id: 06664679
dt: j
an: 2016f.01080
au: Vincent, Jill; Bardini, Caroline; Pierce, Robyn; Pearn, Catherine
ti: Misuse of the equals sign: an entrenched practice from early primary years
to tertiary mathematics.
so: Aust. Sr. Math. J. 29, No. 2, 31-39 (2015).
py: 2015
pu: Australian Association of Mathematics Teachers (AAMT), Adelaide, SA
la: EN
cc: H20 H30 E40
ut: equal sign; operational meaning; relational meaning; algebraic expressions
ci:
li:
ab: Summary: In this article, the authors begin by considering symbolic
literacy in mathematics. Next, they examine the origins of misuse of
the equals sign by primary and junior secondary students, where
“$=$” has taken on an operational meaning. They explain that in
algebra, students need both the operational and relational meanings of
the equals sign. When substituting numbers for pronumerals in an
algebraic expression, students are able to rely on their operational
understanding to evaluate the expression. Similarly, it is possible for
students to solve algebraic equations such as $2x + 3 = 11$ without
recourse to the relational meaning, for example, by a guess and check
approach. However, if they fail to understand that the expressions on
each side of an equation are equal, then they have difficulty, for
example, understanding why $x$ can be subtracted from both sides when
solving the equation $2x + 3 = x + 11$. Researchers have found that
students who understand that the equals sign is a relational symbol of
equality are more successful in solving algebraic equations. The
remainder of the article examines a sample of the written solutions of
first semester undergraduate students demonstrating inappropriate use
of the equals sign in a major Australian university’s Calculus 1
course. The article concludes that the notion of expecting symbols to
have meaning and a habit of checking the meaning of the symbols used is
an aspect of working mathematically that needs to be cultivated at all
levels: primary, secondary and tertiary. In particular, ensuring that
students understand the relational role of the equals sign is an
important step in developing symbol sense. (ERIC)
rv: