Making Math Feedback Count Part 2: Enhancing Student Progress in Math
By Dr. Sherri Lorton
In Part 1 of this series, we explored the powerful role of data in guiding math instruction. We illustrated why tying data collection and feedback to standards supports planning and the feedback process. Now, in Part 2, we dive deeper into the various types of data that can inform feedback practices, particularly in mathematics, and provide specifics on how teachers can incorporate simple practices in their classrooms. Each data type provides unique insights into a student’s understanding, from formative assessments to diagnostic tools, helping teachers tailor their feedback to meet specific needs. By integrating multiple data sources – such as assessments, observations, and diagnostic tools – educators can craft feedback that is timely, actionable, and designed to encourage student growth. This post will explore these data types in detail and outline how to use them to provide feedback that corrects mistakes and promotes a deeper understanding of mathematical concepts.
Types of Data to Inform Feedback
Several types of data can be used to assess student progress against math standards, each offering unique insights into a student’s understanding:
Formative Assessment Data
These are informal checks for understanding that occur throughout a lesson or unit, such as exit tickets, quick quizzes, and class discussions. Formative assessments allow teachers to gauge students’ understanding in real-time and provide immediate, targeted feedback. For example, if a student struggles to understand place value, a teacher can quickly address the misconception with a corrective task or explanation.
Summative Assessment Data
These assessments, such as end-of-unit tests or standardized tests, provide an overview of how well a student has mastered a set of standards. While summative assessments are generally used for grading purposes, they can also serve as a tool for identifying patterns of strengths and weaknesses across the class. If a significant portion of the class struggles with a certain standard, teachers can use this data to modify instruction for future lessons. This data can also be used by coaches, administrators, or the curriculum department at the district level to identify strengths/weaknesses in instructional practices or curriculum.
Observational Data
Teachers’ observations during daily math activities, such as group work or individual problem-solving, offer qualitative data that can complement more formal assessments. Observations allow teachers to identify students’ problem-solving processes and offer feedback on strategies that can improve their efficiency or understanding. Some ways to make observations more useful include making descriptors explicit, creating organized lists, or using portfolios. Creating very explicit descriptors makes the statements easy for students to understand. Creating a hard copy or electronic version with a list of the descriptors and keeping them in an easily accessible location (iPad, laptop, clipboard, or binder) allows you to refer to it quickly when you plan and teach whole class or small group lessons. Using portfolio binders for each student and organizing them into a bookcase or on a counter where you and students can easily access them is another way to keep track of student progress. All of these will provide solid documentation that can be used when meeting with students, parents, or other teachers.
Diagnostic Data
Tools like diagnostic assessments or universal screeners can help teachers identify students’ baseline skills and pinpoint gaps in understanding before beginning new content. These assessments, which are often administered at the start of the year or before a new unit, provide crucial insight into where students need the most support.
Effective Feedback Practices Based on Data
Once data is gathered, educators must translate that information into actionable and supportive feedback. Effective feedback should:
1. Be Specific and Goal-Oriented
General feedback like “good job” or “try harder” does not give students the guidance they need. Instead, feedback should be focused on specific aspects of the standard, such as, “You accurately added the numbers, but you made an error with the placement of the decimal point. Let’s review how decimals work when adding.” This feedback helps students understand the exact error and what they need to do to improve.
2. Promote Self-Reflection
Encouraging students to reflect on their own work can help them internalize feedback and understand their areas for growth. Teachers can ask questions like, “What strategy did you use to solve this problem? How might you approach this differently next time?”
3. Be Timely and Frequent
Feedback is most effective when provided in a timely manner, allowing students to act on it while the learning is still fresh in their minds. Frequent feedback also ensures that students receive ongoing support and guidance, which is critical for long-term success. While feedback can come from notes on assignments or assessments, other quick ways include using whiteboards to complete a problem and show your answer or checking work with a peer.
4. Encourage Growth
Feedback should focus not only on the errors students have made but also on how they can improve moving forward. Dweck’s (2006) research on growth mindset shows that feedback fosters resilience and a positive attitude toward learning when it emphasizes effort, strategy, and learning from mistakes. A positive attitude toward math helps break the stereotype that math is inherently difficult or only for certain people. Hattie’s research (2009) also underscores the importance of feedback as a high-impact strategy for promoting student achievement, highlighting that feedback tied to specific learning outcomes can dramatically improve student performance.
Final Thoughts
In conclusion, the strategic use of diverse data types – from formative assessments to diagnostic tools – can significantly enhance the feedback process in math instruction. When teachers leverage data to provide specific, timely, and growth-oriented feedback, they empower students to recognize and address their own learning gaps. Moreover, feedback that encourages self-reflection and focuses on improvement fosters a growth mindset, which is essential for building students’ confidence and perseverance in math. By incorporating various data sources into feedback practices, educators can create a dynamic learning environment where students receive the support they need to continuously develop their mathematical skills and reach their full potential. As we’ve seen, data-informed feedback is not just about correcting errors – it’s about providing the foundation for lifelong learning and academic resilience.
References
Dweck, C. (2006). Mindset: The New Psychology of Success. Random House.Hattie, J. (2009). Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement. Routledge.
