id: 05668524
dt: j
an: 2010c.00342
au: Steel, Wayne
ti: Links between algebra and arithmetic.
so: Math. Teach. Inc. Micromath 2008, No. 211, 14-16 (2008).
py: 2008
pu: Association of Teachers of Mathematics (ATM), Derby
la: EN
cc: H23 C33
ut: mathematics activities; arithmetic; elementary algebra; grade 10;
mathematical concepts; equations; mathematical logic; interviews;
concept formation; interviews
ci:
li:
ab: Summary: General Certificate of Secondary Education (GCSE) mathematics
assessment previously included a piece of coursework that required
learners to develop a general equation to describe the relationship
between two groups of numbers on a number grid. In this author’s
experience, it became clear that Year 10 students often struggled to
form a link between arithmetic patterns and algebraic generalities.
Also, his work with sixth-form students highlighted situations where
they were uncomfortable with manipulating algebraic expressions without
changing the variables to x and y, which suggested that even these
quite capable mathematicians saw algebra as a distinct process separate
from other areas of mathematics. In this article, the author
investigates a class of 20 Year 10 students of average ability on two
aspects of their use of algebra ‒ as a description of a general
arithmetic connection/progression and as a valid method of proof that a
connection exists ‒ using the process known as the "clinical
interview", allowing him to gain as much information as possible about
each student’s understanding of the concepts involved. (Contains 3
figures.) (ERIC)
rv: