id: 06664348
dt: j
an: 2016f.00712
au: Dominguez, Higinio
ti: Mirrors \& windows into student noticing.
so: Teach. Child. Math. 22, No. 6, 358-365 (2016).
py: 2016
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: D52 C32 D42 D72 C52 C62
ut: noticing; problem solving; participation; cultural diversity; socioeconomic
status; problem posing; word problems; difficulties; language
ci:
li: http://www.nctm.org/Publications/Teaching-Children-Mathematics/2016/Vol22/Issue6/Mirrors-_-Windows-Into-Student-Noticing/
ab: Summary: In many classrooms, students solve problems posed by others ‒
teachers, textbooks, and test materials. These problems typically
describe a contrived situation followed by a question about an unknown
that students are expected to resolve. Unsurprisingly, many students
avoid reading these problems for meaning and instead engage in a
suspension of sense making characterized by rule-following behavior and
keyword searches. Problems in everyday situations, however, do not come
preformulated. Instead, these problems and the reasoning that they
instantiate develop simultaneously as problem solvers informally
question the situation and begin to formulate conjectures and possible
pathways for solving these problems. Word problem difficulties have
been investigated primarily by looking at what students do or do not
do, including looking at student errors or students’ failure to use
linguistic knowledge. These explanations suggest that students, not the
problems need to change. In this article, the author suggests using a
windows-and-mirrors framework for encouraging students to be problem
posers. Like a window, a problem should be an opportunity for students
and teachers to look out for what makes sense to solve the problem.
Simultaneously, like a mirror, a problem should be an opportunity for
students and teachers to look into what students notice as relevant for
solving a problem. Readjusting the window and/or the mirror ‒ as it
is recognized in word problems ‒ signifies reformulating a problem.
Reformulating problems is important because asking students to solve
preformulated problems has shown that students do not make sensible
connections of mathematics to situations. When such experiences repeat
every day, students develop self-perceptions that they are not good at
math. The aim of this article is to explain how to help culturally
diverse and socioeconomically disempowered students use problem posing
to reflect their knowledge and gain insight into new knowledge. This
article discusses four research-based strategies that can support all
students in problem posing: (1) Let students specify some quantities;
(2) Let students frame problem questions; (3) Promote problem posing at
various points; and (4) Invite students to interpret representations.
The author also provides questions that can elicit student noticing by
restoring experiential mirrors and opening mathematical windows. (ERIC)
rv: