The issue for this paper is to discuss what can explain that students in different grades seem to experience a phenomenon in more or less the same way and thus, need to discern the same critical aspects in teaching. Data comes from a three-year-long learning study project conducted in four different Swedish schools, in K–9: preschool, grade 4, 6 and 9 respectively.  

Understanding what students yet need to learn in relation to a specific content is of importance if to organize a teaching situation where students can work in a zone of proximal development (Vygotsky, 1986). Within the theory of variation the concept of critical aspects is regarded as bearing such information for teachers to use when designing teaching (Marton, 2005; Runesson, 2013).

In the research project we used phenomenography as a theoretical framework in search for critical aspects. Phenomenography is a research approach aiming to understand qualitatively different ways of experiencing a phenomenon. A basic assumption is that we, on the basis of what we have experienced in life, what situations and problems we encountered, experience a phenomenon in a specific way (Marton, 1981; Eriksson, 1999). But the ways we experience a phenomenon do not vary very much. This is believed to be because the contexts and activities do not vary at all. A phenomenographical analysis tends to result in a limited but qualitatively different way of experiencing a phenomenon (Eriksson, 1999). Critical aspects can be identified when comparing different ways of experiencing a phenomenon.

The research question addressed in this paper is what possible explanations can be found that students in different grades seem to experience a phenomenon in more or less the same way and thus, need to discern the same critical aspects in teaching.

In order to identify critical aspects groups of students from each grade were interviewed when presented algebraic expressions and some possible answers. The interviews were transcribed and phenomenographically analysed.

The results indicates that regardless of earlier schooling the students experienced the phenomenon of algebraic expressions in a similar way and thus same critical aspects were identified as needed to discern for the students in the four grades. Based on the analysis three different critical aspects were identified. Students from preschool class and grade 4 were interviewed during the first project year and the students from Grade 6 and 10 the second project year. The analysis from the first project year resulted in critical aspects common for the students and that was not so surprising since we knew that these students had not yet experienced algebraic expressions. However almost the same critical aspects were identified in the analysis of the interviewed students in Grade 6 and 9 during second project year. This was more of a surprise since the students had met algebraic expressions in school.

The discussion will focus on these findings in relation to what possible experiences student may have of discerning aspects of algebraic expressions in relation to the content of mathematical education.