According to John Hattie, feedback is one of the most powerful influences on improved academic achievement. After his synthesis of more than 900 meta-analyses, he found that feedback had one of the highest effects on student learning. Feedback can be one of our most effective instructional strategies for improving student performance, because it has been shown to accelerate the rate and amount of learning.
Feedback is the information we provide students about how they are performing relative to a goal. Feedback does not include judgments or evaluation; rather, it tells students what effects their actions have on their goals. It clearly articulates for students what they understand and where they still need to demonstrate proficiency, and guides them to use specific strategies for improvement.
According to author Dylan Wiliam, "Feedback involves a change of focus from what the teacher is putting into the process to what the learner is getting out of it." Feedback should help the learner answer the questions: Where am I headed? How am I doing? And where do I go next?
Teachers may choose to provide feedback on any of the following:
Feedback is also provided to the teacher by the student. When teachers listen to students and learn what they know, what they understand, where they are confused, and when they are disengaged, amazing learning occurs for both teacher and student.
Feedback is tied to a learning target and success criteria. Before feedback is delivered, students should understand the learning target and the indicators for success. When students can compare their work with a clearly understood criterion for success, they are more likely to accept and value the feedback, and they begin generating their own feedback for learning.
Feedback is based on evidence. Teachers should ensure the tasks they assign align with the learning targets. Feedback should be specific and based on observations of the student's processes and work, not on inferences, and it should focus on the quality of the work, not the learner.
Feedback informs the student where they are relative to the criteria for success. Using work samples at different levels of proficiency helps students understand what quality work looks like. In time, students become adept at recognizing strengths and areas of opportunity in their own work.
Feedback is actionable. The most effective feedback is meaningful, specific, and useful; it provides information that allows the student to take action and answers the question, "What do I need to do more or less of next time?" It should target one important thing that, if changed, would immediately yield noticeable improvement.
Feedback is comprehensible. Feedback should engage and motivate students, be usable, and not overwhelming. When students are used to short, frequent conferences, they have a greater awareness of the role feedback plays in their learning. Ask students to repeat back the comments to confirm they know what to do next.
Feedback is timely and ongoing. To be effective, feedback needs to be delivered when the student is engaged in the work and there is still time to make improvements. Once feedback is given, students need the immediate opportunity to use it.
Norris and Schuhl recommend using assessing questions when students are stuck and advancing questions for students ready to move beyond the standards.
Applying these tenets of high-quality feedback in the mathematics classroom is critically important to our students' success. Our feedback should not only promote learning of the math content but also strengthen students' application of the mathematical practices. In addition to specific content and skills, feedback should focus on the Standards of Mathematical Practice, which emphasize students' ability to:
When feedback is centered on mathematical practices, students grow in the habits of mind needed to be mathematically proficient. At the start of a conference, quickly review the work the student has done, including the strategies they are using, and note what the student has done well along with any areas of confusion. You might start the discussion with:
With these openers, the feedback is tied to the student's work and based on evidence, not on the learner. Be sure to ask high-quality questions to probe student thinking. In their book Engage in the Mathematical Practices, authors Kit Norris and Sarah Schuhl identify two types of probing questions: assessing questions that scaffold instruction for students who are stuck, and advancing questions that further learning for students ready to move beyond the standard.
It is really helpful to identify an anchor problem and solution that exemplifies the work you expect students to do. Students do best when they know exactly what is expected of them, through rubrics, checklists, or an annotated example. Providing an anchor problem not only lifts the quality of student work but also provides guidance about what to do next.
It is important that students understand the teacher is not the only source of feedback in the math classroom. Providing opportunities for students to engage in dialogue with their peers helps clarify their thinking. When talking with a partner, students have the chance to listen to and reflect on the mathematical arguments of their classmates. Taking time to analyze and discuss errors can increase engagement and promote conceptual understanding. One way to leverage errors is to project anonymous work samples that include flawed thinking and lead the class through a discussion, building a culture of risk-taking and a recognition that we can all learn from our mistakes.
The goal of our standards is to produce students who are college and career ready, and feedback is one of our most powerful tools to help them get there.
When effectively used, feedback provides students with accurate information about what they understand and can do, as well as areas where they still need to build proficiency. In the mathematics classroom, quality questioning is at the heart of effective feedback. When students make comparisons between their work and the criteria for success, they identify for themselves what is working and the steps they need to take for improvement.
Clayton, Heather. "Learning Targets." Making the Standards Come Alive!, 2017.
Hattie, John. Visible Learning for Teachers: Maintaining Impact on Learning. New York: Routledge, 2012.
Norris, Kit, and Sarah Schuhl. Engage in the Mathematical Practices: Strategies to Build Numeracy and Literacy with K-5 Learners. Bloomington, IN: Solution Tree Press, 2016.
Vagle, Nicole Dimich. Design in 5: Essential Phases to Create Engaging Assessment Practice. Bloomington, IN: Solution Tree Press, 2015.
Wiggins, Grant. "Seven Keys to Effective Feedback." Educational Leadership, September 2012.