Test-driven teaching and care for mathematics learning

Abstract

In Icelandic secondary schools, students take frequent tests and submit homework for which they are graded. The tests have a significant impact on teaching and learning because students are often very busy succeeding on exams, and teachers spend considerable time and energy preparing exams, preparing students for exams and reviewing exams (Hafdís Ingvarsdóttir, 2018; Laufey Petrea Magnúsdóttir, 2015). I discuss this test-driven teaching method based on the philosophical perspective of care for mathematics learning (Watson, 2021). That perspective combines two ideas about mathematics teaching: caring for students and caring for mathematics. I also explicitly include the dimension of caring for the community in this concept.

Caring for students is conceptualised in the philosophical tradition of care ethics (Held, 2006; Noddings, 2012) while caring for mathematics is a notion borrowed from the research tradition in mathematics education (Hackenberg, 2005; Mason, 2009; Mason & Hanna, 2016; Watson, 2021). Caring for students entails listening to them to understand their experiences and the needs they express. It includes feeling a pull to meet the student’s needs, and then the teacher must respond to the students. They can then try to meet the expressed needs, but sometimes, the teacher may have reason not to. For example, the teacher may not want to help students avoid tackling mathematical challenges. In every case, the caring teacher must cultivate a caring relationship through a continued dialogue. Caring for mathematics involves respecting and promoting the values and norms of the discipline, seeing it as a meaning-making and truth-seeking process of conjecturing and convincing one’s self and others through reasoning. In addition, I argue that care for mathematics learning cannot be isolated from its context inside the educational system, where the instrumental value of academic certificates and credentials (especially those related to mathematics) may overshadow the use value of the disciplines (Williams, 2012).

After discussing the available research on test-driven mathematics teaching in Icelandic upper-secondary schools, I introduce and explain the perspective of care for mathematics learning. I discuss the research method based on research from the inside (Mason 1998, 2002) and reflective analysis based on care for mathematics learning. Research from the inside includes collecting brief but vivid accounts of incidents upon which I reflect.

I present eight short accounts of incidents related to tests and grading from my mathematics teaching in Icelandic high schools, which I interpret through the lens of care for mathematics learning. Some of the accounts depict students’ deep concern with the instrumental value of mathematics, leading their attention away from enjoyment and engagement with mathematics toward efforts to minimise the risk of low grades or failure. Some accounts illustrate my concern for my relationships with students and the emotional weight of these relationships, including disappointment with having failed to connect students with mathematics. Some accounts highlight my and other teachers’ concern over accountability and the integrity of the grading systems. The accounts thus shed light on what caring for mathematics education entails and the possibilities for practising such care in test-driven teaching.

The accounts highlight a triple tension that mathematics teachers face if they want to pursue care for mathematics learning. First, they must try to meet the needs expressed by students and cultivate relationships with them. Second, they seek to honour mathematics values and immerse students in exploring, truth-seeking and reasoning. Third, they strive to meet the requirements of the school system and society for measurable results from the teaching. An analysis of the accounts through the care for mathematics learning lens shows that test-driven teaching undermined my and my students’ care for mathematics learning. I conclude that test-driven teaching does not reflect care for the wider society.