Descriptive Feedback and Differentiation: A Natural Connection Astrid Fossum, Mathematics Teaching Specialist, Milwaukee Public Schools, Sharonda M. Harris, Curriculum and Instruction Math Supervisor, Milwaukee Public Schools, The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No

Mathematics FrameworkDistributed Leadership Teacher Learning Continuum Student Learning Continuum

In this session participants will… Engage in analyzing student work samples with the purpose of identifying similar strategies and misconceptions and group students accordingly. Participate in writing effective descriptive feedback, focusing on feedback as a tool to differentiate instruction.

MPS Learning Target: Number Operations and Relationships Use strategies fluently to make estimates, solve, and pose real-world problems (e.g., single and multi-step) for all operations, to compare and rename numbers, and to find factors and multiples.

Wisconsin Assessment Framework for Mathematics Subskill Descriptors Sub-skill B.b: Computation Use all operations in everyday situations to solve single or multi-step word problems. Solve three- and four-digit addition and subtraction with regrouping; multiplication of two-digit by one-digit numbers; division with single-digit divisors and two-digit dividends and with two-step or mixed operation problems with single-digit numbers. Determine reasonableness of answers.

C.A.B.S. (Classroom Assessments Based on Standards) Write a word problem for 52 ÷ 7 and then solve your problem. As you solve the problem, explain your reasoning and show your answer.

Research “Improved formative assessment helps low achievers more than other students and reduces the range of achievement while raising achievement overall.” “Firm evidence shows that formative assessment is an essential component of classroom work and that its development can raise standards of achievement.” Black, P. & Wiliam, D (1998). Inside the Black Box: Raising Standards through classroom assessment. Phi Delta Kappan, 808(2),

Types of Feedback Motivational Feedback Evaluative Feedback Descriptive Feedback Effective Descriptive Feedback

Descriptive Feedback Goal is to improve student achievement by telling the learner what steps to take in order to move forward in the learning process. Feedback that is intended to tell the learner what needs to be improved. Gives specific guidance as to how to improve the learners’ reasoning. “You accurately found the number of students in 4th grade who said ice cream was their favorite. You now need to divide this number by the total number of students to get the percent who said ice cream was their favorite.”

Effective descriptive feedback Goal is for students to internalize the effective feedback. Feedback that is intended to be used by the learner to independently move their reasoning to the next level. “I agree with the pattern that you have identified in the table. I am not convinced that the rule you wrote works for all the values in the table. How could you prove this?”

What is the teacher differentiating? Content: What students will learn and the materials that represent that. Process: Activities through which students make sense of key ideas using essential skills. Product: How students demonstrate and extend what they understand and can do as a result of learning. Learning environment: The classroom conditions that set the tone and expectations of learning. Tomlinson, 1999

“Once students realize that information from both teacher feedback and their own self- assessment can help them improve, they will process material more deeply, persist longer, and try harder. In short, they will become more self- regulated learners.” Brookhart, 2007

Process… Do the math prompt Identify the key mathematics Identify expectations and anticipated misconceptions Analyze student work samples Group work according to mathematical features Provide descriptive and/or effective descriptive feedback to groups of students Students and teachers work on task while utilizing feedback statements Determine next steps for the teaching and learning of mathematics

Resources Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through assessment. Phi Delta Kappan, 80(2), Brookhart, S.M., (2007). Feedback That Fits. Educational Leadership, 65(4), Brookhart, S.M., (2008). How to Give Effective Feedback To Your Students. Alexandria, VA: Association for Supervision and Curriculum Development. Marzano, R., Pickering D., & Pollock, J., (2001). Classroom Instruction that Works: Research Based Strategies for Increasing Student Achievement. Alexandria, VA: McREL. Stiggins, R.J., Arter, J., Chappuis, J., & Chappuis, S. (2005). Assessment FOR Learning: An Action Guide for School Leaders. Portland, OR: Assessment Training Institute. Tomlinson, C., & Eidson C. (2003). Differentiation in Practice: A Resource Guide for Differentiating Curriculum, Grades K-5. Alexandria, VA: Association for Supervision and Curriculum Development. Tomlinson, C. (1999). The Differentiated Classroom: Responding to the Needs of All Learners. Alexandria, VA: Association for Supervision and Curriculum Development. Wiggins, G., & McTighe, J. (1998). Understanding by Design. Alexandria, VA: Association for Supervision and Curriculum Development. The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. EHR