China is the best in Mathematics

Chinese mathematicians are the best in the world. Since 1999, China has consistently topped the International Mathematics Olympiad (IMO). This is no surprise since China has developed its mathematics independent of Greece and the western civilizations. For example, China has been using the concept of the decimal system since time immemorial. Mathematics is used in ancient China in various applications such as flood forecasting, astronomy, surveying, etc. I would venture to say that mathematics is naturally embedded in the Chinese mind.

The following table shows China’s total dominance of the IMO:

Table 1. China’s rank at the International Mathematics Olympiads: 1999-2008



Many of the topnotch contestants of other countries are also of Chinese descent. This shows that the world has come to realize that Mathematics is the realm of the Chinese.

Even here in the Philippines, Filipinos with Chinese descent show excellence in Mathematics. They are admired for their genius and love for Mathematics. The Philippines was put in the limelight of the world of Mathematics through the efforts of Dr. Simon L.Chua, a Filipino with Chinese roots. He is the first Filipino to receive the International Paul Erdos Award in 2006 for leading in the development of mathematical challenges in the Philippines. He is the president of the Mathematics Trainers' Guild (MTG), an organization that trains talented young Filipinos in Mathematics. Through the leadership of Dr. Chua, the MTG with its dedicated officers, sent these young Filipino Math wizards to international competitions and has won numerous awards and medals.

What is the secret of the excellence of the Chinese in mathematics? It is an enigma. They are simply very good with numbers.

Math Olympiad - Part 2

In this post, I will investigate whether a county's team score in IMO is dependent (or independent) on translating IMO contest questions into one's native language.

The null hypothesis is:
Ho: Team Points in Math Olympiad is independent of Language (With Translation to Native Language) of Contest Question

The alternative hypothesis is:
H1: Team Points in Math Olympiad is NOT independent of Language (With Translation to Native Language) of Contest Question

The following tables are derived from IMO 2007 data:

Table 1. Observed frequencies by Team Points Interval by IMO Questions with/without translation to Native Language: IMO 2007


Table 2. Expected frequencies by Team Points Interval by IMO Questions with/without translation to Native Language: IMO 2007


Computing the test statistic yields the following:

Table 3. Results of Chi-Square computation: IMO 2007


CONCLUSION

Since the Computed Chi-square statistic (16.94) is greater than the Tabular Chi-square value at α = 0.05 (9.448) and α = 0.01 (13.277), we reject the null hypothesis.

We conclude that the each country's score at the Math Olympiad is NOT independent of the language (whether Translated to native tongue or not) of the contest question.

In plain language, the Math Olympiad team scores are dependent on whether the contest questions are translated into the native language of participating countries. For an insight on whether translation of IMO questions to native language affects the team scores in positive or negative manner, let’s take a look on the mean scores.

Table 4. Count and Average Score for IMO Questions with or without translation: IMO 2007



The difference in average team score of countries with translation and those that don’t is 36 points. It is likely that translating IMO questions to one’s native tongue could significantly increase team scores.

Math Olympiad - Part 1

The Philippines has been participating in the International Math Olympiad (IMO) for more than a decade now. Based on the available records, the country has consistently ranked in the lowest decile of participating countries.

The following shows the ranking of countries in the IMO from 1995 to 2007 (Presentation of countries is based on the 2007 ranking):

Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Russia	1	2	3	3	5	2	2.5	2	1.5	6	4.5	4	3
China	2	1	1	1	2	1	1	1	1.5		29	16	19
South Korea	3.5	3	5	12	6	6	4.5	4	7	12	11	8	7
Vietnam	3.5	13	15	4	4	5	10	5.5	3	9	10	7	4
U.S.A.	5	5	2	2	3	3	2.5	3	10	3.5	4.5	2	11
Japan	6.5	7	8	8	9	16.5	13	15	13	14	48.5	25.5	27
Ukraine	6.5	22	9.5	11	14	20	8	13	12	8	6	18	23
North Korea	8
Bulgaria	9.5	21	11	5	1	4	4.5	5.5	5	2	26	52	44
Taiwan	9.5	10	7	6	16	7	9	8	9	5	14	20	12
Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Romania	11	6	6	10	7	8	15	11.5	4	11	7.5	1	2
Hong Kong	12.5	14	17	30	29	24	19.5	28	33.5	25	79
Iran	12.5	8	4	9	17.5	11	18	10	8	1	63	70	53
Thailand	14	15.5	23	35	19.5	22	22.5	29.5	47.5	42	52	47	34
Germany	15	4	12	25	17.5	10	14	20.5	17	16	28	30	48
Hungary	16	17	9.5	7	10.5	12.5	21	9	11	3.5	30.5	27	20
Turkey	17	19.5	21.5	32	8	14.5	11	18.5	16	17.5	25	19	25
Poland	18	11	27.5	16	22	22	19.5	32.5	19	21	20.5	13	16
Belarus	19	23	18	13	19.5	14.5	12	7	6	19	55	58	64
Moldova	20	9	21.5	17	30.5	49	40	26	56	50	58	41	36.5
Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Italy	21	12	24	49.5	50	33	46.5	50	23	38	22.5	15	13
Australia	22	26	25	27	26.5	26	25	16	15	13	34.5	34.5	32.5
Serbia and Montenegro	23	38	39	22.5	23
Brazil	24	29	34	22.5	26.5	22	16	48.5	29.5	30.5	74
India	25	35	36	14	15	9	7	14	18	7	60.5	56	68
Georgia	26	33.5	37	28	32	34	38.5	36	38	36	32.5	36	30
Canada	27	15.5	19	22.5	12.5	12.5	24	17	31.5	20	7.5	11.5	6
Kazakhstan	28.5	31	26	22.5	12.5	16.5	6	24	35	35	12	11.5	9
United Kingdom	28.5	19.5	13	20	10.5	27	32	22	20	17.5	16	5	10
Colombia	30	50.5	27.5	29	39	37	42	44.5	49.5	41	66	71	70
Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Lithuania	31	33.5	53
Peru	32	40	29	64	60.5	51	41	65.5	78.5	46	53.5
Greece	33	56	50	26	30.5	47	30	56	47.5	32	13	10	15
Mongolia	34.5	45		19	25	35.5	32	40.5	25.5	30.5	30.5	44.5	42
Uzbekistan	34.5	57		45	52.5	49	27	38	59		67
Singapore	36	27	14	18	36	30	29	37	36.5	22.5	41.5	25.5	27
Mexico	37.5	24	31	37	41	46	46.5	32.5	52.5	44.5	32.5	53.5	58.5
Slovakia	37.5	18	20	31	35	25	48	18.5	21	33.5	36	17	21.5
Slovenia	39	36.5	56	49.5	75	58	67	34.5	58	51	50	44.5	60
Czech Republic	40	48.5	16	34	34	28	45	42	49.5	15	40	66	55
Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Sweden	41	43	61	46	48	49	69	31	41.5	47	19	40	35
Austria	42	42	40.5	59.5	59	56.5	55	39	29.5	48	9	23	21.5
France	43.5	28	32	38	24	19	28	48.5	33.5	26.5	34.5	39	36.5
Norway	43.5	66	64	59.5	42	44	50	57	39.5	61	44	37.5	52
Belgium	45	52.5	40.5	42.5	37.5	52.5	69	53.5	54.5	39	17	21	27
Croatia	46	54	34	40	33	45	35	34.5	41.5	22.5	1	6	1
Argentina	47	31	46	39	28.5	31	22.5	25	45	29	82
Armenia	48.5	36.5	34	36	43.5	67	53	20.5	39.5	26.5	37.5	29	29
Macau	48.5	59.5	64	42.5	58	56.5	64	76.5	60.5	64	56	49.5	62
Israel	50.5	25	30	15	21	18	17	11.5	25.5	24	68	61	61
Netherlands	50.5	63	47.5	61	64	54	54	46.5	31.5	44.5	37.5	59	45
Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Azerbaijan	53	48.5	49	47	40	65	73	65.5	66.5	54	43	42	43
Bosnia-Herzegovina	53	41	56	70	43.5	62	51	29.5	43.5	33.5	41.5	31	47
Indonesia	53		42.5	54	37.5	64	60.5	51	64.5	68	15	14	14
Macedonia	55	63	54	48	47	43	43	43	36.5	40	46.5	49.5	31
Mozambique	56	90	90	82.5
Estonia	57	45	45	44	54	40.5	37	58	69	43	58	49.5	49
Albania	58.5	50.5	60	56	71	70.5	72	75	66.5		71.5	67.5
Switzerland	58.5	31	42.5	56	67.5	60.5	57	40.5	24	57	58	62	39.5
Latvia	60	52.5	47.5	52.5	50	40.5	38.5	46.5	22	37	75	67.5	65.5
Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Finland	61	39	56	64	56	38	64	52	43.5	63	53.5	55	56
Portugal	62	47	70	77	73	78	78	72.5	70	72.5	71.5	63	67
Ireland	63.5	67	51	66	74	70.5	64	69	62	59	3	9	8
Turkmenistan	63.5	61	64	62	60.5	59	66		77			72.5
Denmark	65	69	44	68	66	55	69	61	54.5	66	80	69	58.5
Spain	66	45	58.5	56	46	60.5	58	68	46	59	64	49.5	51
Kyrgyzstan	67	77	58.5	52.5	50	75.5	79	76.5	76	69	77	75	73
South Africa	68	63	62	33	45	32	36	27	27.5	28	39	43	41
Cyprus	69	81	77	64	71	68	34	65.5	64.5	56	24	34.5	32.5
Trinidad and Tobago	70	73.5	78	76	62.5	72.5	60.5	59	68	59	65	60	63
Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Tajikistan	71	72	79.5
Costa Rica	72	78.5	66.5
Iceland	73	59.5	72	72	62.5	66	74	60	60.5	52.5	2	3	5
Ecuador	75.5	70.5	75	81	77	82	83	74			18	28	17.5
El Salvador	75.5	78.5	71
Luxembourg	75.5	82.5	87.5	71	69	79	80	53.5	71	65	51	32	50
Malaysia	75.5	70.5	76	73	67.5	69	60.5	65.5	63	62	69.5	72.5	72
Pakistan	78.5	76	81.5
Paraguay	78.5	68	79.5	82.5	82	80	82			72.5	77
Bangladesh	80	80	87.5
Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Morocco	81	65	74	41	56	63	52	55	57	52.5	60.5	65	24
Cambodia	82
Sri Lanka	83	55	68	74	81	77	71	72.5	81	74		53.5	71
Philippines	84		69	79	79	74	75	70.5	73	70.5	73	74	65.5
New Zealand	85	58	38	58	56	35.5	44	62.5	52.5	49	48.5	37.5	46
Montenegro	86
Cuba	87		52	78	76	39	26	44.5	27.5	67	27	46	38
Lithuania	88.5	89	81.5	51	52.5	42	56	62.5	51	55	22.5	33	39.5
Venezuela	88.5	73.5	73	80	78	52.5	49	79.5	80	75	81
Puerto Rico	90	84.5	84	69	71	75.5		81.5			77
Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Saudi Arabia	91	88	87.5	85
Chile	92
Bolivia	93	86.5	91
Brunei								81.5			62	57	69
Guatemala			85			81	76	79.5	75		45	22	54
Kuwait		86.5	87.5	84	80	83	81	78	78.5	76	46.5	64	57
Nigeria		84.5
Panama		75
Tunisia			83	75		72.5	60.5		74
Uruguay		82.5	66.5	67	65	84	77	70.5	72	70.5	69.5
Yugoslavia						29	32	23	14	10	20.5	24	17.5
# of countries	102	99	100	94	91	93	92	91	90	85	91	84	82

The world is too big to compare the Philippines' IMO performance with the top performing countries. So I generated the following table to see how well we performed compared with ASEAN neighbors:

Country	2007	2006	2005	2004	2003	2002	2001	2000	1999	1998	1997	1996	1995
Vietnam	3.5	13	15	4	4	5	10	5.5	3	9	10	7	4
Thailand	14	15.5	23	35	19.5	22	22.5	29.5	47.5	42	52	47	34
Singapore	36	27	14	18	36	30	29	37	36.5	22.5	41.5	25.5	27
Indonesia	53		42.5	54	37.5	64	60.5	51	64.5	68	15	14	14
Malaysia	75.5	70.5	76	73	67.5	69	60.5	65.5	63	62	69.5	72.5	72
Cambodia	82
Philippines	84		69	79	79	74	75	70.5	73	70.5	73	74	65.5
Brunei								81.5			62	57	69

As of IMO 2007, the Philippines is at the bottom of ASEAN countries.

What is the (MATH) problem of the Philippines? How do we solve this? Let me count the ways.

Filipino math lovers may look into the following ways:

1. Process of selecting IMO contestants.
Is it open to all students? Is it grassroots-based? Sana kagaya ng Metrobank-MTAP-DepEd Math Challenge setup. Lahat sana may pagkakataong sumali.

Although most of the good math students are in private schools, I believe that there are very good public school math students that are left undiscovered or were not given even a small chance to participate. My haunch is that the most talented math students are in public schools. The laws of probability should support my haunch.

2. Math questions during selection and training of Philippine representatives.
Are we giving them the IMO-type questions during the selection and training processes? Many of the questions in a few math contests that we have in the Philippines are computation type. Such type of math questions is perfect for Metrobank-MTAP-DepEd Math Challenge.

For IMO, the questions are out-of-the-box type. One year training is recommended for prospective Philippine representatives.

3. Philippine Education System is inadequate.
Most of the countries that participate have at least 12 years of pre-University education (elementary to high school). Kulang tayo ng 2 years. Two years of additional math would spell the difference. Talo tayo sa competition kasi hilaw pa ang mga bata.

4. IMO questions could be translated into Filipino

I presume that the Filipino representatives use the English IMO questions during the olympiad. Other countries have the IMO questions translated into their own language. Bakit hindi rin sa Pilipino?

Studying Math in your native language would enable deeper understanding of the subject. Learning it in a foreign language (English) would hinder absorption of basic concepts. Hirap ka na nga sa Math tapos iintindihin mo pa yung English questions. Doble ang difficulties.

At saka baka magkaibang compartment sa utak ang language at Math. Baka left brain ang Math tapos right brain ang language. Hinuha ko lang yung ha.

I studied the data of the IMO 2007 and made a crude statistical test whether there is any relationship between IMO scores of a country and countries with IMO questions translations. the results should be interesting. But that would be the subject of another post.

For Math lovers these are food for thought.

Sana ang 1st Olympic Gold ng Pinas ay sa Math.

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