Transitioning from "It Looks Like" to "It Has To Be" in Geometrical Workspaces: affect and near-to-me attention

Within a practitioner researcher framework, this paper draws on a particular mathematics education theory and aspects of neuroscience to show that, from a learner’s perspective, moving to a deductive reasoning style appropriate to basic Euclidean geometry, can be facilitated, or impeded, by emotion and/or directed attention. This shows that the issue of a person’s deductive reasoning is not a merely cognitive one, but can involve affective aspects related to perception – particularly perception of nearby sense data – and emotion. The mathematics education theory that has been used is that of the Espace de Travail Mathématique, the English translation of which is known as Mathematical Working Spaces (MWS). The aspects of neuroscience that have been used pertain to the distinct processing streams known as top-down and bottom-up attention. The practitioner research perspective is aligned with Mason’s teaching-practice-based ‘noticing’; qualitative data analysed in this report include individual interviews with school teachers on in-service courses and reflective notes from teaching. Basic Euclidean geometry is used as the medium for investigating transition from ‘it looks like’ to a reasoned ‘it has to be’

Talking the talk…but walking the walk? How do non-specialist mathematics teachers come to see themselves as mathematics teachers?

In order to address the shortage of mathematics teachers in England, the UK government has funded various in-service subject knowledge courses for practising teachers, who are not mathematics specialists. These courses aim to develop these teachers’ mathematical subject knowledge (e.g., DfE 2014). In this TAS session we will report on a research project which was set up to investigate how teachers on the in-service programmes offered by our institution developed as teachers of mathematics. We orientated our research around a central research query: How do already qualified, non-specialist mathematics teachers come to see themselves as mathematics teachers? Our previous work (Crisan and Rodd 2011) found that at the end of the course these teachers’ mathematical work showed that they still lacked fluency with mathematics and were far from having secure subject knowledge. However, familiarity with and learning of new maths topics on the course increased their confidence in themselves as learners of mathematics. As the non-specialist mathematics teachers’ confidence in their own mathematical ability increased, we noticed a change on how they talked about themselves as potential mathematics teachers. The teachers became preoccupied with whether and how they will be recognised as mathematics teachers by their colleagues on the course, current school or potential employing schools and mathematics departments. We have many forms of data from the course participants: mathematical work, interviews, teaching observations, written narratives, for example. Analysis of data considers the participants’ developing mathematics teacher identity in terms of ‘engagement, imagination and alignment’ (Wenger 1998). We will be presenting excerpts from some of our case studies to illustrate how the participants negotiated their own trajectories of learning towards a new identity, that of mathematics teachers

Teachers of mathematics to mathematics teachers: a TDA Mathematics Development Programme for Teachers

To address the shortage of mathematics teachers in England, serving teachers, qualified in subjects other than mathematics yet teaching secondary mathematics, were eligible to participate in a Mathematics Development Programme for Teachers (MDPT) commissioned and funded by the Teacher Development Agency (TDA). A research project was set up to investigate how teachers in our 2010-11 cohort developed into mathematics teachers within this Programme. This report indicates how (1) learning new mathematics, (2) developing a view on the nature of mathematics and (3) teaching mathematics in different ways, contribute to a mathematics teacher identity, yet there was a discrepancy between the teachers’ espoused confidence in being a mathematics teacher and their technical mathematical competence

Multilevel governance challenges in transitioning towards a national approach for REDD+:Evidence from 23 subnational REDD+ initiatives

Although REDD+ was conceived as a national approach to reducing emissions from deforestation and forest degradation, many of the early advances have been at the subnational level. It is critical to link these subnational efforts to emerging national REDD+ frameworks, including with respect to finance and benefit distribution, setting reference levels, measurement, reporting and verification (MRV), land policy and safeguards. We use evidence from interviews with proponents from 23 subnational REDD+ initiatives in six countries to characterize the multilevel governance challenges for REDD+. We analyse the differences in perceived challenges between subnational jurisdictional programs and project-based initiatives, and then analyse proponents’ perceptions of the relationship between government policies at multiple levels and these REDD+ initiatives. We find important multilevel governance challenges related to vertical coordination and information sharing and horizontal and inter-sectoral tensions, as well as concerns over accountability, equity and justice. Though the shift to a nested, jurisdictional or national REDD+ is sometimes approached as a technical design issue, this must be accompanied by an understanding of the interests and power relations among actors at different levels. We outline challenges and suggest priority areas for future research and policy, as countries move towards a national REDD+ system

The Role of Sleep in Learning New Meanings for Familiar Words through Stories

Adults often learn new meanings for familiar words, and in doing so they must integrate information about the newly-acquired meanings with existing knowledge about the prior meanings of the words in their mental lexicon. Numerous studies have confirmed the importance of sleep for learning novel word forms (e.g., “cathedruke”) either with or without associated meanings. By teaching participants new meanings for familiar word forms, this is the first study to focus exclusively on the specific role of sleep on learning word meanings. In two experiments participants were trained on new meanings for familiar words through a naturalistic story reading paradigm to minimize explicit learning strategies. Experiment 1 confirmed the benefit of sleep for recall and recognition of word meanings, with better retention after 12 hours including overnight sleep than 12 hours awake. Experiment 2, which was preregistered, further explored this sleep benefit. Recall performance was best in the condition in which participants slept immediately after exposure and were tested soon after they woke up, compared with three conditions which all included an extended period of wake during which they would encounter their normal language environment. The results are consistent with the view that, at least under these learning conditions, a benefit of sleep arises due to passive protection from linguistic interference while asleep, rather than being due to active consolidation

The park is ruining our livelihoods. We support the park! Unravelling the paradox of attitudes to protected areas

Despite considerable field-based innovation and academic scrutiny, the nexus between conservation approaches, local support for parks and park effectiveness remains quite puzzling. Common approaches to understanding notions of environmental justice are to understand distributional and procedural issues, representation in decision making, and recognition of authorities and claims. We took a different approach and analysed environmental justice claims through institutional, ideational and psychological lenses. We sought to understand how the national park could have such broad support from local communities despite their acknowledgement that it severely curtailed their livelihoods. We conducted 100 household interviews in three villages that border Nam Et-Phou Louey National Protected Area. Our study found that villagers 1) hold on to broken promises by the State for agricultural activities and alternative revenues without fully changing forest use behaviours; 2) were influenced heavily by the ‘educational’ programmes by the State; 3) accepted the authority of the State and lack of participation in decision-making based on historical experiences and values; 4) justified their burdens by over-emphasising the positive aspects of the park. Our findings present a complementary framework to explain environmental justice claims, allowing for a nuanced analysis of how people respond to justices and injustices, and specifically how injustices can be identified through proven social science concepts

Pupil Dilation Is Sensitive to Semantic Ambiguity and Acoustic Degradation

Speech comprehension is challenged by background noise, acoustic interference, and linguistic factors, such as the presence of words with more than one meaning (homonyms and homophones). Previous work suggests that homophony in spoken language increases cognitive demand. Here, we measured pupil dilation—a physiological index of cognitive demand—while listeners heard high-ambiguity sentences, containing words with more than one meaning, or well-matched low-ambiguity sentences without ambiguous words. This semantic-ambiguity manipulation was crossed with an acoustic manipulation in two experiments. In Experiment 1, sentences were masked with 30-talker babble at 0 and +6 dB signal-to-noise ratio (SNR), and in Experiment 2, sentences were heard with or without a pink noise masker at –2 dB SNR. Speech comprehension was measured by asking listeners to judge the semantic relatedness of a visual probe word to the previous sentence. In both experiments, comprehension was lower for high- than for low-ambiguity sentences when SNRs were low. Pupils dilated more when sentences included ambiguous words, even when no noise was added (Experiment 2). Pupil also dilated more when SNRs were low. The effect of masking was larger than the effect of ambiguity for performance and pupil responses. This work demonstrates that the presence of homophones, a condition that is ubiquitous in natural language, increases cognitive demand and reduces intelligibility of speech heard with a noisy background

Learning in lectures: Multiple representations

Lectures remain the lynchpin of mathematics teaching at university even with advances in information technology and access to the internet. This paper examines the requirements for learning mathematics and shows how important it is for lecturers to be aware of the different modes of presentation they are using. Ways to assist students to make the connections between different representations are considered, with particular reference to students whose first language is not English

Why Clowns Taste Funny: The Relationship between Humor and Semantic Ambiguity

What makes us laugh? One crucial component of many jokes is the disambiguation of words with multiple meanings. In this functional MRI study of normal participants, the neural mechanisms that underlie our experience of getting a joke that depends on the resolution of semantically ambiguous words were explored. Jokes that contained ambiguous words were compared with sentences that contained ambiguous words but were not funny, as well as to matched verbal jokes that did not depend on semantic ambiguity. The results confirm that both the left inferior temporal gyrus and left inferior frontal gyrus are involved in processing the semantic aspects of language comprehension, while a more widespread network that includes both of these regions and the temporoparietal junction bilaterally is involved in processing humorous verbal jokes when compared with matched nonhumorous material. In addition, hearing jokes was associated with increased activity in a network of subcortical regions, including the amygdala, the ventral striatum, and the midbrain, that have been implicated in experiencing positive reward. Moreover, activity in these regions correlated with the subjective ratings of funniness of the presented material. These results allow a more precise account of how the neural and cognitive processes that are involved in ambiguity resolution contribute to the appreciation of jokes that depend on semantic ambiguity