Feedback essential to helping students succeed in mathematics


By Jeani Gollihue

If you were asked to list some things that you felt impact student achievement, what comes to mind?

The graphic above shows some typical teacher responses to that question. But are these really the most effective factors? Not according to John Hattie. Hattie, an education researcher, has cited more than 900 meta-analysis studies and used them to quantitate attributes of teachers and schools.

The numerical value assigned to each characteristic is called the effect size and the larger the positive number, the larger the positive impact that factor has on student achievement.

In John Hattie’s book, “Visible Learning for Teachers – Maximizing Impact on Learning,” he provides a list of attributes and their corresponding effect sizes. Come to find out, many of the factors teachers believe are most important do positively impact students, but not at the effect size one would think.

So what does make the most impact according to Hattie? Here are the 10 attributes which Hattie’s research deems as the most effective. As a teacher, the tool I wield the most on this list is feedback.

Students need feedback on their work to know what they are doing correctly and what they need to do better or differently. Feedback in math is especially crucial. If a student does 10 problems incorrectly before I get to his or her desk, it will take me more time to break the bad habit than to teach the skill from scratch. How can teachers incorporate feedback to students more efficiently in our every day instruction?

One thing teachers should remember is that formative assessment and feedback go hand in hand. Without frequent assessment, teachers will not realize the mistakes in time to give the appropriate feedback. My friend Ann Booth, a prominent Kentucky math educator, often said “Formative assessment should be a check-up, not an autopsy.” Regular check-ups with appropriate feedback can steer students back in the correct direction.

Here are some ideas on how to incorporate feedback efficiently that I have used for my students:

Post-It Notes: I gobble them up at every free table because I use thousands of them. I place them beside an incorrect problem with comments and corrections. English teachers use this concept all the time by inserting comments in the margins of electronic copies of writings.

Highlighters: Highlight the part of a problem that is incorrect, then show what should have gone in that place.

Sort quizzes: I sort into three categories. Sticker quizzes are perfect, middle quizzes have small errors that can be corrected as described above, but quizzes with stars on the top contain fundamental errors that need some one-to-one instruction. Distributing quizzes while students are working on an assignment gives me time to talk with students about their quizzes. This type of formative assessment needs to happen often to catch misconceptions before they become nearly unbreakable bad habits. When students make mistakes on formative assessments, I allow them to retake, explain away or redo the problems for full credit. I want students to see these as opportunities for growth and not as failure.

Student Peer Helpers: I have one for each of my Algebra I classes. Peer tutors help me conference with starred quiz holders, monitor class work, field questions when I am busy with other students and help me differentiate instruction. At my current school, peer tutors are volunteers and receive no credit for this class, but they use it as volunteer hours for scholarships. If students are going to receive credit, in the past I have required them to keep a daily journal, write a two-page reflection each grading period and I factor in attendance for their grade.

Shuffle groups: I got this idea from my friend Ben Zimmerman. If you can get students in a group to actually work together, the conversation itself can be instructional and offer feedback. In a shuffle group, each student must turn in the assignment. Papers from each group are paper-clipped together, but I only grade one paper from the group. Everyone in the group gets the same grade based on the one paper graded. Students are more likely to help each other under these conditions. When I grade the selected paper, I grade it thoroughly and give in-depth feedback. Students in the group review the graded paper together.

Want went wrong? Questions: These make good bell-ringers or quiz questions. Put an incorrectly worked problem on the board and ask the students to explain to the pretend student what went wrong. Sometimes I will give them two or three incorrect answers to the same problem. They must correct the problems, explain what the pretend students did wrong and give a score out of 10. This helps me know if they understand which mistakes were the most important. When possible, I use actual mistakes made by students in that class.

Teaching students to self-assess and monitor their own performance is not only a way to provide immediate feedback, but it also gives them ownership in the education process.

Here are some ways I try to get students to monitor their own work:

IPE days (Instruction, Practice, Extenstion): As I go over targets for each unit, students evaluate how they think they are doing on each target. A few days before a test, we have an IPE day. Students can choose to practice topics they feel shaky on (I provide problems with solutions), get additional instruction or tackle some challenging extension problems of the topic. Students who chose to work on the extension problems also help me answer questions for the instruction group.

Expert stations: Similar to IPE days but a little less formal. I pick two or three students to be “experts” for each objective and set them up in various places in the room. I identify what that station is. Students are given a worksheet with problems from different objectives. They work on the problems from the objectives they feel are their weaknesses. If they get stuck, they visit the appropriate station. Station experts are given a few extenstion-type questions to work during slack time.

Self-Evalulation opportunities: For every assignment I give I try to have some type of feedback the student can use to self-assess. From odd exercises, answer banks and answer keys hung up around the room to corny Algebra with Pizzazz puzzle sheets, a student should know if the answer they have for a problem is correct. Sometimes if I am using the textbook, I will assign problems in multiples of three. Students have some odd problems to use for self-evaluation, and some even ones that I know they didn’t just copy from the back of the book.

These ideas are some ways I have tried to incorporate feedback into instruction, but just working it in doesn’t make it effective feedback. According to an article on Edutopia by Marianne Stenger, “5 Research-Based Tips for Providing Students with Meaningful Feedback,” there are some tips to consider if teachers want their feedback to students to be meaningful.

  1. Be as specific as possible. “Great job!” doesn’t provide insight to what was great. Instead, try something like “I like how you … .”
  2. The sooner the better. This is tough, but as mentioned above, feedback after 50 incorrect repetitions isn’t going to be as effective as immediate feedback.
  3. Address the learner’s advancement toward a goal. “Look how much better you are doing on these problems than Monday. You just have to work on this one thing … .” Using learning targets also lets the student see where he/she is in the scheme of things.
  4. Present feedback carefully. Remind students often that feedback isn’t a personal attack on them, but instead a way for me as their teacher to communicate with them one-on-one, whether in person or through written communication. I try to point out something the student has done well before jumping into issues. “You got off to a great start when you …, but right here you need to … .”
  5. Involve learners in the process. “Here is the solution worked out, can you see where you went wrong?” “How should you have done this?” “Can you think of anything you have tried on another problem that could work here?”

Hattie tells us that feedback has a significant impact and Stenger reminds us of how to make feedback more meaningful. But because not all students are created alike, we cannot expect whole group instruction to meet the needs of every learner. It is our job to provide educaton to each individual and feedback gives us an incredible opportunity to do just that.


Jeani Gollihue
Jeani Gollihue

Jeani Gollihue retired from Greenup County High School after 22 years in the classroom and five years as a curriculum resource teacher. She currently is teaching Algebra 1, AP Calculus AB & BC at Russell High School (Russell Independent). Gollihue has served on three Kentucky Department of Education math committees, has done some reviewing and editing for Illustrative Mathematics and has twice been named a state finalist for the Presidential Award for Excellence in Math and Science Teaching.