中学水平数学教育的关键领域

JinStar academic Math course will focus on helping pupils developing fluency, working mathematically and reason mathematically. Pupils will be taught to: 

今之星7-9年级数学课程中，我们将重点培养学生的灵活运算能力、数学理性能力和解决问题的能力。其中包括：

• Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots;

  巩固学生在KS2（小学高年级）阶段积累的数学能力，并扩展他们对数字系统的理解，以及处理小数、分数、 幂和根相关计算的能力；

• Select and use appropriate calculation strategies to solve increasingly complex problems;

      拓展学生通过预先评估及多步骤运算解决问题的能力，并应用于日常生活；

• Begin to model situations mathematically and express the results using a range of formal mathematical representations；

  启发学生以数学的方式对情景进行描述的能力，并使用一系列正式数学表达来展示结果；

• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

  引导学生拥有选择恰当的概念、方法和技术去解决不同寻常问题的能力

Word problems in mathematics often pose a challenge because they require that students read and comprehend the text of the problem, identify the question that needs to be answered, and finally create and solve a numerical equation.

英文数学应用题对绝大多数学生来说，都是一种挑战。因为如果想要解题，学生先要真正读懂并理解题面文本的意思，才能确定答题的方向，进而得出正确结论或成功解决问题。

Many students who have English as a second language, may have difficulty reading and understanding the written content in a word problem. If a student is learning English as a second language, he might not yet know key terminology needed to solve the equation.

很多非英语母语的学生在阅读和理解英文数学应用题的时候，往往觉得困难重重，因为他们通常并不知道那些能够解决问题的关键术语用英文怎么说。

By teaching the key terminology first to students, we then work through worded maths problems with our students by teaching students in this way, they have the terminology and vocabulary to understand the maths problems. We find that often student’s mathematical ability is very good, it is the understanding of the maths vocabulary which needs developing.

因此，我们的课程会优先讲解习题中涉及的关键术语，再和学生们一起解决数学应用题本身。通过这种递进式的教学方法，学生们就能够通过自身积累的术语和词汇，去循序渐进地独立解决一些英文数学应用题。我们发现，中国学生的数学解题能力通常都很优秀，他们只是需要进一步提高对英文数学关键术语词汇的理解。

Once students learn the key terminology used in mathematical word problems, it will be easier to learn how to write numerical equations. It is very important for our teachers to provide our students with opportunities to learn and practice key vocabulary words.

一旦学生学会了如何使用数学应用题中的关键术语，就拥有了更加灵活自如解决数学习题的能力。因此，对我们的授课教师而言，为学生提供学习和练习数学关键词汇的机会非常重要。当然，想要更好地学习和解决英文数学题，也不能靠死记硬背关键词汇，理解词汇在数学题中的语言意义也至关重要。

What research has found is that if we ask students to only rely on knowing that certain key words signal specific operations, we can actually lead them away from trying to understand the problems. They will tend to look only for those words and whatever numbers are in the problem, even if they are not relevant to the answer. This will not help them be mathematically proficient later, even when they are proficient with English.

通过我们的调查发现，如果只要求学生死记硬背关键词汇与特定解题方法的搭配，反而会弱化他们对问题的理解能力。他们在读题时会下意识搜寻熟悉的词汇和数字，即使这些内容与最终解题的思路和答案并没有什么关系。一旦养成这样的学习思路，就算学生的英语水平再好，也无助于他们在数学学习方面的成长。

Our process with teaching worded maths problems, is to read the problem several times with the student then discuss what the problem is trying to solve.  Finally, we look at mathematically working out the problem to get the answer.  Teaching students to read questions thoroughly is a skill not only necessary for maths – this skill is applicable to all subjects.  We want students to know the meaning of the words, but also to see them in the context of the whole problem.

我们在实际教学中采取的教学方法是，通过带领学生多次阅读题面，然后引导他们去思考究竟要解决的是什么问题。这样的教学思路能够引导学生自主思考、主动搜寻可用的数学工具或研究方式以获得最终答案。能够深入剖析并理解题面的能力，不仅可以应用于数学学习中，还能够广泛应用于各个科目的学习实践中。我们希望学生不仅能够从单字含义的层面去理解关键词汇，也能在整个题目文本的语境下去理解它们。