Improving How Students Analyze Their Work

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One of my goals this year was to have students analyze their own work, make observations and improve. These observations have improved this year by a light margin. For example, students get back their graded paper and look over how they did. Most students look at the top for their points or some type of feedback. Some look for where something was marked incorrectly, while others look for a place in their binder to place the paper. The good news is that students are looking at their graded papers with a more critical eye. That’s a win in my book. Students are starting to observe where they needed to elaborate or change a procedure. That’s good, but the time spent looking at what to change is still minimal.

This year I introduced the NY/M model. Students were a bit hesitant at first, but I’m finding some pockets of success. Those pockets are not just related to the new model, but also a whole range of opportunities that have been put in place for students to understand where a mistake might’ve occurred. Ideally, I’d like to have students identify how the mistake or error happened and to curb that action in the future. Don’t get me wrong, I’m all for making mistakes in order to learn, but some errors impact an entire answer and I’d like students to be able to identify where that’s happening. Being able to self-reflect in order to improve is a beneficial skill.

In an attempt to provide multiple opportunities for error analysis, I’ve intentionally planned for students to identify their own math misconceptions. This has taken many different forms. I believe that students that can identify math misconceptions may be better able to proceed without making them in the future. Three tools/strategies that have been helpful in this endeavor are found below.

  • Nearpod has been a useful too this year. Specifically, having students show their work using the draw tool has helped other students identify misconceptions within their own understanding. Displaying the work on the whiteboard without a name has been especially helpful, as a student might not be embarrassed, yet the class can still learn from that particular person. I’ve used this as an opportunity to look at positive elements of student work and also look for areas that need some bolstering.
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What do you notice?

 

  • Lately I’ve been giving feedback on student papers and incorporating that into my agendas. Before passing back the papers I review the misconception list and answer questions then. I then pass out the papers and students complete the NY/M process. Generally, students make very similar errors and I attempt to address this while reviewing the agenda. This has decreased the amount of questions that students ask related to why/how to improve their answer to receive a M.

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  • On the paper I’m making a renewed effort to write feedback on homework and projects. The feedback takes many different forms and isn’t necessarily in a narrative form. Sometimes I ask question and other times I might circle/underline a specific portion that needs strengthening. This method often elicits student questions as it’s not as clear-cut as other methods. Regardless, it’s another way for students to analyze their work, make changes and turn it back in a second time.

Why is this important to me? Well, I believe that students should be provided additional opportunities to showcase their understanding. At times, I feel as though there’s a gap between what math work they show and what they’re capable of showing. Giving feedback, along with another opportunity to improve, tends to help my students show a real-time understanding of a particular concept. Ideally, this would seamlessly work and all students would move from an NYàM. It’s not all roses though. I’d say at least 50% of the students improve on their second attempt, but I’d like to see more. I believe we’re making progress and have more to go, but I believe we’re on the right track. I’m encouraged to see that this model is slowly and slightly changing the review, redo and improve cycle. This has me thinking of how to expand on it for next year. Stay tuned!

Reflection

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It’s official.  The 2015-16 school year has concluded.  The final bell rang last week I’m starting to look at my summer book list. My reading takes on different forms during the summer.  I have a few books on hold at the local library just for that purpose.  I’m looking forward to digging into those later this week.  Before reading these I enjoy catching up on blogs that I missed during the last hectic month of the school year.  This year I’m also looking back at my personal goals for this past year.

As I reflect back on the school year I often categorize how classes went that year.  Were the classes successful?  How did students learn?  Did I create an environment that optimized student learning and their curiosity?  Did I leave a lasting impact that students will remember?  How many of these students will invite me to their graduation.  Okay, the last one was a joke.  Kind of.  I tend to reflect back on these questions as well as others.  Last August I wrote a post about the goals that I had for the new school year.  This post is designed to reflect on those goals.


 

1.  I plan on taking the first few days of school to engage students in community building activities. The class will be completing a “get to know you” survey and set expectations for the class. We’ll also be completing the marshmallow challenge and have some rich conversations around math and mindset. I feel like instructional strategies make little impact if students have a fixed mindset. The same could be said for teachers. Before delving into content I want to ensure that the classroom community is moving in the right direction.

Looking back, I was ambitious with my planning.  At the time I thought this was a realistic goal.  I started off the school year with community builders.  We completed the marshmallow challenge and other activities.  I didn’t actually survey the students.  Instead, students wrote in their journals about math experiences.  I reviewed their journal entries and had brief conversations with each student.  The students felt comfortable in the classroom and seemed to develop rapport with each other.

I didn’t get into the rich discussions about math mindset as much.  Having a growth mindset has been emphasized in my district but the practice of it in individual classrooms vary. This is also a byproduct of the mindsets coming from other students, at home and at school. Honestly, it was challenging to not dive into content immediately.   Regardless, the classroom community was set on a sound foundation.  That foundation played a pivotal role throughout the rest of the school year.

2. I‘d like to make learning more visible in the classroom. I’m planning on having students use math journals to reflect and document their learning journey. I’m also planning on using effect size data to show student growth over time. To do this I’ll need to create additional pre-assessments to analyze pre/post data. I’m also planning on moving away from letter grades on unit assessments. Instead, I’m going to have students reflect more on the skills being learned in class.  This is a change from past practices so a lot of modeling may be needed.

I had students use math journals this year.  I intentionally had students use them to reflect on assignments/projects throughout the year – more so at the beginning of the year.  I also dabbled with students using foldables this school year.  The foldables were used primarily for process-oriented skills involving conversions.  These were glued or taped into the student math journals.  By the end of the school year the math journals were thick and looked like scrapbooks.  I’m looking at changing this format next year.

I used effect-size with one of my classes this year.  Students took  a pre-assessment and explored a particular concept for around three weeks.  After the three weeks, they took the same pre-assessment.  I calculated the effect-size and placed the data in a spreadsheet that was shared with my teaching team and administrator. I felt like this was good practice as my district is moving towards effect-size next school year.  Students received both the pre-assessment and assessment back at the end of the unit to see how much progress was made.

My unit tests didn’t include letter grades on the top of them.  This seemed to bother some students as they wanted to know their exact grade.  By the end of the year, all some students weren’t as concerned about the percent/grade.  I emphasized, as much as I could, that the skills were the focus.  I believe progress was made in this area and I’d like to keep this practice intact for next year.


I tend to agree with the philosophy that deep reflection can lead to growth.  I’m looking forward to the new school year in August and have some new goals that I’d like to put in place.  For now, it’s time to reflect and recharge before the new school year comes around the bend.

Reflecting on Effort

Last Monday my school started its third trimester marking period. As this new trimester begins students were given time to reflect on the past trimester. While the students brainstormed what to write I gave each one their personal file.

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For as long as I can remember teachers at my school have kept a file for every student in their class. This all-important file holds paper assessments, report cards and anecdotal notes taken throughout the year.  This file is also what’s usually laid out during parent teacher conferences.

To the students surprise, I gave each one their own file for the reflection opportunity.  Prio to handing out the files I made sure there wasn’t anything confidential in the files.  Students were then asked to analyze all of their assessments and reflect on the second trimester. Students paged through their assessments and journal entries and filled out the sheet below.

Click for file
Click for file

I set aside about 30 minutes for students to look through their personal file and write their response. I wanted the students to analyze their own effort level. It’s interesting how students took on an ownership role as they took the file.  They took this role seriously.

Business Meeting?

Some of the students took the entire amount of time while others needed more. When students finished they brought up their file and journal to discuss their views with me.  I  had a brief conversation with the students about their reflection and asked them questions related to their effort level.  The students and I discussed how the statement below applies to what they produce in class.

Effective Effor

Although there’s room for improvement, I feel like the class is making positive strides in being able to reflect on experiences without solely looking at the grade.  During one brief conference I asked a student whether they felt like effort in math class eventually leads to achievement.  The student responded, “Not completely, but effort level impacts my overall grade.”  Sometimes I find this to be a perception battle of grades/points vs learning experiences.  Providing students opportunities to reflect can help balance this perception.

Class Math Discussions

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Making time for quality math discussions

A few years ago I remember my school district emphasizing the need to use more of a math workshop approach in the elementary classrooms. The school district even invited a math workshop specialist to present on all the different ways to set up groups and organize guided math.  Some of the teachers gleaned the information and used parts of the model in their own classroom.   The consensus was that some of the guided math approach was better than none at all.

As the years passed the idea of math workshop started to change. Teachers started to change the math instruction block to incorporate small group instruction. Whole group instruction still occurred, just in shorter bursts. The small groups consisted of around 5-6 students and rotated every 10 – 15 minutes.   The groups didn’t meet everyday – that’s almost impossible. I remember barely making it through two rotations 2-3 times per week. The organization involved seemed overwhelming, but doable. This workshop model was modified depending on how the teacher organized their math class. After a couple of years the district changed it’s focus to emphasize reading instruction. One small part of the reading instruction is designed for students to share their understanding with others. After hearing about this type of model I decided to merge this type of model within my math classroom.

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As the district changed its initiatives my math model also started to change. Instead of fully devoting time to small group math practice, I decided to incorporate a math discussion within the teacher group for a portion of the time. Half of the time in the small group was used to work on direct problems associated with a standard, while the other time was set aside to discuss the math concept in detail. Over time the conversation started to eat up a larger potion of my small group time. This discussion component ended up becoming more formal after I found the conversations started to impact students’ understanding of math.  The questions that I asked were often related to vocabulary or about a particular strategy that was used to find a solution. Students were given opportunities to answer the question and ask each other questions in the process. For the most part students were on task, but I’d have to reign in or rephrase responses as needed.  I also found myself planning questions to intentionally ask during the small group time. I had to use some type of timer system to rotate groups at the right time. Most of all I felt like students were able to offer their input in a low-risk environment and discuss math while receiving some type of feedback from everyone involved. Also, students were starting to use some of our more formal math conversations in their written explanations. What I’m finding is that I need to be more intentional in creating opportunities for these classroom conversations to happen. They seem to open up additional learning opportunities that were closed off before. I feel as though slowing down the pace and delving deeper into math concepts has brought about this opportunity

Side note: I’ve also used this strategy with a whole-class discussion.  Although it’s benefiting students I need to refine the logistics of using this strategy for the entire class.  Also, I’ve experimented with Math Talks this year – definitely something that I want to explore a bit more in the next few months.

 

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?

 

End of the Year Survey Data

At some point during the last week of the school year I generally have my classes take a survey.  The survey is designed to provide feedback and to reflect on learning experiences that have occurred throughout the year.  The survey is composed of questions about the class in particular, favorite memories, different learning experiences, and feedback on how I’m perceived. For the past few years the classes and I review the survey data together before the students write their final reflections. For this post I took out the learning experience pieces and am focusing in on teacher perception.

Survey Directions:

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I read through the directions with the class and answered a few clarifying questions.  Students weren’t required to submit their name.  Students took about 20 – 30 minutes to complete the survey.  I averaged the classes together and the results are below.

Results

I’ll be showing the class the chart above tomorrow.  Before doing that, I’m going ask the students what they think are the top 3.  In the past I usually compile the list into the “top 3” and then the class discusses the results and implications on how these categories impact learning in the classroom.  This is always a rich discussion that evolves into an understanding that feeling safe and respected in a classroom often encourages academic risk taking. Here are the top 3 we will be discussing tomorrow:

  • The teacher is fair to all students in the classroom – 1.154 / 10
  • The teacher uses technology to teach the class – 1.179 / 10
  • The teacher shows that she/he really loves to teach and learn – 1.359 / 10

I’ll then show the bottom 3:

  • The teacher gives choices to complete an assignment – 5.39 / 10
  • The teacher allows opportunities for students to reflect on their learning – 3.256 / 10
  • The teacher gives assignments that connect to the real world – 2.821 / 10

During this time the class will be tackling questions about what’s important in a typical classroom.  The class discussions during this time are so important.  This type of reflective thinking is purposefully planned to encourage students to take part in understanding how their environment and mindset plays a pivotal role in the learning process.

My takeaways

I think teachers can be extremely critical of their own practice.  I tend to focus more on the areas of improvement, but I think it’s important to share this data with the students as one way to model a growth-mindset.  I was surprised to see that reflecting on learning scored lower than others. By low, I just mean it wasn’t rated as highly as others. This year I’ve utilized student reflection sheets, but only really using them after assessments.  I feel like I need to merge more opportunities for students to reflect throughout a math unit of study, not just at the end.  I’m also willing to explore different avenues to reflect.  Instead of using the same sheet, possibly using multiple forms of reflection may help.  This is something I’m going to work on over the summer and have in place for next school year.

Also, what’s interesting is that as grade levels progress from lower elementary to upper elementary, assignments connecting to the real world decrease.  I’m not totally surprised as there’s a large emphasis on algebraic equations for my upper elementary classes.  The algebra concepts and practices are often disconnected from practical use. Again, I’d like to find a way to change this perception.

I’m excited to see that students feel safe and feel like I’m fair in the classroom.  The environment and having positive rapport with students can go a long way in having students exceed their own expectations.  Also, even though it wasn’t in the top 3, I’m proud to see that students feel that they can use technology to demonstrate their learning.  This has been a huge emphasis this year with my student content creation theme.

Overall, using student survey data can be a valuable experience.  The transparency that it provides can encourage students to take additional risks.  Looking towards next year, I might want to give a similar survey earlier in the year and then closer to the end.  That way we can look at the growth of the class.  Regardless, I feel like the moments we have to reflect on our learning experiences and survey data are well spent.  This time can can help revisit learning experiences and offer an opportunity to cement an authentic enjoyment in understanding mathematics.

 

Reflection before report cards

photo credit: woodleywonderworks via photopin cc
photo credit: woodleywonderworks via photopin cc

Last Thursday marked the end of the first trimester grading period.  After a few unit assessments, quizzes and special projects, my students are given a report card.  The report card splits into two categories: academic grades and behavior skills.  I tend to give my students their report card a few days before it’s actually sent home.  Once the reports cards are passed out I find that students focus only on the letter grade. Not the personal teacher comments, learning strands, checked boxes, but the letter grade is what gets the focus. Over the past few years I’ve challenged this type of thinking and laser-like focus on grades.  I’m slowly but surely moving my class towards a standards-based grading model, although the district requires teachers to use a traditional A-F model.

Before passing out the report cards this year, I gave my students an opportunity to journal about their math journey so far.  Math journaling has been a larger part of my teaching this school year. Students use math journals in my class to complete different types of math problems and for self-reflection.  I try to have the students journal approximately once every two weeks. During the journal time I turn off the lights in the classroom, turn on some music in the background and allow the students to go anywhere in the room to write up their response to the journal prompt. Some students stay at their desk while others find a hide-out in the corner of the room, on a comfy chair, or underneath a table.  As the year has progressed students are beginning to ask to have additional time to journal.

This year I gave each student their academic file before journaling. Enclosed in the file were all the past unit assessments and quizzes that took place during the first grading period.  Students were asked to analyze their own file and answer the questions below in their math journal.

  • What learning experiences stand out in your mind?
  • What do you feel are your strengths?
  • What would you consider a “growth” area for the next grading period?
  • What is one SMART goal that targets one growth area?
  • Create an illustration that matches any of the prompts above

After the students respond, I’ll review the responses and write short comments back to each student.  This does take some time, but definitely worthwhile.  I generally comment on their strength and ask questions that encourage students to reflect on their progress and growth areas.  This process also gives me an insight into what a particular student thinks and values.  By analyzing their own data, reflecting on progress made, and creating an action plan, I feel students are better prepared to take ownership of their own learning.