Learners’ difficulties with proof have been ascribed to their lack of understanding of functions that proof performs in mathematics, namely, verification, explanation, communication, discovery, and systematization. However, the extant mathematics education literature on validation of instruments designed to measure learners’ beliefs about the functions of proof is scant. The purpose of this mixed methods study was to use the Standards for Educational and Psychological Testing (as discussed by the American Educational Research Association/American Psychological Association/National Council on Measurement in Education (AERA/APA/NCME), 2014) as a theoretical and methodological platform to support arguments for the validity of the learners’ beliefs about the functions of proof (BAFP) instrument. Scale items were generated from de Villiers’ model and a review of the literature, panel of experts, and key informants. The resulting instrument, comprising 28 Likert-scale items and 5 open questions that assessed the five functions of proof, was administered to 87 grade 11 learners in one high school in the Pinetown Education District, KwaZulu-Natal, South Africa. The results put the validity of the scores on the BAFP instrument into question. The study was an exploration of validity arguments based on the evidence from various data sources. Confirmatory factor analysis with a larger sample in a different context needs to be conducted to warrant the use of the BAFP instrument. The key contribution of this study to the field is that it sheds light on the complexities of instrument validation; the scope of the effort may explain why comprehensive validation efforts have not been documented extensively in literature.

学习者在证明方面的困难归因于他们对证明在数学中所发挥的功能缺乏理解，即验证，解释，交流，发现和系统化。但是，关于用于验证学习者对证明功能的信念的工具验证的现有数学教育文献很少。这项混合方法研究的目的是使用教育和心理测试标准（如美国教育研究协会/美国心理学会/美国国家计量教育委员会（AERA / APA / NCME）所讨论，2014年）作为理论和方法平台来支持关于学习者对功能信念的有效性的论证证明（BAFP）工具。量表项目是根据de Villiers的模型以及对文献，专家小组和主要信息提供者的评论得出的。所生成的工具包括28个李克特量表项目和5个评估证明的五个功能的未解决问题，已在南非夸祖鲁-纳塔尔省Pinetown教育区的一所中学中，对87位11年级学习者进行了管理。结果使BAFP仪器上分数的有效性受到质疑。这项研究是基于来自各种数据源的证据对有效性论证进行的探索。需要对不同背景下的较大样本进行验证性因素分析，以确保使用BAFP仪器。这项研究对该领域的关键贡献在于，它揭示了仪器验证的复杂性。这项工作的范围可以解释为什么没有在文献中广泛记录全面的验证工作。