Observing for Mathematical Proficiency in Secondary Mathematics Education

Abstract

One of the critical aspects of a mathematics teacher’s work is analysing learners’ mathematical work. Mathematics tasks can prompt the development of different students’ mathematical abilities, and it is of relevance to address the various promoted skills when assessing students’ mathematical work. However, this is a challenging task, given that students’ work is commonly based on procedural knowledge, which is only one of the skills students can work on. Attentive to teachers’ needs to assess students’ learning (summatively and formatively), this chapter uses Kilpatrick J, Swafford J, Findell B, The strands of mathematical proficiency. In: Kilpatrick J, Swafford J, Findell B (eds) Adding it up: helping children learn mathematics [electronic resource]. National Academy Press, Washington, DC, pp 115–155, 2001) model of mathematical proficiency to study examples of students’ work when solving mathematical tasks. From those examples we observe how the five strands of mathematical proficiency are demonstrated by learners as they bring forward various mathematics through their mathematical work. By observing students’ work on mathematical proficiency, teachers are able to acknowledge students’ mathematical abilities, address students’ difficulties, assist students’ knowledge development and, as a consequence, plan and structure their classes and activities focused on students’ needs.