Abstract
ABSTRACT Most students need to learn to solve equations as a part of their education, but far from all succeed. In this study we investigate the potential impact of variation in the choice of numbers as coefficients when students in upper secondary school solve linear equations. A test with linear equations was distributed to 111 16-year-old vocational students and phenomenographic interviews were performed with 23 of them. The findings show that exchanging coefficients (e.g., changing a and b in a = b ⋅ x ) from natural numbers to other numbers significantly changes how equations with the same structure are handled, despite access to a calculator. A framework of five conceptions is described explaining how numbers are experienced in the foreground or background of attention, partly depending on what meaning the equation is given. The results indicate that number types need to be considered, not only in teaching arithmetic, but also in algebra.
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