id: 06326890
dt: j
an: 2014e.00620
au: Wasserman, Nicholas H.
ti: Introducing algebraic structures through solving equations: vertical
content knowledge for K-12 mathematics teachers.
so: PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 24, No. 3, 191-214
(2014).
py: 2014
pu: Taylor \& Francis, Philadelphia, PA
la: EN
cc: H49 H39 C29
ut: algebra; group axioms; field axioms; structure sense; solving equations
ci:
li: doi:10.1080/10511970.2013.857374
ab: Summary: Algebraic structures are a necessary aspect of algebraic thinking
for K-12 students and teachers. An approach for introducing the
algebraic structure of groups and fields through the arithmetic
properties required for solving simple equations is summarized; the
collective (not individual) importance of these axioms as a foundation
for algebraic thinking is discussed by way of an example of an abstract
group. Results of this approach in a mathematics for teachers course
are presented, with K-12 teachers ($n=12$) having increased their
content knowledge both about arithmetic properties and abstract
algebra, as well as having their teaching beliefs and intended
practices influenced. Implications for classroom teaching about a
vertical slice of the K-12 curriculum related to algebraic structure
are examined.
rv: