Powerful vocational mathematics knowing

Abstract

The aim of this thesis is to illuminate vocational mathematics knowing within the context of building and construction-work education. The overall purpose is to contribute to the understanding of how mathematics, as manifested in vocational practice, can be articulated in educational contexts in ways that acknowledge both conceptual and contextual depth The thesis comprises three studies. The first, a phenomenographic interview study, explores mathematics teachers’ and vocational teachers’ various perceptions of educationally significant vocational mathematics knowing. The findings indicate that teachers, in different ways and to varying degrees, recognise the complexity of integrating aspects spanning a variety of domains. Teachers further describe mathematics as an essential component of students’ holistic vocational ‘Bildung’, illuminating values such as critical thinking, confidence, creativity, and adaptability. The second study aims to further explore how this kind of knowing is explicitly expressed in vocational problem solving. The empirical data consists of teachers’ descriptions of the understanding required by students when approaching such problems, together with students’ own discussions while working on constructionrelated mathematical tasks. Drawing on the conceptual framework developed within the phenomenography and variation theory research tradition (VTL), the results identify a set of critical aspects that are necessary to discern in order to understand and engage with mathematically rich construction-work situations in powerful ways. The study concludes that handling such problems requires coordinating both theoretical and practical forms of knowledge, originating from mathematics, other disciplinary areas, and vocational practice. The findings further highlight the importance of addressing both context-specific elements and conceptually coherent knowledge structures within vocational education. Building on insights from the second study, a vocationally relevant mathematical concept (similarity) was selected for further analysis in the third study. This study aims to illuminate learning opportunities afforded in mathematics textbooks for Grade 10, using variation theory as an analytical tool. According to variation theory, students’ opportunities to learn depend on patterns of variation. The analysis reveals that the textbooks make different sets of aspects possible to discern. While one textbook provides organised opportunities to practice a specific procedure for solving standardised tasks, another also makes it possible to discern essential aspects of the similarity concept. Finally, when all three studies are considered together, the thesis argues that the learning opportunities afforded in mathematics textbooks for vocational students, particularly when the focus remains on delimited procedural skills and standard tasks, are insufficient for developing the kind of conceptual flexibility and contextual awareness that characterise powerful vocational mathematics knowing, as described and exemplified throughout the thesis. Acknowledgments Writing this doctoral