Reflection and Math Goals

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Two of my classes took assessments this week.  These are considered unit assessments and are related to math skills that the class has been working on over the past 1-2 months.  My fourth grade class just finished up a fraction unit, while fifth graders ended a unit on equations. I tend to grade the tests and then pass them back in the next day or two.  Seeing that it takes so much class time to give these tests (and the grading) I want students to be able to use these assessments.  By using them, I mean that students should be able to look at them with formative lens and purposefully reflect on the results.  Usually the assessment process looks like this:

Stage 1

  • Assessments are passed back to students
  • Students review their score and are excited or disappointed
  • Students try to figure out how everyone else did

Stage 2

  • Teacher reviews the assessment solutions with the class
  • Students ask questions about why or maybe how they can get additional credit
  • Students see where fixable mistakes exist

Stage 3

  • Students receive their math journals
  • Students fill out a reflection sheet looking at skill strengths and areas to improve
  • Students indicate the most memorable activity and why
  • The teacher and student meet and sign-off on the test analysis and reflection portion

 

Okay, so stages 1-3 have been happening in my classroom for the past seven or so years.  It’s become part of my classroom’s math routine.  I see benefits in having students reflect on their progress on assessments, but I also want students to look at an assessment beyond the grade itself.  I’ve blogged about this evolution before. I stopped putting actual letter grades on assessments because of this.  I also considered taking off the point totals as well, but ended up keeping them since it was on the grade report anyway.

I see value in the student reflection component.  I believe students feel empowered when they’re given more control, choice, and access in the classroom.  This year I’ve added my own stage 4.  I’ve added this for a couple different reasons.  One, I’ve noticed that students that don’t necessarily meet their own expectations are really hard on themselves.  They often react negatively on the reflection component and I don’t want students to feel worse after reflecting on their performance.  I want this to be a valuable experience and growth opportunity.  Two, my students have kept their math journal for multiple years.  Some of them are jam packed with notes, reflections, and foldables.  You’d be surprised at how much is in some of these journals.  One thing that students continually tell me is that they love going back in their journal and looking at what they completed over the past few years.  They see that their mathematical writing has changed as well as the concepts that they’ve encountered.  It’s similar to a math yearbook to many of my students.  My third reason is that I’ve always been interested in how students perceive themselves as math students.  Over the years, I’ve emphasized that creating an individual math identity is important. I emphasize this at my school’s back to school session. This math identity shouldn’t come from a parent, but instilled within.  Being able to see students for multiple years allows me more of an opportunity to do this.  Also,  I’m excited to share this at NCTM and learn with other educators about the goal setting and monitoring process. This has been an area of growth for me as I’m continually refining the student math reflection process.

So, here’s stage four:

Stage 4

  • Students review and rate their perceived effort level and attention to detail
  • Students provide an example of where their effort level increased
  • Students create a math goal that will be achieved by the end of the year
  • Student indicate how they know that the goal will be met
  • The teacher and student sign-off on the reflection sheet

 


 

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Don’t get me wrong, this type of reflection is time consuming.  Whenever I discuss this process with other teachers I get quite a few questions about how to find the time.   Meeting 1:1 with kids to discuss their goal takes time and usually the other students are in stations or working on something independently. I can usually finish up meeting with the kids over 1-2 classes.  Instruction still occurs during this time, it’s just not a whole-group model.

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I’ve attempted many strategies to move kids away from comparing their score with others.  One strategy that seemed to work well was to have students go to stations and then I passed out the assessments.  I realized later that they just compared the results when they left the classroom.  I want to shift the paradigm to more of an individual growth model.  It’s a challenge.  Through the years, I believe progress has been made in this, but more needs to be done.

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The student math goals are interesting.  I had to have a brief mini lesson on the topic of math goal setting as many students wanted to initially make a goal of “getting everything right on the next test.”  I think many students were more interested in thinking of what their parents wanted and not necessarily a specific goal for themselves. Keep in mind these are 3-5th graders.  After a few different attempts, students started to make goals that were more skill focused.  Some students are now writing goals about “becoming better a dividing fractions”, “divide decimals accurately”, “become better at solving for x with one-step equations.”  While conferring with the kids I’m reminding them that the goals need to be measurable.

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After the assessment students review their math journals and monitor whether they’ve met their goal or not.  If not, they write down why or possibly change their goal.  I’ll then meet with the student and sign-off on the goal.  My next step is to involve parents in the goal and have a more frequent monitoring process.

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Better Student Reflections

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This year I’ve attempted to incorporate more student reflection opportunities in math classes.  This reflection has taken on different forms.  Reflecting on math practices is evident through classroom conversations and through student math journals  I feel as though a heavy dose of student reflection can go a long way in having students build awareness of their strengths and areas that need bolstering.  My focus this year has been geared towards students reflecting on their unit assessments.  I want students to understand that reflecting on past performances and setting goals can help them improve going forward.  I don’t believe all elementary students come to this conclusion all on their own.

At the beginning of the year I analyzed all the different methods to promote student reflection opportunities.  The timing of student reflection matters. My classes generally have approximately 11 unit assessments throughout the year.  Having formal reflection points after the assessments provide a number of checkpoints along the way.  I decided to start by finding/creating student self-reflection templates.

My student reflection sheets have changed over time.  The evolution of what was created can be found below.

1.)

Students identified corrected answers and showed reasoning.
Students identified corrected answers and showed reasoning.

At the beginning of the year students were asked to find problems that were incorrect and delve deeper into the reasoning. Students had to seek out why a problem was incorrect and explain how to find a correct solution.  This offered little interaction between the student and teacher, although some students would come up to the teacher to get further clarification on specific concepts.

2.)

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Positive elements

The above portion was added to the first and helped students focus on positive elements of their performance while still addressing areas of improvement.

3.)

Persevere and stay focused component
Persevere and stay focused component

One major area that I thought needed strengthening was in the perseverance department.  The above section was added to help students find strategies that they could use when approaching a complex problem.

4.)

Analyzing specific math concepts
Analyzing specific math concepts

Around the third unit assessment I decided to merge a more standards-based grading approach.  I had students identify which problems were associated with certain math strands.  Students then analyzed those results to look at possibly setting a relative math goal.

5.)

Written reflection and growth mindset
Written reflection and growth mindset

By this time students were becoming more reflective learners.  I liked what I was seeing and felt like students were benefiting from this reflection opportunity.  I added more pieces that emphasized having a growth mindset – e.g. connecting to achievement.  This was also the first time that I had students and teachers sign-off on the reflection.  I was able to have short discussions with the students about their assessment.

6.)

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Identifying areas of strength/concerns
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Student goal setting piece

Around the fifth unit assessment I added a goal setting part to the reflection sheets.  I haven’t tweaked the reflection sheet much since then  feel the results are positive.  Students are not as infatuated with the letter grade, but more focused on specific concept areas of the test.

I’ve used this sheet for the last few unit assessments.  It’s in a Word format so feel free to edit it and make it your own.  There’ll never be a perfect student reflection sheet but this has worked well for my students.  Moreover, students are able to look back through their math journals and see their own growth over time.

Last week I passed back a graded unit assessment back to a group of fourth grade students.  Each student took a peek at their paper, looked over their problems and grabbed their math journals.  Students found a comfy place in the room to reflect on their results and set goals for the next unit.  After students finished the reflection they brought the sheet up to me to discuss the reflection and next steps.  We both signed-off on the reflection and the students move on to another activity.

This process of math reflection seems to help my students.  It does take up around 30-45 minutes or so, but I feel like it’s time well spent.

How do you use student reflection in the math classroom?

 

Math Autobiography

Math Autobiographies

The start of the school year is coming up quickly.   Very soon schools across the country will be bustling with staff, students and parents.  I’m not setting up my classroom until mid August so I’ve prepped materials all this week.  During the past few weeks my RSS feed (R.I.P. Google Reader, hello Feedly) has been filling up with passionate posts related to goal setting. These posts have allowed me time to reflect on my classroom and put together a few initiatives for the fall.  One of my goals revolves around the concept of math reflections.

I’m always advocating for interdisciplinary units of study in the classroom, so incorporating student reflections is one way that I integrate math and language arts.  Even at the elementary level, student reflections have so much potential.  In fact, I worked with a group of first grade students last year on reflecting on our learning experiences near the end of the year.  As an introduction we started by talking about the words “My Mathematical Journey” that’s displayed on the outside of my classroom door.  We called it our “scrapbooking” time, as most of their parents had some form of a scrapbook and the idea connected to reflections.

My upper elementary classes already use math journals, but we haven’t delved into math autobiographies … yet.  Ideally, I’d like to have students create an autobiography of their mathematical journey so far.  While the journey hasn’t been long, it’s still worthwhile to discuss and reflect upon.   While researching a few options I came across these sites:


  • John Burk’s post – This post gives some practical questions to ask students when discussing students’ math experiences.  I actually started at this site and branched out to the sites below.
  • Algebra 1 Blog – This blog contains essay prompts with student replies.  This is a prime site if you’re looking for student examples, as there’s over 100 sample responses.
  • Math Autobiography Slideshare – I was thinking that this example might be one way to construct a math autobiography.  Adding pictures, narration, etc. might be a decent way to present a student’s math journey.  I found that this Prezi is also another method that could be used in the elementary classroom.

There are a lot of resources and examples available on the topic of math autobiographies. Most are geared towards middle school and beyond, most likely because of the writing component involved.  So, I’m going to use a few ideas from the above links to adapt the autobiography assignment for my students.

To start, I’m going to give my students a digital camera.  Why?  Similar to Matt Gomez, I believe the digital camera can be an amazing tech tool in the classroom.   Students will take pictures of themselves in different poses:  with math manipulatives, books, the classroom, etc.  I’ll print out the authentic pictures (hopefully in color) and students will write captions under each picture.  Students will place their own pictures and captions in their own math journal in chronological order.  I believe the photos can all be glued into each student’s math journal.  As the year progresses the students might want to add more photos and captions to extend their math autobiography.

In a few months I’m hoping to write a another blog post showing the results of this idea.

photo credit: This Year’s Love via photopin cc