Guest article written by: Shirley Vigil, Associate Professor, American Public University
Students tend to fall into two clear camps when it comes to mathematics: those who say, “I’m bad at math” or “I just don’t understand math,” and those who say, “I love math” or “I do very well at math.” Rarely do I see students who feel neutral. From years of teaching, however, I have learned that many students labeled “mathphobic” can be guided to understand, appreciate, and even gain confidence in math through targeted instruction and practice.
A central principle in helping reluctant learners is relevance. When mathematical concepts are tied to everyday situations, students are more likely to engage. Framing problems as realistic scenarios shifts the focus from abstract manipulation of symbols to solving meaningful tasks. That relevance allows students to first apply non-mathematical reasoning—what some researchers call off-line thinking—and then connect that reasoning to formal mathematical methods.1
Course design plays a major role in this approach. Assignments should be crafted so learners see that they are solving situational problems, not just “doing math” for its own sake. For example, a budgeting exercise, distance-rate-time scenario, or a statistical summary of a small survey can ground abstract concepts in familiar contexts. When students concentrate on the situation, they naturally ask which mathematical tools apply, which makes the mathematics feel purposeful rather than arbitrary.
That said, relevance alone can sometimes backfire. Some resourceful students will intuit answers heuristically—by trial, estimation, or pattern recognition—without using formal methods. While those strategies can lead to correct results, as an instructor I want students to learn and apply mathematical procedures and reasoning so they can tackle more complex problems and generalize their skills. The aim is to move students from intuitive solutions to systematic mathematical problem-solving.
One effective teaching strategy is to explicitly translate language into mathematical operations. Teach students to map common words and phrases to symbols and relationships: “is” or “equals” translates to the equal sign, “more than” or “greater than” becomes an inequality, and terms like “total,” “difference,” or “product” suggest particular operations. Making these language-to-symbol connections reduces confusion and demystifies word problems, allowing learners to convert real-world descriptions into equations they can solve.
Practice is essential. Many students believe they can read a textbook and immediately apply new concepts, but building mathematical skill requires repeated, deliberate practice to form reliable neural connections. Even students who enjoy math benefit from continual practice when learning a new topic. Regular exercises, varied examples, and incremental increases in difficulty help students recognize which concept applies in different situations.
In my teaching experience, students who initially resist math often become capable and confident learners given three things: clear, relevant instruction; ample, varied practice; and encouragement that builds self-confidence. Years of being told they “aren’t math people” can obscure a student’s potential. With thoughtful pedagogy and opportunities to succeed, that potential frequently emerges.
Practical techniques instructors can use include presenting problems within meaningful contexts, teaching explicit translation between language and mathematical notation, offering worked examples alongside guided practice, and giving timely feedback so students learn from mistakes. Encouraging a growth mindset—emphasizing that proficiency develops through effort and strategy rather than innate talent—also helps students persist and improve.
Ultimately, teaching mathematics effectively is about connection: connecting everyday experience to formal methods, connecting language to symbols, and connecting effortful practice to growing competence. When educators design lessons that acknowledge students’ prior thinking and provide clear bridges to mathematical tools, more learners move from avoidance to understanding and even appreciation of mathematics.
1Devlin, Keith, 2000. The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. Weidenfeld & Nicolson: Basic Books.
About the Author
Shirley Vigil is an Associate Professor at American Public University, where she teaches courses including College Trigonometry, College Algebra, Contemporary Math, and Statistics. She holds a BS and a PhD in Industrial and Systems Engineering and an MS in Electrical Engineering from the University of Alabama (Huntsville and Birmingham, respectively). She is a licensed Professional Engineer in the State of Alabama.