This paper studies grade 7 (age 13) students' expressed understanding about the equal sign/notion of equivalence in order to investigate what aspects of the concept that could be seen as an established knowledge at lower secondary school/middle school. Using items from different instruments and combining these to a new one that covered a broad…

Based on the wide-ranging liberal reforms introduced in the early 1990s, Sweden has become one of the most prominent realizations of Milton Friedman's proposal for market-based schooling. From 1991 to 2012, the percentage of Swedish ninth-grade students attending independent, voucher-financed, private schools increased from 2.8% to 14.2%. A recent…