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.

Reflection and Math Goals

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

Stage 1

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

Stage 2

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

Stage 3

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

 

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

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

So, here’s stage four:

Stage 4

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

 


 

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

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

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

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

Differentiated Instruction

Image by Luigi Diamanti

As an educator, part of my job is to meet students’ academic needs.  Every educator, at one time or another, asks the question – how can I meet the needs of all the students that enter my classroom?  That’s a tough questions to answer, with multiple answers, depending on your philosophy of education.  To start, you need to understand the current skill level of your students.  You might want to give some type of pre-assessment to determine what type of skills that the students possess. A lot of vital data can be extracted by analyzing student assessment data.  Student assessment data can often drive school-wide instructional decisions.  Once assessment data has been collected and analyzed, you can begin to start to differentiate and individualize instruction.  Differentiated instruction is an educational buzz word that has been around for quite some time now.  What does it actually mean and isn’t it subjective?  Here are a few definitions:


“Differentiated instruction is a teaching theory based on the premise that instructional approaches should vary and be adapted in relation to individual and diverse students in classrooms” – Carol Anne Tomlinson

Differentiating instruction ….”Maximize(s) each student’s growth by recognizing that students have different ways of learning, different interests, and different ways of responding to instruction”  – Diane Ravitch

“Rather than simply teaching to the middle by providing a single avenue for learning for all students in a class, teachers using differentiated instruction match tasks, activities, and assessments with their students’ interests, abilities, and learning preferences” Jennipher Willoughby


Throughout this post, I’m going to show one way to differentiate instruction in the classroom. Specifically, via a flexible grouping strategy.

After utilizing a pre-assessment, or some type of formative assessment, you can use the results to begin to group the students based on skill level.  Generally, different “flexible” groups are created based on the skill level of each student. Each group will work towards achieving or mastering specific skills related to the curriculum.  For example, one group might work on basic computation strategies related to practical application problems, another might practice critical thinking skills, and another group may complete enrichment projects related to statistics.  What each group works on should focus on improving students’ skills.  Student groups are fluid and can change throughout the school year as additional student data is collected.  Individuals in each group will set their own goals through a goal setting process.  By engaging in goal setting, students are given the opportunity to gain responsibility for their own learning.  Shifting some of the responsibility to the student gives ownership, therefore assisting in intrinsically motivating a student to achieve their goal.

This is only one form of differentiated instruction.  I’ve provided a list of resources on differentiated instruction below.

Disclaimer (unfortunate but necessary) : The thoughts and opinions expressed in these pages are my own, and not necessarily the opinions of my employers.