id: 05534032
dt: j
an: 2009b.00230
au: Canada, Dan; Gilbert, Mike; Adolphson, Keith
ti: Investigating mathematical thinking and discourse with ratio triplets.
so: Math. Teach. Middle Sch. 14, No. 1, 12-17 (2008).
py: 2008
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: D53 F83
ut: ratio; problem posing; context; classroom techniques; mathematical logic;
teaching methods; logical thinking
ci:
li:
ab: Summary: Teachers know that real mathematical understanding includes the
higher-level skills of comparing, contrasting, and making connections
among different computational approaches. What mathematical connections
can students make when asked to explore a task that is posed in three
different ways? This article describes a unique task structure that
helps to foster classroom discourse and reveal studentsâ€™ mathematical
conceptions. The activity, called Ratio Triplets, referred to a set of
three versions of one particular mathematics problem. Although the task
centers on a fairly common type of proportional reasoning task, the
authors found that using different versions of the task afforded a good
opportunity for students to consider the meaning of ratios in multiple
ways. Here, the authors describe the three versions and how they used
them in class. Then, they profile some of the variations in
mathematical thinking that students demonstrated. Examples from each
version are provided. Finally, the authors highlight the benefits
gained from having students discuss all three versions. (Contains 5
figures.) (ERIC)
rv: