Thinking About Math Misconceptions

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My students have about one month of school left.  It’s hard to believe that the 2016-17 school year will soon be over.  This year I’ve been attempting to have my kids think more about their mathematical understanding.  Putting aside time to do this hasn’t been easy and there’s been a struggle, but I believe we’re making progress.  One of the most impactful pieces to this has been the inclusion of a more standards-based approach when it comes to student work.

One way in which I’ve had students think more about their thinking is to give students opportunities to redo assignments.  Students are given a second attempt to complete an assignment after they complete a reflection sheet.  The sheet is below.

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The goal is to improve and move from the NY – not yet to a M- Met.  Students are required to analyze their assignment and staple on the NY–>M sheet before turning it back in.  I’ve changed this sheet over the past few months as I started to notice that some students were a lot more successful at redoing their assignments and receiving full credit than others.

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I decided to have a a brief classroom discussion to talk about how analyzing our math work can help us identify where we should target improvement efforts.  I put two slides up on the whiteboard to frame the discussion.

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Indicates what the student wrote and how it impacted the second attempt.

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The class discussed the two slides and the student responses.  I emphasized the need to critically analyze their work before redoing it a second time.  Being specific with the comments also plays a role in how well a student performs again.  I also thought it might be a decent idea to start discussing key misconceptions before the class gets back their assignments.  This already happens, but spending more time discussing prevalent misconceptions beyond “simple errors” might be helpful moving forward.  I’m sure I’ll refine the reflection sheets over the summer, but I like the progress that students are making along their mathematical journey.

 

 

Tinkering with Second Attempts

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I believe teachers are always tinkering to see what works best.  I’m in the midst of doing just that with my NY/M strategy.  Near the beginning of the year I noticed that students would take quizzes and focus on the top third of the page.  Near the top, often right next to the assignment title would be a score.  That score would mean the world to the kid. Students would take a look at the point value and immediately make an evaluation based on that that score alone.   The internalization and analysis that I’d hope for wouldn’t happen.  So this year I decided to move a bit closer to a standards-based model with assignments.  Students would be allowed to redo an assignment for credit.

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At first this strategy seemed to make a huge difference.  Students took more risks and it seemed to curb some of their anxiety.  In the most positive cases, I’d write specific feedback on the students’ papers and place a NY at the top of the paper.  Students would redo the sheet and put it back into the turn in bin.  The less-than-perfect cases would involve me putting  a NY at the top of the page without additional markings.  In all honestly, sometimes the errors were careless mistakes and didn’t require much feedback on my part.  Regardless, students were turning back in the NYs and around 60-70% would receive Ms in return.  This was good news.  Although I was glad that this strategy seemed to be working, I started noticing a trend.

Some students would put less effort in completing the assignment the first time knowing that they’d have another opportunity.  Also, students would redo an assignment and not truly analyze what they did wrong in the first place, so they ended up netting zero.  This started to discourage me and that’s when I started tinkering again.   I asked a few different people on Twitter about the logistics behind retakes in their math class.  One person stated that her students fill out a form before retaking the assignment, while another mentioned that the student would be required to get extra help before the retake. I don’t believe there’s  a right or wrong answer to this.  I believe that there needs to be some type of reflection/feedback that occurs before the retake.  That could help students become more aware of what happened during the first attempt and prepare them a bit better for the second.  Being aware of where a hiccup happened is usually the first step in the reflection process.  So starting this week my students will be filling out the sheet below before retaking a quiz.

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I’ll probably continue to tinker with the wording, but it’s a start.  I want students to be able to analyze their first attempt and find the reason behind the retake.  Sometimes, the reason is because of a simple mistake, but I’d like kids to move beyond that as most reasons for the second attempt are mathematical.  I’m looking forward to seeing how this works during the last third of the school year.

 

We’re Back in Business

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Students are scheduled to enter my school tomorrow morning.  It’s been a whole two weeks since I’ve seen my students.  Tomorrow, routines will be reestablished, backpacks will be filled, students will be chattering about their break, and students and teachers alike will get back into school mode after a brief hiatus.  As  tomorrow approaches, I’m reflecting on what my classes have accomplished and what still is on the plate ahead of us.  I spent a good amount of time yesterday planning out the next week of instruction and it confirmed my anxiousness to know that the school year is over half-way completed.  As I look over the next few months, I’m finding curriculum pacing guides, standardized testing, school performances and field trips all impact my instruction to a certain degree.  This happens every year and it has me thinking of what time I truly have left with the kids. I’m also aware that these next few months directly impact students in meaningful ways.  For some, this will be my last year with a group of fifth graders that I’ve seen since they were in second grade. I want to ensure that I make the most of that time remaining.  That doesn’t necessarily mean speeding through the curriculum.  I’m hoping to gives students opportunities during the next few months to make connections, reflect and set goals.  As we all come back tomorrow, I want to communicate the following to my kids:


1.)  The learning experiences that you’ll encounter in the next few months are intentionally designed for you to make meaningful math connections.  Perseverance will be key in helping you create these connections.  You might find that you don’t understand a particular concept when we introduce it.  That’s okay.  Learning is a process and we’re all in this together.

2.)  Group projects, individual assignments and standardized tests are on the calendar and will be approaching in the next few months.  Keep in mind that I believe you’ll will show your potential on all of these. The scores and marks will help teachers and your parents have a better understanding of your strengths and areas that might need to be bolstered.  Also keep in mind that the scores are a number and don’t represent who you are as a person.

3.)  Let’s celebrate a milestone.  We’ve worked hard and have made significant progress since September. Each student in here has made gains and I want us to reflect a bit on our success. There’s more to accomplish, of course, but reflecting on our past growth can also encourage us to move forward with additional confidence.


I’d like to communicate this to all my classes at some point tomorrow.  I won’t necessarily read off a script, but I feel like flushing it out on here is a decent starting point.

It’s time to get back into the routine of setting my alarm clock to wake up extra early.  I’ll be joining the trove of educators heading back into their schools this week.  I’m looking forward to tomorrow.

Self-Reported Grades

The first trimester grading period ended about a week ago.  Soon, students will receive their report card grades and teacher comments.  The majority of teachers in my school have been carefully crafting the right words to be placed on the report card.  These comments often communicate how the students are learning compared to the standard, possible struggles, and next steps to improve their learning journey.  The report cards are usually sent home via backpack and most students gravitate towards the letter grade that is at the top of the report card.  My school isn’t standards-based so that letter grade is often a place of emphasis. The rest of the report cards components come secondary.  I’ve noticed this trend for years.  This year I’m changing up this process to help students understand and reflect on their own learning before they receive their actual report cards.  I decided to create an activity based on Hattie’s self-reported grades influencer.

In preparation for this activity I filled out each report card with comments that I thought were appropriate.  These comments mentioned the scope and sequence of math skills explored during the trimester.  They also communicated what students could bolster during the second trimester. I left the actual grade portion of the report card blank.  I also left the MS, LS, AC and NI blank.  These were for students to fill out.

I gave each student their partially filled out report card and student file.  The student file contains all of the unit assessments for the first trimester.  Students were also asked to use their math reflection journal during this activity.  This tended to help empower the students as they were given all the tools needed to fill out their own report card.  Before students started to assess themselves I decided to review what the MS, LS, AC and NI meant.

screen-shot-2016-11-13-at-7-21-40-amThis took the most time, but I feel like it was worthwhile as students were connecting how particular math skills fit within certain learning goals. They started to analyze their unit assessments, journal and reflection sheets to determine whether they mastered the skill or not.

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After students filled out their report card I met with them 1:1 for about five minutes.  We had a productive conversation regarding where the student assessed themselves.  Sometimes the students were right on point, while other times they were very critical of their own performance.  The process of reviewing their own performance brought a new meaning to the actual report card.  Some students also asked questions about the comments and asked that certain items to be taken out or added.

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When the report cards come out I find the students have a few different reactions.  Some students shove the report card into their backpack while others critically analyze their results in preparation to answer questions from their parents. In an instant, the amount of effort and time spent in crafting the right words can easily be ignored or highlighted.  I’m thinking that this activity will help students to start to see their report in a different light.  Self-assessing takes time, but this is an activity that I plan on using during the second and third trimesters.