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The majority of children in mainstream (no fee, poorly resourced, African language dominant) public schools in South Africa fall significantly behind curricular norms in mathematics by Grade 3; the early learning gap grows across time. The provision of quality instructional materials is a well-recognised component of effective strategies to improve early grade mathematics in low- and middle-income contexts. However, there has been little explication of what constitutes quality instructional materials, nor long-term design work to contribute theory to this instructional design challenge. Across 15 years, the author has been working in an education design hub with teacher educators and teachers in the rural Eastern Cape, with the goal of improving early grade mathematics. The gains in mathematics performance have been among the most significant reported in research literature. This paper presents the design principles emerging from the work. Engaging the theoretical layers discussed by diSessa and Cobb, the paper contributes to design theory by emphasising the relationship between explicit instructional assumptions and design principles, integrating four ontological categories (motive, pedagogy, language use and mathematical meaning-making). Since 2011, the Department of Basic Education has provided learner workbooks to support teaching and learning in foundation phase mathematics at system scale. It is hoped that this paper will contribute to the ongoing development of this vital national resource. The paper makes explicit instructional assumptions and design principles (available for critique, adaptation, and refinement), and provides a more nuanced framework through which to assess and improve materials across time. [ABSTRACT FROM AUTHOR]

Research on mathematical equivalence, and to some extent, on number structure in early grade mathematics, has shown that most students at primary and secondary levels understand these concepts instrumentally rather than relationally. The study reported in this paper uses a design research approach to explore both mathematical equivalence and number structure in a primary pre-service teacher education programme at a university in South Africa and reports on an intervention strategy intended to culminate in developing design principles comprising guidelines for the effective teaching of number structure and mathematics equivalence in primary pre-service teacher education programmes. The mixed method study comprises 70 first-year primary pre-service teachers (PSTs) and a teacher educator. The PSTs wrote pre- and post-tests, and were interviewed following the pre-test. Skemp's notion of relational and instrumental understanding guided the design of the intervention and the analysis of the data. The results from the study indicates that PSTs' understanding of the notion of equivalence is similar to what has been reported for students in schools, and that there were some learning gains in the post-test results. Based on the findings from the study in general, some emergent design principles are proposed. [ABSTRACT FROM AUTHOR]

Test validation may more aptly be conceived of as the process of designing language tests responsibly. While a good test gains in reputation as it is administered over time, the early stages of its validation are perhaps the most critical. There is now general agreement that the validation process should be reported in the form of an argument that brings together multiple sets of evidence to justify the design and implementation of the measurement instrument, the language test. The format of such integration is, however, still contestable ground. Referring to an example of language test design and development, this paper seeks to demonstrate how a framework for responsible test design may be employed to achieve such an integrated argument, as well as how two of the methodological tools most frequently employed to muster empirical evidence for validating test design, namely classical test theory (CTT) and Rasch analyses, complement each other in designing tests responsibly. While most language tests designed in South Africa have used CTT, the employment of Rasch analyses has been more limited. A secondary aim of the paper is therefore to provide applied linguists who work in the subfield of language testing with an example of how the latter kind of analysis can complement the former. In all, however, these disparate approaches must be integrated into the theoretical justification for the development of language tests, in order to satisfy a number of conditions for their responsible design. [ABSTRACT FROM AUTHOR]

Increasing human demands for ecosystem services due to climate change, population growth, poverty, lack of employment, tourism, and concomitant coastal property development threatens adaptive capacity in South Africa's coastlines. Adaptation strategies frequently propose ecosystem-based adaptation (EBA) as a model for transformative change. However, several studies point to difficulties implementing EBA across the world. The aim of this paper is to assess to what extent social-ecological systems approaches and common pool resource (CPR) governance theories could inform EBA. Data obtained from interviews and surveys with policy makers and residents in South Africa's Garden Route District were interpreted using the robustness framework (RF) and the design principles (DPs), two common tools for analyzing CPR governance. We found that the Garden Route coast is threatened by negative interactions between hard public and private infrastructures and ecological infrastructures (the cornerstone of EBA) which are driven by weak local government bodies and asymmetrical power relations. By coding the data for elements/interactions within the RF and then identifying and mapping the DPs onto the RF, we also revealed ways to leverage transformative EBA in the Garden Route. Our analyses suggest that the interactions between human-made and ecological infrastructures, as well as power relation, should be at the core of any development debate. Trade-offs should aim for maximum congruence between sustainability and equity in ecosystem services provisioning. This paper provides some considerations for researchers and decision makers to leverage transformative EBA that could potentially apply to areas experiencing similar challenges. [ABSTRACT FROM AUTHOR]