Speaking by Numbers

As teachers of math and Spanish, we have both been approached on countless occasions by adults — friends, colleagues, parents — who share variations on the following statement regarding world language study: “I took seven years of Spanish, and I can’t speak a word.” Or in the case of math: “I’m just not a math person.” Frequently, these confessions of having had a negative experience with our subjects are accompanied by sadness, regret, and perhaps even guilt on the part of the speaker. Parents who confide in us feel especially culpable for not having learned conjugations in Spanish, or algebraic notation, and they often look at us with hope, eager to hear that things have changed — that their children will not suffer the same fate.

The good news for parents and their children studying world languages and math today is that research shows that a student’s positive affect is of paramount importance to results (Krashen, 1982). This research underscores our own findings: that it is imperative for students to feel not only comfortable but also competent and able to take risks. Over time, the subjects we teach have unfortunately become loaded with negative overtones. Perceptions of math and world languages have been adversely affected, at least in part, by outdated methodologies and a misunderstanding about the way in which the adolescent learns best. As a result, we have both felt a strong need to “rebrand” our language and math study by modeling fun, engagement, and the joy that can be felt as we play while learning our subjects. And when students are having fun doing the “work” of a subject, they are very likely to be “on task,” engaged, and participatory in positive ways that contribute to the goals of the class.

Mythbusting

Language study as an “elite” subject
Students who struggle in world language study often claim that they just “don’t get” the language. Their parents often echo this sentiment by claiming that they also don’t “have an ear” for language. While this claim is patently untrue (since these parents speak English with no problem!), it is indicative of a deeper problem in language education. These statements reveal a stereotypical attitude that maintains that language study is for the “elite” and suited only for students with a highly developed ear or special set of cognitive skills. Indeed, for many years, language study was only available at the secondary level, when students are supposedly mature enough to handle the study of verb paradigms and grammatical structures. Certain languages have cycled through historical periods of elite status: Latin at the turn of the last century, followed by French, Russian during the time of Sputnik, Japanese in the 1980s, now Chinese. The truth is: all students can (and do) learn languages, and all languages are worthy of study, if the right motivation is present and solid, research-based methodologies are utilized. It is the job of the language teacher to find ways to develop motivation in and convey this sentiment to students. Along with the task of designing and developing lessons to teach languages, our (not-so-minor) role must be to frame language study as enjoyable and worthy of effort, and to instill a reasonable expectation of success in our students.

Mathphobia
When I meet people for the first time and tell them that I’m a math teacher, they often roll their eyes and exclaim, “I hated math!” In fact, it seems that the memory of math class resonates strongly with them, and not often positively. Hating math seems to be a badge that many adults wear proudly. It implies that they are survivors of a war, and look at them now! They not only survived math classes, but they also succeeded in life despite their battle with them. Moreover, it seems that those who did well in math class did so despite their distaste for it. Many others state that they are “just not good at math,” as though being good math is something that only an elite few are born with.

For many of us, learning math entailed memorizing a series of long and meaningless algorithms, and the beauty and creativity of the subject was long lost on us.

These are some of many reasons why we need to rethink what we do in the math classroom.

The Affective Filter
In his writings, linguist and researcher Stephen Krashen posits the affective filter hypothesis (1981). He claims that variables such as anxiety, self-confidence, and motivation have an effect on a student’s acquisition of language. Krashen believes that students who are confident, anxiety free, and motivated are better able to learn languages and that it is imperative for teachers to establish a comfortable and safe environment in our classrooms in order to keep students’ affective filters down. It is when students are tense, feel criticized, or are just unmotivated that their affective filters go up and little or no learning can get through. Krashen’s ideas mesh well with Maslow’s Hierarchy of Needs theory of psychology. Like Krashen, Maslow believes that a student’s physiological, safety, love/belonging, and esteem needs must be met before that student can reach self-actualization, or a place where learning can best be accomplished.

“Math Myth”
One popular myth about math is that there are certain people who are “math people” — those who can do math well — and everybody else. Studies vary widely in examining what qualities lead to the attainment of math ability. Some research points to the emergence of math abilities in infants and even animals. In his book,The Math Instinct: Why You’re a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs), Keith Devlin, a mathematician at Stanford Univer­sity, presented a 1992 study by Karen Wynn that showed that very young children have a reliable sense of quantity of a small collection of objects, even before they have the language to describe it. If humans are born with a math instinct, we may conclude that there are those of us whose innate sense of numbers is stronger than that of others. However, a study by Kou Murayama, a research psychologist at the University of California at Los Angeles, indicates that hard work in math is even more important for success than innate number skills. Students who are motivated in math are more likely to be successful math students when they reach high school than those who score higher on an IQ test in fifth grade but do not have the motivation to work hard.

Thus, we can conclude that anybody can learn math. It is our responsibility as math teachers to help students develop the motivation, persistence, and what Duckworth et. al (2007) define as “grit” to achieve. Allowing students to take risks and providing them with the tools and the environment in which they can find joy in math will foster the passion needed for success.

What Works

Lowering Filters and Raising
Motivation
In teaching world languages, it is important to provide students with a safe space in which they can feel comfortable taking risks. After all, speaking a new language with different sounds to one’s home tongue can be cause for anxiety. Especially in middle school, when one of the main goals of the adolescent student is to “fit in” and not be seen as different, speaking a new language can feel risky. Furthermore, making mistakes in the study of a new language is a given. How do we educators design activities and lessons that help students to feel safe in taking these risks?

Modeling is one important means of making students feel comfortable in the classroom. If the teacher is willing to model risk-taking behaviors, students will be more likely to follow suit. Teachers must also model the joy and enthusiasm that they feel toward their languages/subjects. If the teacher isn’t excited, it’s unlikely that the students will be. And, perhaps most importantly, teachers must be willing to make mistakes and to laugh at themselves. It is liberating for students to see their teachers make an errors — and acknowledge them without negative feelings attached. This type of modeling can set the tone for the classroom community. It is also helpful to establish “rules” at the start of the school year that include reference to the behaviors that are accepted — and expected — in the class. Below is an excerpt from the “class contract” for middle school students. It is read through on the first day of school and sent home to be shared with and signed by parents on the first night as homework.

How to Succeed in Spanish Class
In order to get the most out of this class, let’s agree on the following rules:
Listen. Listening is important in the language classroom. Listen to your classmates, and to the teacher — and we will all listen to you when it’s your turn to speak! You can learn a lot by paying attention to others when they speak in class, so listen up!

Participate. We learn language best when we use it — a lot — so raise your hand, volunteer to do a dialog or skit, share your answers to homework. The more you speak, the better your pronunciation, syntax, and vocabulary will become in Spanish.
Respect. We are all in this together, and yet we all have different strengths, talents, and skills. The goal of this class is to grow and improve, and to do this, we will all have to try new things. This will mean making mistakes — lots of them! We must all be respectful and supportive of each other as we take this journey together. For this reason, teasing or making fun of classmates will not be allowed in our class. All for one, and one for all.

Gaming in the Language Classroom
Another effective way of lowering the affective filter with adolescent students is to incorporate games and game design into lessons. Much to the lament of many parents and educators, middle school students spend an inordinate amount of time playing games — video or internet based or otherwise. But games are not in and of themselves a bad thing. In fact, teachers can leverage the excitement of games in the classroom by designing activities that involve quests, rewards, and good feedback.

Games designer and advocate Jane McGonigal (2011) writes passionately about the potential of games for educational purposes. She describes optimal-experience design as a game that has “compelling goals, interesting obstacles, and a well-designed feedback system” (p. 126). Students play games because they are excited by a meaningful task or goal and they have a reasonable expectation of reaching that goal. In the case of videogames, they play games over and over again in order to learn something new to help them move on to new challenges. They seem not to be dissuaded by failure and, in fact, are more willing to take risks if it means progressing in the game. They are always aware of their progress because all well-designed games have an intense and clear feedback loop that lets players know where they are in the game and how far they still need to go. These traits of a good game can be incorporated into the classroom experience so that students feel more motivated and connected to their learning.

An example of a world language game is one based upon the Paris-Dakar rally. Middle school students of Spanish and French were organized into teams across several different seventh-grade classrooms. Each team consisted of several students from both languages in an effort to foster collaboration and teamwork. A huge map of Europe and Africa was displayed in the front hallway of our school, with specific cities highlighted in red:

Students were required to design a “car” for their team using a 3” x 5” index card. These cars were placed on the map around Paris, and then the race was ready to begin. Each day, students were asked questions or given tasks in their respective languages. On some days, they were simple questions involving new vocabulary or cultural topics. On others, the questions required students to move around the school to find hidden objects (using directions in French or Spanish) or to interact with adults in order to find out some information (again, in French or Spanish). Each day, depending on the success of their tasks, students’ cars would move to the next city on the map. This “race” took place over the course of two weeks and had students feeling passionate and engaged. Through the game, students learned geography, cultural topics, and some history, while strengthening both their productive (speaking and writing) and receptive (listening and reading) skills in the target language.

Risk Taking in Math
As with teaching world languages, a classroom environment that is supportive and joyful is one in which students feel safe taking risks. When students feel validated and encouraged to explore new mathematical concepts, they can feel comfortable making mistakes and learning from them. The ideal math classroom is one where relationships among the students and between the students and the teacher are strong and trusting, and where laughter and mathematical play and experimentation are not only permitted but also encouraged. Indeed, humor is an essential component of a vibrant math class. It is important to laugh often in open enjoyment of each other and the process of learning. Math class should be a happy place. The teacher must model a ready enthusiasm for all things mathematical, wonder aloud at a particularly beautiful mathematical structure, and speak readily of her love for math challenges. Teachers shouldn’t mind making mistakes in front of the students, as students need to see how making errors can lead to greater understanding. While it is important to be precise in math — it is working with an eye to detail that leads to a correct solution — distinguishing precision from perfectionism is important. As learners, we don’t need to be perfect. Rather, we should accept mistakes as providing opportunities for learning. Praising a student’s process rather than just the product (no math pun intended) reinforces the notion that risk taking is important and supported.

In an ideal math classroom, it feels that the class functions as a team, cheering when one succeeds and expressing encouragement when someone else tries a problem-solving strategy that might not work. The teacher, too, must praise risk taking, offering positive feedback when a student tries an approach that is different from the one being taught.

Differentiation
As in all classes, there will always be a range in the skills of learners in a particular math class. Even when grouped homogeneously, there are going to be students who speed ahead and others who need more reinforcement to master skills. It is good practice to anticipate the needs of different learners and to be prepared to meet a student’s particular needs. Having a range of problems readily at hand to offer to those who are ready to move ahead is one way to keep those students motivated. On the other hand, it is also important to carve out time for students who need more reinforcement and help them not feel overwhelmed. Some teachers choose a time during the day to meet individually with students and provide extra support. Having quiet one-on-one time with students helps to build supportive relationships so that they feel comfortable asking for help or asking to be challenged.

Empowering students to take risks and take control over their learning is a valuable goal for teachers striving to establish a rigorous and exciting class environment. A fun way to do this is to invite students to teach and create math challenges for one another and to take a role in leading discussions and problem-solving strategy sessions. When students have a meaningful voice in their own learning and in their peers’, they become motivated learners who feel responsible for one another. Such a math class may feel a bit chaotic and messy as students grapple aloud with complex concepts and problems, share ideas with each other, and argue over different problem-solving strategies. While being a little chaotic, this math class will be very engaging, fun, and productive.

It is common knowledge that students learn better when they are self-motivated, able to take risks and make mistakes, and feel successful. When engaged, students are less apt to disrupt class or distract others. Our mantra is that learning can be — and should be — joyful. We were both inspired to come into teaching at least in part by our own passionate teachers. They possessed an infectious spirit that made us love their subjects through the magnetism of their excitement. As educators who enjoy teaching, are fascinated by our subjects, and also love kids, we aim to convey these very positive feelings to our students. While being a happy teacher is not enough to eliminate all classroom-management challenges, a safe, inviting, and enthusiastic climate sets the right tone for good teaching and learning.

This is not to say that we don’t have our challenging days. Like students, we too have outside lives that we sometimes can’t help but bring into school. As the adults, though, we set the tone and climate of the classroom, and so it is critical that we are ever cognizant of our power to influence our students’ experiences in school. Educator and psychologist Haim Ginott writes the following about his own realization of the immense power that teachers wield in the classroom:

“I have come to the frightening conclusion that I am the decisive element. It is my personal approach that creates the climate. It is my daily mood that makes the weather. I possess tremendous power to make life miserable or joyous. I can be a tool of torture or an instrument of inspiration, I can humiliate or humor, hurt or heal. In all situations, it is my response that decides whether a crisis is escalated or de-escalated and a person is humanized or dehumanized. If we treat people as they are, we make them worse. If we treat people as they ought to be, we help them become what they are capable of becoming.” — Haim G. Ginott, Teacher and Child: A Book for Parents and Teachers

In addition to developing engaging learning activities, establishing a comfortable and safe environment, and modeling our own passion for our subjects, we must be mindful of the power we have to influence the hearts and minds of our students. In so doing, we open our subjects up to all students — not just the few and the proud.

References
Devlin, Keith. The Math Instinct: Why You’re a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs). New York: Thunder’s Mouth Press, 2005. Print.
Duckworth, A. L., Peterson, C., Matthews, M. D., & Kelly, D. R. (2007). “Grit: Perseverance and passion for long-term goals.” Journal of Personality and Social Psychology, 92(6), 1087-1101.(pdf)
Ginott, G. Teacher and Child: A Book for Parents and Teachers. New York: Macmillan, 1975.
Krashen, S. D. (1982). Principles and Practice in Second Language Acquisition. Oxford: Pergamon. http://www.sdkrashen.com/Principles_and_Practice/Principles_and_Practice.pdf.
“Like Math? Thank Your Motivation, Not IQ.” Scientific American, 28 Dec., 2012. Retrieved from: http://www.scientificamerican.com/article.cfm?id=like-math-thank-your-moti
Maslow, A. H. (1943). “A theory of human motivation.” Psychological Review, 50(4), 370-96. Retrieved from http://psychclassics.yorku.ca/Maslow/motivation.htm
McGonigal, J. (2011). Reality is Broken. New York: Penguin.

Martha Edelson is a math teacher and Lori Langer de Ramirez is a Spanish teacher at The Dalton School, New York. Langer de Ramirez’s website, http://miscositas.com, is full of free resources for language teachers.