
06326890
j
2014e.00620
Wasserman, Nicholas H.
Introducing algebraic structures through solving equations: vertical content knowledge for K12 mathematics teachers.
PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 24, No. 3, 191214 (2014).
2014
Taylor \& Francis, Philadelphia, PA
EN
H49
H39
C29
algebra
group axioms
field axioms
structure sense
solving equations
doi:10.1080/10511970.2013.857374
Summary: Algebraic structures are a necessary aspect of algebraic thinking for K12 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 K12 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 K12 curriculum related to algebraic structure are examined.