id: 06434946
dt: j
an: 2015c.00801
au: Nagle, Courtney; Moore-Russo, Deborah
ti: The concept of slope: comparing teachers’ concept images and
instructional content.
so: Investig. Math. Learn. 6, No. 2, 1-18 (2013).
py: 2013
pu: Research Council on Mathematics Learning (RCML), Memphis, TN; Taylor \&
Francis (Routledge), Philadelphia, PA
la: EN
cc: I29 I49 C39 D39
ut: slope; teachers’ concept images; teachers’ content knowledge; rates of
change; derivative; instructional knowledge; linear functions;
non-linear functions
ci: ME 1999d.02385
li:
ab: Summary: In the field of mathematics education, understanding teachers’
content knowledge and studying the relationship between content
knowledge and instructional are both crucial. Teachers need a robust
understanding of key mathematical topics and connections to make
informed choices about which instruction tasks will be assigned and how
the content will be represented. {\it L. Ma} [Knowing and teaching
elementary mathematics. Teachers’ understanding of fundamental
mathematics in China and the United States. Mahwah, NJ: Lawrence
Erlbaum (1999; ME 1999d.02385)] described this profound understanding
of fundamental mathematics as how accomplished teachers conceptualize
key ideas in mathematics with a deep and flexible understanding so that
they are able to represent those ideas in multiple ways and to
recognize how those ideas fit into the preK‒16 curriculum. Slope is a
fundamental topic in the secondary mathematics curricula. Unit rate and
proportional relationship introduced in sixth grade prepare students
for interpreting equations such as $y = 2x-3$ as functions with
particular, linear behavior in eight grade. The focus on relationships
with constant rate of change leads to distinctions between linear and
non-linear functions and the idea of average rate of change in high
school. Ultimately, these ideas prepare students for instantaneous
rates of change and the concept of a derivative in calculus. The
diversity of conceptualizations and representations of slope across the
secondary mathematics curriculum presents a challenge for secondary
teachers. These teachers must work flexibly and fluently with various
representations in the many contexts in order for their students to
build a coherent, connected conceptualization of slope. Since secondary
mathematics teachers need a deep understanding of slope to mediate
students’ conceptual development of this key topic, the study
reported here investigates both how teachers think about and present
slope.
rv: