If people care about ideas in the same way they care about people, as Noddings (2005) claims we do, a model of relationship between people can illuminate the relationship between a student and ideas in mathematics. In this paper, Noddings’ ethic of care (2003), particularly her model of relationship,  is used to position the traditional or typical high-school mathematics textbook as an agent in relationship with a student. Following this, extended problem solving activities such as those proposed by Gutstein and Peterson (2006) and Boaler (2009), particularly the creativity inherent in them, are positioned as agents in relationship with students. I argue that the first relationship is fatal to many students and that the second is fruitful.

To begin this argument, I outline principal features of an ethic of care (Noddings, 2003, 1993; Skoe, 2008). Within a consideration of an ethic of care, caring is not regarded solely as an individual attribute. Also recognised is the significant role played by the cared-for, whose response influences the next offer from the one-caring. Especially relevant to the argument presented in this paper is the relationship between the two parties; the one-caring and the one-cared-for.

In the application of Noddings’ model I employ in this paper, the student initially holds the place of the one-caring, and the mathematics textbook holds the place of the cared-for. As in human relationships, they continually exchange positions; the one-cared for becomes the one-caring; the one-caring becomes the one-cared-for; and so on. It is a relationship of mutuality that thrives or dies depending on the contributions made by both parties.

De Freitas (2008) notes the attachment to mastery and submission in school mathematics. Mastery and submission are relations characteristic of dictatorship. Through the mastery/submission model, the textbook makes offers which are pre-determined, fixed and immoveable. Once the student has read the first few pages, the textbook is predictable; each section contains a carefully worked example which the student is directed to repeat many times over.  Further, all expected responses (correct answers) to these dully predictable offers are listed in the back of the textbook. Johansson (2007) found that the teacher even defers to the textbook when s/he disagrees with it. Consequently, the traditional high school mathematics textbook dicates the relationship with the student, in the same way a dictator controls the relationship with his subordinates.

In contrast, a creative mathematical environment, such as the exploratory problem solving activities proposed by Boaler (2009) and Gutstein and Peterson (2006)  allows students to make a move (an offer) of their own choice  to the mathematics. The mathematics responds in a far less predictable manner. Perhaps in this response of the mathematics the student sees an important insight, or perceives a new and unusual difficulty. The response from the mathematics is uncertain and dynamic. This offer by the mathematics is a gift, not the order/instruction typical of textbook-based mathematics. The series of offers and responses between students and exploratory problem based mathematics is a dynamic process as uncertain as any human relationship.  However it is a more pleasureable and engaging relationship for many students than submission to a dictatorship.  

Boaler, J, (2009). The elephant in the classroom; Helping children learn and love maths. Souvenir Press, London. De Freitas, E. (2008) Mathematics and its other: (dis)locating the feminine. Gender and Education, 20 (3), pp 281–290. Denzin, N.K., & Lincoln, Y.S. (2003). Introduction: The discipline and practice of qualitative research. In N. Denzin & Y. Lincoln (Eds.), Collecting and interpreting qualitative materials (2nd ed., pp. 1-46). Thousand Oaks, CA: Sage) Gutstein, E and Peterson, B (2006) (Eds) .Rethinking mathematics : teaching social justice by the numbers. Milwaukee, Wis. Rethinking Schools. Johansson, M. (2007) Mathematical meaning making and textbook tasks. For the Leaning of Mathematics, 27 (1), pp 45-51. Noddings, N. (2005). The challenge to care in schools : An alternative approach to education. New York, N.Y. ; London : Teachers College Press Noddings, N. (2003). Caring: A feminine approach to ethics and moral education (2nd ed.). Berkeley: University of California Press. Noddings, N. (1993). Caring: A feminist perspective. In K. A. Strike & P. L. Ternasky (Eds.), Ethics for Professionals in Education: Perspectives for Preparation and Practice (pp. 43-53). New York: Teachers College Press. Skoe, E. (2008). Care, Inventory of (Ethic of Care Interview), In F., Clark Power; R. J., Nuzzi; D., Narvaez; D. K., Lapsley & T. C., Hunt (eds.), Moral Education: A Handbook. Volume 1. A-L. Praeger. kapittel C. s 57 - 58