Accelerating Math Learning Through Real-World Connections: Answering the Key Questions

It's often difficult to grasp concepts that seem irrelevant to our lives. Just as travelers in foreign lands can feel disoriented when encountering unfamiliar cultural practices, math students can feel perplexed and overwhelmed when venturing into new mathematical territory. For struggling students, equations on the blackboard can quickly become a jumble of meaningless symbols. This article explores how real-world connections can preemptively address this issue, fostering a deeper understanding and appreciation for mathematics by linking concepts to students' experiences and interests.

The Power of Real-World Connections

Real-world connection 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 connections are incorporated into lessons, students have the opportunity to see how math fits into their daily lives. By grounding mathematical concepts in familiar contexts, educators can make the subject more accessible and engaging. This approach helps students understand the relevance of what they are learning, answering the age-old question: "When will I ever need this?" before it even arises.

Does Real-World Connection Lead to Better Academic Results?

While a definitive scholarly consensus may be lacking, many teachers observe improvements in their classrooms when implementing real-world connections. One study that asked teachers from various grade levels to list the advantages and disadvantages of real-world connections revealed that most teachers felt there were no significant disadvantages. Some of the disadvantages they did list are easily remedied. The advantages 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.

Building a "Web of Understanding"

To illustrate how this web is formed, Diana V. shares an example: “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.

This example highlights how real-world connections move away from rote learning, which studies suggest is ineffective.

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Intentional Discourse and Productive Struggle

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. The students also practice productive struggle in the candy bar exercise. 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. This collaborative problem-solving fosters critical thinking, communication, and perseverance.

Practical Examples in the Classroom

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. Here are a few examples:

Water Conservation: Krista Dunlop-Shepard, a bilingual teacher for grades first through sixth in Toronto, had her students practice their adding and subtracting skills by measuring the flow of water in the sinks and toilets. They also asked custodians how much water they use daily to mop the floors. After students reviewed their calculations, Dunlop-Shepard tasked them with thinking of ways they could conserve water. Students with varying goals and interests were able to see the relevance of math in their lives.
Cooking and Baking: Gabi Sanfilippo’s fifth grade students practiced “halving, tripling, or quadrupling recipes based on how many people they’d cook or bake for” over the holidays.
Candy Graphing: Dottie Wright Berzin added a sweet twist to her graphing lessons by asking her students to bring their favorite Halloween candy to class. Together, they used their candy to build different kinds of graphs (such as coordinate graphs and tally charts) that ranked the treats from least favorite to most favorite. Students then developed advertising campaigns based on their data. Part of this exercise could also involve thinking critically about how to work with limited resources. If students were given a budget, they could be tasked with deciding how much money they would allocate for marketing each kind of candy. As a final step, they could write and present an evidence-based business case that defends their budgetary decisions.
Historical Volume Calculations: Real-world connection is indeed one of the most effective ways to bridge the gap between math and other subjects. For example, math helped one English teacher illustrate the tragic loss of human life during the Holocaust. While teaching Elie Wiesel’s classic novella Night, she asked her seniors to calculate the volume of 11 million pennies (the estimated number of Holocaust victims). Not only does this exercise help students grasp the extent of the Holocaust, it disabuses them of the notion that math and literature are diametrically opposed, which fuels the myth that there are “STEM people” and “humanities people.” In that construct, if you are good at one subject you cannot be good at the other.

Strategies for Implementing Real-World Connections

There are many effective ways to teach real-world connection in the math class. Here are a few concrete strategies:

Incorporate Student Interests: 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.
CRA Approach: During the concrete stage, students participate in a hands-on activity with an everyday object. 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.
Problem-Based Learning: Another way teachers can incorporate real-world connection into their lessons is through problem-based learning, in which individuals work in groups to solve open-ended problems. They not only work collaboratively, but they also practice intentional discourse with each other. And the teacher can get creative and make the activity fun for the entire class. For instance, the teacher using placekicking as a real-world example can ask her class 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 the class breaks off into groups, they will feel like something important rests on their calculations.
Meaningful Personal Items: 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 class 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.

Connecting Math to STEM Careers

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. 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.

Developing Essential Life Skills

Even for students with no interest in STEM careers, real-world connection can help them develop important values and traits. 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.

A World Without "When Will I Ever Need Math?"

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.

STEMscopes Math: A Resource for Real-World Learning

STEMscopes Math is an all-new approach to math instruction. Built from the ground up by practicing educators using the flexible 5E lesson model, STEMscopes Math provides you with everything you need to create a meaningful learning experience that empowers your students with 21st-century skills to succeed in future STEM careers.

STEMscopes Math is leveling up with 6th-8th grade and Algebra I curriculum! Not every school has access to math manipulatives or enough to support all learners. With virtual manipulatives and PhET Simulations, teacher can enhance equity, empower learning at home, and delight digital natives. Every STEMscopes Math lesson is built from the ground up to the standards. Chunking information into bite-size pieces, we make our units (called “scopes”) digestible and engaging.

Key Features of STEMscopes Math

Home: Build your own content knowledge, analyze the standards, and gain an understanding of everything the scope has to offer here in the Home section.
Engage: The Engage section is all about laying the foundation for learning. You begin this section by pre-assessing students and filling knowledge gaps.
Explore: This is where students dig into the meat of the content. The Explore section provides scaffolded hands-on activities that build toward mastery of the standards. Each Explore provides prompts for rich mathematical discourse and student reasoning, along with an Exit Ticket.
Explain: Paired with Explore, the Explain section offers a variety of resources that help connect the experiences of the Explore activities to the academic content students need to know.
Elaborate: Workstations are a go! The Elaborate section makes differentiation a cinch with ready-made activities-digital and paper-based games, spiraled review, career connections, literacy connections, and more-perfect for rotations! *Instructional elements in STEMscopes Mathematics are intended to work together.
Evaluate: Get the data you need from the assessment tools provided in the Evaluate section. From multiple choice-based assessments to an open-ended reasoning prompt, there’s an evaluation for every student’s learning style.
Intervention: Useful during Elaborate or as an after-school support, Intervention contains a small hands-on activity designed to target students’ conceptual misunderstanding while building their math skills.

Accelerate Learning: Fostering a Love for Learning

At Accelerate Learning, we believe that curiosity is the driving force behind discovery. Our award-winning, hands-on, interactive STEM programs are designed to engage students’ natural inquisitiveness, turning questions into exploration and exploration into understanding. We equip educators with the tools, resources, and support they need to inspire students and enhance STEM learning. We’re dedicated to fostering a love for learning through interactive, hands-on experiences. All of our programs are research- and evidence-based to ensure students meet their potential and achieve measurable growth.

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