The purpose of this methodological paper was twofold: to develop an objective instrument to measure Grade 11 learners� functional understandings of proof in mathematics in a Dinaledi school (specially selected poor performing school) in South Africa, and evaluate the reliability and validity of the instrument. A curriculum geared toward reflecting the mathematics discipline needs to incorporate the functions of deductive proof in mathematics. The Mathematics curriculum in secondary schools provide teachers with specific aims. The South African Mathematics Curriculum requires that learners develop a deep understanding of proof. However, the lack of an instrument designed to measure functional understandings of proof in mathematics weakens the ability to assess progress towards the fulfilment of this aim. This is an exploratory study conducted in two stages: theoretical development of subscales and items and field-testing the instrument and psychometric evaluation of the instrument by randomly surveying two groups: 37 Mathematics and 37 Mathematical Literacy participants. Initially, a 31-item instrument, Functional Understandings of Proof (FUPS) questionnaire was developed. A panel of experts evaluated content validity and the known-groups method was adopted to assess construct validity. A content validity index of 0.80 was achieved among the experts. A t test for independent samples revealed a statistically significant difference between Mathematics and Mathematical Literacy participants. Further, chi-square tests revealed non-significant association between functional understandings of proof and gender, (1, n = 74) = 1.37, exact p = 0.744 and functional understandings of proof and Home Language, (1, n = 74) = 3.500, exact p = 0.082. As a consequence, values of the effect size for gender and Home Language were respectively = 0.043 and = 0.217. Six negatively-worded items whose correlations were between 0.20 and 0.90 and non-significant thus suggesting that there were some possible conceptual misconceptions among the participants, were deleted. Cronbach�s alpha coefficient of 0.886. In the final analysis, a 25-item FUPS instrument was developed and validated.

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