派不到M1 或M2數

eviepa

前幾天到過圖書館除了看過M1 中統計學的模擬試題，也看過2010年A Level中的Mathematics and Statistics裡統計學部分。Maths & Stat是AS Level，在大學收生時當半科A Level看待，應是會考與A Level剛好中間的深度。

M1的統計學模擬試題出得很straight forward，只要你在坊間打開任何一本《統計學入門》的書，都會發覺當中的例題和M1的試題很相似。換句話講，就算學生對expected value、standard deviation、normal distribution、poisson distribution等概念不甚了了，只要操熟課本的試題，仍然能答對不少題目。當然，要取高分還得要了解背後概念。這個部分不算太難。

相對地，AS Level的Maths & Stat的題目就出得很深，變化大很多，需要對所學過的概念有深入的了解才能答得好。

大抵上，文憑試的深度像會考多過香港A Level。不知道和英國的A Level的比較又如何？

雙儿

原帖由 eviepa 於 11-7-30 06:58 發表
雙兒/cow：

我當年理科班的所有同學都修A Maths。他們當中，Modern Maths取A的有15人，其他的都是B或C。至於A Maths，則有幾個A，拿D、E的也有一些。這個格局不止我的一屆，前後幾屆也大概如此。數字上較支持cow的說法，A Maths無 ...

I'm just not certain Cow is right or wrong. I just want some statistical proof. Your memory may be right but then your school is a much better school than you described before because statistically the average number of As per school is less than 10. You also ignore the complication that when a student takes both additional maths and maths, naturally he will devote more time on "maths" in general and statistically we have to discount this distortion when comparing an A-maths student's performance in maths against a non-A-maths student in maths if we want to know what if the amount of preparation is the more or less the same.

ANChan59

cow and eveipa's comment are logical observation and deduction on the maths issue.

cow

原帖由 雙儿 於 11-7-30 09:04 發表
You also ignore the complication that when a student takes both additional maths and maths, naturally he will devote more time on "maths" in general and statistically we have to discount this distortion when comparing an A-maths student's performance in maths against a non-A-maths student in maths if we want to know what if the amount of preparation is the more or less the same.

We just need to compare in general whether it is easy for students to get good results in Maths or in A.Maths. We don't need to consider how much time they spend on 'Maths' in general . However you have got a very good point that the time of students spending on Maths and A.Maths is relevant.

For me as an example, I put more than double if not triple time in A.Maths than in Maths but my Maths result is still higher than my A.Maths. My classmates also spent more than in A.Maths. Therefore, adding such a factor, A.Maths is even more difficult to get a good result.

cow

// devote more time on "maths" in general

BookloverJ,
I think 雙儿 means devote more time on A.Maths and Maths and other maths.

eviepa

Your memory may be right but then your school is a much better school than you described before because statistically the average number of As per school is less than 10.

雙兒：

我讀的中學很可能是一間超級增值學校。年復一年收取升中試考得五年制中學的較弱學生，但每年考會都有很好的成績。聽一個老師說，我們是天主教教區直轄中學裡，會考成績最好的一間。

cow

原帖由 eviepa 於 11-7-31 10:00 發表
我們是天主教教區直轄中學裡，會考成績最好的一間。

eviepa,
以你提供的A.Maths和Maths成績, 恐怕貴校(以A.Maths和Maths而言)當年(~1980)並不是天主教教區直轄中學裡，會考成績最好的一間。
會考成績最好應是聖若瑟英文中學, 其次是觀塘瑪利諾書院/伍華書院.

eviepa

Cow,

謝謝你的指正。我讀中學時，從來沒有詳細求證過這位老師的講法。不過，我的母校是其中一間好學校就是肯定的。

你大概不知天主教教區直轄學校是那些。

天主教總部在中環明愛。而直屬天主教教區的學校，當年有大概十八間，當中大概沒有一間可以稱得上是名校。裡面包括高主教、聖貞德、彩虹村天主教、長沙灣天主教等。每兩年，圍內都會有一個聯校運動會。

記憶中，聖若瑟英文中學、觀塘瑪利諾書院肯定不在此列。伍華好像是其中之一。

cow

eviepa,

也多謝你的指正。聖若瑟英文中學和觀塘瑪利諾書院應是後期才由天主教教區管理。

伍華是其中之一, 當年可以稱得上是地區名校。貴母校當年會考成績可能不及伍華, 但現在一定比伍華好.

[ 本帖最後由 cow 於 11-8-1 06:58 編輯 ]

雙儿

I always thought boys are better at numbers but you guys have disappointed me. I know I can be wrong but I need proof, not just you guys keeping on saying I'm wrong.

Let me exaggerate it a bit. If we keep other things unchanged and just relax the grading of additional maths further like IGCSE. If we had 30% candidates getting an A, you would then agree additional maths is easier in terms of getting a good grade. Now, we know the A% is significantly higher but we also know that the students taking additional maths are more capable in maths in general. Is this factor fully explained by the higher A% and A-C% in additional maths. This is the question.

I am beginning to understand why our perspectives are different. It is because you are men and I am a woman.

If we look at Queen's College, that is exactly the picture you want: the students are significantly better in maths than in additional maths.
The pattern is at odds with the overall statistics.
http://www.qc.edu.hk/

However, if we look at girls' schools, like Marymount http://www.mss.edu.hk/Achievement/hkcee/ce2010/ce2010.pdf or True Light http://www.tlmshk.edu.hk/academic3.php, the picture is just the opposite. This supports my belief that more hardworking students and girls perform better in additional maths, and maths has a better differentiating power than additional maths in telling whether the student is good at maths in general.

Beside, the performance of top schools will conform to the beliefs of you guys but the performance of less than top schools tend to behave otherwise.

Although my query has not been solved yet, I am prepared to let it rest. But next time, I expect you guys slightly more rigorous in your reasoning. Boys are supposed to be better in maths and logic.

[ 本帖最後由 雙儿 於 11-8-1 15:14 編輯 ]

雙儿

原帖由 eviepa 於 11-7-31 10:00 發表



雙兒：

我讀的中學很可能是一間超級增值學校。年復一年收取升中試考得五年制中學的較弱學生，但每年考會都有很好的成績。聽一個老師說，我們是天主教教區直轄中學裡，會考成績最好的一間。 ...

Eviepa

I'm not saying your memory is wrong. But with over 10As for a class, your school's result is almost on a par with QC.

雙儿

cow

雙儿,

For MSS
A.Maths(A-C):slightly greater than 70%
Mahts(A-C):slightly less than 70%
A.Maths (for small number of students only)
Maths (for all students)

For A.Maths group students, should be near 100% got A-C in Maths. For non-A.Maths group (including Arts and Science students) may be less than 50% got A-C.

We should focus on the A.Maths group students that the average grade of Maths should be higher than A.Maths.

------------------
An analysis of the regression of science stream
matriculation results on certificate of education
examination performances in Hong Kong.
(p39-40)
hub.hku.hk/bitstream/10722/40781/1/FullText.pdf


iii) the mean of performance in C.E.E. Mathematics is 7.3 corresponding to a grade lying between B and A which is exceptionally high, and the standard deviation of 0.73 is abnormally low - such reduced variability of the predictor would most probably hamper its predictive value for the
criterion;

iv) approximately 7/9 of the students in the sample sat for C.E.E. Additional Mathematics, and the attained mean of performance is 6.1, which is much lower than that of Mathematics; and

[ 本帖最後由 cow 於 11-8-1 16:44 編輯 ]

雙儿

原帖由 cow 於 11-8-1 16:19 發表
雙儿,

For MSS
A.Maths(A-C):slightly greater than 70%
Mahts(A-C):slightly less than 70%
A.Maths (for small number of students only)
Maths (for all students)

For A.Maths group students, should be near ...

Cow

I'm starting to like you as I always think it is often not the cleverest one who will reach the destination but the most persevering one. You may be a 火頭軍, but this is what it takes to get to the bottom of everything.

I know the case of Marymount is not convincing. I used that as an in-between example to show the pattern transition from a top boys' school like QC to a less-than-top girls' school like true light which shows a more dramatic result biased to additional maths.

The study you show is useless I'm afraid. I'd have agreed with you easily if it had been 1982 now. The study is outdated as the data it used were those of 1981. According to Table 1 in the paper, the A-C percentages was 22.17% for maths and 24.06% for additional maths. Without thinking I would certainly agree additional maths was more difficult then, in 1981. I suspect this is also the reason why you guys have a similar impression. But in the 2010 data we used earlier on, the A-C% was 28% for maths and 39% for additional maths. Will this make you think again?

Cow, you're getting better, but not good enough, yet.

雙儿

[ 本帖最後由 雙儿 於 11-8-1 19:23 編輯 ]

eviepa

Eviepa

I'm not saying your memory is wrong. But with over 10As for a class, your school's result is almost on a par with QC.

雙儿

理科班40%人數學取A，大概和名校有段大距離吧？當年這間男校，三班中只有一班理科。不用多講，最強的差不多都進了理科。於是，會考時，這15個A就是A的總數了。文科最強也只是B。

雙儿

原帖由 BookloverJ 於 11-8-2 09:24 發表


雙儿,

I found Cow is very sincere throughout the discussion, how come you call him a 火頭軍.

Your snobbish attitude towards others is really irritating and annoying.

I was serious when I said I was starting to like Cow; I was half joking when I said he is 火頭軍.My original wording is "you may be a 火頭軍, but this is what it takes to get to the bottom of everything." It's pretty positive, isn't it. 其它人願做火頭軍，雙儿也未必有興趣相陪。

Snobbish? personality-wise absolutely yes, but definitely not towards Cow; condescending? a bit as I'm much senior than Cow in age. I do enjoy helping Cow to become more vigorous in his thinking. Condescending again, I'm afraid.

As to you, just learn to ignore the people you don't like, will you? The easiest thing to do is to invoke 雙儿版規 and ignore 雙儿 completely.

[ 本帖最後由 雙儿 於 11-8-2 14:32 編輯 ]

雙儿

Cow

I was wrong when I said that the 1982 HKU paper you quoted is useless. When I showed our posts to my husband over breakfast this morning, he suggested right away we may have stumbled on something useful.

You mentioned the mean score of maths in the study is 7.3 but the mean score of additional maths is only 6.1 in 1981. Then I said it is useless as the A-C percentages were 22.17% for maths and 24.06% for additional maths in 1981, but the A-C% was 28% for maths and 39% for additional maths in 2010. My husband said we could do a very rough adjustment for the grade inflation of this period and see what the picture would be like in 2010. We multiply the maths score 7.3 by the factor of 28%/22.17%, then we have an adjusted score of 9.2; we multiply the additional maths score 6.1 by the factor of 39%/24.06%, then we have an adjusted score of 9.9.

It’s rough but it paints the overall picture. It shows, at least compared to the past, additional maths was not as difficult as before in terms of getting a good grade.

After all, it looks more like it is me who is the火頭軍. Thanks Cow, your perseverance has also made me think harder.

雙儿

ANChan59

....deleted.....

[ 本帖最後由 ANChan59 於 11-8-3 09:08 編輯 ]

cow

http://www.hkeaa.edu.hk/doclibra ... /alexamstat08_6.pdf
2008首次報考HKAL Pure Maths的日校考生有6557其中有6475人有考HKCEE A.Maths.
HKCEE Maths:
A. 1359
B. 2730
C. 2138
D:   320
E:       9
F:       1

HKCEE A.Maths:
A:   712
B: 1449
C: 2231
D: 1710
E:    346
F:      22
U:       5

http://www.hkeaa.edu.hk/doclibra ... 7/alexamrep07_6.pdf
2007首次報考HKAL Pure Maths的日校考生有6507其中有6413人有考HKCEE A.Maths.
HKCEE Maths:
A. 1426
B. 2702
C. 2097
D:  271
E:    10
F:      1

HKCEE A.Maths:
A:  830
B: 1457
C: 2249
D: 1500
E:   360
F:     15
U:      2