Why Teaching Standard Algorithms Too Early Can Hurt Your Students’ Math Journey

Are you struggling to teach your students the standard algorithm for addition, subtraction, multiplication, or division? You’re not alone! While standard algorithms are an essential part of the curriculum, introducing them too early can create unnecessary challenges for your students—and even harm their understanding of math. Let’s dive into why this happens and explore strategies to build a stronger conceptual understanding of math in your classroom.

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Build Conceptual Understanding of Math First

Did you know the Common Core Standards don’t expect students to master the standard algorithm for addition and subtraction until the end of fourth grade? The multiplication algorithm is introduced by the end of fifth grade, and long division comes in sixth grade. However, many curriculums present these algorithms far earlier than recommended.

When students are pushed to memorize steps before they understand the why behind them, they may struggle to make sense of math. Instead of fostering a solid foundation, this approach creates “math robots” who can follow procedures without understanding their purpose.

In my classroom, I’ve found that slowing down and focusing on conceptual understanding of math first leads to amazing results. Before introducing the algorithm, my students use tools and invented strategies like base-ten blocks, visual models, and number lines to explore addition, subtraction, multiplication, and division. They gain a deeper understanding of numbers, build confidence, and develop flexible thinking.

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Focus on Problem Solving

Math is about more than getting the “right answer.” It’s about thinking critically, making connections, and solving problems in creative ways. By emphasizing problem-solving before algorithms, you give your students the chance to grapple with numbers and discover strategies that work for them.

For example, when teaching multi-digit addition and subtraction in second and third grades, my students experiment with place value strategies, such as breaking numbers apart or drawing visual models. They share their approaches with peers, discuss their reasoning, and gain insights from each other. This collaborative process helps them understand how numbers work together—and they often amaze me with their innovative solutions!

One of the ways I consistantly practice this in my classroom is through Number Talks. These short mental math activities give students the opportunity to think about math flexibly, learn from peers, and gain a greater conceptual understanding of math concepts.

When we skip this stage and introduce algorithms too early, students lose the chance to engage in this kind of exploration. Instead, they become focused on memorizing steps, which can limit their ability to think critically and solve problems in meaningful ways.

Here is a sample number talk from Whitney’s third grade classroom. Even though this is practicing multiplication, notice ALL the different ways students developed to solve the problems.

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The Role of Algorithms in Math

Algorithms aren’t the enemy—they serve an essential purpose in math. They provide a reliable method for solving problems efficiently, especially as students tackle more complex calculations in middle and high school. But algorithms rely on a foundation of number sense and conceptual understanding of math. Without this groundwork, students may struggle to apply these methods effectively (especially when math gets more complex).

If you are trying to teach algorithms and you teach anything less than fourth grade, you may want to stop and focus on building a conceptual understanding of math concepts instead.

In my classroom, I remind myself that teaching the algorithm is not the goal—it’s just one tool in a larger math toolbox. By delaying the introduction of algorithms until students are ready, we ensure they can use them confidently and accurately without sacrificing their understanding of the underlying math concepts.

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The Bigger Goal: Building Problem Solvers

At the end of the day, our ultimate goal as math teachers is to develop confident, capable problem solvers. When we prioritize conceptual understanding of math and encourage creative problem-solving, we prepare students for success—not just in math, but in life.

Here’s what this looks like in action:

• Encourage Exploration: Let students solve problems in multiple ways (even if they are not the most efficient strategies) and encourage them to share their thinking with peers.
• Celebrate Mistakes: Create a classroom culture where mistakes are valued as opportunities to learn and grow.
• Focus on Progression: Use the Common Core Standards as a guide, building a conceptual understanding of math in the early grades and saving algorithms for later.

Math is a journey, not a race. By giving your students the time and tools to explore, question, and make meaning of numbers, you’re helping them build a foundation that will support them through every math challenge to come.

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Your Takeaway

Introducing standard algorithms too early may feel like you’re helping students master math faster—but in reality, it can hold them back. By focusing on conceptual understanding first, you empower your students to become flexible, confident thinkers who can tackle any problem that comes their way.

I hope that we are making you feel better (especially now that you can take teaching these memorized steps off of your plate of everything to cover if you aren’t teaching 4th, 5th, and 6th grade).

In fourth grade, the common core standards say that students should learn the standard algorithm for addition and subtraction (so lower grades need to really build a conceptual understanding of addition and subtraction to make it easier for 4th grade teachers to teach the algorithm). The fifth grade standards have students learning the standard algorithm for multiplication (so lower grades need to build the conceptual understanding of multiplication to make it easier for 5th grade teachers to teach the standard algorithm). Students are not supposed to learn the standard algorithm for long division until sixth grade! We have so much time to work on building a strong conceptual understanding and not rushing to memorized steps.

Let’s teach math in a way that sparks curiosity and celebrates discovery. When we prioritize problem-solving over procedures, we create classrooms full of mathematicians ready to take on the world!

Also, if you are looking for more creative ways to explore math and encourage thinking about math in different ways, try Math Talks! These are great for getting kids to think creatively about math and explain their thinking. Download our Math Talk Guide to help you get started with math talks in your elementary classroom.