新任教师设计数学游戏之能力探究

摘要

本文考察中学数学新任教师如何通过设计基于游戏的数学任务来发展问题提出（problem posing）技能。研究在一门研究生层次的教师教育课程中展开，14 位职业生涯早期的教师两两结对，共同探索数学游戏、分析其内在结构，并创制可直接用于课堂的原创任务。研究采用质性个案研究取径，聚焦两组具有代表性的搭档：一组对经典的 NIM 游戏展开了反思性探究，另一组则设计了两款以奇偶性为基础的新颖策略游戏。研究发现回应了三个问题：教师如何把数学游戏作为创造性任务设计的工具加以运用；设计过程如何支撑教学洞察与教师身份的发展；以及在任务创制过程中浮现出何种形态的数学推理与教学推理。参与者报告了创造力的提升、概念理解的深化、策略推理能力的增长，以及不断演进的教学能动感。本研究强调，把结构化的问题设计机会整合进数学教师教育项目，是培育反思型、创新型、以学生为中心的教育者的一条重要路径。

Abstract

This paper investigates how novice secondary-school mathematics teachers develop problem-posing skills through the design of game-based mathematical tasks. Conducted within a graduate-level teacher education course, the study engaged 14 early-career teachers working in pairs to explore mathematical games, analyze their underlying structures, and create original classroom-ready tasks. Using a qualitative case study approach, we focus on two representative pairs: one that undertook a reflective inquiry into the classical NIM game and another that designed two novel, parity-based strategy games. The findings address how teachers engage with mathematical games as tools for creative task design, how the design process supports pedagogical insight and the development of teacher identity, and what forms of mathematical and instructional reasoning emerge during task creation. Participants reported heightened creativity, deeper conceptual understanding, strategic reasoning, and an evolving sense of pedagogical agency. The study underscores the value of integrating structured opportunities for problem design into mathematics teacher education programs as a means of cultivating reflective, innovative, and student-centered educators.