| 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. |
