Two developments have contributed to the convergence of views about the benefits of real-life and inquiry-based pedagogies in mathematics learning. First, the mathematics teaching community is increasingly focused on the learning of mathematics that involves the transfer of prior knowledge to novel problem-solving situations, a key element in recent characterizations of the notion of "Numeracy." Second, research about human cognition in domain-specific learning suggests that problem-solving activity provides better contexts in which to observe the construction of creative connections of disparate information. The question is how can we examine the above cognitive processes, as these are played out in Numeracy contexts? (Tan, "Educ Res Policy Pract" 6:101-114, 2007) identified "dialogue" and "inquiry" as important themes of the psychology that girds problem-based learning. In this report, we take up Tan's suggestion that research needs to make learner's cognition more visible by immersing a cohort of Malaysian and Australian students in arithmetic word problems. Students were required to explain and justify their solutions. The frameworks of "dialogue" representation and schema guided our analyses that focused on students' readings, explanations, representations and reflections about a given set of problem contexts. Results showed that both the groups experienced difficulty in representing far-transfer numeracy problems. However, Australian children tended to develop longer and more varied explanations in comparison to their Malaysian counterparts. Potential implications for classroom practices, policy-making and future research directions are explored.