数学概念的形成与发展以及数学概念的转变日益成为教育心理学领域和数学教育领域共同关注的热点。数学知识的获得与内化不仅是促进个体抽象逻辑思维发展的必要途径，也是学生将来进入中学、大学学习物理、化学等学科的必要基础。本研究从数学认知发展的角度结合我国数学教育的现状，以比例推理为研究对象，进行了三方面的研究。 研究1通过自编的比例推理测试材料考查了324名小学4～6年级学生在解决比例问题时所采用的各种策略，以及不同类型的问题情境对学生所用策略的影响。结果表明：（1）学生在解决比例问题时所采用的策略会体现出一定的层次性特征，分别是对应－非对应、内在－相间以及具体算法策略。各种算法策略的有效性水平存在显著差异。其中正确的除法和可同化减法策略在各种策略中的频数最高。（2）不同年级学生在具体算法策略的使用上存在显著差异，四年级策略有效性水平最低，且策略频数最为分散，而六年级采用正确策略的频数最高，其中正确的除法策略占主要优势。（3）问题情境会对学生解决比例问题的策略产生显著影响。学生在合成的测度情境中具体算法策略的有效性水平最高，其次为关联的集合，而在缩放问题情境中使用无效策略的频数最多。学生在合成的测度和关联的集合情境中更多地采用内在策略，而在缩放问题上倾向于采用相间策略。 研究2从与比例推理密切相关的数学思维出发，探讨了不同思维水平对学生解决比例问题的影响机制，结果表明：（1）处于相对思维的被试会更多地采用有效策略，问题情境与相对思维之间具有交互作用，当面对熟悉的问题时，相对思维对比例推理的影响不显著，而面对陌生的问题时，相对思维高的学生会更多地采用有效策略。（2）对共变与非共变的判别与比例推理中相对应的数量关系的关联最为密切，而非线性关系和非比例线性关系对比例推理的影响不能一概而论，对于能够正确判别这两种共变关系的被试，在解决比例问题时找出对应的数量组合的可能性要高，而无法进行正确判别的被试，在找出对应的数量组合时并不具有劣势。 研究3分析了不同问题情境中个体在比例推理上发展的异步性。结果表明：（1）采用相对思维的被试在比例问题解决上具有更稳定的水平，在不同情境中存在发展阶段变化的人数较少。（2）学生在合成的测度与关联的集合问题中的发展阶段更为一致，而在缩放问题上则滞后于前两者。

Nowadays conceptual formation and development in math and conceptual change in math is a focused topic more and more regarded by mathematical educator and educational psychologist. The acquirement and interiorization of mathematical knowledge not only is the necessary process to promote the development of individuals’ logical thinking, but also is the foundation of physics and chemistry in middle school and university. This study discussed three main aspects about proportional reasoning in terms of development in mathematical cogniton as well as the current status in mathematical education in China. In the first study, a adapted examination was used to explore 324 primary students’ characteristics of strategies using in proportional reasoning task, and the correlation between their strategies using and different problem contexts. The result showed that: (1) There would be somehow a three-hiberarchy construction in the strategies used by pupils in proportional reasoning tasks, which included corresponding vs. non-corresponding strategies, within vs. between strategies, and the algorithmic strategies. There was differentiation in the efficiency between the different algorithmic strategies, and the correct division and assimilated substraction has the most frequency in all kinds of algorithmic strategies. (2) There were significant differences between three grades in algorithmic strategies using. Pupils in grade 4 with the most discrete distributions in frequency of algorithmic strategies performed worst on proportional reasoning tasks. Pupils in grade 6 had the best performance and they had a main predominance in using correct division. (3) Problem contexts had significant effect on the performance of proportional reasoning tasks. Algorithmic strategies used by pupils in well-chunked measures problems had the most efficiency, associated sets were in the next place, and pupils performed worst in strechers & shrinkers problems. Pupils used more within strategies in well-chunked measures and associated sets problems, and used more between strategies in strechers & shrinkers problems. The second study was designed to explore the influence of mathematical thinking on proportional reasoning, The results revealed that: (1) Pupils with high levels of relative thinking would used more efficient algorithmic strategies. Problem contexts and relative thinking had significant interaction on the proportional reasoning, i.e. there were no significant differences between pupils with different levels of relative thinking when they solved familiar problems, but pupils in high levels of relatives thinking would performed better when they solved unacquainted problems. (2) There were the closest relationship between the judgement of covariation or non-covariation and the judgement of correspondent quantities or non-correspondent quantities in proportional reasoning tasks. It was more possible for pupils who can judge the non-linear covariation and non-proportion covariation correctly to discover the correspondent quantities, but pupils who couldn’t give the correct judgement didn’t perform worse on discover the correspondent quantities. The third study analyzed the asynchronism of development on proportional reasoning across different problem contexts. The results showed that: (1) Pupils who were in the high levels of relative thinking would have steady performance on proportional reasoning tasks, and they seldom transfered among different stages within three problem contexts. (2) The developmental sequences of proportional reasoning were more coherent in well-chunked measures and associated sets problems than in strechers & shrinkers problems, as well as pupils in the latter lagged behind the two formers.