The dimensions of prospective elementary and middle school teachers’ problem posing for integer addition and subtraction

Elementary and middle school prospective teachers participated in semi-structured problem posing for integer addition and subtraction. The prospective teachers ( n = 98) posed a variety of different stories, but this paper focuses on the temperature stories they posed. Results include descriptions of their posed temperature stories through the lens of the various dimensions (i.e., problem types, realism, consistency, correctness). Prospective teachers posed mainly state-translation-state problem types and rarely posed state-state-distance, state-state-translation, or translation-translation-translation problem types. They often changed the structure of their number sentences. Although they posed mostly realistic and mathematically correct temperature stories, the stories compromised realism or consistency in order to use state-translation-state problem types. Coordinating of the various dimensions (e.g., problem types, consistency) when problem posing requires flexibility with problem types. This work highlights the complexity of posing temperature stories, and coordinating the various dimensions highlights the need for prospective teachers to experience problem posing. Implications for problem posing with integers and temperature are extended to all contexts that inherently support translation and relativity. In the discussion, we coordinate the different problem types with various number sentences and dimensions. Unpacking the various dimensions illuminates prospective teachers’ thinking and offers a way of considering integers and contexts.