The influence of numbers when students solve equations

Abstract

Is it possible that some students’ primary difficulty with equation-solving is neither handling the literal symbols nor the equality, but the numbers used as coefficients? It is well known that many students find algebra a difficult topic, and there is much research on how students experience this strand of mathematics, with indications of how it can be taught. Still, a perspective not often fronted in this research – that has been suggested as an area potentially important – is how numbers, other than natural numbers, in algebra, are perceived by students. Such kinds of numbers (negative numbers and decimal fractions) have been used in this thesis to explore how the numbers influence students’ equation-solving. Two studies with a phenomenographic approach have explored how students (n1=5, n2=23) perceive linear equations of similar structure but with different kinds of numbers as coefficients, e.g., 819 = 39 ∙ 𝑥 and 0.12 = 0.4 ∙ 𝑥. In the second study, a test was also used to investigate the magnitude of the influence of a change of coefficients for 110 students while solving equations with a calculator. The findings show that equations with decimal fractions and negative numbers are less likely to be solved by these students, and decimal fractions as coefficients can even make a student unable to recognize a kind of equation they just solved with natural numbers. The interviews display that, depending on the number in a linear equation, some students focus on different aspects of the equation, and that the numbers influence what meaning the students see in the equation and how they can justify their solution. Following the phenomenographic approach, differences in the way that students experience the equations were specified, and critical aspects were formulated. This implies a wider use of different kinds of numbers in teaching algebra, as different kinds of numbers hold different challenges, thereby also varying learning potential, for students.