Towards a socio-ecological perspective of mathematics education

In this theoretical research report we propose a socio-ecological perspective, as relevant for research in mathematics education that takes account of our complex, precarious present and imagined future, while recognising its historical roots. We discuss briefly work that considers the social, political and ecological, and build from this scholarship. A ‘socio-ecological’ perspective considers the social and ecological as entangled, and mathematics (education) as both shaping and shaped by these entanglements. This is a mathematics (education) that gains meaning from questions that emerge in socio-ecological relations. We ground our theoretical argument using a project located in a community living in a polluted region of Mexico, where a river is central to the questions motivating community activism and our research

A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equation

Concerns have been expressed that although learners may solve linear equations correctly they cannot draw on mathematically valid resources to explain their solutions or use their strategies in unfamiliar situations. This article provides a detailed qualitative analysis of the thinking of 15 Grade 8 and Grade 9 learners as they talk about their solutions to linear equations in interviews. The article stems from a study that describes whether learners use mathematically endorsable narratives to explain and justify their solutions. Sfard’s theory of commognition is used to develop a framework for analysis of their discourse. The findings show that all learners use ritualised rather than explorative discourse, characterised by applying strict rules to operations with disobjectified entities. The only mathematical objects they produce endorsed narratives about are positive integers. Thus they do not meet the relevant curriculum requirements. Nevertheless, the analytic tools – adapted from Sfard specifically for the study of linear equations – give a particularly nuanced account of differences in the learners’ ritualised discourse. For example, some learners used endorsed narratives about negative integers, algebraic terms and the structure of an equation when prompted by the interviewer. There is not sufficient evidence to suggest that any learners are in transition to explorative discourse. However, the article shows that learner discourse is a rich resource for teachers to understand the extent to which learners are thinking exploratively, and offers suggestions for how their thinking can be shifted. This is an opportunity for teacher professional development and further research

Student perspectives on group work in support of the learning of mathematics at high school and at a university of technology

This is an Accepted Manuscript of an article published by Taylor & Francis in African Journal of Research in Mathematics, Science and Technology Education on 20 August 2013, available online: http://www.tandfonline.com/10.1080/10288457.2010.10740681.Debates on improving performance in science and engineering at higher education institutions have stressed the need for institutions to adopt pedagogic practices appropriate for the setting. In this paper we contribute to this debate by presenting the results of empirical research conducted in a first-year foundation mathematics course for Civil Engineering students at a University of Technology in South Africa. Using the perspective of learning as participation in a community as a theoretical framework, the paper focuses on a particular type of student learning community, that is, small group work for the learning of mathematics. We use individual interviews to investigate students' perspectives on small group work in support of their learning of mathematics at high school and in the foundation mathematics course. The results suggest that students have considerable experience of working in groups inside and outside the classroom at school, and they identify conditions conducive for group work, including having a sense of belonging in a group. They value group work for providing support that may not be provided by the lecturer, for example, by obtaining alternative explanations (often in their home language), sharing ideas on problem solving, and getting immediate feedback. We argue that higher education institutions should draw on students' experience of group work and create the space for this type of student learning community both inside and outside the mathematics classroom. We also use the empirical results to develop the notion of “community” as described in the theoretical perspective of learning

(Re)imagining spatialities for equity in mathematics education

Contemporary discourse about the ‘opening’/‘closing’ of schools and what is ‘inside’/‘outside’ the curriculum potentially exacerbates existing inequities in mathematics education. This paper explores how different spatial imaginaries might advance or hinder efforts to deeply and systematically pursue equity. We use critical postcolonial thought for our (re)imaginings in the South African context. We argue that viewing the school, the mathematics curriculum, and language as nouned, bounded, spatial objects highlights what needs attention and for whom, but also points to the indelible, structural nature of exclusion. We propose a notion of spatiality as experienced encountering. This recognises all people and their practices as strategic agents, and emphasises relations between people, but also between the mind, body and Earth.Online Paper Presentation is available at: https://zivahub.uct.ac.za/articles/presentation/_Re_Imagining_Spatialities_for_Equity_in_Mathematics_Education_MES11/1657859

Successful students’ negotiation of township schooling in contemporary South Africa

This article draws on data from a larger longitudinal qualitative case study which is tracking the progress of students over the course of their undergraduate degrees at a South African university. For this paper, we used background questionnaires and semi-structured interviews with 62 first-year students from working-class, township schools who were first registered for Extended Degree Programmes in 2009. The article draws on post-structuralist theory on learning and identity to describe and analyse the participants’ perspectives on how they negotiated their high school contexts. We analyse the subject positions in which participants invested, as well as how they negotiated their way through social networks and used resources. Our data illustrate the ways in which students had to carry the burden of negotiating their way through home, school and neighbourhood spaces that were generally not conducive to learning. Nevertheless, participants consciously positioned themselves as agents. They were resilient, motivated and took highly strategic adult decisions about their learning. We argue that a focus on how successful students negotiate their environments challenges the pathologising paradigm of “disadvantage” that characterises research and debates in higher education. It also offers an additional lens for admissions processes and for providing appropriate intervention strategies in the tertiary setting

MIKE-SHE integrated groundwater and surface water model used to simulate scenario hydrology for input to DRIFT-ARID: the Mokolo River case study

A fully integrated, physically-based MIKE SHE/MIKE11 model was developed for the Mokolo River basin flow system to simulate key hydraulic and hydrologic indicator inputs to the Downstream Response to Imposed Flow Transformation for Arid Rivers (DRIFT-ARID) decision support system (DSS). The DRIFT-ARID tool is used in this study to define environmental water requirements (EWR) for non-perennial river flow systems in South Africa to facilitate ecosystembased management of water resources as required by the National Water Act (Act No. 36 of 1998). Fifty years of distributed daily climate data (1950 to 2000) were used to calibrate the model against decades of daily discharge data at various gauges, measurements of Mokolo Dam stage levels, and one-time groundwater level measurements at hundreds of wells throughout the basin. Though the calibrated model captures much of the seasonal and post-event stream discharge response characteristics, lack of sub-daily climate and stream discharge data limits the ability to calibrate the model to event-level system response (i.e. peak flows). In addition, lack of basic subsurface hydrogeologic characterisation and transient groundwater level data limits the ability to calibrate the groundwater flow model, and therefore baseflow response, to a high level. Despite these limitations, the calibrated model was used to simulate changes in hydrologic and hydraulic indicators at five study sites within the basin for five 50-year land-use change scenarios, including a present-day (with dam), natural conditions (no development/irrigation), and conversion of present-day irrigation to game farm, mine/city expansion, and a combination of the last two. Challenges and recommendations for simulating the range of non-perennial systems are presented.Keywords: hydrology, non-perennial, MIKE SHE, integrated surface and groundwater modellin

Supporting families managing childhood eczema:Developing and optimising Eczema Care Online using qualitative research

Background: childhood eczema is often poorly controlled due to under-use of emollients and topical corticosteroids. Parents/carers report practical and psychosocial barriers to managing their child’s eczema, including child resistance. Online interventions could potentially support parents/carers; however, rigorous research developing such interventions has been limited. Aim: to develop an online behavioural intervention to help parents/carers manage and co-manage their child’s eczema. Design and setting: Intervention development using a theory-, evidence- and Person-Based Approach with qualitative research. Methods: a systematic review and qualitative synthesis (32 studies) and interviews with parents/carers (N=30) were used to identify barriers and facilitators to effective eczema management, and a prototype intervention was developed. Think-aloud interviews with parents/carers (N=25) were then used to optimise the intervention to increase its acceptability and feasibility. Results: qualitative research identified that parents/carers had concerns about using emollients and topical corticosteroids; incomplete knowledge and skills around managing eczema; and reluctance to transitioning to co-managing eczema with their child. Think-aloud interviews highlighted that while experienced parents/carers felt they knew how to manage eczema, some information about how to use treatments was still new. Techniques for addressing barriers included: providing a rationale explaining how emollients and topical corticosteroids work; demonstrating how to use treatments; and highlighting that the intervention provided new, up-to-date information. Conclusions: parents/carers need support in effectively managing and co-managing their child’s eczema. The key output of this research is Eczema Care Online (ECO) for Families; an online intervention for parents/carers of children with eczema, which is being evaluated in a randomised trial

DRIFT-ARID: A method for assessing environmental water requirements (EWRs) for non-perennial rivers

Environmental water requirement (EWR) assessment methods, for ascertaining how much water should be retained in rivers to sustain ecological functioning and desired levels of biodiversity, have mostly been developed for perennial rivers. Despite non-perennial rivers comprising about 30–50% of the world’s freshwater systems, data on their hydrology, biota and ecological functioning are sparse. Current EWR assessments require hydrological and other data that may not be available for such rivers and some adaptation in the methods used seems necessary. DRIFT is an EWR method for perennial (or near-perennial) rivers that has been developed in South Africa over the past two decades and is now widely applied nationally and internationally. When applied to the semi-permanent Mokolo River, challenges particular to, or accentuated by, non-perennial rivers included the reliable simulation of hydrological data, the extent of acceptable extrapolation of data, difficulties in predicting surface-water connectivity along the river, and the location and resilience of pools, as well as whether it was possible to identify a reference (natural) condition. DRIFT-ARID, reported on here, is an adaptation of the DRIFT approach to begin addressing these and other issues. It consists of 11 phases containing 29 activities.Keywords: EWR, non-perennial, DRIFT, DS

Eczema Care Online: development and qualitative optimisation of an online behavioural intervention to support self-management in young people with eczema.

OBJECTIVES: To describe the development of Eczema Care Online (ECO), an online behaviour change intervention for young people with eczema (phase I); and explore and optimise the acceptability of ECO among this target group using think-aloud interviews (phase II). METHODS: Theory-based, evidence-based and person-based approaches to intervention development were used. In phase I, a qualitative systematic review and qualitative interviews developed an in-depth understanding of the needs and challenges of young people with eczema. Guiding principles highlighted key intervention design objectives and features to address the needs of this target group to maximise user engagement. Behavioural analysis and logic modelling developed ECO's hypothesised programme theory. In phase II, qualitative think-aloud interviews were carried out with 28 young people with eczema and the intervention was optimised based on their feedback. RESULTS: The final intervention aimed to reduce eczema severity by supporting treatment use (emollients, topical corticosteroids/topical calcineurin inhibitors), management of irritants/triggers, emotional management and reducing scratching. Generally, young people expressed positive views of intervention content and design in think-aloud interviews. Quotes and stories from other young people with eczema and ECO's focus on living with eczema (not just topical treatments) were valuable for normalising eczema. Young people believed ECO addressed knowledge gaps they had from childhood and the safety information about topical corticosteroids was reassuring. Negative feedback was used to modify ECO. CONCLUSIONS: A prototype of the ECO intervention was developed using rigorous and complementary intervention development approaches. Subsequent think-aloud interviews helped optimise the intervention, demonstrated ECO is likely to be acceptable to this target group, and provided support for our guiding principles including key design objectives and features to consider when developing interventions for this population. A randomised controlled trial and process evaluation of the intervention is underway to assess effectiveness and explore user engagement with the intervention's behavioural goals