Undergraduate mathematics instructors often report that students make careless errors or have not previously learned key mathematical ideas and strategies. The purpose of this study is to explore evidence of an alternative explanation that at least some of these "errors" may result from students' application of conceptions developed in…

Currently Australian pre-service teachers' levels of personal numeracy are under a great deal of scrutiny. There are calls for universities to raise entry standards into teaching degrees and counter-calls that the output of universities should be gauged rather than inputs. In 2015, doubts about the ability of graduate teachers to convey the…

People frequently continue to use inaccurate information in their reasoning even after a credible retraction has been presented. This phenomenon is often referred to as the continued influence effect of misinformation. The repetition of the original misconception within a retraction could contribute to this phenomenon, as it could inadvertently…

"Specific Mathematics Assessment that Reveal Thinking" (abbreviated as "smart tests") provide an on-line formative assessment of middle years students. They aim to put information from research on students' understanding directly into the hands of teachers, by providing quick automated diagnosis of learning for all students in…

Mathematics educators have had a long standing interest in students' understanding of decimal numbers. Most studies of students' understanding of decimals have been conducted within Western cultural settings. Similar research in other countries is important for a number of reasons, perhaps most importantly because it can provide insights that may…

A recent international study of pre-service teachers identified that proportional reasoning was problematic for pre-service teachers. Proportional reasoning is an important topic in the middle years of schooling and therefore it is critical that teachers understand this topic and can rely on their Mathematical Content Knowledge (MCK) when…