This work is part of a larger project that seeks to understand how students blend (integrate) chemistry and mathematics as they work through chemical kinetics problems. Here we focus on four students from our larger sample: two students that demonstrated more instances of blending chemistry and mathematics in their interviews ("high-frequency…

We examine a commonly suggested proof construction strategy from the mathematics education literature--that students first produce a graphical argument and then work to construct a verbal-symbolic proof based on that graphical argument. The work of students who produce such graphical arguments when solving proof construction tasks was analyzed to…

This study aims to examine the effects of a course module aimed at improving pre-service mathematics teachers' (PMTs) proof schemes. This study used designed-based research. Participants of the course were 22 PMTs in a teacher preparation program. We obtained data from two surveys, one of which consists of proof questions. The other requires…

Nearly all young people in the United States aspire to a college degree, but many fail to complete college in a timely manner. Does this lack of attainment reflect abandoned college plans? I analyze mixed-methods data from a five-year study of 700 low-income mothers at two Louisiana community colleges. Hurricane Katrina displaced respondents and…

Combinatorial proof serves both as an important topic in combinatorics and as a type of proof with certain properties and constraints. We report on a teaching experiment in which undergraduate students (who were novice provers) engaged in combinatorial reasoning as they proved binomial identities. We highlight ways of understanding that were…

The coming of "brand society" and the onset of mediatization spur universities to strategize their visual identity and pay particular attention to their icon. Resulting from branding initiatives, university icons are visual self-representations and material-cum-symbolic forms of organizational identity. In this work we ask: What identity…

Researching students' responses to tasks at different year levels and in varied curriculum contexts can provide insights that relate their understandings to prior learning experiences and teaching approaches. In this article, we discuss evidence of students from three curriculum contexts (English, Australian, and Israeli) (n = 350) ways of…

Functional thinking is an established route into algebra. However, the learning mechanisms that support the transition from arithmetic to functional thinking remain unclear. In the current study we explored children's pre-instructional intuitive reactions to functional thinking content, relying on a conceptual change perspective and using mixed…

This paper explores how in-service teachers enrolled in a graduate proof course interpret, understand, and use generic examples as part of their proving and justification activities. Generic examples, which are capable of proving and justifying with strong explanatory power, are particularly important for teachers considering teaching proof in…

Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

The global rise of a neoliberal "new politics of parenting" discursively constructs parents in poverty as the reason for, and remedy to, child poverty. This allows for Early Childhood Education and Care (ECEC) to become a key policy lever by using human technologies to intervene in and regulate the lives of parents and children in…

Two logic problems are analyzed. (DT)

The literature on cities in the developing world equates segregation with the proliferation of enclaves and slums and tends to overlook how the people associated with those places are further segregated in public spaces and enclaves. To account for the symbolic partitioning of Metro Manila, I document the segregating practices of the residents of…

The translation of problems into symbolic form and solution by truth table methods are described. (SD)

Processes of national research assessment, such as Excellence in Research for Australia (ERA) are a type of audit technology that confronts and steers established institutional identities and traditions. This nexus between policy and practice drives boundary work that diffracts prevailing policy logics, organisational practices, and habits of…