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!  

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.

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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Data Landmarks and Context

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One of my classes is working on a unit related to data displays and number systems. Around a week ago the class was putting together sets of numbers to match data landmarks.  This was a challenge as students had to think differently.  The class was also asked which data landmark better represents a student’s performance.   I was meaning to write a post then, but a number of things came up and it never happened.  Fast forward a week and here we are.   

Students were given two sets of scores from two different students. 

Jack’s scores:  85, 81, 78, 100, 84, 89 

Sonja’s scores:  55, 87, 91, 92, 68, 93 

Students were asked to find the median and mean for each student.  For the most part, students were able to identify both of these landmarks.  Here comes the kicker … now students needed to determine which landmark better represents each student’s performance, mean or median?  This was a challenging prompt for a couple reasons.   

  • Students weren’t accustomed to using the word represent in this context.  Students were taking the view that the students should get the higher grade and that would be the mean or median. They explained that the student should receive the higher grade because they (the person) is a hard worker and deserves to be rewarded with the highest score. 
  • Students thought of the word represents as the typical score.  When discussing the mean earlier in the year the word typical would often come up as a synonym. 
  • Students looked at the last score as the most recent and thought that should be the final representation.  My school is heading in the direction of standards-based grading so that’s maybe why students took that approach.  I don’t know. 
  • Students looked at the lowest and highest score of each set of data and reviewed the range to help them pick the median or mean 

 

After struggling a bit, the class came together and we discussed a few possible solutions.  The class agreed that the question allows a lot of room for interpretation and context certainly matters.  The fruitful conversation brought about a change in perspective for some as students started to see this type of math differently than just numbers sprawled across a page.  The numbers had meaning and the context drives the answer.   

A little later in the week students were asked the following prompt: 

If you were the teacher in Jack and Sonja’s class, would you use the median or the mean to calculate students’ grades?  Explain. 

This was a bit confusing at first, but students made progress in understanding the context and how it helped determine which landmark to use.  Again, I had answers related to the teacher wanting to give the higher score to help students with confidence.  Other students used the data landmarks to find the average.  I felt like students were more comfortable using the average as they could say that they used every data point, therefore making sure all assignments counted for something.   

I’m looking forward to next week as we dive into histograms. 

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.