id: 06467673
dt: j
an: 2015e.00437
au: Isler, Isil; Marum, Tim; Stephens, Ana; Blanton, Maria; Knuth, Eric;
Gardiner, Angela Murphy
ti: The string task: not just for high school.
so: Teach. Child. Math. 21, No. 5, 282-292 (2014).
py: 2014
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: D82 I22 U62
ut: mathematical concepts; concept formation; activities; manipulative
materials; functional thinking; visualization
ci:
li: http://www.nctm.org/publications/article.aspx?id=43584
ab: Summary: The study of functions has traditionally received the most
attention at the secondary level, both in curricula and in standards
documents ‒ for example, the Common Core State Standards for
Mathematics and [{\it National Council of Teachers of Mathematics},
Principles and standards for school mathematics. Reston, VA: NCTM
(2000)]. However, the growing acceptance of algebra as a K‒12 strand
of thinking by math education researchers and in standards documents,
along with the view that the study of functions is an important route
into learning algebra, raises the importance of developing children’s
understanding of functions in the elementary grades. What might it look
like to engage students in functional thinking in the elementary
grades? Elementary school curricula often include a focus on simple
patterning activities (e.g., recursive number sequences, such as 2, 4,
6, 8, \dots) in which only one variable is observed. However, an
exclusive focus on this type of activity might hinder the development
of students’ reasoning about how two or more quantities vary
simultaneously, a key component of functional thinking. {\it M. L.
Blanton} et al. [Developing essential understandings of algebraic
thinking. Grades 3‒5. Reston, VA: NCTM (2011)] argue that elementary
school students are in fact capable of engaging in this type of
thinking. Furthermore, they point out that focusing on functional
thinking provides a context for students to understand the role of
variable as varying quantity. This article supports {\it M. L. Blanton}
et al.’s [loc. cit.] argument by sharing a classroom episode as well
as pre-instruction and post-instruction data from a yearlong teaching
experiment. The authors discuss some of the crucial elements they
believe contributed to students’ growing abilities to engage in
functional thinking. They also discuss connections made among various
representations, another important benefit of having students engage in
functional thinking. (ERIC)
rv: