98. The culture of math teaching December 11, 2011
Posted by Bettina Hansel in Education and Culture.Tags: math
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What is important to learn?
In the USA, math has long been seen as a difficult subject, and often as one that only some people can master. But math, unlike subjects such as philosophy, anthropology, geography, or sometimes foreign languages, is almost always a required course of study both in high school and college in the United States. And quite regularly, many students fail to learn the concepts and formulas that the math courses require. I have been attending a conference this week about new approaches to teaching and learning basic math concepts for under-prepared college students in the USA. The approach we are taking has been inspired in part by some research of Japanese teaching and learning styles, which seemed to the American researcher to be a very innovative approach. Yet the Japanese teachers insisted that their methodology in fact came from the USA.
My thoughts about math and culture lately have come both from my participation in this project and from my husband’s recent career change that is leading him to take more math than he ever thought he’d need. I tend to believe that further study into almost any field is valuable, but algebra seemed to be the subject I had most forgotten and least used over the years since my last course in college algebra. Still, this project intrigued me, and never being one to spurn an intellectual challenge, I became obsessed with one of the sample algebra problems being considered for the course. The problem dealt with creating a formula to describe relationship between decibels of rock music over time and hearing loss. I could graph several different values and understood that there was an exponential relationship here, but I didn’t seem to be able to put this in an equation true for all cases.
Educational systems are cultures, and as such teachers, administrators, students and the larger society make decisions about students should learn and how best to teach it, basing these decisions on values, beliefs and assumptions that are deeply bound to various other aspects of the culture and how it defines and interprets both history and recent experience. Mathematical concepts and numeric relationships are broadly universal, but there is no such universal consensus about when or how to teach math and to whom.
The methodology for teaching math that we are exploring in this group is one that really begs the question: Does everyone really need to take algebra? Determined to refute the idea that some people cannot understand math, this method focuses largely on understanding how the students think. It relies on the belief that students who are pushed to think about real-world problems and to figure out for themselves how they might be solved, and are not just given solutions to memorize, will in fact be able to discover for themselves various solutions to the problem. The practice of thinking through problems and finding solutions is seen as more valuable to the students in developing their competence with numbers and mathematical concepts.
This seems very much in keeping with current academic culture in the US that embraces “student-centered” learning over “sage on the stage” teaching which is seen as the traditional model. With a basis in “real-world” problems, this method also endorses the value of education that leads to application rather than emphasizing abstract thinking and knowledge for its own sake.
I must admit that I am intrigued with the new approach and more than ready to question the value of traditional algebra and traditional approaches to teaching to try something new with the students who seem to fail repeatedly in math classes. And yet I am sure that my own ability to think logically, grasp concepts and solve problems was also formed soundly by the algebra, geometry, and trigonometry lectures I received in Cuban-accented English, illustrated only with chalk on a board. What made her such a good math teacher? I have pondered this off an on over the past months since I learned of her death earlier this year. Was it simply the way she organized and presented the material? Was it somehow helpful that she had to translate her own knowledge into our language? All I know is that anytime I see an algebraic equation, I hear it in my mind in a strong Spanish accent. And I’m not the only one to do so.
Gracias, doctora. No le olvidaré jamás.
97. Group encounters across cultures. July 23, 2011
Posted by Bettina Hansel in Culture and Communication.Tags: exchange students, telephone calls
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In the 1980s, the exchange organization I worked for very much discouraged exchange students from telephoning home. The same was true of my daughter’s summer camp. Since there was only the camp phone number — no cell phones back then — the camp controlled the telephone use. In both cases, it was firmly believed that the parents’ calls to their children interfered with the children’s adjustment abroad or to the camp. That is what years of experience had told them: You can’t fully participate in the social life and the culture here if you’re constantly communicating back home. From a research perspective, I both respect the wisdom of years of experience and doubt the validity of a conclusion that isn’t based on some firm data. But until someone randomly assigns some exchange students or campers to endless phone class back home while another randomly selected group has their cell phones confiscated and monitors the adjustment of those in each group, we may tend to rely on the wisdom of experience even as it becomes increasingly hard to control the contact back home. But how would such research about cell phone use define adjustment success? It would most certainly be a measure of the individual student or camper’s satisfaction, learning, and interaction with others.
Coming from a very individualistic society, and having worked for an exchange program that sent individual students abroad to live with a host family, it’s not surprising that I have usually thought of the cross-cultural experience in terms of the individual from one culture who comes in contact with another culture. But I realize that this approach really misses the point. It may be even more common for a group from one culture to come in contact with another culture, and it is in this situation where cross cultural navigational skills are surely tested since your individual behavior is always on display to your own group.
Thinking back to exchange students (or summer campers), it makes perfect sense that one of the most frequently reported outcomes of their experience is an increased sense of autonomy and independence. A common re-entry adjustment issue for exchange students is the fact that their friends and family back home have very little interest in understanding the intense experience they just had bonding with other people in another culture. How totally different their experience would be if they were not the lone explorers of this new and fascinating cultural space, but rather came to the experience along with their parents and siblings! Yet it could still be an enriching experience for the family.
Inserting a group from one culture into another culture, whether a study abroad group, a group of refugees, an ex-patriot family, or even a group of New York work colleagues headed on a business trip to California, is a seriously different experience from that of the solo sojourner or the foreign manager from the head office. It isn’t a question of limiting or controlling the level of contact with those back home — they are they with you, and the social and cultural context that you share will also be present constantly as the group navigates the cultural waters of the new culture. It is not possible, or even desirable, to dismantle the social hierarchy of your home group because it is your group, not just you personally, that needs to shift to accommodate the demands of the other culture.
The goal in these cases is not typically to integrate individually into the other culture (though this may be the goal for some group study abroad programs). Rather, the group will seek to maintain its own culture’s goals and interests, and to enrich the group with the experience and interaction with the other culture. If this is a peace-building encounter, it is especially important that the group maintains its integrity and identity. The leader cannot force cultural adaptations and concessions to the host culture that the group as a whole does not want nor understand. In some cases, one member of the group may serve as a linguistic or cultural translator, but that may not be the same individual who leads the group or makes decisions.
A group cultural exchange calls on the individual members to consider their own culture in the context of the host culture. I have no model for this, but I would look for an outcome in which group behaviors became more flexible, and the group as a whole became more aware of its cultural context while considering how to integrate new possible futures.
96. Nixon in China January 31, 2011
Posted by Bettina Hansel in Reflections.Tags: Nixon in China
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It was in February in 1972 when Nixon went to China. I was a university student then, with not much use for Nixon, but with a naive interest in China. In high school I had checked out a translation of Mao’s “little red book” from the library, and read it cover to cover in the course of three weeks or so. I thought I needed some balance to the information I was getting filtered through my mother’s ultra-conservative journals and the television news. I deliberately did much of my reading in public places, believing that just reading Mao would make me seem rebellious.
I remember almost nothing of what I read, but seeing the last dress rehearsal today of the Metropolitan Opera’s production of John Adams’ opera, Nixon in China, I remember how it felt to read that book. Being quite young, I felt certain that I was living on the cusp of great changes. And no doubt I was. Nixon in China reminded me how much my life has been shaped not just by the one week the Nixons spent in China, but by the culture of 1972 and the years on either side of it.
An iconic song written just seven years earlier simply took the fear of China for granted as something to compare to our own social ills in the USA.
Think of all the hate there is in Red China
Then take a look around to Selma, Alabama
You may leave here for 4 days in space
But when you return, it’s the same old place
The poundin’ of the drums, the pride and disgrace
You can bury your dead, but don’t leave a trace
Hate your next-door neighbor, but don’t forget to say grace
And… tell me over and over and over and over again, my friend
You don’t believe
We’re on the eve
Of destruction
This is the context that I bring with me to the opera; the intensity of my own youth and a particular worldview of that time from the center of the United States. I don’t have a decent feel even now for the Chinese context for this meeting. All of my news — such as it was — came from US sources. While I recognized the references to the Long March and the Cultural Revolution, I don’t know enough about the Chinese view of the Nixon visit. I did not watch any of it on television in spite of its broadcast on “the three networks” the Nixon character mentions in the opera. I didn’t have a television in my dorm room and I was too wrapped up in my studies and in my social life to think about watching this news.
Since this performance was a dress rehearsal, the concert hall was filled with school groups. I wonder what context these students are bringing with them. Have they been told some of the background by their teachers or parents or, especially for the youngest there, their grandparents? History classes have seldom been able to provide me the rich awareness of a prevailing social reality that I brought to this opera, so I expect they bring their own more modern contexts. Perhaps the opera rests on the emotions and thoughts expressed in the lyrics and music sung by the characters, both American and Chinese. In spite of extensive research, much of this still stems from the imagination of the opera’s creative team, especially the lyricist, Alice Goodman who brings a touching and odd poetry to the conversations and inner thoughts of this cast of characters. I was left wondering about the emotional life of human beings in positions of power: what it means for them, how they see themselves, and what they worry about.
* * *
As I read the news today across another ocean, Egypt faces a massive protest movement that seems poised to change the shape of that country dramatically, though perhaps not entirely in the way the young protesters may hope. I can’t help but find myself pulled to read the news stories and even the tweets that provide too little and too often. If not an opera, then certainly there is epic poetry waiting to be written.
