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.

Building Awareness and Knowledge

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During the past couple weeks I’ve created a brief routine of reading in the mornings. Sitting out on the deck, reading a book and slowly drinking my coffee has been time well spent.  I’m taking advantage now since this won’t be happening once school starts in about a month. One of the books is related to culturally responsive teaching and the other I’m just starting to dig into is about white fragility.  Both books are somewhat similar and I’ve been able to spend a decent amount of time reflecting on systematic education practices.

One particular takeaway in chapter four of CRT was related to building awareness and knowledge before making judgements. The author makes the case that teachers should widen their interpretation aperture when interacting with students. Aperture refers to the amount of light that is allowed in and out while taking pictures. Aperture is used instead of lens in this context. Widening that interpretation aperture takes time and a process is involved. The paraphrased process below is from the Mindful Reflection Protocol by Dray and Wisneski.


1.) The author discusses replaying student and teacher interactions in your mind.  That replay involves describing what’s seen. It can be challenging to replay conflicting interactions, but keep in mind that the replay is neutral – it’s stating the facts.

2.) Make assumptions and attempt to interpret the behaviors.  Teachers have to make so many decisions everyday and generally the interpretation falls into two categories:  intentional or non-intentional – positive or negative.  Behavior interpretation has the potential to be a sticky situation as it depends on the aperture of the teacher.

3.) The author suggests to offer alternative explanations.  What would a child behave in ____ way.  Do cultural norms or beliefs play a role in why the behavior happened?  How are directives given at home?  After reviewing the assumptions a couple times it’s time to check the explanation.  Explain the observation with other teachers.

4.) Hear from their perspective and check your explanation.  It might be helpful to go outside of your team to discuss this to receive alternative perspectives.  Here’s where it takes an extra effort to research and build more of an awareness of cross-cultural knowledge.  Trainings and PD can play a role with this.

5.) Make a plan of how to address similar behaviors and continue to review when you might be overgeneralizing situations.


Next week I’ll be reading about how to recognize common triggers and look at building learning partnership.  I’m also going to to be diving into chapter two of White Fragility.

 

 

Reflections on 2018-19

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It has been about a month since school let out and I’ve been enjoying the summer so far.  I’ve been reading, working on the lawn, painting and took a vacation.  During the last month I decided to focus my time on things not related to school work.  This balance of time tends to give me a better perspective when I do come back to working on items related to school.  Now I’m starting to see school supplies (already!) in stores and am looking back at how the school year went last year.  Every year I attempt to gather information about my students and how they perceived the school year as a whole.  I give a survey and use that information moving forward for the next year.  I decided to wait a bit over the summer to look over the results.

Back in June I gave a survey to all of my students in 3-5th grade.  The survey was related to instruction models and preferences.  This year I intentionally varied my models throughout the year and didn’t stick with one particular tool for activities.  I started off the survey with a brief question about their favorite math topic this year.

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Before giving the survey I went into detail about each topic.  The purple is measurement and I’m not sure why it didn’t show up with my advanced table Gform add-on. The next question was related to why they felt this was their favorite topic. Here are a few responses:

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Next time I’m going to put a minimum character limit to extract more information.

The next section, which was the largest, was related to instruction models/activities. Students rated them (1-5) 1 being the least effective for learning and 5 being the most.  A brief explanation of the items is in each caption.

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Teacher gives prompt and students discuss as a group and share out responses to the class

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Used for retrieval practice – students used this individually and in groups of two

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Similar to Kahoot, but more self-paced – used to reinforce concepts

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Similar to Number Talks – prompt is displayed and class discusses concept

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Used  for notation on slides and showing student’s work to the entire class

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Used K-5 math for whole class or independent exploration of math concepts

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Students are digitally randomized into groups and then they work on a particular task with that partner.  Students report out their responses afterwards.

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I display work (sometimes student work) on the document camera and the class discusses strategies


I had 59 students take the survey, but I have 65 + students in 3-5th grade.  Some of them were out for other activities during the time the survey took place.  Something to consider … some of these activities were used more frequently so students had a larger sample size.  Overall though, it seems students enjoyed most of the tools/activities for learning about mathematics.  I think it should be mentioned that there’s a difference between a tool and strategy and I might be blending the lines a bit in this post.

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The tools in the box were used independently or with a partner.  They also required some type of technology (iPad, Chromebook), while the other four didn’t.  I think having a blend between the tools/strategies is helpful and students aren’t dependent on using one medium to show their learning.  I’m looking forward to diving more into this data as the summer progresses.

 

Scale Factor – Part Two

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During the last week of school one of my classes explored dilatations.  It was a rather short lesson since there were only a couple days of school left.  After some review, I pulled out a project from last year and thought might be applicable since it addressed the same standard for that particular day. I looked it over and made a few changes so this year it would run smoother.  Here’s what changed:

  • I had the students create an exact 4cm by 6cm grid using rulers.  This was different than my initial project.  I made sure to check each grid before students moved on to the next step.  I’m not a fan of having a simple mistake or unclear directions derail an entire project (which it did for some last year) – so I decided to check each students initial grid.

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  • I also created a random piece to the amount of dilation this time around.  This picture is from last year’s post.update.pngLast year students already knew the grid to use and basically used a “paint by number” approach to fill in each square.  Although that was fun, it didn’t really hit the objectives as much as I’d like.  I had students roll a die to determine the dilation this time.  This gave four different options for students.

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  • I put together a criteria for success component where students could check-off items when completed.  I set up the different dimension papers on one of the tables so students could easily grab them depending on their dilation.  I also added a short debrief piece near the end of the project where students discussed how they increased the size of the image.

These changes helped improve this particular project and I believe it created a better learning experience for the students.   There are times where I completely scrap a project and other times I make tweaks in order to make it better.  I opted for the second option this time around.

* Next year I’m planning on updating the project to include dilations that involve reducing the size of an image.

Reflections and Takeaways

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The school year is coming to a close. This Monday would’ve been the last day but the midwest weather had other plans and an additional three days were added to the schedule. Classroom walls are starting to look bare and teachers are packing away their things for the summer. Boxes and labeled containers have started to accumulate in classrooms as some teachers know that they’ll be moving classrooms.  As I pack up my room I’m reflecting on this past year. Here are a few takeaways and potential changes that I’m contemplating over the summer.


Takeaways – I’ll keep these winners for next year

  • Give out study guides at the beginning of a unit

After reading Making it Stick last summer I decided to give out my unit study guides at the beginning of a unit.  It takes my classes around 1-2 months to complete each unit of study and I used to give out and review the study guides (basically chapter reviews) the day before the test.  This year I gave them out during the beginning of the unit and students worked on them throughout and then the class reviewed them together the day before the test.  I had to make a trade-off seeing that students would need to complete them at home or if we had extra class time, but that didn’t seem to be an issue.  Also, I gained about an extra day of instruction per unit by using this so it ended up being a winner in my book.

  • Create an agenda slide for each class

For the last couple years I’ve used an online planner to create my plans for each class.  I’ve found it helps me with organizing the structures of lessons a bit more and allows for a quick copy and paste to a slide for students to see.  The goal is in the left corner and it’s something that the class reviews each day.  Most of the students look at the activities for the day and then take out the materials that might be needed.  This year I had a handful of students with special needs and this visual cue seemed to help with anxiety related to the expectation for that particular day.  Plus it helped keep me organized, which is why I did it in the first place.  Do I always follow the agenda – nope, but it’s there to provide structure and an expected outcome.

  • Use math routines more consistently 

This year my 3-5th grade classes used math routines from day one until the end of the school year (counting these last four days).  I also used them during test days. There’s something important about starting with the math and the students expecting to start the day with a specific task.  My third grades used Estimation 180, fourth Who am I, and fifth AlgebraByExample.  It became part of our daily routine and I believe it helped with cycling through concepts and skills throughout the school year.  I plan on continuing to do this next year.

  • Instructional Balance

My classes this year have been much more balanced as far as math instruction is concerned.  This year I used Desmos, Quizziz and Nearpod more frequently and relied less on problems from the text book or worksheets (making sure to state that there’s nothing wrong with a worksheet).  Having that interleaved practice and time to discuss topics with partners has benefited students as they apply their math learning in different situations.  I’ve also changed the sequence in which some math topics are taught and gave students more time to explore concepts with manipluatives first before diving into more of the abstract.


Potential Giveaways – I might change these for next year

  • Homework

Ugh.  That sticky issue of homework has come up again.  This year I gave students homework around 2-3 times per week at the beginning of the year.  I slowly started giving less and ended up with 1-2 times per week during Feb-May.  I found that it was beneficial for those students that completed it, although the students I wanted to complete it rarely brought it back.  Also, I found myself giving homework to increase the amount of time in my math class – not a good reason.  A few years back I decided to give students links to the homework incase that they forgot it at school.  It still wouldn’t be completed.  I’ll still be giving homework next year, but I’m thinking of changing the format to be more of a retrieval practice model.  What that looks like will depends on the next couple months.

  • Projects

My students completed a couple different projects this year.  In a few instances I believe the time in which students worked could’ve been more structured.  I’d like to create more of a daily schedule for these projects and include time where students “check-in” with the teacher to ensure that we all finish.  Unfinished student projects feel like a failure and I’d like to limit these.

  • Grade Less and More Accurately

Next year I’d like to have specific points within a units to formatively check how students are in relation to the standards.  These won’t be formally entered into the grade book, but used for students to reflect on their progress and for me to look at where I need to emphasize my instruction.  I used a reflection tool that was helpful for my third graders this year and I’m planning on extending it to other grade levels.  Who thought emojis could be so powerful?  Also, every year around this time I wonder if the students’ grades actually reflect where students are in relation to the standard?  Sometimes yes, other times no.  At some point in time my district will be consistently using standards-based grading, but we’re certainly not there yet.  I’m hoping that this will help students and parents to see where students are on a continuum compared to the expected standards.  In the meantime, we still have the letter system that parents and students have grown so accustomed to and expect to see when the report cards are delivered.


Events that spurred growth – I’d like to continue to seek out these opportunities

  • Conferences

This year I had the opportunity to co-present at IAGC on the the topic of math routines with my colleague Cheryl. Most of my learning came in the time creating the presentation and discussing potential ideas.  The conference was well attended despite the extremely cold temperatures.  I had a sub for the day but ended up not needing them since school was canceled – go figure.  I also had the opportunity to travel to Wisconsin and attend WMC to present on feedback routines.  I was only able to attend one day, but it was great and meeting many members of my PLN face-to-face was amazing and long overdue.  Special shoutout to Adrianne , Sonja , Mary and Chris for being so welcoming and I enjoyed our conversations.

This past week I received confirmation that I’ll be able to attend all three days of NCTM in Chicago.  I’m in the process of putting together a couple proposals and look forward to meeting, sharing and learning with colleagues.  Attending conferences and meeting with other educators outside of my district brings a different perspective.  That different perspective and ideas is refreshing and helps me think of ways to improve my practice in ways that I didn’t think of before.

  • Book studies

Last year I participated in a Making it Stick summer book study and it was a great experience.  It’s one thing to read a book solo and another to read it along with other educators.  There’s an accountability piece that keeps me reading and more critically analyzing what I’m taking away from what I’m reading.  I’m looking forward to Culturally Responsive Teaching And The Brain this summer.  The book arrived at my doorstep about a week ago and I’m looking into diving in with my highlighter next week.

  • Podcasts

I recently started listening to Podcasts and have found a couple that I’ve been sticking with over the last couple months.  These podcasts help me think about practices that I could improve and just gives me a different perspective in general.  Right now I’m listening to The Cult of Pedagogy, Estimation 180, The Creative Classroom and The Minimalists.  I’m sure my list will change over these summer as more non-education related podcasts enter my queue.  I need to have more of balance with the types of podcasts I listen to but this is a start.


 

Student Self-Reflection and Common Math Errors

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My fourth grade students took their first unit assessment of the year last Wednesday.  This is the first class to take an assessment this school year.  The unit took around four weeks and explored topics such as area, volume, number sentences, and a few different pre-algebra skills.  This year I’ve been approaching student reflection and unit assessments differently.

Students were given their study guide during the first couple days of the first unit.  The study guide included questions that covered topics that would be taught throughout the unit.  At first students were confused about how to complete items that we haven’t covered yet.  Eventually students became more comfortable with the new study guide procedure as we explored topics and they completed the study guide as the unit progressed.  There were a couple of students that lost their study guides, but they were able to print it off from my school website.  I reviewed the study guide with the class the day before the test.  It took around 10-15 minutes to review, instead of around 40-50, which has been the norm in the past.

After students finished the study guide the class reviewed the skills that were going to be assessed.  Students informally rated where they were at in relation to the skill.  I decided to move in this direction as I’m finding that reflection on achievement or perceived achievement doesn’t always have to happen after the assessment.

Students took the test and I passed back the results the next day.  Like in past years, I have my students fill out a test reflection and goal setting page.  This page is placed in their math journals and I review it with each student.  I decided to use Pam’s idea on lagging homework/coding and add this to my student reflections.  Last year my students used a reflection sheet that indicated problems that were correct or incorrect and they developed goals based on what they perceived as strengths and improvement areas.  This year I’m attempting to go deeper and have students look at not only correct/incorrect, but also at error analysis.

So I handed back the tests and displayed an image on the whiteboard.

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I told the students that we’d be using coding in math today.  I reviewed the different symbols and what they represented with a test that was already graded.  Each question would be given a code of correct, label / calculation error, misconception, or math explanation. I gave multiples examples of what these might look like on an assessment.   I spent the bulk of my time introducing this tool to the misconception symbol (or as some students say the “X-Men” symbol) to the students.  After a decent amount of time discussing what that looks like, students had a good feel for why they might use the math explanation symbol.

I then passed out the sheet to the students.

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Students went through their individual test and coded each question based on the key.  At first many students wanted to use the label/ calculation error code for wrong answers, but then they stopped and really looked at why their answer didn’t meet the expectation. In some cases, yes, it was a label issue.  Other times it was an insufficient math explanation.  Most of the students were actually looking at their test through  different lens.  Some were still fixated on the grade and points, but I could see a shift in perception for others.  That’s an #eduwin in my book.

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After students filled out the top portion of the reflection sheet they moved to the rest of the sheet.

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Students filled out the remaining part of the reflection sheet.  They then brought up their test and math journal to review the entry.  At this time I discussed the students’ reflection and perception of their math journey and I made a few suggestions in preparation for the next unit.

At some point I’d like create an “If This Than That” type of process for students as they code their results.  For example, If a student is finding that their math explanations need improvement then they can ________________ .  This type of growth focus might also help students see themselves as more owners of their learning.  I’m looking forward to using this same process with my third and fifth grade classes next week.

Third Grade Math Confidence

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My third grade students have been working on rounding and estimating this week.  It’s been a challenge as these concepts are fairly new to the entire class.  We’ve only been in school for only three weeks but I feel like we’re in stride now.  Kids and teachers both are in a routines and tests are already on the schedule.

Back to rounding and estimating.   So students have been struggling a bit with these two concepts as we head towards using the standard algorithm. With that struggle comes a shake in math confidence.  Students needed to be reminded of our class expectation of “lean into the struggle” many times during the past week.  It’s interesting how a student’s math confidence changes throughout a unit, or even throughout the year.  This third grade class in particular is working on becoming more aware of their math performance compared to what’s expected.  In order to reach that goal, I dug back into my files and found a simple, yet powerful tool that might help students on this awareness math journey.

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Basically, students first read the top row goal. They were then given a die to create an example of the goal.  During this process students circled one of the emoji symbols to indicate their confidence level.  The extremely giddy emoji indicates that they could teach another student how to complete the goal.  The OK smiley means that you’re fairly confident, but feel like you might not be able to answer a similar question in a different context.  The straight line emoji means that you’re confidence is lacking and you might need some extra help.  This paper wasn’t graded and that was communicated to the students.

Regardless of the emoji that is circled, students are required to attempt each goal.  Some students were very elaborate with explaining their thinking, while others tried to make their answer as concise as possible.  After completing this students submitted their work to an online portfolio system so parents can also observe progress that’s been made.  So far it’s been a success.  I’d like to use this simple tool for the rest of the first unit and possibly the next.  It takes time, but as usual in education, the teacher has to decide whether it’s worth that time or not.  In my case, the student reflection has meaning and it’s directly tied to the goals of the class.  I’m looking forward to seeing how these responses change over time. Feel free to click here for a copy of the sheet if you’d like one.