Math Materials: Math Competencies Test for Teachers (Part 5)

This is (the LAST) Part V of a material on Math Competencies Test for Teachers.

Math Materials: Math Competencies Test for Teachers (Part 4)

This is Part IV of a material on Math Competencies Test for Teachers.

Math Materials: Math Competencies Test for Teachers (Part 3)

This is Part III of a material on Math Competencies Test for Teachers.

Math Materials: Math Competencies Test for Teachers (Part 2)

This is Part II of a material on Math Competencies Test for Teachers.

I hope this would be of help to Math teachers out there.

Math Materials: Math Competencies Test for Teachers (Part 1)

My wife compiles Math materials. We will begin sharing these so that people will begin to appreciate and love Math.

Today we will share a material on Math Competencies Test for Teachers. We are not the authors of the test. But we are sharing it to help.

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.