Sida Liu

Math is a language. It allows us to express ideas precisely and concisely, solve problems, or simply enjoy the fun of playing with patterns. Yet, traditional education often teaches math as a rigid set of rules, overwhelming students with exercises before they can connect with it meaningfully.

What if we taught math as a second language?

When teaching a second language, we have two options. One way is to begin with vocabulary and grammar—similar to how math is traditionally taught. But a more natural approach is to start with conversations, stories, or playful interactions, letting learners discover patterns and build intuition. When students feel ready, they are invited to participate.

Many students fear math because they never get a chance to experience its flow. They encounter it first as rules, without enough time to grasp its underlying patterns. If teachers approached math like a second language, students could observe math in action before being asked to solve problems on their own.

A teacher fluent in math—like a native speaker in language—could model problem-solving aloud on the board, visualing their thought process and transforming expressions step-by-step without the pressure for students to understand immediately. This approach is similar to the teaching style of Khan Academy, where problems are solved aloud, offering students a chance to follow along at their own pace. For further engagement, teachers could invite students to suggest their own problems, solving them in front of the class, to demonstrate that math is not a monster but a playful friend.

At its core, math is about equivalence—the idea that one expression can be transformed into many others, forming a web of equivalent expressions. Solving a problem is like finding a valid path through this web, from one expression to another. But one doesn’t always have to solve problems to engage with math, like exploring a new language, one can wander through the web of expressions for the joy of discovery.

This math-as-a-second-language approach invites students into math through curiosity, observation, and play. At first glance, a rule-first teaching method might seem more efficient, but it often shuts students out too soon, leaving many feeling disconnected. By immersing students in the process of mathematical thinking, we keep the door open for them to experience math naturally—just as they would with a second language.

Teaching Amharic using a Rule-first Method

Just for fun, I used AI to generate an example of learning Amharic, a Semitic language spoken in Ethiopia, by learning some rules first.

“በላ” means “to eat”. It changes depending on who is performing the action, for example, “እበላ” for “I eat”, “ይበላ” for “He eats”, “ትበላ” for “You eat” (both singular and plural). Now please pay attention to what is the correct form of “to eat” if we are eating, it is not ““እበላ” but “እንበላ”.

Does it feel disconnected? But remember, it is not a difficult problem at all! In fact, any native Amharic speaker can answer this with their eyes closed. How discouraging!