It is difficult to understand something that you think has no relevance to your life. Travelers to foreign countries, for example, often experience a sense of disorientation when they observe cultural practices without having a point of reference. Math students are very much the same. As they journey into new mathematical territory, they often feel perplexed and overwhelmed. In the eyes of struggling students, equations on the blackboard can quickly transmogrify into a welter of meaningless symbols. Eventually, they will ask the question every math teacher dreads hearing: “When will I ever need this?”
Provides teachers a way to answer this question preemptively. It is a method that fosters an understanding and appreciation for numbers by focusing on the relationship between mathematical concepts and students’ experiences and interests. When real-world connection is incorporated into lessons, students have the opportunity to see how math fits into their daily lives. In turn, math becomes a visible phenomenon in their routines instead of a set of abstract rules and concepts confined to the classroom.
But does real-world connection lead to better academic results? While there may be no scholarly consensus regarding this question, many teachers see improvement in their classroom by following this method. One study asked teachers from a range of grade levels to list the advantages and disadvantages of real-world connection. The advantages they cited included:
- Increases motivation and interest in mathematics
- Helps to improve conceptual, meaningful, permanent learning
- Develops students’ mathematical process skills (reasoning, communication, problem-solving, and analytical thinking)
- Helps students build a consciousness of their future career choices by showing occupational fields in which mathematics is used
- Helps students develop a positive attitude toward mathematics
- Facilitates generalization and abstraction of mathematical ideas and concepts
When asked to list the disadvantages, most teachers said that “There is no significant disadvantage.” Some of the disadvantages they did list are easily remedied. For instance, teachers said that real-world connection can be a limitation “If examples are unrealistic and not related to students’ experiences.” And some were worried that students will conclude that “mathematics is only limited to real life.” More serious issues—such as the concern that teachers are not trained to teach real-world connection—can be addressed in university teaching curricula and professional development seminars.
The advantages of real-world connection may stem from the fact that students get plenty of opportunities to enrich their “web of understanding”—a network of concepts that grows as students build on their skills and knowledge. Developing a web of understanding stands in contrast to learning by rote, which too often leads to questions about math’s relevancy. To illustrate how this web is formed, Diana V. Lambdin uses the example of a fifth-grade teacher posing the following scenario to a classroom:
“Suppose 39 students want to share 5 candy bars fairly. How much can each student get?” Students suggest two ways to divide the candy bars: 39 by 5 and 5 by 39. When the teacher polls her students, most of them agree on the former equation. However, the students soon realize that it will leave them with an unequal number of pieces. They discuss a few solutions. None of them work until one student solves the problem by drawing equally segmented chocolate bars on the board. Another student then offers an alternative solution that also works. By solving this real-world problem, students naturally “revealed and worked through a number of confusions and misconceptions about fractions and divisions” (Lambdin 5).
If the students learned division by rote instead, they might miss the chance to make the connection between fractions and divisions.
Indeed, real-world connection leaves little room for rote learning, which studies indicate is ineffective. Real-world connection does, however, facilitate intentional discourse.
According to the National Council of Teachers of Mathematics, intentional discourse entails “students comparing and contrasting ideas and methods, constructing viable arguments, critiquing each other’s reasoning, and helping each other make sense of mathematics.”'
Lamdin’s story about the 5th graders dividing the candy bars is an excellent example of intentional discourse. Thinking aloud with this familiar item in mind, students respectfully explained why flawed solutions wouldn’t work. Through open dialogue, they taught each other. Here, communication is a learning opportunity. As one former math coach Dean Ballard writes, “Communication about mathematics among students … is the vehicle for bringing thinking to the surface, clarifying ideas, moving ideas forward, revealing misconceptions, and making key mathematical connections clear, transferable, and memorable” (5).
The students also practice productive struggle in the candy bar exercise. “Productive struggle is the process of effortful learning that develops grit and problem solving.”
When solving new mathematical problems, students are expected to fail in their initial attempts, just as the students dividing the candy bar did. Through their struggle, students cultivate grit—a valuable trait in both mathematics and life. They also build confidence in their abilities to solve mathematical problems. And a confident student is naturally “more willing to tackle challenging problems” (Lambdin 10).
Examples of Real-World Connection
There is no shortage of practical examples teachers can use while operating under the real-world connection model. Teachers across the world devise clever real-world examples every day. Many of these examples have the added benefit of allowing restless students to leave their desks and move around.
Best Practices for Using Real-World Connection
There are many effective ways to teach real-world connection in the math class. Some of them have already been discussed, such as facilitating dialogue and connecting math to careers.
Teachers should also devise real-world examples that include students’ interests. Students are more likely to focus when their hobbies are involved. A Texas high school math teacher in an avid football town, for instance, may use place kicking to introduce parametric equations to her class. With some imagination, even popular entertainment, such as television shows or pop music, can be incorporated into math lessons.
Real-world connection lends itself to the three-step method known as Concrete-Representational-Abstract (CRA), which teachers have found to be highly effective in the classroom.
- During the concrete stage, students participate in a hands-on activity with an everyday object. Our football-town teacher, for example, may start by having the students kick field goals on the gridiron.
- Moving on to the representational stage, she could discuss the trajectory of the football through videos and illustrations.
- Finally, she can introduce algebraic notations and expressions—the abstract stage.
CRA provides a well-defined structure for implementing real-world connection into the classroom, and real-world connection provides a context that is safe and familiar to students. It eases them into new mathematical concepts before they start to get frustrated and dismiss them as irrelevant.
Another way teachers can incorporate real-world connection into their lessons is through problem-based learning, in which students work in groups to solve open-ended problems. Students not only work collaboratively, they practice intentional discourse with each other. And the teacher can get creative and make the activity fun for students. For instance, the teacher using placekicking as a real-world example can ask her students to imagine that their school is playing for the state championship. The game has come down to a clutch 64-yard kick, which would also break the Texas record for longest field goal. The teacher can turn this activity into a competition by dividing the class into small groups and instructing them to design an equation they think will result in victory. The winners need to produce not only a championship formula, but a formula that yields the cleanest kick—a perfect arc that drops squarely between the uprights. As students break off into groups, they will feel like something important rests on their calculations. This elaborate scenario demonstrates just some of the possibilities of coupling real-world connection with problem-based learning.
While applying real-world connections in the classroom, teachers can also incorporate experiences that are personally meaningful to students. Imagine, for example, an elementary teacher who wants her students to get hands-on experience measuring the dimensions of real objects. She could ask them to bring in three special items from home. These items could be family pictures, stuffed animals, heirlooms (with parents’ permission), and anything else of sentimental value. While measuring items that are important to them, students are more likely to feel invested in the activity.
Implications of Teaching Real-World Connection
Of course, winning the attention of students in the classroom is only the first step toward inspiring the next generation of STEM professionals. Ultimately, educators want students to see STEM as a viable career path, and real-world connection introduces them to possible careers in STEM. For example, high school students learning algebra in a real-world context may be asked to use quadratic equations to maximize profit for their favorite clothing brand. This exercise affords the teacher an excellent opportunity to introduce his class to careers in data science, which requires mastery of algebra.
The teacher can even talk about the shortage of data scientists in the job market and their attractive salaries. Alternatively, he could poll the class on their favorite athletes and discuss how sports scientists could use algebraic expressions to improve their performances. In this light, real-world connection doesn’t just indicate the concrete implications of math in ordinary life. It also highlights STEM careers and demonstrates that math plays a part in virtually any industry students can imagine. With this knowledge, students can get a head start on pursuing a STEM-related career.
Even for students with no interest in STEM careers, real-world connection can help them develop important values and traits. Along with learning basic arithmetic to do essential things like budgeting, students can sharpen their critical thinking by problem solving in real-world contexts.
Imagine, for example, a group of students using linear equations to predict the profits for a new potato chip company with limited resources. There is one girl in the group who knows she wants to be a police officer when she grows up. Although she has no interest in math or business, she contributes to the group and welcomes her classmates’ help when she struggles. She works through the mechanics of a challenging problem and applies her understanding to it while collaborating and communicating with her team. In this one exercise, she practices team work, communication, and productive struggle. She also develops the grit she’ll need to succeed later on. When she begins her law-enforcement training, she’ll have the character traits she’ll need to become an outstanding police officer.
If real-world connection becomes standard practice in classrooms, it is easy to imagine a world without that vexing question, “When will I ever need math?” Before students even ask, teachers can supply several examples of professionals and ordinary people using math in their daily lives. Of course, real-world connection does not replace the teaching of abstract math; real-world connection instead supplements it. It shows students that math is a way of understanding the world around them and their place in it.