id: 06512806
dt: j
an: 2016a.00150
au: Lapp, Douglas, A.; Ermete, Marie; Brackett, Natasha; Powell, Karli
ti: Linked representations in algebra: developing symbolic meaning.
so: Math. Teach. (Reston) 107, No. 4, 306-312 (2013).
py: 2013
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: C34 H34 I24
ut: modes of representation; dynamic linking; concept formation; research;
upper secondary; interviews; mathematical language; notation; abstract
reasoning; mathematical ability; quadratic equations; parabolas; zeros;
solving equations; graph of a function; concepts; understanding;
symbolic meaning; calculators
ci:
li: http://www.nctm.org/Publications/mathematics-teacher/2013/Vol107/Issue4/Connecting-Research-to-Teaching_-Linked-Representations-in-Algebra_-Developing-Symbolic-Meaning/
ab: From the text: The use of symbols provides mathematics with enormous power.
From the learnerâ€™s perspective, however, symbols can present enormous
obstacles. Using symbols to encapsulate big ideas allows readers to see
various stages of arguments within one field of view. However, for many
learners, unpacking symbolization poses a significant hurdle in the
development of conceptual understanding. Here we compare and contrast
symbolic reasoning approaches that algebra students used when solving
equations. What is a root of an equation, and how is it related to
various representations? More generally, what does it mean for a value
to be a solution to an equation? These are standard questions that we
expect students to be able to address and discuss. Although many
students maybe able to solve equations, far too many have limited
conceptual understanding and rely primarily on procedural knowledge of
the equation-solving process.
rv: