges between teachers and students or students and students, go beyond
describing a summary of steps in solving a problem; problem solving strategies
are linked to mathematical argument. At Seneca Valley Middle School, roles of
teachers includes establishing norms
wherein differences are expected and respected; where disagreements are
resolved by reasoned arguments; and where mathematical reasoning is a practice
to be learned, not an innate ability (Ball, Goffney, & Bass, 2005).
Discursive participation and the related
teacher practices that influence student learning are largely affected by the
mathematical task selected by the teacher.
It is the mathematical task, a set of problems or a single complex
problem, itself that focuses attention on a particular mathematical idea and
defines the intellectual challenge on which students will attend during a
mathematics class (Stein, Grover, & Henningsen, 1996). The kind of task selected can promote or
discourage students to explore deeply the intended mathematical goal and is
closely related to norms in which students will engage and the opportunity for
deep conceptual understanding (Doyle,1988; Stein, Smith, Henningsen, &
Silver, 2000).
Seneca
Valley teachers are considering the task’s cognitive demand,that is the level
and type of thinking that a task has the potential to engage in a student. In
general, low-level cognitive demand tasks are algorithmic in nature. They involve using or producing previously
learned facts or procedures. There is
little ambiguity about the direction or steps needed for solution and they are
generally not connected to concepts underlying the procedure. The focus is primarily on obtaining a correct
answer with little need for explanation.
Conversely, tasks that require students to explore and understand
mathematical concepts, processes, or relationships, requiring that students
develop meaning through the use of multiple representations and analysis, while
accessing prior relevant knowledge fall into the category of high-level
cognitive demand. These tasks often require students to use non-algorithmic thinking
while persevering to develop solution strategies. Further, equity is served as students profit
from the alternate representations of classmates’ vision of the mathematical
ideas. The task itself provides the reason that talk is needed at all. Properly
chosen, it offers the opportunity for everyone to make a contribution to both
individual and group success.
For additional information please contact
Andrea Peck at Seneca Valley MS
