Knowing and Teaching Elementary Mathematics ckli/Courses/m150-1.pdfKnowing and Teaching Elementary Mathematics ... she became the principal of the local school. ... Knowing and Teaching Elementary Mathematics Introduction ...

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<ul><li><p>Knowing and Teaching Elementary MathematicsIntroduction</p><p>Chi-Kwong LiThe College of William and Mary</p><p>September, 2007</p><p>Chi-Kwong Li</p></li><li><p>Chinese view of Eduction</p><p>Before Cultural Revolution (1966-69)</p><p>Four important types of professions</p><p>Scholars</p><p>Farmers</p><p>Workers</p><p>Merchants</p><p>During and post cultural revolution</p><p>The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.</p><p>All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).</p><p>Educated people were sent to countryside to be re-educated bypeople in the countryside.</p><p>Chi-Kwong Li</p></li><li><p>Chinese view of Eduction</p><p>Before Cultural Revolution (1966-69)</p><p>Four important types of professions</p><p>Scholars</p><p>Farmers</p><p>Workers</p><p>Merchants</p><p>During and post cultural revolution</p><p>The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.</p><p>All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).</p><p>Educated people were sent to countryside to be re-educated bypeople in the countryside.</p><p>Chi-Kwong Li</p></li><li><p>Chinese view of Eduction</p><p>Before Cultural Revolution (1966-69)</p><p>Four important types of professions</p><p>Scholars</p><p>Farmers</p><p>Workers</p><p>Merchants</p><p>During and post cultural revolution</p><p>The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.</p><p>All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).</p><p>Educated people were sent to countryside to be re-educated bypeople in the countryside.</p><p>Chi-Kwong Li</p></li><li><p>Chinese view of Eduction</p><p>Before Cultural Revolution (1966-69)</p><p>Four important types of professions</p><p>Scholars</p><p>Farmers</p><p>Workers</p><p>Merchants</p><p>During and post cultural revolution</p><p>The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.</p><p>All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).</p><p>Educated people were sent to countryside to be re-educated bypeople in the countryside.</p><p>Chi-Kwong Li</p></li><li><p>Chinese view of Eduction</p><p>Before Cultural Revolution (1966-69)</p><p>Four important types of professions</p><p>Scholars</p><p>Farmers</p><p>Workers</p><p>Merchants</p><p>During and post cultural revolution</p><p>The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.</p><p>All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).</p><p>Educated people were sent to countryside to be re-educated bypeople in the countryside.</p><p>Chi-Kwong Li</p></li><li><p>Chinese view of Eduction</p><p>Before Cultural Revolution (1966-69)</p><p>Four important types of professions</p><p>Scholars</p><p>Farmers</p><p>Workers</p><p>Merchants</p><p>During and post cultural revolution</p><p>The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.</p><p>All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).</p><p>Educated people were sent to countryside to be re-educated bypeople in the countryside.</p><p>Chi-Kwong Li</p></li><li><p>Chinese view of Eduction</p><p>Before Cultural Revolution (1966-69)</p><p>Four important types of professions</p><p>Scholars</p><p>Farmers</p><p>Workers</p><p>Merchants</p><p>During and post cultural revolution</p><p>The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.</p><p>All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).</p><p>Educated people were sent to countryside to be re-educated bypeople in the countryside.</p><p>Chi-Kwong Li</p></li><li><p>Chinese view of Eduction</p><p>Before Cultural Revolution (1966-69)</p><p>Four important types of professions</p><p>Scholars</p><p>Farmers</p><p>Workers</p><p>Merchants</p><p>During and post cultural revolution</p><p>The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.</p><p>All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).</p><p>Educated people were sent to countryside to be re-educated bypeople in the countryside.</p><p>Chi-Kwong Li</p></li><li><p>Chinese view of Eduction</p><p>Before Cultural Revolution (1966-69)</p><p>Four important types of professions</p><p>Scholars</p><p>Farmers</p><p>Workers</p><p>Merchants</p><p>During and post cultural revolution</p><p>The cultural revolution was motivated by the power strugglebetween Zedong Mao and Shaoqi Liu.</p><p>All the old custom and tradition were challenged and destroyed (sothat Liu could be challenged and removed from power).</p><p>Educated people were sent to countryside to be re-educated bypeople in the countryside.</p><p>Chi-Kwong Li</p></li><li><p>Background of Liping Ma</p><p>As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.</p><p>Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).</p><p>Soon, she became the principal of the local school.</p><p>A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.</p><p>After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.</p><p>She finished her study, and her thesis grew into this influential book.</p><p>Chi-Kwong Li</p></li><li><p>Background of Liping Ma</p><p>As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.</p><p>Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).</p><p>Soon, she became the principal of the local school.</p><p>A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.</p><p>After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.</p><p>She finished her study, and her thesis grew into this influential book.</p><p>Chi-Kwong Li</p></li><li><p>Background of Liping Ma</p><p>As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.</p><p>Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).</p><p>Soon, she became the principal of the local school.</p><p>A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.</p><p>After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.</p><p>She finished her study, and her thesis grew into this influential book.</p><p>Chi-Kwong Li</p></li><li><p>Background of Liping Ma</p><p>As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.</p><p>Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).</p><p>Soon, she became the principal of the local school.</p><p>A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.</p><p>After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.</p><p>She finished her study, and her thesis grew into this influential book.</p><p>Chi-Kwong Li</p></li><li><p>Background of Liping Ma</p><p>As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.</p><p>Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).</p><p>Soon, she became the principal of the local school.</p><p>A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.</p><p>After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.</p><p>She finished her study, and her thesis grew into this influential book.</p><p>Chi-Kwong Li</p></li><li><p>Background of Liping Ma</p><p>As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.</p><p>Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).</p><p>Soon, she became the principal of the local school.</p><p>A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.</p><p>After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.</p><p>She finished her study, and her thesis grew into this influential book.</p><p>Chi-Kwong Li</p></li><li><p>Background of Liping Ma</p><p>As an eighth grader in Shanghai, she was sent to the countryside tobe re-educated by peasants.</p><p>Instead of working in the field, she was asked to teach in the localschool (two classes of all subjects).</p><p>Soon, she became the principal of the local school.</p><p>A few years later, she returned to Shanghai and studied moreeducational theory from Professor Liu.</p><p>After getting a master degree, she went to US in 1988 to pursue aPh.D. in mathematical education at Michigan State University andStanford University.</p><p>She finished her study, and her thesis grew into this influential book.</p><p>Chi-Kwong Li</p></li><li><p>The study of Liping Ma</p><p>Chinese students typically outperform US students.</p><p>Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.</p><p>To explain this paradox, Liping Ma studied teachers understandingof fundamental mathematics in China and the US.</p><p>Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.</p><p>Two motivating examples</p><p>In teaching division with fractions, how to explain 1 34 divided by12 .</p><p>Can one make up a good story?</p><p>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.</p><p>Chi-Kwong Li</p></li><li><p>The study of Liping Ma</p><p>Chinese students typically outperform US students.</p><p>Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.</p><p>To explain this paradox, Liping Ma studied teachers understandingof fundamental mathematics in China and the US.</p><p>Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.</p><p>Two motivating examples</p><p>In teaching division with fractions, how to explain 1 34 divided by12 .</p><p>Can one make up a good story?</p><p>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.</p><p>Chi-Kwong Li</p></li><li><p>The study of Liping Ma</p><p>Chinese students typically outperform US students.</p><p>Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.</p><p>To explain this paradox, Liping Ma studied teachers understandingof fundamental mathematics in China and the US.</p><p>Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.</p><p>Two motivating examples</p><p>In teaching division with fractions, how to explain 1 34 divided by12 .</p><p>Can one make up a good story?</p><p>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.</p><p>Chi-Kwong Li</p></li><li><p>The study of Liping Ma</p><p>Chinese students typically outperform US students.</p><p>Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.</p><p>To explain this paradox, Liping Ma studied teachers understandingof fundamental mathematics in China and the US.</p><p>Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.</p><p>Two motivating examples</p><p>In teaching division with fractions, how to explain 1 34 divided by12 .</p><p>Can one make up a good story?</p><p>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.</p><p>Chi-Kwong Li</p></li><li><p>The study of Liping Ma</p><p>Chinese students typically outperform US students.</p><p>Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.</p><p>To explain this paradox, Liping Ma studied teachers understandingof fundamental mathematics in China and the US.</p><p>Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.</p><p>Two motivating examples</p><p>In teaching division with fractions, how to explain 1 34 divided by12 .</p><p>Can one make up a good story?</p><p>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.</p><p>Chi-Kwong Li</p></li><li><p>The study of Liping Ma</p><p>Chinese students typically outperform US students.</p><p>Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.</p><p>To explain this paradox, Liping Ma studied teachers understandingof fundamental mathematics in China and the US.</p><p>Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.</p><p>Two motivating examples</p><p>In teaching division with fractions, how to explain 1 34 divided by12 .</p><p>Can one make up a good story?</p><p>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.</p><p>Chi-Kwong Li</p></li><li><p>The study of Liping Ma</p><p>Chinese students typically outperform US students.</p><p>Chinese teachers (in those days) only had 9 year education, plus 2year teacher training vs. US teachers often had college degrees.</p><p>To explain this paradox, Liping Ma studied teachers understandingof fundamental mathematics in China and the US.</p><p>Previous explanations: learning gap, difference in cultural contexts,parental expectations, number-word systems, school organization,amount of time spent learning mathematics, mathematics curricula.</p><p>Two motivating examples</p><p>In teaching division with fractions, how to explain 1 34 divided by12 .</p><p>Can one make up a good story?</p><p>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.</p><p>Chi-Kwong Li</p></li><li><p>The study of Liping Ma</p><p>Chinese students typically outperform US students.</p><p>Chinese teachers (in those days) only had 9 year education, plus 2year teacher tr...</p></li></ul>

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