TY - JOUR

T1 - Deficit or difference? The role of students' epistemologies of mathematics in their interactions with proof.

AU - Solomon, Y. J.

N1 - Small-scale study which explores undergraduate mathematics students' beliefs about mathematics knowledge and learning, based on interview data. Considers issues of the status and understanding of proof in the transition from school to university mathematics and suggests a theoretical analysis of the problem which challenges the common assumption of deficit in school teaching and proposes instead that university practices render the process of creating and validating mathematical knowledge invisible to students. Contributes to theory of personal epistemologies and communities of practice in the field of mathematics/higher education, combining psychology, education and socio-cultural theory. This paper was reviewed by two expert referees in addition to the journal editorial board. RAE_import_type : Journal article RAE_uoa_type : Education

PY - 2006/3/1

Y1 - 2006/3/1

N2 - The ability to handle proof is the focus of a number of well-documented complaints regarding students' difficulties in encountering degree-level mathematics. However, in addition to observing that proof is currently marginalised in the UK pre-university mathematics curriculum with a consequent skills deficit for the new undergraduate mathematics student, we need to look more closely at the nature of the gap between expert practice and the student experience in order to gain a full explanation. The paper presents a discussion of first-year undergraduate students' personal epistemologies of mathematics and mathematics learning with illustrative examples from 12 student interviews. Their perceptions of the mathematics community of practice and their own position in it with respect to its values, assumptions and norms support the view that undergraduate interactions with proof are more completely understood as a function of institutional practices which foreground particular epistemological frameworks while obscuring others. It is argued that enabling students to access the academic proof procedure in the transition from pre-university to undergraduate mathematics is a question of fostering an epistemic fluency which allows them to recognise and engage in the process of creating and validating mathematical knowledge.

AB - The ability to handle proof is the focus of a number of well-documented complaints regarding students' difficulties in encountering degree-level mathematics. However, in addition to observing that proof is currently marginalised in the UK pre-university mathematics curriculum with a consequent skills deficit for the new undergraduate mathematics student, we need to look more closely at the nature of the gap between expert practice and the student experience in order to gain a full explanation. The paper presents a discussion of first-year undergraduate students' personal epistemologies of mathematics and mathematics learning with illustrative examples from 12 student interviews. Their perceptions of the mathematics community of practice and their own position in it with respect to its values, assumptions and norms support the view that undergraduate interactions with proof are more completely understood as a function of institutional practices which foreground particular epistemological frameworks while obscuring others. It is argued that enabling students to access the academic proof procedure in the transition from pre-university to undergraduate mathematics is a question of fostering an epistemic fluency which allows them to recognise and engage in the process of creating and validating mathematical knowledge.

KW - epistemic fluency - epistemologies - mathematics community of practice - proof - transition from pre-university to undergraduate mathematics

U2 - 10.1007/s10649-006-6927-1

DO - 10.1007/s10649-006-6927-1

M3 - Journal article

VL - 61

SP - 373

EP - 393

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

SN - 0013-1954

IS - 3

ER -