Read Chat Reflect Week 2: Feedback

Call me weird or what ... I feel excited about this week's "Read Chat Reflect!"  So excited I'm already reading the article for the week and thinking about how it applies in my class.

The first sentence that caught my eye in "How Am I Doing?" is "Her paper did not tell her what she was good at or what she needed to keep working on—the marks did not function as effective feedback."  I know students get nothing from the papers I return to them other than a grade.  In my mind, feedback has to happen way before I take up a paper ... and when I do take one up, it's usually a summative activity.  If students want to make corrections or work on that same assignment I invite them to tutorials, and we talk through their errors.

The next thought that I've been pondering this afternoon is this, "Absent a learning target, students will believe that the goal is to complete the activity."  Learning targets are huge in our school.  In fact we not only have targets but also criteria for success! When I joined this school I was familiar with learning targets - I was ready to roll.  And then I heard all the talk about criteria for success and I felt like I was starting over.  Once I got the hang of it, it made sense to me.  So ... the learning target on Monday is, "I can solve equations with rational expressions."  The criteria for success include:

1. Find a common denominator for every fraction in the equation.
2. Multiply every term in the equation by the common denominator.
3. Simplify the equation (distribute and combine like terms where necessary)
4. Solve the simplified equation.
5. Check the solution to determine if it works or if it is extraneous.

One way to look at criteria for success is as steps.  As I teach I need to assess each step to determine which students have the individual steps and to remediate immediately those that do not.  This is tricky.  Sometimes we use individual whiteboards and check step by step.  Other times students work through problems, and then I ask them to self-report ... on which step are they struggling.  I go to the list as in my example ... how are you doing with step 1?  Step 2?  Etc.  I try to modify examples based on that feedback that students give to me.

Two other thoughts caught my attention in this article ... Effective feedback occurs during the learning, while there is still time to act on it. And, Effective feedback does not do the thinking for the student.

I can't wait until test day to give feedback.  Students need feedback while they are learning the math skills.  And when I give feedback, I can't do the work for them.  I have a bad habit of taking a student's pencil in my hand and writing the next step or two.  I know this is not good.  It's better if I have an EXPO marker in my hand, write something on their desk - that will help them figure out the next step on their own if my questions are enough to lead them there.

I wish there was a good article or book on feedback specifically in math class. Suggestions???

Student Reflection and Criteria for Success

In chapter Chapter 3, "Clarifying, Sharing, and Understanding Learning Intentions and Success Criteria: from Embedded Formative Assessment, Wiliam explores the value in and techniques for sharing learning intentions and success criteria with students.

Can students assess themselves against a set of criteria during the unit so that at the end of the unit, they have reflected on all of the criteria?  

What would this look like for me?  My goals for students would be task specific (solving equations) and process focused (being able to show steps clearly and accurately).

At the end of our unit on solving multi-step equations, students will need to be able to solve equations with grouping symbols and/or variables on both sides of the equal signs.

Learning Goal:  I can solve multi-step linear equations.

Steps to Success:

1. I can use the distributive property if the equation has grouping symbols.
2. I can simplify each expression on either side of the equal sign by combining like terms.
3. I can isolate the variable by adding the inverse to both sides of the equation.
4. I can isolate the variable by multiplying the inverse on both sides of the equation.
5. I can substitute my solution back into the original equation to check my work.

In order to experience success, students will need to know the terms that I highlighted in the success criteria.  They will also have already mastered one and two-step equations.

In developing this lesson, students will put together interactive foldable on solving equations.  An example of those notes are here.  Along with the "flip book," students will have a list of vocabulary words and the steps to success outlined above.  I'll put those items on a self-assessment sheet so that students can rate their own understanding before, during and after the unit.

During the lesson sequence, I will check for understanding on each step of success.  In addition, as we are solving equations, and students ask for help, I will ask them on which success step they are struggling.  In this way, students will be encouraged to become familiar with the five steps.

After routine practice, I plan to assign an error analysis task.  In that task, I will give students equations that have been worked out step by step but that also include at least one error.  Students will identify the errors and correct the work.  This example is not my work ... but I would create something like this!  "Using Error Analysis to Teach Equation Solving" by Kathy Hawes, published by NCTM in 2007 has good ideas for teaching solving equations.  A copy of this article is online here. 

How do you share your learning intentions and criteria of success with students?