A Formative Assessment Cycle involves: 1.Teaching a lesson to achieve objectives. The lesson includes a planned assessment to check if the objective has been learned. 2.Gathering and analyzing data from the assessment by both the teacher and the student. 3.Formulating a new lesson in response to the data. A new objective may be formulated or the teacher and students continue to work towards the original objective(s). The teacher may adjust the teaching strategy. The Formative Assessment Cycle A math skill that is in the original problem Explaining how to solve a problem Analyze a written explanation. Analysis Teacher and students will analyze the data together while it is displayed anonymously. Lesson The lesson is the instruction of the math concept, as well as how to write an explanation and the expectations used to grade it from 1 to 4. Objective The assessment Students are asked to solve a math problem and write explanations for their solution. They will then be asked to assess their classmates’ explanations. Student Grading of Open Responses Using feedback from assessment to customize instruction and increase student learning Christine O’Connor – Oak Middle School in Shrewsbury, MA Cristina Heffernan – ASSISTment Program Zach Broderick – Worcester Polytechnic Institute Next Objective/Lesson/Assessment The response lesson will involve reviewing the students’ writing in class. The teacher will make a point of focusing not only on the quality of the writing but also on the math content involved in the problem. This will be assessed by: 1. Giving another math problem using that skill and 2. Doing this cycle again to re-assess the students’ explanations. Objectives: Student Will… Solve a complex word problem using the Pythagorean theorem Explain how they arrive at their answers Analyze classmates’ explanations and grade them Lesson: 1.In previous weeks students learned the Pythagorean theorem. 2.Students were also given instruction on how to write an explanation of their solutions Documentation of Assessment Part 1: Here are the answers to the questions as well as the typed explanations on how the students solved the problem. Due to time constraints the class only looked at part C since that is the one where only 9% of the students got the numerical part correct. The Assessment: Part 1: Students are asked to solve the 3 part problem called “Arsenio’s Open Response”. They input their answer as well as an explanation of how they solved the problem. Figure 1 shows part C of the problem. Part 2: Follow up question: On a scale of 1-4, students critique 5 randomly selected responses written by their classmates shown on the projector anonymously. Next Lesson: Class discussion. With 10 minutes left in class, Ms. O’Connor is now ready to address any misconceptions about part C of the Arsinio problem. She has lots of data to choose from and she chooses to discuss because the answer is wrong and because it is not clear if it should get a 3 or a 4—one person even thought it was wrong! In analyzing the misconceptions, she will be able to address the mathematics in the problem (Objective 1). There is also a wide range of clarity on the grading explanations and she wants to discuss this as well (Objectives 2 and 3). Objectives: In this case, they stay the same. Solve a complex word problem using the Pythagorean theorem Explain how they arrive at their answers Analyze responses and grade them The Assessment: Students will be given another open-ended problem that uses the Pythagorean Theorem. The Reflection loop will be done again using ASSISTment. The plan in action: January 13th, 2009 Ms. O’Connor’s 8th Grade Math Class Documentation of Assessment Part 2: The students graded the explanations from above on a scale of 1 to 4 and explained how they got their answers. This is the last part of the assessment data for this plan. These examples show students grading an explanation of a wrong answer, 72131, and of a correct answer, Student grades of explanations Student grades of explanations 72131