Van Hiele Ideas and the Realistic Mathematical Education: a few approximations

Abstract This article originated in a research that investigated possible relations between the principles of Realistic Mathematical Education assessment and the learning process phases proposed by Dina Van Hiele-Geldof and Pierre Van Hiele, seeking approaches. The work was developed in a research perspective of theoretical nature, of the speculative type. It highlights the educational aspect of Van Hiele's work, in particular, the learning process phases: information, guided guidance, exploitation, free orientation, and integration. It considers that the learning process phases of Van Hiele's approach are another auxiliary element in the elaboration of mathematical knowledge from situations that can be mathematized, developed through a guided reinvention process based on information collected in assessment situations.

摘要：本文源自一项研究，该研究旨在探索现实主义数学教育（Realistic Mathematical Education）评估原则与迪娜·范·艾尔勒-盖尔多夫（Dina Van Hiele-Geldof）、皮埃尔·范·艾尔勒（Pierre Van Hiele）提出的学习过程阶段之间的潜在关联，并寻求可行的实施路径。本研究属于理论思辨类的研究范畴，着重阐释范·艾尔勒理论成果的教育维度，尤其聚焦其提出的学习过程五阶段：信息（Information）阶段、引导指导（Guided Guidance）阶段、拓展运用（Exploitation）阶段、自由定向（Free Orientation）阶段以及整合（Integration）阶段。本研究认为，范·艾尔勒理论中的学习过程阶段，是依托可数学化的情境构建数学知识的又一辅助要素，此类知识可通过基于评估情境收集的信息开展的引导式再创造过程得以形成。