A longstanding problem in mathematics education has been to determine the knowledge that teachers need in order to teach mathematics effectively. It is generally agreed that teachers need a more advanced knowledge of the mathematical content that they are teaching. That is, teachers must know more about the content that they are teaching than their students and also know more than simply how to "do the math" at a particular grade level. At the same time, research does not clearly indicate what advanced mathematical knowledge (AMK) is useful in teaching or how it can be developed and identified in teachers. In particular, the potential AMK that is useful for teaching is too vast to be enumerated and may involve a great deal of tacit knowledge, which might be difficult to detect through observations of practice alone. In the last decade, researchers have identified that teaching practice entails a specialized knowledge of mathematics but the role of advanced mathematical knowledge in teaching practice remains unclear. However, the construct of horizon content knowledge (HCK) has emerged in the literature as a promising tool for characterizing AMK as it relates specifically to teaching practice. I propose an operationalization of HCK and then use that as a lens for analyzing the knowledge resources that a fourth and fifth grade teacher draw on in their encounters with the mathematical horizon. The analysis identifies what factors contribute to teachers' encounters with the horizon, characterizes the knowledge resources, or HCK, that teachers draw on to make sense of mathematics they engage with during their horizon encounters, and explores how HCK affords and constrains teachers' ability to navigate mathematical territory. My findings suggest that experienced teachers' HCK includes a situated, professional teaching knowledge that, while sometimes non-mathematical in nature, informs their understanding of mathematical content and teaching decisions. This professional teaching knowledge guides how teachers use and generate mathematical structures that sometimes align with established mathematical structures and in other cases do not. These findings have implications regarding the way in which the development of AMK is approached relative to teacher education, ongoing professional development, and curriculum design.

The South African Department of Basic Education and Department of Higher Education and Training (2011a) made a call for the development of mathematics knowledge and practice standards in the foundation phase to serve as guidelines for the preparation of foundation phase teachers in the different higher education institutions. The purpose of the study in hand was to develop draft knowledge and practice standards in the number domain for the preparation of foundation phase teachers (referred to as mathematics knowledge and practice standards). These standards have to be refined and improved in further studies and should in the end serve as knowledge and practice standards for the preparation of foundation phase teachers in South Africa. Through a conceptual qualitative research methodology the researcher purposefully collected documents and analysed them through content analysis. The data-gathering process took place in three phases. During the first phase, policy documents with regard to general standards for teacher preparation, written school curriculum documents and mathematical standards for the preparation of foundation phase teachers in South Africa, the United States of America, Australia and the Netherlands were gathered. The second phase involved the purposeful gathering of articles, research reports and teacher preparation textbooks with regard to the preparation of foundation phase teachers to teach the number domain. During the first and second phases of data gathering, the documents were analysed according to mathematical knowledge for teaching as described by Ball, Thames and Phelps (2008) and the first draft of mathematical knowledge and practice standards was compiled. During the third data-gathering phase, critical evaluation reports were gathered from experts in the field of mathematics education (including researchers at universities and practising foundation phase teachers). The critical evaluation includes gaps/shortcomings in the draft mathematics knowledge and practice standards, as well as comments with regard to the clarity, applicability and functionality of the document. The draft mathematics knowledge and practice standards (MKPSs) for the preparation of foundation phase teachers include: Standard 1: Common content knowledge – The foundation phase teacher has a clear understanding of the common content knowledge of the number domain. Standard 2: Specialised content knowledge – The foundation phase teacher has a clear understanding of the specialised content of the number domain. Standard 3: Knowledge at the mathematical horizon – The foundation phase teacher understands how mathematical themes in the number domain relate to other themes in the different foundation phase year groups and in other phases. Standard 4: Knowledge of content and teaching – The foundation phase teacher is able to plan lessons and knows how to teach the number domain. Standard 5: Knowledge of content and learners – The foundation phase teacher knows the foundation phase learners and knows how they learn the number domain. Standard 6: Knowledge of content and the curriculum – The foundation phase teacher understands the South African school curriculum, as well as international trends in the school curriculum concerning the number domain. Those experts in the field of mathematics education in the foundation phase who participated in the study all indicated that the mathematics knowledge and practice standards in the number domain have the potential to boost the preparation of foundation phase teachers in South Africa. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

The South African Department of Basic Education and Department of Higher Education and Training (2011a) made a call for the development of mathematics knowledge and practice standards in the foundation phase to serve as guidelines for the preparation of foundation phase teachers in the different higher education institutions. The purpose of the study in hand was to develop draft knowledge and practice standards in the number domain for the preparation of foundation phase teachers (referred to as mathematics knowledge and practice standards). These standards have to be refined and improved in further studies and should in the end serve as knowledge and practice standards for the preparation of foundation phase teachers in South Africa. Through a conceptual qualitative research methodology the researcher purposefully collected documents and analysed them through content analysis. The data-gathering process took place in three phases. During the first phase, policy documents with regard to general standards for teacher preparation, written school curriculum documents and mathematical standards for the preparation of foundation phase teachers in South Africa, the United States of America, Australia and the Netherlands were gathered. The second phase involved the purposeful gathering of articles, research reports and teacher preparation textbooks with regard to the preparation of foundation phase teachers to teach the number domain. During the first and second phases of data gathering, the documents were analysed according to mathematical knowledge for teaching as described by Ball, Thames and Phelps (2008) and the first draft of mathematical knowledge and practice standards was compiled. During the third data-gathering phase, critical evaluation reports were gathered from experts in the field of mathematics education (including researchers at universities and practising foundation phase teachers). The critical evaluation includes gaps/shortcomings in the draft mathematics knowledge and practice standards, as well as comments with regard to the clarity, applicability and functionality of the document. The draft mathematics knowledge and practice standards (MKPSs) for the preparation of foundation phase teachers include: Standard 1: Common content knowledge – The foundation phase teacher has a clear understanding of the common content knowledge of the number domain. Standard 2: Specialised content knowledge – The foundation phase teacher has a clear understanding of the specialised content of the number domain. Standard 3: Knowledge at the mathematical horizon – The foundation phase teacher understands how mathematical themes in the number domain relate to other themes in the different foundation phase year groups and in other phases. Standard 4: Knowledge of content and teaching – The foundation phase teacher is able to plan lessons and knows how to teach the number domain. Standard 5: Knowledge of content and learners – The foundation phase teacher knows the foundation phase learners and knows how they learn the number domain. Standard 6: Knowledge of content and the curriculum – The foundation phase teacher understands the South African school curriculum, as well as international trends in the school curriculum concerning the number domain. Those experts in the field of mathematics education in the foundation phase who participated in the study all indicated that the mathematics knowledge and practice standards in the number domain have the potential to boost the preparation of foundation phase teachers in South Africa. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014