数学知识观视角下学习进阶的再审视

Re-examination of Advanced Learning from the Perspective of Mathematical Knowledge View

数学学习进阶主要描述学生对数学知识或技能在一段时间内的发展历程,学习进阶的明确可以推动形成性评价、教学、学习的一致性,可以帮助教师承前启后地对照学习目标设计评价任务、分析评价结果、确定学习差距。对数学知识观的学科审视发现,数学知识兼备科学和人文的特点,数学知识具有发现性和发明性。建构数学学习进阶包括个体经验、朴素尝试,逐步内化、产生冲突,形成概念、内化运用,知识整合、拓展延伸。当然,数学学习进阶的建构过程,不是简单的从无到有的过程,也不是将现存的要素进行简单机械组合而必定实现的过程,其过程具有主体作用性、整合生成性、渐进性和未竟性、深度性和开放性等特点。

Advanced learning of ma thematics mainly describes the development of students'mathematical knowledge or skills over a period of time.The clear understanding of advanced learning can promote consistency in formative evaluation,teaching and learning,and help teachers design evaluation tasks,analyze evaluation results,and det ermine learning gaps based on learning objectives.A disciplinary examination of mathematical knowledge view reveals that mathematical knowledge combines the characteristics of science and humanities and has the characteristics of discovery and invention.The method of constructing advanced mathematical learning includes:individual experience,simple attempts,gradual internalization and generating conflict,forming concepts and int ernalzing applications,knowledge integration and expansion and extension.Of course,the construction is not a simple process from scratch,nor is it a process of mechanically combining existing elements.It has characteristics of subjectivity,integration and generation,gradualness and unfinished,depth and openness.