Giving and receiving effective feedback is a pivotal tool across all levels of education and teaching. In mathematics education, constructive feedback enhances students’ understanding, builds their mathematical skills, and helps to foster a deeper connection between educators and their students.

This article explores what feedback is, how we can ensure the feedback we give our students is specific and actionable and, as teachers, how we, too, can constructively receive feedback.

What is feedback?

Feedback in maths goes beyond praise, criticism, reward or punishment. A mere ‘good job’ or ‘try again’ falls short of offering the constructive guidance required for improvement.

Effective feedback should:

• be clear and concise
• explain what the student did well, their strengths and what they understood
• point out and explain any misunderstandings
• suggest ways to improve or move forward.

In explicit teaching, feedback should be specific and actionable.

Specific: I know what needs to be done.

Actionable: I know what I need to do to move ahead.

Students should know precisely what needs improvement and how to achieve it. This not only clarifies the path to success, it also makes the feedback process more motivating for the individual student.

Why is it important?

Feedback in maths education serves various essential purposes:

• Promoting learning: It is a powerful catalyst for academic growth.
• Building motivation: Constructive feedback can inspire students to strive for excellence.
• Fostering relationships: Feedback provides an excellent opportunity for teachers to connect with students on a deeper level.

The human element: empathy and trust

Delivering feedback is not a formulaic, one-size-fits-all process. As with all elements of teaching, many factors influence how we interact with our students and how we establish what kind of feedback will work best for them.

Two key ingredients to delivering meaningful feedback are empathy and trust.

Without empathy and trust, feedback can feel invasive, critical and unwarranted. If we build a safe learning environment built on empathy and trust, our feedback will be more effective and our students more motivated for improvement.

When delivering feedback, avoid emotional reactions and remember that the level of trust in your classroom will significantly impact how your feedback is received.

Integrating feedback into planning

To create space for feedback, when planning teaching educators should:

• Set clear goals and success criteria: Determine what you aim to achieve with your students.
• Anticipate misconceptions: Be prepared to address common misunderstandings.
• Deliberate noticing: Continuously assess your students and their understanding, both academically and emotionally.
• Establish empathy and trust: Deliberate noticing allows teachers to connect with their students on a deeper level.

Feedback goes both ways

Teachers are often very adept at giving feedback but are not always so comfortable on the receiving end of it. Be open to receiving feedback from students, both sought feedback and inferred feedback.

Sought feedback: Give your students regular opportunities to share with you what is and isn’t working. Encourage them to be specific.

Inferred feedback: Where teachers identify students may not be fully comprehending the material. Roving around the classroom will give you more opportunities to pick up on your students’ inferred feedback.

Asking your students for feedback is a great way to improve your practice and also provides an opportunity as the teacher to model how to receive feedback. Giving and receiving purposeful feedback will help to create a learning environment that encourages open communication.

Feedback in mathematics education is not a one-size-fits-all approach but a human-centred process rooted in empathy, trust and a genuine desire for improvement. By embracing these principles and making space for feedback in teaching, educators can create a supportive environment where every student can excel in mathematics.