Student Reflections

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My fifth graders finished up a math unit around a week ago.  The unit took around 1-2 months and students explored topics pertaining to decimals, percentages and box plots. Near the end of November I had a discussion with Jack about student reflections and previewing units.  Jack shared a Tweet by Chrissy about cool-down bins.

I thought the idea had potential and decided to use it as part of my end-of-unit reflections. My students completed the test reflections and I added the bin language near the bottom.

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The class discussed what each category meant and I answered questions.  I think the most challenging part was communicating the difference between practitioner and expert.

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Some students mentioned that you could complete the task without any help, but still not be an expert.  Other students said that they still wouldn’t consider themselves an expert even if they could teach other students a skill.  Still tweaking this idea.  The class is still working on this type of reflection, but I believe we’re making progress.  I’m hoping to use this throughout the rest of the school year.  Students can then reflect back and look at the progress that was made.  One of the goals this year is for student to become better at accurately assessing their math understanding compared to the standard.


Side note:  One small win during the past week. I was able to combine two second grade classes to complete an array polygraph last week.  Another teacher and I had around 35 students complete the polygraph together for around 20 minutes.  It was great to see partners use math vocabulary to try to guess the arrays.  Words like factor, row, column and product were all be used during the process.

We have two more weeks of school and then two weeks of break. Let’s finish 2019 on a strong note!  

Monitoring Progress Towards Goals

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Around two weeks ago my students finished up a math unit and started a new one.  Students previewed the next unit by reviewing a study guide and looking ahead at the skills in their consumable math journals.  They then made appropriate goals based on the preview.  I spoke with the students afterwards and helped them reshape the goals to be more aligned to what’ll be explored during the next unit.  I wrote about this process here and then started to think about next steps.

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Some students created goals related to topics that we haven’t explored yet, while others felt more prepared to answer.  My students around about a 1/3 through the current unit. This week students checked on their progress towards the goal.  My intention was for students to become more aware of their goal and the progress made towards its completion.

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I think in the future I’d like to create some type of scale where students identify the progress made towards the goal instead of a met/not prompt.  I’m looking forward to revisiting and refining this idea as the year progresses.

 

Math Reflections and Sentence Stems

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My students just finished up the first trimester yesterday.  So we’re about a third of the way through the school year. In my mind this is a perfect time to reflect on the progress that has been made over the last couple months.  All of my classes started near the end of August and many of my classes have recently completed the second or third unit. It’s been a great journey so far and we’ve made progress.

Last week I had a class conversation about progress and what it looks like in math class. We discussed growth and how it doesn’t look the same to everyone.  To help facilitate the conversation I had students reflect on their unit assessments.  Usually, I’d have students fill out a form indicating questions that were incorrect and then they’d code the errors.  Students would then set a goal for the next unit.  That process is detailed here.

This time around I wanted my students to recognize their growth and how their perceptions change over time.  I also wanted students to preview the next unit and set a goal based on the preview. I modified a journal prompt from a colleague and decided to add sentence stems with space to write.  I didn’t give students much advice or guidance on how to complete this, but I told them that I wanted them to be honest with their responses.  The prompts are meant to have them reflect on their progress.

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Students were able to follow the sentence stems a bit easier than past reflection prompts.   The wonder question was left vague for a reason as it presents a way to indicate student interest and curiosity.

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Most students were able to analyze their unit assessment and look for trends that were positive.  I wanted to communicate that they should be proud of what they accomplish. Some students even looked beyond the test and wrote down that they were proud of how they improved their understanding of x skill.  Other students stuck with the grade on the test and being proud of that aspect.  I really like the “something I want to remember …” piece as it reinforces that what students are working on and developing will be used in the future.

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Some students asked for more lines to write additional pieces that they learned.  Again, I found there tended to be two camps of students.  One group focused on the math concepts/skills, while others focused on the points/questions.

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The “PA” is a pre-algebra activity that we complete to start the math class.  It was interesting to read what students felt was the most difficult as some were more vulnerable than others. This year I’m emphasizing the idea that this class is part of their math journey and that we’re all mathematicians.

The next step was to preview the next unit and start to set a meaningful goal.

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Student went through their math journals and looked for words or skills that didn’t ring a bell.  At first students thought that everything looked fine and confidence was brimming a high level, but then they started to look at the wording.  The next unit explores box plots and percentages.  Based on the words/topics, students made a goal that they’d like to accomplish.

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I appreciate how the above student extended the skill to learn about percentages and sports.

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This particular student wants to become better at the “LCM box method” as it was explored last unit.


Students completed the page and then we discussed it together 1:1.  I asked each student why they felt that the goal was relevant and meaningful.  I’m looking at adding a progress monitoring piece to this goal as the class progresses through unit three.  Ideally, I’d like to revisit the goal every 2-3 weeks to see what progress has been made towards the goal and make adjustments as needed.  By doing this, I believe students are taking more of an ownership role as they can see progress made towards the goal.

You can find the entire template for the sheet here.  Feel free to leave in the comments how you’d use this or if you have questions.

Feedback and Reflection Opportunities

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Over the past few years I’ve emphasized the use of student feedback, reflection and goal setting in my classroom.  Trying to find an adequate balance for this has been a challenge.  This school year I’m looking at different mediums in which students can reflect on their math progress.  Reflecting on individual progress and determining where students are at in the progression can lead to powerful outcomes.  This year I’m looking at different ways to encourage students to make more meaningful reflections that lead to actionable goals.


Math journals

Each student has a math journal.  These journals take the form of a 70 count spiral notebooks. The journals are primarily used to reflect on assessment performance.  My class has eight unit assessments per grade level and there’s a reflection sheet designated for each one.  I’ve written about the different sheets and journals: (1)(2)(3).  Students then complete the sheet and bring their test along with their reflection to the teacher to review.  At that point the teacher and students work together to develop a math goal for the next unit.

Peers

Students work together often in my class.  I use a randomizer and group students so they tend to have different partners daily.  After they complete a task I give the students a couple minutes to discuss with their partner the effort level and challenge of a particular assignment.  I tend to use a timer and encourage students to be honest in the process.  Hearing how other students feel about the effort and challenge level can help students be more aware of the struggle that is part of the process.  Certainly not all, but I’ve seen some students thrive with this type of reflection.

Independent

Before students complete a project teachers give a sheet indicating the criteria for success. This looks like a checklist with statement indicating what’s needed to meet the expectation of a particular assignments.  As students complete each component they reflect on whether they’ve met the criteria and place a check.  Students will attach the criteria for success sheet to their assignment

Digital Platform

Along with the criteria for success, students may submit a project to a digital platform like SeeSaw or Canvas. Other students in the class are randomly selected to give feedback on other projects.  Students follow a prompt that asks whether a student has met the criteria for success or not.  They then re-check the work and ask a question or provide a positive comment about the work.  After the comments are submitted, the original poster reviews the comment, reflects and responds to the question or comment.


 

Each one of these mediums has pros and cons.  I’m finding that the classroom environment plays a major role in how comfortable students are in sharing their thoughts with the class.  Some students are much more willing to independently reflect and speak with the teachers than others.  I find that students take more of an ownership role when they analyze their own performance in context and make steps to improve.  Bypassing the “I’m good at math” or “I’m bad at math” type of thinking can be a challenge, but providing ample opportunities to reflect can move students away from generalizing and be more specific about their analysis.

The next step in my process is to take these reflection opportunities and transition it to meaningful individual goal setting.

Math Responses and Discussions

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Last year I experimented with a couple different ways to encourage students to discuss mathematics.  I used a form of a number talk last year and found some success.  Students were engaged the conversations were more productive than in the past.  I also noticed that not all students participated in the conversation.  Even with manipulatives, some students participated minimally and shied away from being called on.  I found that some students dominated the discussion more than others.  This was taking place in most of my classes and I kept on reinforcing the importance of having a positive classroom climate where mistakes were honored.  I thought emphasizing the climate and providing support would help encourage participation from everyone involved. For some that worked, others not so much.

This year is a bit different.  I’m still using a form of number talks with success.  I’m still looking for ways to help improve this process.  I also introduced a more organized way to incorporate math discussion prompts with students.  I first organized students into groups using a randomizing student spreadsheet.

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Students are put into groups and a destination in the classroom.  I put a new slide on the whiteboard once everyone finds their assigned location.

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Students get into their groups and identify themselves as partner A or B.  Usually I use the spreadsheet to indicate the partners.  Partner A starts with the first prompt and I display it on the whiteboard.

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I click the timer and partner A has 40 seconds to respond to the prompt while partner B listens.  After the 40 seconds I pick a few different people in class and ask them about their thoughts about the prompt and their answer.  Partner B then gets a different prompt.

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Partner B gets to respond to the prompt while partner A listens.  I’ve toyed around with 20 – 40 seconds and have landed on 40 because it gives students an ample amount of time, but also the limit encourages them to be concise.  Students usually go through 2-3 questions each and then we have a whole class debrief session.  So far students have been receptive to this medium and I’m hoping to expand it to other classes that I teach.

Files referenced in this post:

 

Finding the Difference

My second grade math group started this week.  I gave a pre-test on Monday and found that students had some trouble with the word difference.  Many of the second graders saw the word difference and immediately thought subtraction. I could see why students would see this as a quick search reveals difference as being “The result of subtracting one number from another” and “How much one number differs from another.”  I think most students in my class focused on the first definition rather than the latter.  While discussing the word more than a few students brought up that they knew how to find the difference using a method.  It ended up being the standard subtraction algorithm.

On  Wednesday students were introduced to part of a 100 grid and asked to use it to find the difference between two numbers.  Some of the students started to see that difference could be interpreted as distance between.

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Students used two different colors to locate and identify the numbers.  Students then counted the space between the two numbers.  They used hops while moving to the right and then down.

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30 + 3 = 33

Another student used the grid to show a different way to find the difference.

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3 + 30 = 33

I showed both methods under the document camera and the class discussed how both could work.  Students were then asked to place their strategy on a number line.

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Another student raised their hand and wanted to show the class something that they created.

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Next week the class will be investigating regrouping strategies.

Categorizing Numbers and Number Lines

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This week my students explored how to categorize numbers. By then end of the week students were expected identify integers and rational numbers and apply them to real-world contexts. The class reviewed what and where to place numbers on a number line and how to classify them as whole, counting, integers, rational, and/or irrational numbers.  This was an introductory lesson and the term rational and irrational were new to them.  After a brief class conversation about the differences between rational and irrational numbers the class took a deeper dive into how to identify the characteristics of each classification.  The class looked at a few true/false statements:

  • Is 1,000,000 a counting number?
  • Is 1,000,000 an integer?
  • Is every rational number in an integer?
  • Is zero is a counting number?

The class went through these types of questions and were able to respond and justify their answers.  The questions started to get more challenging as students needed to circle  multiples answers.

  • Circle all of the numbers that belong to each set.

Integers:   4.5       2/3     102     -6       8       0

 

This was more challenging and took some time to categorize each number to see if it fit accordingly.  Students were then asked to place numbers on vertical and horizontal number lines.  I was glad to see how well the students responded to the vertical number line as I don’t believe they get enough practice with those.

Students had about 20 minutes left and one project to complete.  I introduced students to a number line project.  I ended up going with Google Draw for this project because I don’t have enough access to iPads at the time and I was able to checkout a Chromebook cart for this particular lesson.  Students were given a prompt to use dice to create numbers and fractions to place on a number line.  They rolled and found their numbers.  Students used their Chrombooks to access bit.ly/mrcoaty.

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Students make a copy of the Google Drawing and added their numbers to the number line.  It took some work to manage the tools involved in this platform.

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I explained what each icon meant and how they could use it to make the number line their own.  It wasn’t as smooth of a transition as I thought it’d be, but students persisted and were eventually able to place the numbers they created on the number line and dragged the label to each number.  Students were then expected to take their drawing, save it as an image and place it in their individual SeeSaw account.

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Not all students finished this in class and I sent it home as optional homework for students to complete.  The above example is from one student that took it home and completed it before putting it into their SeeSaw account.

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