Broadening the Content and Curriculum Horizon for all Mathematics Teachers

• In Event: Defining and Measuring What Math and Science Teachers Need to Know: Implications for Professional Development

Abstract

The knowledge and understanding that teachers possess about each topic of the mathematics curriculum, as well as their understanding of how topics connect with each other, are important components of teachers’ mathematical knowledge (e.g. Ma, 1999). In this paper we identify and discuss tasks of teaching mathematics that require knowledge of both school mathematics beyond the specific content being taught and of the underlying structures of the discipline. Furthermore, we discuss how teachers’ knowledge at the mathematical horizon may influence how teachers approach teaching and their students’ learning.
Building on the Mathematical Knowledge for Teaching (MKT) framework (Ball, Thames, & Phelps, 2008; Hill, Rowan, & Ball, 2005) we investigate knowledge that “supports a kind of awareness, sensibility, disposition that informs, orients and culturally frames instructional practice” (Ball & Bass, 2009). This kind of knowledge, referred to as Horizon Content Knowledge (HCK), involves being cognizant of the large mathematical and curricular landscape in which the present experience and instruction is situated (Ball & Bass, 2009, p. 5). HCK plays a crucial role in teachers’ knowledge and influences their instructional practices, which in turn affect students’ current and future learning. Such knowledge necessarily influences the nature of the tasks teachers set and how they are implemented in the classroom. Therefore, it is important to investigate what constitutes HCK, and the interplay between the different types of knowledge and how they affect practice.
Based on studies in Ireland (Author3), Norway (Authors1, 2011; Authors2, 2009) and Portugal (Author2, 2009; Author2 et al., 2011a, b), we look at how teachers perform their tasks of teaching. Data gathered from classroom practices (audio and video recordings), interviews and results from using measures of MKT are analyzed. Our aim is to get a better understanding of HCK and teachers’ ideas about their needs for HCK in order to be able to fully tackle every aspect of each topic, and to ensure that learning takes place.
With a focus on the HCK domain of MKT, we give examples of teaching situations where teachers’ awareness/lack of awareness of the discipline, influences the work of teaching. We discuss how HCK influences the way in which teachers develop their tasks of teaching and analyze discussions with teachers about the knowledge needed in order to promote teaching for and with understanding. We discuss examples from primary school, where HCK enhanced or would have enhanced the teaching. Examples include teachers considering properties of numbers and operations with reference to a set of numbers used at a particular class level, defining odd and even numbers, defining convex and concave polygons, and proving that any polygon can be triangulated in more than one way.
Results from this study could inform teacher educators about the design of mathematics education courses that take HCK into account, they could provide coherence for professional development programs for teachers of all grade levels, and inform policy makers regarding decisions about teachers’ mathematical knowledge for teaching requirements.

Authors

• Arne Jakobsen, University of Stavanger

• Mark Hoover Thames, University of Michigan

• Miguel Ribeiro

• Sean F. Delaney, Marino Institute of Education