Attending to Precision

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Last week I read through chapter five of Becoming the Math Teacher You Wish You’d Had.  Reading this chapter made me wish that school was still in session.  There were times when I was reading that I stopped and reflected on how I manage expectations in the classroom.  Specifically, I thought about how I emphasize the need to be precise during math lessons.  More often than not, the precision aspect is related to computation mistakes as well as issues related to missing or incorrect units.  I address this so many times during the year.  So many that I can’t count the amount of times that it’s mentioned.  I think most math teachers have been there.  In most cases I’ve observed students being able to show their understanding of a particular concept, but they don’t show it on assessment.  A label might be incorrect or a one-digit calculation completely changes an answer.  I see this all the time with adding units related to linear, square, and cubic measurements.  A student may get the answer correct, but the label doesn’t match.  I have issues when students place cm^2 when the label should be cm^3.  There’s a big difference there and it has me questioning whether the student understands the difference between area and volume.  There has to be a better way than just reminding students to check for errors or make a reasonableness check.

A couple of the examples that were showcased also emphasize using precise language.  Avoiding the word “it” and being specific are highlighted.  I find myself repeating certain phrases in class.  Not using “it” to describe a particular unit would be on my repeat list.  Instead of using that devil of a word, teachers can emphasize and have students label the ambiguous “it” into something more accurate.  Incorrect labels are a killer in my class, so this is something I continually emphasize.

Estimating can also play an important role in attending to precision.  My third grade class uses Estimation180 just about every day.  We made it all the way to day 149 last year.  We were pretty pumped about that much progress.  It was a productive struggle and heartening to see how much progress was made.  As time went on students became more accurate with their estimates.  That thought process transitioned to other aspects of math class.  I asked the students to have reasonableness checks before turning in an assignment.  The check doesn’t always happen, but when it does it’s a golden opportunity.  I’ve had some students use a checklist to record whether they’ve estimated first to see if their answer is reasonable.  Again, it’s not always used but I believe it benefits students.

Games can be great opportunities for students to be reminded to attend to precision.  Some games are great for this, others aren’t and bring an anxiety component to the table.   I was reminded of the negative impact of timed tests and elimination games.  I’m not a fan of timed fact tests in the classroom and haven’t used them for years.  More recently, I’ve used timed Kahoots or other elimination games.   Some students are more engaged when there’s a competition component.  This chapter brings awareness to how emphasizing speed can be damaging.  Most of the time these games are low-risk, but they do bring anxiety and can cause some students to withdraw.

Guided class activities like pattern creation can be helpful in reminding students to attend to precision. Using student-created patterns ( ___, ____, 56, ____, _____ ) to develop unique solutions can be utilized to show understanding of numbers.  Students can create a multitude of patterns with this.  It also challenges students to find a pattern that no one else has.  I’ll be keeping this in mind as I plan out next school year.

It seems that students will always need to be reminded to add correct units, review their work and attend to precision.  Having strategies and tools available to address this will be helpful moving forward.

End of the Year Feedback

 

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My school year ended last Wednesday and I’m now getting around to looking at student survey results.  This year I decided to change up my survey and make it more detail oriented, as I wasn’t really getting enough valuable information before.  Instead of creating my own (like in the past) I came across Pernille’s gem of a survey.  I know that she teaches at a middle school, but I thought the survey would be valuable for my kids just as well.  So I basically copied all the questions into my own Google Form, created a QR code and had students scan the code to complete the survey during the last two days of school.  Students already knew their report cards grades and they were asked to place their names on the feedback survey.  This is the first time that I’ve taken the anonymity out of the equation.  In doing so, I was hoping that students would answer the questions more honestly, which I believe actually ended up being the case.  The survey took around 15-20 minutes of time and it was pleasing to actually see students put effort into this task.  I had 54 total responses.  Of course there were absences, but I thought that size wasn’t bad, seeing that I have approximately 60 kids that I see in grades 3-5 every day.

Like I do every year, I critically analyze the results.  I look at survey results as a risk, but also an opportunity to see what the kids perceive.  They don’t always communicate what they’re thinking and this is a small window-like opportunity to catch their perception.  I tend to question the results every year, but have come to peace with an understanding that I look at trends, not necessarily every number.  Like most data, I find the individual comments to be the most beneficial.  I won’t be delving into that too much here, but here are a couple key findings:

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Students averaged a 3.43 for this question.  Part of me is glad that it wasn’t below three as I don’t want students to perceive the class as being light on challenge.  I want students do be able to put in effort, work hard, set goals and see that their effort has produced results.  This doesn’t always happen.  Also, the word difficulty is subjective and what someone determines as a challenge, they might not consider it difficult.  This is becoming even more evident as my school continues to embrace growth mindset philosophies.

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Okay, the good ole homework question.  I gave homework around 2-3 times a week and it’s used for practice/reinforcement.  Students rated this as a 2.85, which means I should be giving more, right?  Haha.  I believe students analyze this question and compare the amount of homework received in their homeroom vs. my class.  Over the years I’ve given less and less homework.  Early in my teaching career I used to give homework Monday-Friday, but have reduced that amount during the last five years.  It’s interesting to see the students’ perspective on this heavily debated subject.  Maybe next year I could add a question related to whether the homework helped reinforce concepts for students?  We’ll see.

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I really like this question.  It’s risky as I don’t want the numbers to be the same, but it’s also beneficial because I truly want to see how students’ perceptions of their own growth have changed.  The first question came up with an average 7.67, which I was pretty pumped about.  Most students that I see perceive math as something positive.  Having that perception helps my purpose and it’s a also a credit to past teachers.  The second question rang up as a 9.15.  This was a helpful validation to show that students perceptions about math can change over time.  It also emphasizes the larger picture that math is more than rote memorization/processes and it surrounds our daily life.  I also wonder whether removing the anonymity portion influencd this score in some way.

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This question made me a little anxious.  I feel like knowing a student and developing a positive rapport is such an important component.  It came in as a 4.13.  While looking over the data I found that students that didn’t perform as well rated this much lower than those that did.  Spending time asking about students’ lives is important. Time is such  valuable commodity in classrooms and ensuring that you know a bit more about students can benefit all involved.

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Some students said that I could attend their sporting events or ask about what they did over the summer.  Other students said that I could’ve used a survey at the beginning of the year and not just at the end.  Ideally, it’s probably a decent idea to give a perception survey at the beginning of the year to get to know the students.  I didn’t do that this year, but will most likely put one together for next year.  It’s on the docket.

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The responses that I received on the “Anything Else” question surprised me. I’ve never used this before so I wasn’t anticipating results, but I was pleasantly surprised.  About a third of the students mentioned class activities that they enjoyed or told me about how they’ve changed over the school year.  Some students commented about certain math activities that they thought were valuable.  Making it mandatory probably also played a role in why students added more than a “No” to the comment field.  In the future I’ll be adding an “anything else” question to my survey.


Well, now that the school year is over it’s on to planning the next!

Memorable Moments

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My school year ends in about two weeks.  It’s tough to believe, but the school year is almost over.  The kids know it, the administrators do, and so do the teachers.  Classroom decorations are coming down and boxes are being packed. Summer is just around the corner and I’m in reflection mode.  Overall, it’s been a productive year.  I took a few risks and tried out a few new activities this year.  They mostly turned out well, and I’m keeping the majority of them for next year’s classes.  In a week, I’ll be surveying my kids and asking them about their favorite math activities and memorable experiences.  Through this process I’m asking students to reflect on their math experiences this year.  I’m also asking them to comment on how their perception of math has changed over the year.   In years past, some students have commented that they enjoyed certain activities, but what they remember is the activity, not necessarily the math involved.  This often comes up when my elementary students come back to see their teachers after moving on to middle or high school.

Other students comment that they enjoyed more of the procedural aspects of math because they were easier to complete and understand.  Looking back at my own math experience, I don’t really remember getting excited about learning certain math skills/concepts during an activity.  My memory isn’t connected to the particular skills that I learned during these activities.  The activities were meaningful to me and I’m assuming that the skills transferred, but I mostly remember how I felt in math class.   My math teachers, specifically the ones I had after middle school impacted my perception of mathematics.  I remember math activities, how my teacher viewed math, working with other students, math manipulative and math projects.  As my students reflect on their math journey this year I need to keep in mind the influence that teachers have along the way.

On a daily basis, students will use skills and make math connections that align with posted mastery objectives.  What students remember might be completely different than the stated objective for the day.  I feel as though part of my job is to have students make meaningful math connections on a daily basis.  Activities that spur these types of opportunities are beneficial.  Creating opportunities for these memorable math activities is part of the job and it’s one of the reasons that I enjoy opening up my classroom door in the morning.

 

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.

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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.

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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.