The race to cover the curriculum in 180 days is real. Between standardized testing, endless paperwork, and the daily demands of the classroom, it’s no wonder teachers often feel pressured to move fast. To save time, many turn to shortcuts — like teaching algorithms first. Algorithms, those step-by-step procedures to solve math problems, promise quick answers. But here’s the catch: quick answers don’t equal deep understanding.
When we prioritize procedures over understanding, we rob students of the chance to truly grasp math. They may memorize steps for a test, but without a strong foundation, that knowledge often crumbles under new or unfamiliar problems. What if, instead of racing to the algorithm, we focused on building deep, flexible mathematical thinking first? By prioritizing conceptual understanding, we empower students to think, reason, and problem-solve — not just memorize.
Here’s why slowing down to build understanding first is worth every minute.
Understanding Increases Retention
When students are taught algorithms before they develop a deep understanding of math concepts, they often rely on memorizing a series of steps — hoping to land on the right answer. But memorization without understanding is like building a house on sand; it rarely lasts. Without a solid foundation, those memorized steps are easily forgotten. However, when students understand the math, they can connect new learning to what they already know, making it easier to remember and apply later. Even if they forget the exact steps, they can reconstruct the process by drawing a model, breaking apart a number, or using a different strategy. This is the power of conceptual understanding — it leads to long-term retention and the flexibility to apply math in any context.
Understanding Creates Flexible Problem Solvers
A strong conceptual foundation in math empowers students to think flexibly and approach problems in multiple ways. When students understand the why behind a concept, they begin to see connections across different mathematical ideas, allowing them to choose strategies that make the most sense — rather than relying on rote memorization of a single algorithm. This flexibility is a game-changer.
For example, I love giving my 4th-grade students this simple number talk: 1,002 – 998. Students who are heavily dependent on algorithms often default to the standard subtraction method — mentally crossing out the 1, borrowing from the tens place, and working through a series of steps. They get so caught up in the procedure that they miss the simplicity of the problem. They don’t even realize the numbers are only 4 apart.
But when students have a deep understanding of numbers, they approach it differently. They might count up from 998 to 1,002 or simply recognize the difference is 4. This is the power of conceptual understanding — it shifts the focus from blindly following steps to truly thinking about the math. It’s not only faster, but it also fosters confidence and flexible thinking that extends to more complex problems.
Understanding Drives Engagement
Math is so much more than simply following a set of steps — it’s about thinking, reasoning, and making sense of the world around us. When students are given the opportunity to explore mathematical concepts through hands-on experiences, visual models, and real-world applications, they shift from passively receiving information to actively making sense of it. This shift transforms math from something intimidating to something intriguing. Instead of memorizing procedures, students begin to ask questions, make connections, and discover patterns. This curiosity fuels engagement, and that engagement builds persistence — helping students approach math with confidence and a sense of ownership. When math makes sense, students don’t just learn it — they enjoy it.
Understanding Lays the Foundation for Algorithms
When students first build a strong conceptual understanding, algorithms become much easier to grasp — and far more meaningful. Instead of blindly following steps, students understand why each step works and when it makes sense to use a particular method. This deeper understanding also reduces careless mistakes, as students can catch errors by reasoning through the problem rather than relying solely on memorization.
This doesn’t mean algorithms don’t have a place in math instruction — they absolutely do. Algorithms are powerful tools that promote efficiency, but their power is unlocked only when students first understand the math behind them. By allowing students to explore mathematical concepts through concrete manipulatives, visual models, and rich discussions before introducing formal procedures, we set them up for long-term success. When algorithms are built on a foundation of understanding, math becomes clearer, more accessible, and far less intimidating.
By prioritizing conceptual understanding before rushing to the algorithm, we set students up for success—not just in solving problems but in developing a lifelong appreciation and confidence in mathematics. After all, math is not just about getting the right answer—it’s about thinking, reasoning, and understanding.