Fractions are regarded as a challenging mathematical content not only in Tanzania and Sweden, but also in a broader international perspective (Kullberg, 2010). Thus, students around the world continue to struggle with fractions, even after years of instruction (Fazio & Siegler, 2011; Resnick & Singer, 1993). Even in countries where the majority of students achieve reasonably good conceptual understanding, such as Japan and China, fractions are considered a difficult topic (Fazio & Siegler, 2011). One reason for their difficulty is likely that fractions challenge students since many properties of whole numbers that they have learnt are true are not true for all numbers. For example, with fractions, multiplication does not always lead to an answer larger than the multiplicands, division does not always lead to an answer smaller than the dividend, and numbers do not have unique successors. Further, fractions (including decimal fractions) are considered to be the first serious exercises in the type of abstract mathematical reasoning that student will have to master for learning algebra, geometry and other aspects of higher mathematics (see for example Noddings, 2009). Fractions are not only an important stepping-stone for learning advanced mathematics; they are also commonly used in everyday life (Fazio & Siegler, 2011).

Natural Science subjects encompass Biology, Physics and Chemistry in both countries, Tanzania and Sweden. The subject areas are addressed integrated and thematic in the early Grades (1-3) in Sweden and throughout primary school in Tanzania. The three subjects can though be distinguished in the broad content areas of the Tanzanian syllabus: health, environment, living (Biology), non-living (Chemistry and Physics). In addition to the science content the Tanzanian syllabus also includes cross cutting issues such as HIV/AIDS, road safety education, drug abuse, family-life, education and gender. These are either integrated as topics or as sub topics or as the teaching and learning strategies (MoEVT, 2005; Skolverket, 2011). In Sweden each subject have its own syllabus, however the long-term stated capabilities are formulated in almost identical ways. The core content distinguishes one subject from the other. In Chemistry, Matter is a content area in Grade 6 in both countries.

In the following two chapters a meta-study is presented of participating schools in Tanzania and Sweden respectively. The aim of the meta-studies is to contextualize the cases in relation to school development. The Tanzanian meta-study is based upon interviews with some of the participating teachers and thus focuses on school development from a teacher perspective. The Swedish meta-study on the other hand is based upon interviews with some of the Head teachers working at three of the participating schools at the time of the project. In the Swedish metastudy school development is taking the perspective of Head teachers.

Föreliggande rapport grundar sig på tre uppföljningsstudier av försöksverksamheten med gymnasial lärlingsutbildning som genomfördes på uppdrag av Skolverket med en tagning av elever under de tre läsåren 2008/2009, 2009/2010 och 2010/2011. Lärlingsförsöket avslutades läsåret 2011/2012 i och med införandet av gymnasiereformen Gy2011. Då blev lärlingsutbildning en utbildningsform inom de reguljära gymnasiala yrkesprogrammen. Även om försöksverksamheten hade avslutats gick de elever som var antagna läsåret 2010/11 fortsatt kvar inom försöket fram till och med vårterminen 2013.

This report is based on 3 follow-up studies of a pilot project of upper secondary school apprentice education, which were conducted during the academic years 2009/10, 2010/11 and 2012/13 on behalf of the Swedish National Agency for Education. The focus of the studies was the conditions for students’ development of vocational skills in workplace-based education.