Today’s post continues a series offering suggestions on how to best respond when students make mistakes.
‘Focus on Their Ideas’
Sarah Nichols is a national-board-certified teacher and a Utah Teacher Fellow in Salt Lake City:
I teach secondary students with disabilities, many of whom are also English Learners. If I chose to give feedback on all their writing errors, it would be discouraging for the students and time-consuming for me. Instead, I only give feedback on the specific writing skills we practiced before the assignment. Other than that, I focus on their big ideas—are they able to communicate clearly? Have they thought through the prompt? Did they apply what they have learned?
For example, if my learning goal for them involves the correct use of capital letters, I would pay attention to that in addition to recently taught skills that I want them to incorporate. As they work, I provide reminders on those skills and give them structured time and supports to self-check their work. Beyond that, I focus on their ideas more than the way they express those ideas.
I also consider the purpose of their writing. Is the assignment designed to assess their writing skills or their content knowledge? If they are writing to demonstrate their knowledge of the water cycle, it doesn’t make sense for me to take off points or expend a lot of corrective energy on capitalization, conjugation, and punctuation if their writing shows me that they understand evaporation, condensation, and precipitation.
Heavily critiquing work can be discouraging for students. If my goal is to get students to express their ideas in writing, I need them to feel comfortable and confident to do that. By targeting individual skills, I can give feedback for improvement while also providing breathing room for their writing skills to grow and develop.
Math Mistakes
Bobson Wong and Larisa Bukalov teach math at Bayside High School in New York City. They are co-authors of The Math Teacher’s Toolbox: Hundreds of Practical Ideas to Support Your Students and Practical Algebra: A Self-Teaching Guide (3rd edition) and winners of the Math for America Muller Award for Professional Influence in Education:
We often make mistakes in life. When students make mistakes, and they don’t learn how to correct them, they don’t just get discouraged. Often, they will give up before starting because they shut down emotionally. As math teachers, we see students experience “math anxiety”—the feelings of fear and tension when doing math.
Math anxiety isn’t simply an emotional response. It’s also a physiological one that affects heart rate and neural activity. Students who feel anxious about math won’t pay attention to any instruction, no matter how interesting it is. To reduce students’ math anxiety, we’ve learned different strategies for reacting to student mistakes. Here are three common types of student errors and what we do in response.
1. Precision errors: Precision errors are minor mistakes that occur when students don’t read, write, speak, listen, or type carefully. These errors include arithmetic mistakes (such as saying that 3 + 4 equals 6 instead of 7), transposition of numbers (dividing by 42 instead of 24), incorrect symbol use (using the variable x instead of a), incorrect rounding (rounding 36.5 as 36 instead of 37) or calculator mistakes (typing “233” instead of “223”).
Precision errors also include misreading a word (thinking that a measurement is in feet instead of miles) or ignoring a word (not seeing the word “not” in the question “Which statement is not true?”).
When students make precision errors, we ask them to look at their work and the original question to see if their work makes sense. Modeling a self-dialogue helps students to see how they should review their work and identify potential mistakes. We try to limit future precision errors by periodically giving assignments in which students only get credit if they get the correct answer with no mistakes in their work. Online tools like DeltaMath.com or paper assignments like vocabulary quizzes where the exact definitions are required help our students pay closer attention to their work.
2. Conceptual errors: Conceptual errors happen when students do correct procedural work but apply the wrong concept (such as finding the area of a rectangle by adding its length and width instead of multiplying them). Students also make conceptual errors when they misinterpret words (such as thinking that an isosceles triangle has three sides of equal length instead of two).
Since conceptual errors usually occur when students misunderstand an idea, we spend more time and effort to address them than precision errors. When students make conceptual errors, we encourage them to talk through their reasoning using a variety of methods. For example, we ask students “Which method works best here?” or “How would you grade this work?” and implement the “think-pair-share” strategy, in which students think silently on the question before sharing their thoughts with a partner and finally share with the rest of the class.
3. Processing errors: Processing errors take place when the language or notation of a problem is so dense that it requires a great deal of specialized knowledge or reading-comprehension skills to understand it, such as “If f(x) = log3 (x + 1), find f −1(x)” or a long word problem.
Unlike conceptual errors, in which students generally understand a problem but miss one important idea, students who make processing errors often struggle just to get started. To help students process complex mathematical text, we teach students to use techniques that are familiar to many English learners.
For example, we teach students the Three Reads protocol, in which students read a text three times, each time focusing on a different aspect of the text. We encourage students to annotate text, interacting with it so they can understand and remember concepts. We model different methods for students to rewrite text into simpler English or a picture before translating it into mathematical symbols.
All of the strategies we use to address mistakes focus on strengthening mathematical communication skills for all learners. When students become more comfortable reflecting on their work, they express themselves more precisely and accurately. As a result, students become more confident and make fewer errors.
Making Sure ‘That Trust Is Not Broken’
Stephen Katzel is the author of Win Your First Year of Teaching Middle School: Strategies and Tools for Success and Win Your First Year in Teacher Leadership: A Toolkit for Team Leaders and Department Chairs:
Academic feedback on student work throughout the class period teaching or done in writing on assignments is a key component to student growth. Giving students verbal feedback in class is important in their growth as students, but teachers need to be mindful of how academic feedback is given to students to ensure that trust is not broken.
When calling on a student to give an answer in class, it is important to be mindful how to respond if they get the answer incorrect. If a student volunteers to answer a question in your class, it shows that they are engaged in the learning and trust you to respond in an appropriate way, even if they get the answer wrong.
Asking a student, “Did you even read the question?” or saying “John, that was incorrect” doesn’t necessarily inspire that student to participate again nor answer future questions. Responding with specific feedback is important in growing student capabilities and guiding them to the correct answer. For example, “John, I noticed you gave a very strong claim, but I am looking for one more piece of evidence from the text. Would you be able to share an additional piece of evidence from the text?” This type of oral feedback builds student skill sets and allows students to maintain their trust in their teacher.
While giving written feedback to students, the same sentiment applies. While in many cases many assignments can be graded with an “X” for incorrect or “check mark” for correct, in many instances, brief written feedback is necessary and important. If a student submits an assignment that has a written component, giving feedback on a student’s ideas is valuable so that they see you are reading their classwork.
You may be thinking, “I have 150 students, how will I find the time to give written feedback on every assignment?” While this would be a valid point, not every assignment in class that is given necessitates written feedback. Using rubrics to pinpoint specific accolades or suggestions for assignments helps teachers streamline their grading and reporting. Having rubrics for longer assignments allows for teachers and students to have streamlined communication on academic feedback and serves a valuable purpose in student growth.
Handling Errors With English Learners
Margo Gottlieb is the co-founder and lead developer of WIDA at the University of Wisconsin-Madison. She has written, co-written, or co-edited 18 books for Corwin, her latest being Assessing Multilingual Learners: Bridges to Empowerment, 3rd ed. (2024) and Collaborative Assessment for Multilingual Learners and Their Teachers: Pathways to Partnerships (with A. Honigsfeld, 2024):
Error making is a natural and expected part of language and cultural growing for multilingual learners. Ideally, these students are members of a community of learners who interact in a warm, supportive, and trusting environment. In this congenial space, students and teachers are collaborating in designing agreed upon learning targets and negotiating multimodal evidence for showcasing their learning.
Language and content are integrated, one interdependent on the other, and students are focusing on communicating concepts and ideas rather than repeating isolated facts or grammatical structures. Multilingual learners’ histories, experiences, languages, and cultures serve as a backdrop and context for learning, which is built on connected engaging activities.
Let’s assume classrooms support a learning environment where multilingual learners feel comfortable taking risks in developing their language skills and error-making is an accepted part of the learning process. In this safe place of belonging, multilingual learners have access to and use their multiple languages. At times, errors in English are compared with the students’ other languages, leading to students’ increased metalinguistic awareness.
Given this backdrop, the following strategy serves multiple purposes as it is applicable to and can be embedded in instruction and assessment. Overall, it exemplifies how teachers and students can work together to highlight the assets of their students, converting errors into learning opportunities. Although there are numerous ways to tackle the issue of responding to student errors, here’s one that has been effective for students in upper-elementary through high school.
Teachers maintain an ongoing bank of common errors with individual students being detectives who contribute to the class resource. Individual or student pairs are invited to complete the four questions in the chart below or ask and respond to each other’s questions and submit them for review.
Teachers then conference with students and facilitate decisions regarding what constitutes an oral or written error. Finally, those errors that affect meaning, such as grammar or wording, are tagged and placed on the anchor wall. Alternatively, a Google document could be created for the class to share.
Students are welcome to refer to the chart during instruction as a reminder and check what might go in each cell (the italics are suggestions). In addition to the class chart, students could keep a log of their individual errors and offer examples of how to correct them. Used in this capacity, the class chart and/or student log serves as a means of self-assessment and reflection. Over time, teachers and students can create a classroom policy regarding errors, understanding that for multilingual learners, often errors are developmental; therefore, focus on the message, that’s what is most important.
Thanks to Sarah, Bobson, Larisa, Stephen, and Margo for contributing their ideas.
Today’s post answered this question:
How do you respond when students make errors in their work, whether orally or in writing, whether English learner or English-proficient, in any subject?
In Part One, Michelle Makus Shory, Gina Elia, and Francoise Thenoux shared their suggestions.
Consider contributing a question to be answered in a future post. You can send one to me at lferlazzo@epe.org. When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.
You can also contact me on X at @Larryferlazzo or on Bluesky at @larryferlazzo.bsky.social .
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