初高中数学课程存在着很大的差异，为使学生能尽快适应高中学习有必要为学生安排初高中数学学习的过渡知识。可喜的是《普通高中数学课程标准（2017年版）》增设了预备知识，以期帮助学生完成初高中数学学习的过渡。此外教学实践发现初高中数学课程存在断层知识，有许多初高中课标不作要求但高中数学学习需要补充的预备知识。因此为促进中学数学知识的系统性与连贯性，以更好地完成初高中数学衔接工作，有必要在新课标颁布之际对新课标预备知识及新课标下初高中课标不作要求但高中数学学习需要用到的预备知识进行研究。 本文首先从数学课程、教师和学生三方面分析初高中数学衔接的必要性，这是后续研究的起源。接着采用文献法、调查研究法和教学实践法，研究“新课标预备知识”设置的合理性及教学，得出如下结论： （1）设置的合理性：有助于学生思维、知识、心理、学法的过渡，如从形象思维到抽象思维的过渡，逻辑推理思维的提升，从旧知到新知的过渡。故预备知识的设置是合理的。 （2）教学安排参考：相等与不等关系（约4课时）、从函数观点看一元二次方程和不等式（约4课时）放在集合（约5课时）、常用逻辑用语（约6课时）、函数内容前进行教学。 同时，本文采用文献法、调查研究法和统计法，研究新课标下“初高中课标不作要求但高中数学学习需要用到的预备知识”，得出如下结论： （1）补充：乘法公式中的三数和的完全平方公式、立方和与立方差公式；方程中的分式方程、绝对值方程；不等式中的分式不等式、绝对值不等式、高次不等式；因式分解中的十字相乘法、分组分解法；韦达定理；根式化简；分子分母有理化；四心问题。 （2）教学安排：可花时间了解学生对上述预备知识的掌握情况，可在开学前进行专门的衔接补充，也可根据教学需要穿插着进行适当补充，如穿插在新课标预备知识教学中。

There are great differences in Mathematics Curriculum between junior high school and senior middle school. In order to let students adapt to high school as soon as possible, it is necessary to arrange transitional knowledge for primary and high school mathematics learning for students. It is gratifying that the preparatory knowledge was set up in the general high school mathematics curriculum standard (2017 Edition), with a view to helping students complete the transition of mathematics learning in junior high schools. In addition, the teaching practice has found that there is a fault in the knowledge of mathematics in the early and high schools, and there is some preparatory knowledge that the junior high school curriculum standards do not require but the high school mathematics learning needs to be supplemented. Therefore, in order to promote the systematization and coherence of mathematics knowledge in middle school, and to better complete the work of the early and high school mathematics, it is necessary to study the preparatory knowledge of the new curriculum standard and the preparatory knowledge under the new curriculum standard that the junior high school curriculum standards do not require, but needs to be used in high school mathematics learning. This article first analyzes the necessity of the connection of mathematics in early and high school from three aspects: curriculum content, teachers and students, which is the origin of the problem. Then, by using the methods of literature, investigation and teaching practice, study the rationality and teaching of "preparatory knowledge of the new curriculum standard". (1) The rationality of the setting: the first is to help the teaching of the related concepts, avoid the confusion in the teaching of the common logic language, the early teaching and the application of the inequalities; the second is helpful to the transition of the students' thinking, knowledge, learning, psychology and teaching methods: from the image thinking to the abstract thinking, from the weakening of the proof to the strengthening of logical reasoning; from the old knowledge to the new knowledge; from the passive to the initiative, from the memory to the understanding; from the familiarity to the strange; from the teacher to the student, from the "fill duck" to "guide the enlightenment", it is reasonable to set up. (2) Teaching arrangement reference: Equality and inequality (about 4 class hours), The equation and inequality of one element and two times from the point of view of the function (about 4 hours), should be placed before set (about 5 hours), common logical terms (about 6 hours), and function content while teaching. At the same time, study the need of supplement about the preparatory knowledge that the junior high school curriculum standards do not require but the high school mathematics needs to learn, and how to arrange the teaching under the new curriculum standard, mainly using the literature method, the investigation and research method, and Statistical method, then draw the following conclusions as reference. (1) Supplement: Multiplication formula: the complete square formula for sum of three numbers, cubic and cubic difference formula; Equation: fractional equation, absolute value equation; Inequality: Fractional Inequality, absolute value inequality, high order inequality; Factorization: cross multiplication, group decomposition method; Weida theorem; Root and fraction: root reduction and molecular denominator rationalization; Four heart problems. (2) Teaching arrangement: Spend time to understand the students' mastery of the afore-mentioned preparatory knowledge through communication or test, which can be supplemented by special connection before the beginning of school, and can be properly supplemented according to the needs of teaching, such as interspersed in the preparatory knowledge teaching of the new curriculum standard.