How do we know when students aren’t grasping a learning concept, and how do we adjust the course? As educators, we’ve been asking this question for a while. What if we could figure out why students weren’t grasping the concept to help them learn better? And what if we could plan to address the most common misunderstandings the first time we teach the concept? This is where misconceptions come into play.
What is a misconception?
Misconceptions are more than just simple mistakes—they reflect deep-seated misunderstandings that can persist without targeted instruction. A student might make an error because they were rushing or distracted, but a misconception is different: it is an incorrect belief about how something works that intuitively makes sense to them.
Understanding and addressing these misconceptions is critical for student success. That’s where ANet’s work comes in. Our approach to analyzing student misconceptions through formative assessments provides teachers invaluable insights into student thinking, allowing for more effective interventions.
Understanding and Identifying Student Misconceptions
One of the most powerful ways to understand student misconceptions is through distractor rationale—the
reasoning behind why students choose specific incorrect answers. Think of distractor rationale as a personalized map. It helps educators understand where students are and how to get them somewhere else.
ANet has built a system that carefully designs assessment items so incorrect answer choices (distractors) are rooted in common misconceptions rather than random errors. This allows teachers to pinpoint why a student got a question wrong and adjust instruction accordingly.
Our content experts develop these distractors by drawing on their deep understanding of learning concepts, grade-level progressions, and instructional practices. Each item undergoes a rigorous review process to ensure it captures the most likely misconceptions students may develop. After assessments are administered, student response patterns are analyzed to refine distractors further and ensure they reflect students’ misunderstandings.
Misconceptions in Action
Let’s consider this sixth-grade math problem:
Karim began his day by drinking 1 ⅛ cup of milk at breakfast. By the end of the day, he drank a total of 2 ⅔ cups of milk. Which equation and solution correctly represent the amount of milk Karim drank after breakfast?
The correct answer is 1 ⅛ + m = 2 ⅔ with m = 1 13/24.
A common misconception students chose is m= 3 19/24 because students were focusing on isolating the variable to solve the equation and used addition instead of subtraction. While they chose the incorrect procedure to solve the problem, this choice highlights that they may have a deeper conceptual misunderstanding of the relational nature of equations. By identifying these patterns, teachers can address specific misconceptions in future lessons.
Recently, we helped teachers plan for misconceptions and identified two instructional shifts to address this specific misconception.
- Nix this! Describing an equal sign as an operational symbol leading to “the answer is.” Instead, an equal sign is a relational symbol that indicates the expressions on each side of the symbol have the same value. Help students AVOID this misconception by ASKING: What value of the variable makes the statement TRUE (equal)?
- Nix This! To solve an equation, move things to the other side to get the variable alone. Instead:
- Determine the value of the variable that makes the equation TRUE.
- The value of a variable that makes the equation TRUE is called the solution.
- Use inverse operations to rewrite the equation in different ways to reveal the value more clearly.
- Help students AVOID this misconception by ASKING: What value of the variable makes the equation true?
By focusing on making the equation true rather than instructing students to only solve the problem, they begin to understand the relational nature of equations.
Why Misconceptions Are a Game-Changer in K-12 Education
ANet’s clear misconception and distractor rationale empower educators with a structured approach to addressing learning gaps. Our professional learning and job-embedded coaching helps educators:
- Close Read the Benchmark – Understand the standard and connected concepts students need to grasp.
- Do the Math – Identify required strategies, representations, and mathematical language.
- Understand Common Misconceptions – Use data to predict where students might struggle.
- Adapt Instruction – Adjust lesson plans to target and correct misconceptions directly.
Educators can ensure that their instruction remains rigorous and aligned with High-Quality Instructional Materials (HQIM) by integrating misconception-driven insights into their planning. Addressing misconceptions also helps counteract biases that might lower student expectations, promoting a more equitable learning environment.
Changing The Way Students Learn
Misconceptions in math are a natural part of learning, but when left unaddressed, they can create long-term obstacles for students. By focusing on why students make errors rather than just identifying what they got wrong, ANet helps educators deliver more precise and impactful instruction. Our work supports teachers in maintaining the rigor of their instructional materials, more closely utilizing their HQIM, and making informed adaptations that enhance student learning.
ANet’s unique combination of professional learning, job-embedded coaching, and assessments provides a powerful path forward for educators who want to transform their approach to student learning. Let's work together to turn misconceptions into meaningful learning moments.