Abstract
Confidence assessment (CA), in which students state alongside each of their answers a confidence level expressing how certain they are, has been employed successfully within higher education. However, it has not been widely explored with school pupils. This study examined how school mathematics pupils (N = 345) in five different secondary schools in England responded to the use of a CA instrument designed to incentivise the eliciting of truthful confidence ratings in the topic of directed (positive and negative) numbers. Pupils readily understood the negative marking aspect of the CA process and their facility correlated with their mean confidence with r = .546, N = 336, p < .001, indicating that pupils were generally well calibrated. Pupils’ comments indicated that the vast majority were positive about the CA approach, despite its dramatic differences from more usual assessment practices in UK schools. Some pupils felt that CA promoted deeper thinking, increased their confidence and had a potential role to play in classroom formative assessment.
Highlights
Fluency in important mathematical procedures is recognised as a critical goal within the learning of school mathematics (Gardiner, 2014; National Council of Teachers of Mathematics [NCTM], 2014)
Finding ways to support the meaningful learning of mathematical procedures and the development of robust fluency with important mathematical skills is an urgent priority for Western mathematics education
As part of a larger body of work exploring different aspects of mathematical fluency, in this study I seek to answer the research questions: 1. How do school mathematics pupils respond to the use of a Confidence assessment (CA) instrument designed to incentivise the eliciting of truthful confidence ratings? How easy or difficult do they find it to understand? How readily or not do they accept it as a formative assessment tool?
Summary
Fluency in important mathematical procedures is recognised as a critical goal within the learning of school mathematics (Gardiner, 2014; National Council of Teachers of Mathematics [NCTM], 2014). C. Foster scale international assessments such as the Programme for International Student Assessment (PISA) and the Trends in International Mathematics and Science Study (TIMSS) succeed in emphasising the development of mathematical fluency without resorting to the low-level rote learning of procedures (Askew, Hodgen, Hossain, & Bretscher, 2010; Fan & Bokhove, 2014; Leung, 2014). The new national curriculum for mathematics in England, for example, emphasises procedural fluency as the first stated aim (Department for Education [DfE], 2013) and provides a political imperative in the UK for developing this important aspect of learning mathematics
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