新定义解答题是北京高考数学试卷中的一类试题，其难度较大，立意较为深刻。实践中，在教师教和学生学两个方面都具有较大挑战。本研究借助对近年高考试题的材料分析以及学生作答过程分析，从数学活动经验的角度对该类题目的特征和学生表现性评价框架进行挖掘，并通过个案研究给出相应的教学策略。本研究归纳了新定义解答题的形式特征、内容特征、过程特征，论证了新定义解答题的解决过程是一个完整的数学活动过程，并从数学活动经验的角度给出了试题表现性评价框架的四个维度——转化、归纳、证明、表达，及其层次水平划分。以此为基础进行的个案研究验证了该框架的有效性，表明在教学中可以分三个阶段对学生表现进行改进——“试题特征教学”、“转化和归纳维度的教学”、“证明和表达维度的教学”。

 

  New definition question is a type of question in the Beijing College Entrance Examination Mathematics Paper, which is difficult and profound. In practice, there are certain difficulties in both teacher teaching and student learning. With the help of the material analysis of questions over the years and the analysis of students’ answers, this research explores the characteristics of such questions and the evaluation framework of students’ performance from the perspective of mathematical activity experience, and gives effective teaching strategies through case studies. This study summarizes the formal features, content features, and process features of the newly defined answering questions, and also demonstrates that the process of solving the newly-defined problem is a complete process of mathematical fundamental activity, and from the perspective of mathematical fundamental activity experience, it provides four dimensions of the evaluation framework for the performance of test questns—transformation, induction, proof, expression, and its different levels of division. A case study based on this has demonstrated the effectiveness of the framework, and student performance can be improved in three stages in teaching of characteristics of questions, teaching of transformation and induction, moreover, teaching of teaching of proof and expression.