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An English teacher co-teaching trigonometry asked students to explain an equation to a child and to turn discrete problems into a story.

©Shutterstock/Evgeny Atamanenko

I had always hated math. Now I suddenly found myself teaching trigonometry. I was an English teacher in Chicago Public Schools with certification in special education, and when my school was facing a shortage of certified special education teachers, I was pulled in mid-year to co-teach a junior-level trigonometry class with the math teacher.

My students struggled with the calculations, thinking they just weren't good at math. Like me, they hated it. What was the point in working and reworking these calculations? What were we trying to figure out anyway? And I originally agreed with them.

Yet trig slowly became my favorite class of the day. After spending years teaching English and reading, I was being challenged to move beyond what I had always been doing. When you're new to something, you have a fresh perspective. You're willing to take risks. You're willing to try anything because you don't know how something should be done.

I worked with my co-teacher to create a series of supplementary lessons through a different lens to let students experience personal meaning and creativity in their math.

Explaining It to a Baby

I found that many students felt frustrated with math because they needed to come to one single correct answer. This was especially hard with my diverse learners, who struggled with multistep equations. Instead of focusing on coming to the correct answer, my students and I focused on the process of getting there.

I brought in some books from Chris Ferrie's Baby University series-books like General Relativity for Babies and Optical Physics for Babies. The idea is that you don't fully know something unless you can break it down so simply that you can explain it to a young child.

That's the task I gave my students. We started by reading Ferrie's board books to see how simple language and illustrations could be used to explain complex subjects. Next, students chose a multistep equation they had initially struggled with. Working in pairs or small groups, they talked through their thinking and the steps needed to solve the equation. Their partners were encouraged to ask questions and get clarification so the ideas were explained at the simplest level.

Using the books as models, students revised and wrote down their explanations to make them so simple that they could be explained to a young child. After they wrote out their explanations, my co-teacher and I challenged them to create short books using card stock and colored pencils. Students worked with their small groups to talk through ideas and illustrate their books. If they struggled, they were able to pair with another student to create a book together.

Sharing with other students helped them explain ideas in new ways, which helped them develop a deeper understanding. Students were pushed to think metacognitively in order to explain their thinking and their process to others, and the class as a whole gained access to varying perspectives in math by hearing their peers' thought processes. And they were all excited to see how they could use writing and art skills in an authentic way in math class.

Putting the 'Story' in 'Story Problem'

The interesting thing often overlooked in math class is that it already includes stories and real-life connections, in the form of story problems. But the story problems are generally discrete-each is an individual unit, and they don't tell a larger story.

Another issue is that the real-life elements usually don't relate to things that are real issues in students' lives. They might include calculating area so that someone can buy new carpet for their home. Or a story problem might be about landscapers planting a new tree, and needing to calculate the length of wire required to support the tree. These might be things the students will do later as adults, but they're not current issues in the teens' experience.

I used story problems as an opportunity to connect math to students' lives by creating fictional math-based stories. First, students would work in small groups to go through the chapter in their math textbook and collect the story problems, writing them on index cards. Next, students would lay out the cards to see the questions as a whole: Out of 10 or more story problems in the chapter, were there five similar ones they could group together? What problem-solving skills were called for to work on these problems?

Looking at these five unconnected stories, students thought why they needed to solve them, and used their reasons to come up with some type of connected ideas. They created backstories for the names in the problems, in the process turning them into more developed characters. They identified challenges or reasons why the characters needed to solve the problem.

Finally, they combined the story problems they had created and developed a longer narrative to connect these scenarios, an overarching story rooted in authentic math story problems. Survival was a common theme: One group wrote about a zombie apocalypse and another imagined an alien invasion, situations in which characters needed to solve the problems and employ skills that would help them survive. It's true that these stories were not rooted in students' actual lives, but they were more engaging than rug purchases or landscaping.

When they used creative writing skills to develop math story problems about things they were interested in, students became more engaged. They wanted to read the other groups' stories and work on the math in them because they had a real investment in the outcome. The stories helped students find motivation because they created an answer to the question "Why do we need to learn this?"

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An English teacher co-teaching trigonometry asked students to explain an equation to a child and to turn discrete problems into a story.

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Foundations of Culturally and Linguistically Responsive Teaching

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Teachers can provide multiple ways for English learners to engage with lessons and demonstrate their understanding.

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Culturally Responsive Teaching

Middle and high school teachers can cultivate student agency to facilitate conversations about difficult subjects in history class.

isgood teaching. Successful and impactful culturally responsive teaching is a village effort, and members of the community can help you hone these skills. Have resources available for students to process their feelings at school (such as time with a guidance counselor) and for families to help with processing at home. The goal is not to be perfect but rather to be aware, flexible, and responsive.

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3 Ways to Enhance Culturally Responsive Teaching

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Middle and high school teachers can cultivate student agency to facilitate conversations about difficult subjects in history class.

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Teachers who understand both the collectivistic value system of Latino culture and the individualistic culture of U.S. schools can use practices that honor both home and school.

I wanted to understand my students better so I started studying Mexican culture. Then I realized that the children in my class came from many distinct regions, each with different histories and traditions. I just knew that I would never know enough. I had to give up trying.-Kindergarten teacher

This kindergarten teacher voiced the frustration experienced by many teachers. However, she had a different outlook after attending a workshop called Bridging Cultures, which focused on a basic value system common to Latino cultures that transcends languages, histories, and traditions: collectivism (Triandis, 1989). Collectivism is common in Mexico and in Central and South America, particularly among the rural poor who have had limited formal education. Because many Latino immigrants come to the United States with this kind of background, understanding collectivism becomes invaluable for teachers serving immigrant Latino children.

Collectivism Versus Individualism

Collectivism is a cluster of interrelated values that emphasize the interdependence of family members (fig. 1). Within this value system, children are taught to be helpful to others and to contribute to the success of any group they belong to-beginning with the family. Even knowledge of the physical world is placed within a social context.

Figure 1. Features of Individualism and Collectivism

Bridging Cultures with Classroom Strategies - table

The child as an individual

The child as part of the family

Independence

Helpfulness and interdependence

Individual achievement

Group success

Scientific information disengaged from social contexts

Scientific information embedded in social experiences

Authors' note: This represents a partial list of features associated with each value system. For additional qualities, please see Hofstede (1980), Triandis, H. (1989), Rothstein-Fisch, (1998).

In contrast, schools foster individualism, viewing the child as an individual who should be developing independence and valuing individual achievement (Greenfield, 1994). Unlike collectivism, which emphasizes the social context of learning and knowledge, individualism emphasizes information disengaged from its social context (Hofstede, 1980). When collectivistic students encounter individualistic schools, conflicts that are based on hidden values and assumptions can occur: A kindergarten teacher was showing her class an actual chicken egg that would be hatching soon. She was explaining the physical properties of the egg, and she asked the children to describe eggs by thinking about the times they had cooked and eaten eggs. One of the children tried three times to talk about how she cooked eggs with her grandmother, but the teacher disregarded these comments in favor of a child who explained how eggs look white and yellow when they are cracked. (Greenfield, Raeff, &amp; Quiroz, 1995, p. 44)

The first child's answer was typical of the associations encouraged in collectivistic cultures, where objects are most meaningful when they are used in connection with social interactions. However, the teacher expected students to describe eggs as isolated physical entities and did not value the object as a connection among people in social relationships.

The teacher was unaware that her question was ambiguous. Children who shared her orientation assumed that she was interested in the physical properties of the eggs, even though she had not made that point explicit. Children who did not share her orientation made different assumptions. They assumed that she was interested in the object as a mediator of social relationships (Greenfield, Raeff, &amp; Quiroz, 1995).

To help teachers understand the assumptions underlying individualism and collectivism, we developed the Bridging Cultures Project as a research-based, professional development program. We introduced elementary school teachers serving large immigrant Latino populations to a new way of understanding the values that influence behaviors.

When teachers understood that helpfulness is highly valued in collectivistic cultures, they questioned certain classroom practices. For example, in collectivistic households, older children are expected to help younger ones, even when it means putting aside their own task. But teachers often assign individual children to classroom roles, such as chalkboard cleaner or attendance monitor. When friends help one another, teachers may admonish them, saying, "That's Marco's job. You have your own job to do!"

However, once teachers understood the importance of helpfulness in collectivistic cultures, they no longer considered the helpfulness that children learned at home a discipline problem. Teachers began to appoint two children to each task or to allow children to help one another. Clean-up time became pleasant because children helped until the class was clean. These classroom changes increased efficiency, task completion, and classroom harmony. Teachers supported children for being helpful instead of punishing them for interfering with a classmate's responsibility. Helpfulness, a child development goal important to Latino immigrant parents, was valued at school.

Sharing Group Success

A 3rd grade Bridging Cultures teacher, Amanda Perez, mindful of the collectivistic orientation, initiated curriculum changes to systematically expand group learning. First, she increased choral reading so that it became a regular part of daily language arts. Trying out their burgeoning English skills in a group allowed the limited English proficient students to practice the rhythm and the sound of English without being spotlighted.

Perez also used the value of helpfulness in an academic context. At the end of each reading session, she gave each child a copy of the homework. The children discussed the questions, but were not allowed to write down the answers until they were at home. In this way, students more proficient in English helped classmates rehearse the homework. This literacy practice and preview resulted in a 100 percent homework return rate, surpassing the teacher's highest expectations. Perez stated, Most teachers keep students isolated by levels. Now I mix them up. I have also learned that helping one another is not cheating! Because of the Bridging Cultures project, their English is improving. It is so nonthreatening because of the group experience.

In math, group celebrations incorporate an element of collectivism while recognizing individual academic achievement. For example, when an individual student advances to the next level of the multiplication table, the child rings a bell, stopping all action in the classroom and allowing everyone to clap. In this way, classmates share individual success, and one child's success becomes a success for the total group. Individual academic achievement, an intrinsic school value, is accomplished, and children are appreciated for their contribution to the group goal of multiplication mastery.

Scientific Information and Social Context

Understanding collectivism can also eliminate problematic assumptions about what constitutes scientific knowledge. For example, 4th and 5th graders in Marie Altchech's class were learning about plants and animals. Before the children took an excursion to a nearby wetlands, a park docent visited the classroom to prepare them. He asked, "What do you know about hummingbirds?" Students began to tell stories about their family's experiences with birds, but the docent became impatient and said, "No more stories!" He expected students to use scientific language to talk about hummingbird anatomy or ecology, that is, to talk about birds out of their social context. When the children were told to stop telling stories, they became silent.

However, in a Bridging Cultures workshop, Altchech had learned about and analyzed the egg example mentioned earlier. She knew that her students would first consider scientific information in the context of shared family experiences. She also knew that the children did possess the ability to describe physical and behavioral aspects of birds, but that this knowledge might be embedded in a social context. She developed a plan to tap both sets of knowledge.

After the docent left, Altchech invited the children to tell their family stories about birds. Her goal was to give them a collectivistic way to engage in scientific discoveries. As the children shared their family experiences, the teacher wrote story highlights on the left side of the chalkboard and scientific aspects of the children's experiences and observations on the right. This process honored the children's stories while producing a rich and dynamic list of topics for scientific discourse. The teacher and the class valued the stories and the scientific information equally.

In one story, a child reported being in the garden with her grandmother when she noticed that hummingbirds seemed to stand still in the air. This family-based story led to a discussion about how the wings of hummingbirds must beat rapidly to sustain their apparent stillness. The children, fascinated by the topic, engaged in scientific discourse, scaffolded by the teacher, about how body mass, metabolism, and food intake are related. Whereas the docent conveyed the message that the storytelling approach was wrong, the teacher validated the students' stories and used them to build a bridge to the scientific culture valued in school.

When teachers understand and respect the collectivistic values of immigrant Latino children, the opportunities for culturally informed learning become limitless. Our examples in classroom management, reading, math, and science demonstrate that educators can design instruction responsive to diverse groups that does not undermine home-based cultural values.

Although the framework of individualism-collectivism is only one tool for understanding cultural differences (and we caution against sweeping generalizations), it does open the door to new ways of thinking and acting for teachers. Instead of advocating cultural sensitivity in a general way, this framework alerts teachers to specific cultural differences that are likely to diverge from school-based practices and values. Most important, the framework encourages teachers to recognize their own practices as cultural in origin rather than as simply the "right way" to do things.

The frustration caused by the feeling of "not knowing enough about each culture" can be abated when teachers use their knowledge of individualism and collectivism to understand the underlying motivation behind specific cultural practices, including those of the school.

References

Greenfield, P. M. (1994). Independence and interdependence as developmental scripts: Implications for theory, research and practice. In P. M. Greenfield &amp; R. Cocking (Eds.), Cross-cultural roots of minority child development. Hillsdale, NJ: Erlbaum.

Greenfield, P. M., Raeff, C., &amp; Quiroz, B. (1995). Cultural values in learning and education. In B. Williams (Ed.), Closing the achievement gap: A vision for changing beliefs and practices. Alexandria, VA: ASCD.

Hofstede, G. (1980). Culture's consequences: International differences of work-related values. Beverly Hills, CA: Sage.

Rothstein-Fisch, C. (1998) Bridging cultures: A pre-service teacher training model. San Francisco: WestEd.

Triandis, H. C. (1989). Cross-cultural studies of individualism and collectivism. Nebraska Symposium on Motivation, 37, 43-133.

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Bridging Cultures with Classroom Strategies

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Teachers who understand both the collectivistic value system of Latino culture and the individualistic culture of U.S. schools can use practices that honor both home and school.