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.

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.

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.

Recently we traveled to Alsace for the Christmas holiday for an overdue reunion with friends. We are “les invités” although frankly, we invited ourselves to join these friends and their family hoping to add to their pleasure but knowing that we also add to the work and expense of the holidays. In French, hôte is a role that applies to both host and guest, so not surprisingly, we fight over who has the right to pay the bill at the restaurant when we go out to eat. We are told not to bring anything with us when we eat at our friends’ home, but we do anyway. Our conversations are sometimes in English and sometimes in French because we all want to practice our language skills. My husband makes great strides in the new language because he never hesitates to try it. He tends to use whatever French words he knows to replace their English counterparts in his conversations. Sometimes he composes complete sentences in French.

Though I am thousands of miles away from my actual home, I do feel immediately “at home” once we are with these long-time friends who will almost always understand my lazy French accidentally sprinkled with Spanish words and US phrasing. It’s not so much that I “make myself at home” but that these friends make me feel that I truly belong with them and among their family as we celebrate Christmas together. So I relax and am comfortable. We are nine in the house for dinner on Christmas Eve with ourselves, our friends, their adult children and their partners and my friend’s mother, who was my host mother for that summer after high school when I lived with their family in Strasbourg. This was the woman (and her daughter) who endured my tears and complaints when I didn’t yet feel at home, when the culture and way of life here seemed strange and even “wrong” to me. They didn’t hesitate to argue with me about small things like the fact that I wanted to shampoo my hair every day, or show impatience when I made them late, but they also never hesitated to include me in family circle. I was simply one of them, and my fondest memories include the many moments when I felt that strong connection.

Strasbourg, France at this time of year calls itself the “Capitol of Christmas” and it is easy to get into this spirit. The air is filled with the citrus and anise scented “vin chaud” or hot wine that is sold for 2 Euro in many of the Christmas market stalls here, alongside ridiculous holiday hats in the shape of storks, delicate glass Christmas ornaments, gingerbread cookies and advent calendars. Buildings are decorated with lights and ribbons, stuffed bears, stars and glass balls. There has been some snow and more is expected. Christmas carols – often American tunes – are played, and children dressed in animal hats or hoods with mittens recount long stories to their parents who gently pull them through the narrow streets. The gray and foggy days end in darkness at 4:30 as the Christmas lights come on in the city as we step carefully on the snow-covered cobblestones. The narrow streets, the cathedral, the snow and decorations all seem to come from a much-loved fairy tale where magic still exists and the princess always gets her prince. We know that life is not always like this, but we set aside those thoughts for a while and let ourselves be drawn into the atmosphere.

You never told me I couldn’t smoke!

Anyone who has read Edward Hall’s work will probably remember that the USA is characterized as a “low-context” culture because we focus largely on what is explicitly expressed in our communication. Just as parents would exhaust themselves trying to expressly forbid every unwanted activity that their daughters or sons might think to do, even a low-context culture cannot construct itself without some shared and unspoken context. Even my mother’s cousin’s belief that anything not expressly forbidden is allowed is an assumption that fails. Why wouldn’t she as easily assume that anything not explicitly allowed is forbidden?

It’s hard to imagine a five-year-old child in the USA who truly believes that her parents would allow her to smoke, and I have no reason to doubt that even in the first half of the 20th Century in the USA, my mother’s cousin also picked up enough information from the context around her to sneak the cigarettes and smoke them outside somewhere away from the view of the kitchen window rather than simply to ask for them, as she would have asked for a drink of water or something to eat. Her defense is disingenuous, a clever way to soften the punishment. I suspect also, that this was not the last time in her life that she pleaded ignorance of the rules in an attempt to avoid the consequence of not following them.  Perhaps it is an indication of the low-context culture in the USA that this often does work.  How could you be expected to know something if you weren’t explicitly told?

But in fact, we are expected to know many things that we aren’t explicitly told, even in the US. Part of growing up is learning to observe and evaluate the social context in which we live as well as participate in it. Of course, parents will teach their children specific rules and manners and provide guidelines for making judgments about new situations, but even at the age of five, children already have picked up much more than their parents ever told them about the society in which they live. They can often distinguish fairly accurately what sorts of behavior one parent will accept that the other will not. They will have noticed the fact that there are norms and values that exist in the larger society that are substantially different from those of their parents and will draw conclusions about the position of their family vis a vis the larger society.

Exchange students and others going abroad to a new country will often try to find the “Dos and Don’ts” — a list of rules to avoid social missteps. Sometimes this can be helpful, especially when the rules are both subtle and unexpected. It’s comforting to have some answers, but a few explicit rules are as inadequate in guiding your social skills in the new culture as the bilingual dictionary you may carry is in guiding your conversations. Much of the knowledge needed to understand and participate in another culture is like what you observe in through your peripheral vision. If you wear blinders to go from Point A to Point B, you only get to Point B. Intercultural learning is seldom about Point B and the narrow path to get there. But if you knew when you were 5 that smoking was forbidden, and no one told you so, you probably still have some of the skill needed to learn a new culture’s unspoken rules.

First the articles: How could I not be drawn to the article accompanying the photo of  little Indonesian children learning how to make coffee? The article highlighted a trend of many wealthy Indonesian parents who choose to send their children to private Indonesian schools that teach only in English. The result, it seems is that these children do not speak Bahasa Indonesian well. This prompts questions about the future language of business, law, medicine, engineering, or literature and the arts in Indonesia. What would it mean for national unity in Indonesia to have the nation’s elite who are not fluent in the national language? And what would it mean for those in the ”other” education system taught in Bahasa?

That same day, the Times printed an article that raises concerns about the equity of the entrance exam for the “Gifted Kindergarten” programs run by the New York City’s Board of Education, particularly when so many parents with resources take their children to private preparation classes that train them to be more poised and confident when meeting with the examiner. Poise and confidence in a 5-year-old do not necessarily relate to unusually high intelligence, but such traits have frequently been socially and culturally encouraged among a certain subset of US parents who may also tend to have decent incomes and are willing to pay a little more for access to a high quality publicly provided education. The Times is perhaps reporting this story about 25 years after I became aware of equity problems in the entrance exam for the gifted program. At that time, friends of mine who had a perfectly bright and appealing young son took him into be tested for the “gifted” kindergarten. He became suddenly shy and hid behind his mother’s skirt, refusing to answer the questions posed to him, even though all the questions were well within his ability. He did not get into the program. Among the children I knew who did get into this program, there were none that I would consider to be child prodigies with special needs; just children who are quick to learn, similar to many others found at the top of their classrooms.

This brings me to the third article, describing the results of  longitudinal research with students who had been randomly assigned to kindergarten classrooms in the 1980s. While nothing could seem to be fairer than assigning students randomly to classrooms, clearly there were different teachers with different levels of skill, and the impact of what some of these classrooms were able to teach the kindergarteners can still be seen today in terms of the incomes earned by these former students compared to those in the other classrooms. What I did not see described is what those teachers did in those classrooms, though the study looks also at the positive effects of having experienced teachers and small class size.

I took this photo a few years ago at the "Junior Festival" in Verona, Italy. I was reminded of it by the image of the Indonesian children making coffee.

I can’t argue that wage-earning power is an irrelevant goal for education, and yet in my experience what a person is paid for the work they do has very little relationship to the value of that work for the good of society — especially at the extremes.  I might want to pick a mix of indicators of achievement, participation in society, and satisfaction with one’s adult life. I’m probably looking for a “wisdom” measure. What constitutes the “success” that education seeks to achieve is bound up in a broad range of cultural values and assumptions. Some of these have to do with beliefs about the ultimate purpose of life; others focus on beliefs about the process of learning and assumptions about intellectual, physical, and moral development. Schools openly promote specific values based on models of behavior and achievement admired in their culture, or in their specific social segment of the larger society. For example, a Catholic school for men in my study sample promotes the idea of the “gentleman” with values such as ”sportsmanship” and a “strong work ethic” but also with strong ”solidarity with those marginalized by poverty and injustice.”   These values are not mentioned by every school, and one has to think that it colors the education there.

As I slowly continue my research in may spare time, I would love to know more about the goals, values and particularly the driving beliefs and assumptions of the Indonesian English-language schools and the “gifted” programs in New York and elsewhere in which a subset of the population is given a special type of academic training that most of the society does not receive. Of course, these would not be the only schools embedded in a system of indirect or unintended consequences.

The article quotes Jay Jacobs, director of a summer camp where “friendship coaches” have been hired to try to split up campers who become to close to one another:

I don’t think it’s particularly healthy for a child to rely on one friend. If something goes awry, it can be devastating. It also limits a child’s ability to explore other options in the world.

It has often been noted that U.S. culture is highly individualistic, but I’ve never before read such a clear statement of this value as it pertains to friendship. It does, of course, fit with an entire genre of popular songs about the “ramblin’ man” who can’t possibly give up his freedom to commit to a married life with just one woman.

Lest readers from other parts of the world assume that the effort to engineer children’s friendship patterns is unchallenged, the article also cites several U.S. psychologists who believe that this is a bad idea. Many Americans do have long-term best friends, of course, but it is also true that friendships among adults in the U.S.A. are often compartmentalized and dependent on setting appointments and “finding the time” to get together. That time together is usually enjoyed and valued, often with regrets that it cannot happen more frequently. The affection and the pleasure in each others company is real, but for many, it seems, life holds stronger priorities, including a close relationship with a spouse or partner, caring for the children, and a career. These “other options in the world” can sometimes limit our ability to build and maintain strong, close friendships.

Some years ago I attended a training program dealing with stress management. One of the suggestions that I recall well was to put telephone calls to friends on your “to-do” list so that you did not get so absorbed in your career that you neglected your friends. This struck me as funny, but it probably is a decent coping strategy and I have resorted to it myself. If my priorities are to be dictated by the calendar and the to-do lists I create for myself at home or at work, it makes sense to make sure that list includes friendship. I would prefer it to be spontaneous, but instead it is chosen.

It was also exciting to know that the community college where I now work was honored with a “Simon Spotlight Award” at the Friday plenary. It was a great way to conclude the conference.

Read more at Eyes on NAFSA

A week ago I was struck by Stan Katz’s blog post at the Chronicle of Higher Education. There seems to be wide agreement that “international education” is crucial, but there seems little consensus on exactly what this means. Katz complains about the language he frequently sees that talks about international education in terms of US competitiveness in a global economy. Those who follow Intercultural Eyes may recognize some of the familiar themes that I have advocated based on my long career of working with intercultural learning through high school exchange programs. For me, international education involves flexibility and communication skills to build relationships across cultures. It demands perceptual skills and self-awareness to recognize subtle variations and nuances of life in a different place. And it requires an attitude that views the self in an international context with humility and respect for all humanity. I am still struggling to find the rubrics to assess these “educational outcomes” than relate more to character development than content. But I also need to clarify my theory about the development of respect, for instance. Or how flexibility is developed: My hypothesis is that flexibility is related to comfort and confidence while rigidity is related to fear and discomfort. But I don’t know this for certain. Courage without fear is only foolishness.

Language and communication skills can be tested, and the IDI is related to perception and awareness as well as attitudes. Anxiety can me assessed, but low anxiety is not equal to bravery. As we seek to assess education, it is important to understand our goals in their cultural context, and to continue to study other cultures to explore new approaches, new theories, new learning objectives. My hope is that we do not simplify our teaching efforts to meet only those goals that are simple to define and measure.

The research I conducted with AFS alumni from the 1980s suggested a relationship between international experiences and intercultural sensitivity, but so often the first experience came from childhood exposure to other countries and cultures, and especially from parents who encouraged their children to meet people from other countries and cultures. The fact that participation in an AFS high school program so often runs in a family reinforces this theme: the motivation is already there.

As a result, I’ve been thinking about motivation, which increasingly strikes me as the most important variable in developing intercutural understanding. While groups involved in violent conflict or even just verbal conflict may grow tired of conflict, they are more likely to be motivated to avoid the other group than to engage them, even though engagement may ultimately be more productive in ending the conflict.

If motivation for study abroad often comes from parents, then why do parents encourage their children to meet people from other cultures? I would guess the impetus is similar to encouraging their children to enjoy music, play sports, read books, go to museums. While there may be an element of “it’s good for you” in the push parents give to these activities, I would suppose that in general, parents who encourage their children to study abroad believe that other cultures are interesting and attractive. 

This caused me to revisit the work of Todd Pittinsky on allophilia. Five years ago when I first learned of his work, allophilia reminded me of the “Reversal” type of defense in the Bennett model, which emphasizes an excessive focus on the flaws of one’s own culture and an idealized view of the other culture. Presentations of Bennett’s model often exclude the dicussion of “Reversal” which is one of three types of “Defense” experiences. Developmentally, Reversal is seen as no more advanced than Defense, but rather is Defense against one’s own culture. Nevertheless, the factor analysis that was used in creating the IDI scales clearly showed that Reversal was a unique scale, seperate from the Defense scales. Though a Reversal outlook still experiences cultures as “Us” versus “Them” it may well be the tipping point that pushes people to engage with other cultures.

Reversal is not exactly allophilia, which focuses on the attraction, comfort, affection, kinship, and engagement with the other culture or group, but there may well be a correlation between the two concepts. Of course, the exchange student who arrives in a new culture with nothing but good things to say about it tends to be more welcomed in the host family than the one who constantly talks about what’s better back home. And that first exchange student may be more motivated to change, to learn, and to form new relationships with people in the other culture. In a newer article, Pittinsky lists some common and simple ways to try to generate interest and familiarity with other cultures in the classroom. These may be some of the same things that parents do to encourage their children to become interested and engaged with other cultures.

Might attitudes of allophila prevent conflict? My guess would be no. My research has found that Defense frequently exists side by side with Reversal in many individuals’ experience of other cultures. A certain level of conflict is even quite compatible within many committed relationships. But the attitudes of allophilia — particularly affection, kinship (or belonging) and engagement — are essential for the kind of personal commitment that would be crucial to maintain a relationship when conflict occurs.