
05668524
j
2010c.00342
Steel, Wayne
Links between algebra and arithmetic.
Math. Teach. Inc. Micromath 2008, No. 211, 1416 (2008).
2008
Association of Teachers of Mathematics (ATM), Derby
EN
H23
C33
mathematics activities
arithmetic
elementary algebra
grade 10
mathematical concepts
equations
mathematical logic
interviews
concept formation
interviews
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 sixthform 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)