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To conceive the infinity of integers, one has to realize: (a) the unending possibility of increasing/decreasing numbers (potential infinity), (b) that the cardinality of the set of numbers is greater than that of any finite set (actual infinity), and (c) that the leap from a finite to an...
The current study examines the personal epistemology of fourth-grade elementary school teachers from Germany (n = 10) and the United States (n = 10) to gain a more nuanced understanding of teachers’ beliefs about knowledge and knowing through a cross-cultural lens. Analyses of semi-structured...
We discuss an emerging program of research on a particular aspect of mathematics learning, students’ learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning trajectories of students by...
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