人工智能时代，好的问题比好的答案更有价值。因此在学校教育中，如何培养下一代学会发现并提出问题需要引起足够重视，而不应仅仅局限于传授知识、解决问题。许多国家义务教育阶段的课程标准中均开始强调数学问题提出在数学学习中的重要性。如美国州际核心数学课程标准、澳大利亚数学课程标准以及我国国家义务教育数学课程标准等均提倡在数学课堂教学和评价过程中重视学生发现和提出问题的能力。但与数学问题解决等传统数学教学活动中所重视的能力相比，对于数学问题提出相关认知与非认知因素方面的评价研究尚处于起步阶段。近年来，运用教育测量与评价相关技术了解学生认知及非认知方面的表现，并通过分析认知与非认知因素间的关系来探索教育实践当中蕴含的普遍规律，是数学教育研究当中的一种新趋势。 本研究通过对八年级学生数学问题提出能力的评估，以及其与数学问题提出自我效能感之间关系的探索，将数学问题提出认知与非认知因素相结合，从一个侧面了解学生在数学问题提出方面的学习现状。基于上述研究目的，本研究的研究问题具体包括以下两方面：1）八年级学生数学问题提出的表现如何？2）八年级学生自我效能感与数学问题提出表现的关系如何? 本研究以教育测量与评价领域中的大规模学业质量测评相关技术为依托，采用质性与量化研究方法相结合的形式展开研究。首先，研究中会通过深度访谈与出声想、文本分析法、德尔菲法等研究方法遴选问题提出相关测评工具并建立评分标准。随后使用单参数Rasch模型、题组效应模型、T检验、卡方检验等方法对八年级学生在数学问题提出任务上的表现进行评价。最后，运用线性回归模型、广义加性模型、分段回归模型以及隐喻法等方法，尝试剖析自我效能感与问题提出表现之间可能存在的线性和非线性关系，以及这一关系如何随个体、环境和行为的不同而变化。本研究的主要发现包括以下几个方面： 1) 绝大部分八年级学生具备提出问题的能力，但提出的问题缺乏独特性和对不确定事物的探索。在参与测试的1762名八年级学生中，有88.8%的学生能够在全部题目情境下提出问题。但能够提出一些具有独特性或者带有探索性质的不确定性数学问题的学生比例分别为21.20%和13.08%。 2) 学生数学问题提出的表现会受到数学情境中知识的复杂程度以及提出问题难度要求的影响。学生在数学问题提出上的表现存在“障碍赛”和“挑战赛”现象，也即当情境背后的数学知识越复杂，八年级学生在问题提出上的表现越不好（“障碍赛”）。而在同一个情境下，对学生提出问题的难度要求越高，问题提出的表现往往越好（“挑战赛”）。 3) 问题解决能力水平不同的学生在数学问题提出上的表现存在显著差异。问题解决能力水平较低的学生在问题提出任务上的表现显著低于问题解决能力水平较高的学生。问题解决能力水平较低的学生提出的绝大部分问题处于具有逻辑关联性、数学特征和数学交流清晰这样的阶段。而对于问题解决能力水平较高的学生，他们提出的问题中数学交流清晰、有独特性和不确定性的比例较高。 4) 任务越具体，自我效能感与数学问题提出表现之间的线性关系程度越高。当询问学生对自身问题提出能力的一般性认识（也即领域特殊性自我效能感）时，学生对自身能力的认识较为笼统，无法有效地与他们的实际表现产生联系。而当为学生提供具体的问题提出任务情境时，他们所形成的对自身能力的判断与他们的实际表现更加契合。 5) 自我效能感与数学问题提出表现之间的关系可能存在拐点。从自我效能感与问题提出之间的线性关系分析可以发现，二者存在着显著但相对较弱的线性相关关系（相关在0.08-0.27之间）。进一步，通过广义加性模型分析发现，无论个体能力水平、环境要求和行为性质不同时，二者之间呈现出一定程度的非线性趋势。并且依据分段回归模型可以找到每一种情况下自我效能感与数学问题提出表现间关系的拐点所处位置以及拐点前后斜率的变化趋势。 6) 当个体问题解决能力水平、环境要求和行为性质不同时，自我效能感与学生能力表现之间存在着“酝酿期”、“发展期”和“瓶颈期”等现象。其中，“酝酿期”一般发生在提出/解决简单问题时自我效能感较低且能力表现也较低的学生群体中，此时受到学生先验经验不足的影响，会出现对自身能力误判的现象。“瓶颈期”一般发生在学生提出/解决较难问题时能力较强的学生群体中，此时学生更容易高估自己的能力。而“发展期”则几乎贯穿于二者之间关系的各种情况，并体现出与自我效能感概念的“契合性”、“存在性”和“中间性”等特征。

In the age of artificial intelligence, good questions are always more valuable than good answers. Therefore, how to cultivate the next generation of students to find and pose problems in schooling systems should be paid enough attention, besides imparting knowledge and solving problems. The importance of mathematical problem posing in mathematical learning has been recognized and emphasized in many countries’ national curricula. For example, whatever in The Common Core State Standards for Mathematics, Chinese National Mathematics Curriculum Standards for Compulsory Education, or The Australian Curriculum Mathematics, mathematical problem posing is regarded as one of the most vital components in the process of teaching and evaluation. However, comparing with mathematical problem solving and other competence which are valued in the traditional mathematics teaching activities, the research about the assessment of cognitive and non-cognitive factors in mathematical problem posing is still fraught with many challenges. In the last several years, using technologies and methods related to educational measurement and evaluation to understand students’ cognitive and non-cognitive performance as well as analyzing the relationship between cognitive and non-cognitive factors to explore the universal law of educational practice, are one of the new trend in research on mathematics education. This study combined the cognitive and non-cognitive factors in mathematical problem posing to understand the current learning status of 8th grade students in mathematical problem posing. Both of the assessment of students’ mathematical problem posing performance and the exploration of its relationship with self-efficacy will be involved in this study. To be more specific, there are two research questions which will help response to the research objectives: 1) How do 8th grade students perform on mathematical problem posing tasks? 2) What is the relationship between self-efficacy and mathematical problem posing for 8th grade students? This research employs methods related to large-scale assessment in education. It is based on a mixed-methods research paradigm, which includes both qualitative and quantitative research methods. First, we utilized Depth Interview, a think-aloud protocol, content analysis, and the Delphi method to help select mathematical problem-posing items and to build up construct assessment rubrics. Second, we used the Rasch model, Testlet response model, t test, and chi-square test to evaluate students’ mathematical problem-posing performance. Furthermore, a linear regression model, generalized additive model, piecewise regression model and metaphorical thinking method were applied to explore the possible relationship between self-efficacy and mathematical problem posing and how the relationship is affected by changes in individual ability, the requirements of the environment, and the nature of behavior. The key findings of the research are as follow: 1) Most of students could pose problems in the given context, while few of them could pose mathematical problems with originality and uncertainty. There are 1762 8th grade students participated in the mathematical problem posing test. 88.8% of the students could pose problems in all problem scenarios, but only 21.20% of them could pose mathematical problems with originality and 13.08% of them could pose mathematical problems with uncertainty. 2) The performance of students’ mathematical problem posing will be affected by the complexity of knowledge in the given scenarios and the requirements of difficulty. There are obstacle race phenomenon and challenging race phenomenon existed when evaluating 8th grade students’ mathematical problem posing performance. The obstacle race phenomenon means that when the knowledge complexity of a task scenario increase, the score of students’ mathematical problem posing will decrease. The challenging race phenomenon means that the more difficult the problem that students are required to pose in a given task scenario, the better the students’ mathematical problem-posing performance will be. 3) Students of different mathematical problem solving levels will perform significantly differently in mathematical problem-posing tasks. The statistical analysis indicates that most of students with a bottom one third on problem solving could only pose mathematical problems with appropriate logical associations, mathematical features, or good mathematical communication. However, the majority of students with a higher level of mathematical problem solving performance could pose mathematical problems with good mathematical communication, originality, and uncertainty feature. 4) The more specific the self-efficacy tasks, the higher the relationship between self-efficacy and mathematical problem posing performance will be in this study. Concretely speaking, when students answered questions about domain specific self-efficacy, the understanding about their problem posing ability are also general and with weak prediction for their actual performance. However, when they were provided task-specific self-efficacy scale, the awareness of their ability would be more predictable for their performance. 5) There is a non-linear relationship between self-efficacy and mathematical problem posing. According to the result of linear regression model, the linearity of those two factors are weak (from 0.08 to 0.27). Furthermore, based on generalized additive model, no matter individual mathematical problem solving ability, environmental requirements and behavior nature are different, there are constantly non-linear relationship existed between them. Under the piecewise regression model we can also find the breakpoint and the trend of the slope before and after the breakpoint in each circumstance. 6) There is a gestation period, a developmental period, and a stagnation period in the relationship between self-efficacy and mathematical problem posing/solving performance when individual ability, environmental requirements and behavior nature are different. The gestation period appeared when both of students’ self-efficacy and performance are relatively low in posing/solving easy problems. Students at this stage may misjudge their ability due to the lack of prior experience. The stagnation period appeared when students’ performance is relatively high in posing/solving difficult problems. At this time they may overestimate their ability. While the developmental period appeared nearly everywhere and embody consistence, existence and intermediateness features.