jjrchome

maoru 发表于 13-7-2012 08:12
小六会考有限制不许用方程式来解题吗

没有。教育部曾明确地澄清过此事：

Different Approaches Taught for Mathematics Techniques
http://www.moe.gov.sg/media/forum/2007/20070217.htm

• Mr Lim Boon Tong had sought clarification on whether mathematics techniques like algebra, other than the model drawing method, could be used in the Primary School Leaving Examination (PSLE) Mathematics. (“Can algebra be used to solve PSLE maths problems”, The Straits Times, 12/2).
• The model drawing method is a powerful approach for problem solving and learning mathematical concepts. By drawing models, pupils can represent the mathematical relationships in a problem pictorially. This helps them understand the problem and plan the steps for the solution.
• The pictorial form also helps pupils visualise what could otherwise be abstract concepts. In this way, model drawing supports the learning of fractions, ratio and percentages. Pupils will find model drawing useful when they solve problems involving these concepts in Primary Five and Six.
• The model drawing method is thus a developmentally sound approach for young children. It is recognised internationally as an effective way for young children to learn problem solving and to have early exposure to algebraic concepts. At Primary Six and Secondary One, pupils can draw upon their earlier experience of using models to help them understand algebraic relationships in problems.
• Other than the model drawing approach, pupils are also taught different problem solving methods. They are encouraged to try different approaches and have the flexibility to choose the method that works best for them in solving the problems. They are also encouraged to present their solutions clearly so that these can be understood.
• While pupils are not required to use algebra to solve word problems in the PSLE Mathematics, they are also not restricted to the use of any one particular method. In the marking of PSLE Mathematics, all mathematically correct solutions are acceptable and there is no loss of marks if a correct algebraic method is used.
• We thank Mr Lim for his feedback.
  

Ho Peng (Ms)
Director, Curriculum Planning and Development
Ministry of Education
Tan Yap Kwang
Chief Executive
Singapore Examinations and Assessment Board

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小学老师是这样告诉孩子的: 可以用方程式，但不提倡。用方程式解题，如果步骤正确但答案错误，将得不到“method mark”。

maoru

jjrchome 发表于 13-7-2012 08:41
没有。教育部曾明确地澄清过此事：

Different Approaches Taught for Mathematics Techniques

你太专业了，谢谢，早知道我早点上网跟你多聊聊，有时候看孩子做不出来时间又赶，我就让他用方程，看来我不能再瞎说了，新加坡的国情跟中国不一样

maoru

jjrchome 发表于 13-7-2012 08:41
没有。教育部曾明确地澄清过此事：

Different Approaches Taught for Mathematics Techniques

还有一点，想跟您聊一下，我的孩子算三角形面积这种图形题的时候从来不写公式，造成很多粗心错误，比如光是底乘以高，忘记再乘以1/2，然后扣分，这样我们简单的题目都保不住，圆的面积也一样，由于不写公式，有时候把半径的平方错带入成直径的平方，导致一些本不该有的错误，他还跟我说，如果写公式，老师和同学会笑话，孩子是不是在新加坡学傻了？每次考试简单的题目都错很多，难题也不保，所以我们的数学成绩一直上不来，现在最后两个月了，我也挺急的，和孩子在学习上产生很多类似的矛盾，想听一下您的意见，谢谢

jjrchome

maoru 发表于 13-7-2012 08:53
还有一点，想跟您聊一下，我的孩子算三角形面积这种图形题的时候从来不写公式，造成很多粗心错误，比如光 ...

首先，方程式是一定要学的，通常小学会教小六学生一些简单的一元一次方程式，解题时可以使用。

事实上现在小学的数学题越来越难，有些题不用方程式是很难解出的。尤其是PSLE考试时，时间紧迫，碰到难题时很多孩子还是选择用方程式来解题。用方程式解题的好处是简单明了快速，运用熟练的话出错的可能性也比较少。

运用方程式时应该尽量打一些“擦边球”，不要使用X, Y之类的符号，不要用二元一次方程。应该尽量让解题方法看起来比较像“普通方法”。下面是一个例子：

莱佛士女小的一道小六试题：

Beaker A and Beaker B contain some water.  If 46.5ml of water is drained from Beaker A, the volume of the water in beaker A will be 60% that of the water in Beaker B.
If 35.2 ml of water is drained out from Beaker B, the volume of the water in Beaker B will be 85% that of the water in Beaker A.
What is the tota volume of water in Beaker  and Beaker B?

解答：

1 u ---> 1 unit

Before draining out water fram Beaker A，
Beaker A : Beaker B --> (3u + 46.5) : 5u

If 35.2ml drained from Beaker B，
Beaker A : Beaker B --> 3u + 46.5 : 5u - 35.2 = 100 : 85
                                     (3u + 46.5) : (5u - 35.2)  = 20 : 17

Equalize/cross-multiply:
(3u + 46.5)x17=(5u - 35.2)x20
51u + 790.5 = 100u - 704
49u=1494.5
1u --> 30.5
Beaker A --> 3 x 30.5 + 46.5 = 138 ml
Beaker B --> 5 x 30.5 = 152.5 ml
Total --> 138+152.5 = 290.5ml

jjrchome

maoru 发表于 13-7-2012 08:53
还有一点，想跟您聊一下，我的孩子算三角形面积这种图形题的时候从来不写公式，造成很多粗心错误，比如光 ...

有些数学题，用“普通方法”解题反而更加简单，此时就不要使用方程式了。

比如下面这道南洋小学2011年Prelim的试题：

In a cinema, the ratio of the number of girls to the number of boys was 3:2. The ratio of the number of woman to the number of boys was 5:4.The ratio of the number of men was 2:5. During the movie, 6 women and 27 men left the cinema. The ratio of the number of woman to the number of men then became 1:2.
a) Express the number of women as a fraction of the number of men at first. Leave your answer in its simplest form.
b) How many children were there in the cinema?

解答：

(a)   Boy: Girl      ---> 2:3  ---> 4:6
       Boy: Women ---> 4:5
       Men :Girl       ---> 5:2 --->15:6
       Men: Women ---> 15:5 ---> 3:1

(b)  Men: Women ---> 3:1 ---> 45:15
      after less 6 women and 27 men ---> (45-27) ：(15-6)=2:1
      I unit ---> 15/5=3
      nos of children ---> 3x(4+6) = 30

jjrchome

还有一些题，如果用二元一次方程的话很容易解开。但是二元一次方程对于多数孩子的来说太难，很容易出错，因此应该把它转化为一元一次方程来解答。比如下面这道万慈小学的数学题：

Laura and Ahmad have some stamps. If Laura gives 80 stamps to Ahmad, he will have five times the number of stamps as she has. If Ahmad gives 120 stamps to Laura, she will have 1/3 as many stamps as Ahmad. How many stamps does Laura have at first?

用二元一次方程：

L -- > nos of Laura's stamp
A -- > nos of Ahmad's stamp

5x(L-80) = A+80    ……(1)
3x(L+120) = A-120 …. (2)

5L-400=A+80        ……(1)
3L+360=A-120      ……(2)

(1)-(2) ---> 2L-760=200
                   2L=960
                   L = 480


用一元一次方程：

u  --- >unit

If Laura gives 80 stamps to Ahmad

L ---> 1u
A ---> 5u

At first,

L ---> 1u+80
A ---> 5u-80

If Ahmad gives 120 stamps to Laura

L ---> 1u+80+120
A ---> 5u-80-120

3x(1u+80+120) = 5u-80-120
3u + 600 = 5u - 200
2u = 800
1u = 400
400+80=480

maoru

jjrchome 发表于 13-7-2012 09:44
还有一些题，如果用二元一次方程的话很容易解开。但是二元一次方程对于多数孩子的来说太难，很容易出错，因 ...

谢谢！想请问你，新加坡老师为什么不让学生写公式？

jjrchome

maoru 发表于 13-7-2012 09:54
谢谢！想请问你，新加坡老师为什么不让学生写公式？

以前新加坡的小学数学和中国差不多，后来教学改革后就变成这样了。现在的方法应该是考虑到多数孩子在小学阶段较难理解和应用方程和代数的概念，因而采用图形和符号的方式以便让孩子更容易理解和找出数学运算中的逻辑关系和集体方法。另外，如果孩子过早学习方程式，可能就会对其产生一定的依赖性，结果是限制了孩子其它方面的思维发展。

对于理解能力较强的孩子，运用方程式解题没有什么不妥之处。但是孩子接触方程式不宜过早，最好是在完全掌握Model Drawing， 比较法、假设法、找不变量等方法以后。

maoru

jjrchome 发表于 13-7-2012 11:42
以前新加坡的小学数学和中国差不多，后来教学改革后就变成这样了。现在的方法应该是考虑到多数孩子在小学 ...

非常感谢！