id: 06455394
dt: j
an: 2015e.00696
au: Colton, Connie; Smith, Wendy M.
ti: Successfully transitioning to linear equations.
so: Math. Teach. (Reston) 107, No. 6, 452-457 (2014).
py: 2014
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: H33 D73
ut: linear equations; algebra; word problems; activities; problem solving;
transition; linear function; graph; equal sign
ci: ME 2010d.00479
li: http://www.nctm.org/publications/article.aspx?id=40434
ab: Summary: The Common Core State Standards for Mathematics asks students in
as early as fourth grade to solve word problems using equations with
variables. Equations studied at this level generate a single solution,
such as the equation $x + 10 = 25$. For students in fifth grade, the
Common Core standard for algebraic thinking expects them to generate
and compare the relationship between two patterns, such as those formed
by $x + 3$ and $x + 6$. The standard goes on to ask students to graph
ordered pairs on a coordinate plane to support their investigation.
Students in sixth grade are asked to evaluate expressions as well as
write and solve equations derived from real-world contexts. These early
expectations lay the foundation for meeting multiple standards outlined
in the Common Core standard for high school algebra. However, for many
students, progressing from modeling situations with equations such as
$3x + 10 = 25$ to equations such as $3x + 10 = y$ creates a seemingly
insurmountable problem. The transition from one-variable equations with
a single solution to linear equations with two variables and infinitely
many solutions presents many challenges. One specific obstacle to
making this transition lies in students’ misunderstanding of the
equals sign. For many students, the equals sign indicates an operation
rather than a relationship [{\it E. R. Ronda}, Math. Educ. Res. J. 21,
No. 1, 31‒53 (2009; ME 2010d.00479)]. Once the concept of relational
equality is sufficiently developed, students can begin the task of
making sense of two-variable equations. Knowledge construction for
understanding linear equations occurs in various stages. Ronda [loc.
cit.] suggests four clearly defined stages of conceptual development,
which range from the most elementary level ‒ being able to evaluate
variables for specific values ‒ to the most complex level ‒ being
able to view the function holistically. (ERIC)
rv: