Introducing a symbolic interactionist approach on teaching mathematics: the case of revoicing as an interactional strategy in the teaching of probability

This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher’s role in the negotiation of meaning. Using methods inspired by grounded theory, patterns of teachers’ interaction are categorized. The results show how teachers’ actions, interpretations and intentions form interactional strategies that guide the negotiation of meaning in the classroom. The theoretical case of revoicing as a teacher action, together with interpretations of mathematical objects from probability theory, is used to exemplify conclusions from the proposed perspective. Data are generated from a lesson sequence with two teachers working with known and unknown constant sample spaces with their classes. In the lessons presented in this article, the focus is on negotiations of the meaning of chance. The analysis revealed how the teachers indicate their interpretations of mathematical objects and intentions to the students to different degrees and, by doing so, create opportunities for the students to ascribe meaning to these objects. The discussion contrasts the findings with possible interpretations from other perspectives on teaching.     

An exploration of the feature-positive effect in adult humans

Experiment 1 compared the acquisition of a feature-positive and a feature-negative discrimination in humans. In the former, an outcome was signaled by two stimuli together, but not by one of these stimuli alone. In the latter, the outcome was signaled by one stimulus alone, but not by two stimuli together. Using a within-group design, the experiment revealed that the feature-positive discrimination was acquired more readily than the feature-negative discrimination. Experiment 2 tested an explanation for these results, based on the Rescorla-Wagner theory, by examining how novel discriminations, based on a combination of a feature-positive and a feature-negative discrimination, were solved. The results did not accord with predictions from the theory. Alternative explanations for the results are considered.     

Theoretical competence models,tests and designs

Educational Assessment, Evaluation and Accountability -     

Infant-directed speech does not always involve exaggerated vowel distinctions: Evidence from Danish

This study compared the acoustic properties of 26 (100% female, 100% monolingual) Danish caregivers' spontaneous speech addressed to their 11- to 24-month-old infants (infant-directed speech, IDS) and an adult experimenter (adult-directed speech, ADS). The data were collected between 2016 and 2018 in Aarhus, Denmark. Prosodic properties of Danish IDS conformed to cross-linguistic patterns, with a higher pitch, greater pitch variability, and slower articulation rate than ADS. However, an acoustic analysis of vocalic properties revealed that Danish IDS had a reduced or similar vowel space, higher within-vowel variability, raised formants, and lower degree of vowel discriminability compared to ADS. None of the measures, except articulation rate, showed age-related differences. These results push for future research to conduct theory-driven comparisons across languages with distinct phonological systems.     

Learning to assess and evaluate complex realities

Educational Assessment, Evaluation and Accountability -     

Creating effective teaching and learning environments: Building a positive behavioural support (PBS) model for UK special schools

The importance of reducing restraint and restrictive interventions in special schools has been recognised across the four nations of the UK. Government guidance for England and Wales, and recommendations produced by Restraint Reduction Scotland, both reference Positive behavioural support (PBS) as an evidence-based approach that can be used to proactively support pupils with, or at risk of, behaviours that challenge. The Department of Education of Northern Ireland recommends the development of behaviour support plans to support children with special education needs and disabilities. Special schools, however, also have a responsibility to set high expectations for every pupil, to provide access to the respective national curricula and to meet individual needs. School-wide positive behavioural support (SW-PBS), originated in the USA in the 1990s in response to a body of evidence that showed improved social and academic outcomes when behavioural interventions were implemented across whole school settings. It is increasingly being adopted in the UK. Drawing upon examples from schools in England and Wales with which the authors are familiar, this paper outlines the rationale for a special schools' model of SW-PBS and illustrates the ways in which this can be adjusted to meet the specific needs of each setting.

Key Points

• Reducing restraint and restrictive interventions in schools is a high priority across all four nations of the UK.
• Special schools also have a responsibility to provide children with special education needs and disabilities positive learning environments that maximise learning opportunities and meet individual needs.
• School-wide positive behaviour support (SW-PBS) provides a useful framework to help special schools meet these expectations.