Knowing and Teaching Elementary MathematicsIntroduction

Chi-Kwong LiThe College of William and Mary

September, 2007

Chi-Kwong Li

Chinese view of Eduction

Before Cultural Revolution (1966-69)

Four important types of professions

Scholars

Farmers

Workers

Merchants

During and post cultural revolution

The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.

All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).

Educated people were sent to countryside to be re-educated bypeople in the countryside.

Chi-Kwong Li

Chinese view of Eduction

Before Cultural Revolution (1966-69)

Four important types of professions

Scholars

Farmers

Workers

Merchants

During and post cultural revolution

The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.

All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).

Educated people were sent to countryside to be re-educated bypeople in the countryside.

Chi-Kwong Li

Chinese view of Eduction

Before Cultural Revolution (1966-69)

Four important types of professions

Scholars

Farmers

Workers

Merchants

During and post cultural revolution

The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.

All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).

Educated people were sent to countryside to be re-educated bypeople in the countryside.

Chi-Kwong Li

Chinese view of Eduction

Before Cultural Revolution (1966-69)

Four important types of professions

Scholars

Farmers

Workers

Merchants

During and post cultural revolution

The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.

All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).

Educated people were sent to countryside to be re-educated bypeople in the countryside.

Chi-Kwong Li

Chinese view of Eduction

Before Cultural Revolution (1966-69)

Four important types of professions

Scholars

Farmers

Workers

Merchants

During and post cultural revolution

The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.

All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).

Educated people were sent to countryside to be re-educated bypeople in the countryside.

Chi-Kwong Li

Chinese view of Eduction

Before Cultural Revolution (1966-69)

Four important types of professions

Scholars

Farmers

Workers

Merchants

During and post cultural revolution

The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.

All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).

Educated people were sent to countryside to be re-educated bypeople in the countryside.

Chi-Kwong Li

Chinese view of Eduction

Before Cultural Revolution (1966-69)

Four important types of professions

Scholars

Farmers

Workers

Merchants

During and post cultural revolution

The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.

All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).

Educated people were sent to countryside to be re-educated bypeople in the countryside.

Chi-Kwong Li

Chinese view of Eduction

Before Cultural Revolution (1966-69)

Four important types of professions

Scholars

Farmers

Workers

Merchants

During and post cultural revolution

The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.

All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).

Educated people were sent to countryside to be re-educated bypeople in the countryside.

Chi-Kwong Li

Chinese view of Eduction

Before Cultural Revolution (1966-69)

Four important types of professions

Scholars

Farmers

Workers

Merchants

During and post cultural revolution

The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.

All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).

Educated people were sent to countryside to be re-educated bypeople in the countryside.

Chi-Kwong Li

Background of Liping Ma

As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.

Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).

Soon, she became the principal of the local school.

A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.

After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.

She finished her study, and her thesis grew into this influential book.

Chi-Kwong Li

Background of Liping Ma

As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.

Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).

Soon, she became the principal of the local school.

A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.

After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.

She finished her study, and her thesis grew into this influential book.

Chi-Kwong Li

Background of Liping Ma

As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.

Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).

Soon, she became the principal of the local school.

A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.

After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.

She finished her study, and her thesis grew into this influential book.

Chi-Kwong Li

Background of Liping Ma

As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.

Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).

Soon, she became the principal of the local school.

A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.

After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.

She finished her study, and her thesis grew into this influential book.

Chi-Kwong Li

Background of Liping Ma

As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.

Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).

Soon, she became the principal of the local school.

A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.

After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.

She finished her study, and her thesis grew into this influential book.

Chi-Kwong Li

Background of Liping Ma

As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.

Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).

Soon, she became the principal of the local school.

A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.

After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.

She finished her study, and her thesis grew into this influential book.

Chi-Kwong Li

Background of Liping Ma

As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.

Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).

Soon, she became the principal of the local school.

A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.

After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.

She finished her study, and her thesis grew into this influential book.

Chi-Kwong Li

The study of Liping Ma

Chinese students typically outperform US students.

Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.

To explain this paradox, Liping Ma studied teachers’ understandingof fundamental mathematics in China and the US.

Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.

Two motivating examples

In teaching division with fractions, how to explain 1 34 divided by 1

2 .Can one make up a good story?

In a visit to an elementary school with a reputation of high qualityeducation, Ma observed that a student mistook that 7 yards 5inches is 89 inches. But the wrong answer was used by the teacherand no one noticed.

Chi-Kwong Li

The study of Liping Ma

Chinese students typically outperform US students.

Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.

To explain this paradox, Liping Ma studied teachers’ understandingof fundamental mathematics in China and the US.

Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.

Two motivating examples

In teaching division with fractions, how to explain 1 34 divided by 1

2 .Can one make up a good story?

In a visit to an elementary school with a reputation of high qualityeducation, Ma observed that a student mistook that 7 yards 5inches is 89 inches. But the wrong answer was used by the teacherand no one noticed.

Chi-Kwong Li

The study of Liping Ma

Chinese students typically outperform US students.

Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.

To explain this paradox, Liping Ma studied teachers’ understandingof fundamental mathematics in China and the US.

Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.

Two motivating examples

In teaching division with fractions, how to explain 1 34 divided by 1

2 .Can one make up a good story?

In a visit to an elementary school with a reputation of high qualityeducation, Ma observed that a student mistook that 7 yards 5inches is 89 inches. But the wrong answer was used by the teacherand no one noticed.

Chi-Kwong Li

The study of Liping Ma

Chinese students typically outperform US students.

Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.

To explain this paradox, Liping Ma studied teachers’ understandingof fundamental mathematics in China and the US.

Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.

Two motivating examples

In teaching division with fractions, how to explain 1 34 divided by 1

2 .Can one make up a good story?

In a visit to an elementary school with a reputation of high qualityeducation, Ma observed that a student mistook that 7 yards 5inches is 89 inches. But the wrong answer was used by the teacherand no one noticed.

Chi-Kwong Li

The study of Liping Ma

Chinese students typically outperform US students.

Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.

To explain this paradox, Liping Ma studied teachers’ understandingof fundamental mathematics in China and the US.

Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.

Two motivating examples

In teaching division with fractions, how to explain 1 34 divided by 1

2 .Can one make up a good story?

In a visit to an elementary school with a reputation of high qualityeducation, Ma observed that a student mistook that 7 yards 5inches is 89 inches. But the wrong answer was used by the teacherand no one noticed.

Chi-Kwong Li

The study of Liping Ma

Chinese students typically outperform US students.

Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.

To explain this paradox, Liping Ma studied teachers’ understandingof fundamental mathematics in China and the US.

Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.

Two motivating examples

In teaching division with fractions, how to explain 1 34 divided by 1

2 .Can one make up a good story?

In a visit to an elementary school with a reputation of high qualityeducation, Ma observed that a student mistook that 7 yards 5inches is 89 inches. But the wrong answer was used by the teacherand no one noticed.

Chi-Kwong Li

The study of Liping Ma

Chinese students typically outperform US students.

Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.

To explain this paradox, Liping Ma studied teachers’ understandingof fundamental mathematics in China and the US.

Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.

Two motivating examples

In teaching division with fractions, how to explain 1 34 divided by 1

2 .Can one make up a good story?

In a visit to an elementary school with a reputation of high qualityeducation, Ma observed that a student mistook that 7 yards 5inches is 89 inches. But the wrong answer was used by the teacherand no one noticed.

Chi-Kwong Li

The study of Liping Ma

Chinese students typically outperform US students.

Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.

To explain this paradox, Liping Ma studied teachers’ understandingof fundamental mathematics in China and the US.

Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.

Two motivating examples

In teaching division with fractions, how to explain 1 34 divided by 1

2 .Can one make up a good story?

In a visit to an elementary school with a reputation of high qualityeducation, Ma observed that a student mistook that 7 yards 5inches is 89 inches. But the wrong answer was used by the teacherand no one noticed.

Chi-Kwong Li

Ma used the questions developed by TELT (Teaching Education andLearning to Teach Study) at the NCRTE (National Center forResearch on Teacher Education) to interviewed teachers from Chinaand US.

The 23 US teachers interviewed by TELT project members weresupposed to be better than average:* 11 experienced (dedicated and confident) teachers participating inthe SummerMath for Teachers Program at Mount Holyoke College.* 12 participants of Graduate Intern Program run by a schooldistrict and U. of New Mexico.

Ma interviewed 72 teachers from 5 elementary schools in Chinaranging from very high to very low quality.

Chapters 1 - 4 presented the interview results.

In Chapter 5, Ma explained the situation using the idea of profoundunderstanding of fundamental mathematics (PUFM).

Chapter 6 described how Chinese teachers achieved PUFM, andwhy US teachers could not.

Chapter 7 proposed possible change in US.

Chi-Kwong Li

Ma used the questions developed by TELT (Teaching Education andLearning to Teach Study) at the NCRTE (National Center forResearch on Teacher Education) to interviewed teachers from Chinaand US.

The 23 US teachers interviewed by TELT project members weresupposed to be better than average:

* 11 experienced (dedicated and confident) teachers participating inthe SummerMath for Teachers Program at Mount Holyoke College.* 12 participants of Graduate Intern Program run by a schooldistrict and U. of New Mexico.

Ma interviewed 72 teachers from 5 elementary schools in Chinaranging from very high to very low quality.

Chapters 1 - 4 presented the interview results.

In Chapter 5, Ma explained the situation using the idea of profoundunderstanding of fundamental mathematics (PUFM).

Chapter 6 described how Chinese teachers achieved PUFM, andwhy US teachers could not.

Chapter 7 proposed possible change in US.

Chi-Kwong Li

Ma used the questions developed by TELT (Teaching Education andLearning to Teach Study) at the NCRTE (National Center forResearch on Teacher Education) to interviewed teachers from Chinaand US.

The 23 US teachers interviewed by TELT project members weresupposed to be better than average:* 11 experienced (dedicated and confident) teachers participating inthe SummerMath for Teachers Program at Mount Holyoke College.

* 12 participants of Graduate Intern Program run by a schooldistrict and U. of New Mexico.

Ma interviewed 72 teachers from 5 elementary schools in Chinaranging from very high to very low quality.

Chapters 1 - 4 presented the interview results.

In Chapter 5, Ma explained the situation using the idea of profoundunderstanding of fundamental mathematics (PUFM).

Chapter 6 described how Chinese teachers achieved PUFM, andwhy US teachers could not.

Chapter 7 proposed possible change in US.

Chi-Kwong Li

Ma used the questions developed by TELT (Teaching Education andLearning to Teach Study) at the NCRTE (National Center forResearch on Teacher Education) to interviewed teachers from Chinaand US.

The 23 US teachers interviewed by TELT project members weresupposed to be better than average:* 11 experienced (dedicated and confident) teachers participating inthe SummerMath for Teachers Program at Mount Holyoke College.* 12 participants of Graduate Intern Program run by a schooldistrict and U. of New Mexico.

Ma interviewed 72 teachers from 5 elementary schools in Chinaranging from very high to very low quality.

Chapters 1 - 4 presented the interview results.

In Chapter 5, Ma explained the situation using the idea of profoundunderstanding of fundamental mathematics (PUFM).

Chapter 6 described how Chinese teachers achieved PUFM, andwhy US teachers could not.

Chapter 7 proposed possible change in US.

Chi-Kwong Li

Ma used the questions developed by TELT (Teaching Education andLearning to Teach Study) at the NCRTE (National Center forResearch on Teacher Education) to interviewed teachers from Chinaand US.

The 23 US teachers interviewed by TELT project members weresupposed to be better than average:* 11 experienced (dedicated and confident) teachers participating inthe SummerMath for Teachers Program at Mount Holyoke College.* 12 participants of Graduate Intern Program run by a schooldistrict and U. of New Mexico.

Ma interviewed 72 teachers from 5 elementary schools in Chinaranging from very high to very low quality.

Chapters 1 - 4 presented the interview results.

In Chapter 5, Ma explained the situation using the idea of profoundunderstanding of fundamental mathematics (PUFM).

Chapter 6 described how Chinese teachers achieved PUFM, andwhy US teachers could not.

Chapter 7 proposed possible change in US.

Chi-Kwong Li

Ma used the questions developed by TELT (Teaching Education andLearning to Teach Study) at the NCRTE (National Center forResearch on Teacher Education) to interviewed teachers from Chinaand US.

The 23 US teachers interviewed by TELT project members weresupposed to be better than average:* 11 experienced (dedicated and confident) teachers participating inthe SummerMath for Teachers Program at Mount Holyoke College.* 12 participants of Graduate Intern Program run by a schooldistrict and U. of New Mexico.

Ma interviewed 72 teachers from 5 elementary schools in Chinaranging from very high to very low quality.

Chapters 1 - 4 presented the interview results.

In Chapter 5, Ma explained the situation using the idea of profoundunderstanding of fundamental mathematics (PUFM).

Chapter 6 described how Chinese teachers achieved PUFM, andwhy US teachers could not.

Chapter 7 proposed possible change in US.

Chi-Kwong Li

Ma used the questions developed by TELT (Teaching Education andLearning to Teach Study) at the NCRTE (National Center forResearch on Teacher Education) to interviewed teachers from Chinaand US.

The 23 US teachers interviewed by TELT project members weresupposed to be better than average:* 11 experienced (dedicated and confident) teachers participating inthe SummerMath for Teachers Program at Mount Holyoke College.* 12 participants of Graduate Intern Program run by a schooldistrict and U. of New Mexico.

Ma interviewed 72 teachers from 5 elementary schools in Chinaranging from very high to very low quality.

Chapters 1 - 4 presented the interview results.

In Chapter 5, Ma explained the situation using the idea of profoundunderstanding of fundamental mathematics (PUFM).

Chapter 6 described how Chinese teachers achieved PUFM, andwhy US teachers could not.

Chapter 7 proposed possible change in US.

Chi-Kwong Li

Ma used the questions developed by TELT (Teaching Education andLearning to Teach Study) at the NCRTE (National Center forResearch on Teacher Education) to interviewed teachers from Chinaand US.

The 23 US teachers interviewed by TELT project members weresupposed to be better than average:* 11 experienced (dedicated and confident) teachers participating inthe SummerMath for Teachers Program at Mount Holyoke College.* 12 participants of Graduate Intern Program run by a schooldistrict and U. of New Mexico.

Ma interviewed 72 teachers from 5 elementary schools in Chinaranging from very high to very low quality.

Chapters 1 - 4 presented the interview results.

In Chapter 5, Ma explained the situation using the idea of profoundunderstanding of fundamental mathematics (PUFM).

Chapter 6 described how Chinese teachers achieved PUFM, andwhy US teachers could not.

Chapter 7 proposed possible change in US.

Chi-Kwong Li

Ma used the questions developed by TELT (Teaching Education andLearning to Teach Study) at the NCRTE (National Center forResearch on Teacher Education) to interviewed teachers from Chinaand US.

The 23 US teachers interviewed by TELT project members weresupposed to be better than average:* 11 experienced (dedicated and confident) teachers participating inthe SummerMath for Teachers Program at Mount Holyoke College.* 12 participants of Graduate Intern Program run by a schooldistrict and U. of New Mexico.

Ma interviewed 72 teachers from 5 elementary schools in Chinaranging from very high to very low quality.

Chapters 1 - 4 presented the interview results.

In Chapter 5, Ma explained the situation using the idea of profoundunderstanding of fundamental mathematics (PUFM).

Chapter 6 described how Chinese teachers achieved PUFM, andwhy US teachers could not.

Chapter 7 proposed possible change in US.

Chi-Kwong Li