Descriptors of the Professional Look Development in the Context of Pattern Generalization

Abstract The objective of this research is to generate descriptors of the development of the competence of professional looking into children's mathematical thinking for prospective teachers (PPT) in the context of pattern generalization. To this end, future teachers were asked to describe the answers of Elementary education students to one problem of the pattern generalization, interpret the students' understanding and propose actions to improve or enlarge the teaching-learning process. From the skills that conceptualize the professional look (identifying, interpreting, and deciding) descriptors of four development levels were generated: (1) PPT that does not identify the relevant mathematical elements in the process of pattern generalization, (2) PPT that identifies the mathematical elements, but does not use these elements to interpret the students understanding, (3) PPT that identifies the elements and uses these elements to interpret the students' understanding and (4) PPT that identifies the elements, uses them to interpret the students' understanding and proposes appropriate actions for the Elementary education students' learning progress. The generated descriptors and the determined levels can be the starting point in establishing a future learning trajectory of the professional look and offering information to the trainers to interpret the PPT progress in the development of the professional look competence of children's mathematical thinking in the context of pattern generalization.

摘要
本研究旨在构建模式概括（pattern generalization）情境下，面向准教师（prospective teachers，后文简称PPT）的儿童数学思维专业审视能力发展描述体系。为此，研究者要求准教师针对一道模式概括问题，描述小学阶段学生的作答表现，解读学生的理解水平，并提出优化或拓展教与学过程的具体举措。基于构成专业审视的核心技能——识别、解读与决策，本研究生成了四个发展水平的描述条目：
1. 未能在模式概括过程中识别相关数学元素的准教师；
2. 能够识别相关数学元素，但未利用这些元素解读学生理解情况的准教师；
3. 能够识别相关数学元素，并利用这些元素解读学生理解情况的准教师；
4. 能够识别相关数学元素，利用其解读学生理解情况，并提出适配小学阶段学生学习发展的恰当教学举措的准教师。
本研究生成的描述条目与确定的发展水平，可为构建专业审视能力的后续学习进阶路径提供基础，同时为培训者提供评估准教师在模式概括情境下儿童数学思维专业审视能力发展进程的依据。