Second Attempts and Error Analysis

 

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I’ve been thinking about student math reflections this week.  That reflection can take on many different forms. Giving students a second attempt to complete an assignment can give them an opportunity to reflect on their original performance. This is often (not not always) part of a standards-based-grading approach.  Some teachers allow students to redo particular assignments.  Some teachers have their students complete a paper form of a reflection and/or redo sheet when they didn’t meet the original expectations.  Students fill out the sheet, redo certain problems that need a second look, staple the sheet and finally turn the work back in.  This process has worked well during the past year, but I’m noticing that students are starting to place general statements in the blank lines.  This NY –> M process was starting to become more paperwork than individual reflection.

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Students would avoid writing simple mistake like the plague (since it explicitly says not to do that :)), but they’d write comments that were very general.  I mean VERY general.  Students would write

  • “I didn’t write the answer correctly”
  • “I had trouble with fractions”
  • “I didn’t write the problem right”

Most of the responses were general, and some students wouldn’t even thoroughly review their work before attaching the second attempt sheet.  Don’t get me wrong though.  The sheet was helpful, but I wanted students to delve deeper into their work and become better, or more aware, of where they didn’t meet the expectations moving forward.  Over the summer I was able to attend sessions and workshops related to student goal setting and student error-analysis.  I believe student reflection and error-analysis can be powerful tools for students as well as teachers.  Knowing this, I revamped the second attempt sheet this week.  Here’s the new look.

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The blue circles were entered on the sheet based on the most common errors that I found on quizzes.  I made sure to model this with the class before students filled them out.  I gave examples of why someone would check each box.  After a number of questions, students felt more comfortable in deciding which circle to check – some even thought that multiple circles could be checked.  Why not?  I noticed that students would determine which circle to check depending on their perspective.  Check out the three submitted sheets below.  They all are for the same problem, but fit different categories.

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This is interesting because students were starting to analyze their results with a more critical eye.  This is progress, positive progress.  Even with that being said, we have a long way to go.  I need to be more clear on how students should differentiate between a simple mistake and directions.  I also need to clarify and give more examples of what a strategy issue means.  I think some students have been using the updated sheet with integrity, while others might not be using them as well since their perception of the categories isn’t clear.  I believe this is more of a teacher and modeling issue than a student issue.  I’m looking forward to creating a few different activities for next week to help students becoming better at categorizing their errors and misconceptions.  At some point I’d like that awareness to lead to action and eventually goal setting.  One step at a time.

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4 Ways to Encourage Student Self-Reflection in Math Class

Math teachers have a variety of tools that can enhance the learning process.  Technology, math manipulatives and problem-based learning activities can all play an important role in a math classroom.  Regardless of the tools or strategies, one of the most powerful motivators that I’ve utilized over the past few years deals with the concept of reflection.  Adults often learn by experiencing events and reflecting on them later.  Generally the reflection lets us make better or more informed decisions in the future.  Many educators blog, which I believe is one form of reflection.  Allowing students opportunities to reflect on their math learning experiences, including celebrations and mistakes can be time that is well spent.  A sense of ownership develops when students begin to understand that their success isn’t only dependent on the teacher or tools within the classroom, but on themselves as well.  Reflection is especially powerful after making mistakes.  By reflecting on math mistakes, whether they are procedural, formula issues, or simple errors, students become aware that mistakes are part of the learning process and shouldn’t be on the taboo list.  How do we give students opportunities to reflect in math? Here are four possible ideas:

  • Math Journals – This is a great way to gauge a student’s understanding of particular math concepts.  I’m continuing to find that students are using their math journals to communicate their conceived strengths and personal concerns.  Students are asked to reflect on their learning experiences in the journal through various journal prompts.  I check the journals periodically and am able to provide feedback to individual students.
  • Student Led Math Conferences – Throughout the year I have personal math conferences with the students.  Students bring their formative assessments to the conference and the student reflects on their progress.  We work together to find areas that need strengthening and write a personal goal related to specific academic concepts.  Students may decide to bring their math journal to their math conference.
  • Class Anchor Charts or Plus/Delta Chart – After a formative assessment or test the class may have a discussion about what problems on the assignment caused concerns.  We then reflect on the processes used to find the answer and have a thorough discussion about the mathematical process.
  • Blogging – Student blogs allow time to reflect on their mathematical process.  Students can blog about how they solved a particular problem and what steps were needed.  I find that blog explanations are especially useful when explaining solutions to problem-based learning activities.  It’s also a stellar documentation tool.   Keep in mind that the blogs may be public and not all students want to wave their mistakes in the air.

photo credit: doctor paradox via photopin cc

How do you encourage student reflections in math class?