Scielo RSS http://www.scielo.org.za/rss.php?pid=2223-768220130002&lang=en vol. 3 num. 2 lang. en http://www.scielo.org.za/img/en/fbpelogp.gif http://www.scielo.org.za http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2223-76822013000200001&lng=en&nrm=iso&tlng=en http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2223-76822013000200002&lng=en&nrm=iso&tlng=en Children's learning of early number bonds is a significant issue in South African schools because evidence shows that flexible and efficient (fluent and reasoned) knowledge of number bonds to 20 correlates with success at the end of primary schooling, yet the evidence is that many South African students are over-reliant on inefficient counting methods. This paper focuses on why and how treating early number bonds as scientific concepts may be the key to raising learners' attainment in these. The paper argues that teacher mediation is crucial and that mediation for learning scientific concepts has to be meaningful, relational and transcendent. This theoretical position is illustrated with examples from a dynamic assessment interview with a Grade 2 learner carried out as part of the Wits Maths Connect - Primary project. It concludes by suggesting the implications for teacher education and professional development. http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2223-76822013000200003&lng=en&nrm=iso&tlng=en This article describes a comprehensive and novel approach to assessment in early numeracy. Topics include the significance of early numeracy, developing a nomenclature for early numeracy, and describing the context for the development of this approach to assessment. The largely unrealised importance of numerals and numeral sequences in early numeracy, the significance of counting and its distinction from saying a number word sequence, the important topics of structuring numbers in the range 1 to 20 and conceptual place value, the Learning Framework in Number and its use in profiling children's early numeracy knowledge, and important assessment tasks are explored. http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2223-76822013000200004&lng=en&nrm=iso&tlng=en Opening up space for authentic inquiry in preschool can influence the extent to which children can make use of their growing mathematical and linguistic understandings to make sense of themselves and the world around them. Authentic inquiry here refers to investigation that arises naturally from the interests and questions of the children as they experience the learning environment. Three authentic examples are presented from the work of four- to five-year-old children in the domains of mathematics and literacy development to illustrate how the two domains need to be viewed as intertwined at the preschool level. Reflections are also offered on the role of the learning environment, the role of curriculum and the role of teachers and other adults in the learning process. This manuscript is based on a plenary address given in Grahamstown, South Africa at the SARAECE Research and Development week: "Strengthening Foundation Phase Education" conference at Rhodes Universityin September 2012. http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2223-76822013000200005&lng=en&nrm=iso&tlng=en The article proposes that cognitive developmental psychology and cognitive neuroscience theory need to feature more prominently in the theoretical frameworks for South African research on language in mathematics learning in the early years of school. I argue that, considering the state of mathematics learning in the foundation phase and the conundrum around the language of learning and teaching debate in the country, we need more integrated theoretical work for equally integrated analyses of learners and learning, moving beyond the practice of drawing from mostly single theories, such as bilingual education theory, or sociocultural theory. The article explains the reasoning behind the proposition for an expansion of the theoretical work in this field, claiming that policy decisions about language of learning and teaching depend on empirical research that includes theories from the cognitive sciences as framework. http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2223-76822013000200006&lng=en&nrm=iso&tlng=en This paper reports on the development of a Learning Pathway for Number (LPN) with the aim of facilitating the teaching and learning of whole number in the early primary grades (Grades R - 4) within the South African educational context. The development of the LPN was based on the Dutch Learning/Teaching Trajectory for Whole Number (Van den Heuvel-Panhuizen, 2001). This paper describes a case study that presents the development of the LPN with three teacher groups (teachers from a school improvement project, teachers from high-performing schools and pre-service student teachers). The LPN is a conceptual framework based on five learning/teaching principles, namely the context, level, activity, interaction and the guidance principles. The benefit of this pedagogic tool adapted and refined for the South African context is that it provides a longitudinal view, highlighting milestones in the learning of number with the aim of deepening learners' conceptual understanding of number over time. This case study reveals the importance of a devise that enables teachers to reflect on their mathematics content and pedagogy and bridges the theory-practice divide. It also highlights the critical issue of language and the use of appropriate terminology and activities in the classroom. http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2223-76822013000200007&lng=en&nrm=iso&tlng=en This paper explores two foundation phase teachers' example spaces (a space in the mind where examples exist) when teaching number-related topics in relation to snapshots of their content knowledge (CK). Data was collected during a pilot primary maths for teaching course that included assessments of teacher content knowledge (CK). An analysis of a content-knowledge focused pre-test developed for the larger study indicated a relatively high score for one teacher and a low score for the other. Using Rowland's (2008) framework, an analysis of classroom practice showed associations between a higher CK and the extent of a teacher's example space and more coherent connections between different representational forms. Although no hard claims or generalisations of the link between teachers' example spaces and their level of mathematics content knowledge can be made here, this study reinforces evidence of the need to increase teachers' CK from a pedagogic perspective in order to raise the level of mathematics teaching and learning in the South African landscape. http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2223-76822013000200008&lng=en&nrm=iso&tlng=en A number of research studies have suggested that specific pedagogic strategies can have a positive impact on learning, and in turn, have a positive impact on school performance, in particular for children being schooled in disadvantaged contexts. This analysis describes and measures how four of these pedagogic strategies identified in research - the pacing of a lesson, the sequence and coherence of a lesson, cognitive demand and the nature of feedback within a lesson - are displayed in higher and lower performing schools located in lower-income communities in the Western Cape. The analysis forms part of a broader research project, SPADE (Schools Performing Above Demographic Expectation), and is based on fifteen video-recorded Grade 3 numeracy lessons. The analysis suggests a relationship between specific pedagogic strategies and higher performance for individual learners and for schools. The analysis also identifies further effective pedagogic strategies in higher performing schools in lower-income communities. http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2223-76822013000200009&lng=en&nrm=iso&tlng=en In this paper we examine the extent of the focus on number sense, enabled and accompanied by the development of efficient strategies for mental maths, in the foundation and intermediate phase. We do this through documentary analysis of the Curriculum and Assessment Policy Statements (CAPS) for these phases and the Annual National Assessments (ANAs). We argue that number sense and mental agility are critical for the development and understanding of algorithms and algebraic thinking introduced in the intermediate phase. However, we note from our work with learners, and broader evidence in the South African landscape, that counting-based strategies in the foundation phase are replaced in the intermediate phase with traditional algorithms. We share experiences in the form of vignettes to illuminate this problem. Whilst literature and the CAPS curriculum emphasise the important role of mental computation within number sense, we note that the ANAs do not include a "mental mathematics" component. This absence in assessment, where assessment often drives teaching, is problematic. We conclude with the suggestion that research be conducted into the viability/appropriateness of an orally administered mental mathematics assessment component in the ANAs as a way to establish a focus on number sense across the foundation and intermediate phases.