Teachers’ appraisals of adjectives relating to mathematics tasks

Curricular implementations are unlikely to deliver the anticipated benefits for mathematics learners if written guidance to teachers is interpreted and enacted differently from the ways that policymakers and curriculum designers intend. One way in which this could happen is in relation to the mathematics tasks that teachers deploy in the classroom. Teachers and curriculum designers have developed an extensive vocabulary for describing tasks, using adjectives such as ‘rich’, ‘open’, ‘real-life’, ‘engaging’ and so on. But do teachers have a shared understanding of what these adjectives mean when they are applied to mathematics tasks? In Study 1 we investigated teachers’ appraisals of adjectives used to describe mathematics tasks, finding that task appraisals vary on seven dimensions, which we termed engagement, demand, routineness, strangeness, inquiry, context and interactivity. In Study 2, focusing on the five most prominent dimensions, we investigated whether teachers have a shared understanding of the meaning of adjectives when applied to mathematics tasks. We found that there was some agreement about inquiry and context, some disagreement about routineness, and clear disagreement about engagement and demand. We conclude that at least some adjectives commonly used to describe tasks are interpreted very differently by different teachers. Implications for how tasks might be discussed meaningfully by teachers, teacher educators and curriculum designers are highlighted

Exploiting unexpected situations in the mathematics classroom

The professional development of mathematics teachers needs to support teachers in orchestrating the mathematics classroom in ways that enable them to respond flexibly and productively to the unexpected. When a situation arises in the classroom which is not connected in an obvious way to the mathematical learning intentions of the lesson, it can be challenging for the teacher to improvise so as to craft this situation into an opportunity for doing and learning mathematics. In this study, as teacher-researcher I maintained a record of unexpected situations as they arose in my own secondary mathematics classroom. Details are given of four unexpected situations which I found ways to exploit mathematically, and these are analysed to highlight factors which may enhance a mathematics teacher’s preparedness for dealing with the unexpected. The results of this study indicate that deviating from the intended lesson to exploit an unexpected situation in which students have shown some interest can lead them into enjoyable and worthwhile mathematical engagement

The consolidation of implicit sequence memory in obstructive sleep apnea

Obstructive Sleep Apnea (OSA) Syndrome is a relatively frequent sleep disorder characterized by disrupted sleep patterns. It is a well-established fact that sleep has beneficial effect on memory consolidation by enhancing neural plasticity. Implicit sequence learning is a prominent component of skill learning. However, the formation and consolidation of this fundamental learning mechanism remains poorly understood in OSA. In the present study we examined the consolidation of different aspects of implicit sequence learning in patients with OSA. We used the Alternating Serial Reaction Time task to measure general skill learning and sequence-specific learning. There were two sessions: a learning phase and a testing phase, separated by a 10-hour offline period with sleep. Our data showed differences in offline changes of general skill learning between the OSA and control group. The control group demonstrated offline improvement from evening to morning, while the OSA group did not. In contrast, we did not observe differences between the groups in offline changes in sequence-specific learning. Our findings suggest that disrupted sleep in OSA differently affects neural circuits involved in the consolidation of sequence learning