Friday Letters-Student Self Reflections

Today's #sunchat on Twitter inspired me to do a blog post explaining my Friday Letters, my students' weekly reflections.

A couple summers ago, post TMC, I remember seeing people tweeting about the idea of Friday Letters.  I think the teacher had her students write her a letter every Friday about different topics.  That is about all I remember, but I have wanted to do that with my students ever since.

Fast forward a year or two and last Spring when I piloted using Google Classroom with my Honors Math 7 class, I had them do Friday Letters for just the last few weeks of schools.  I wanted to try it out on a small scale (and do the Friday Letters digitally on a running google doc) to see how to manage the workflow.

This year I knew I wanted to start the Friday Letters right away and establish it in a meaningful way for student self reflection.  I had not yet chosen my PPG (Professional Practice Goal) at the beginning of the school year when I started Friday Letters, but was very happy to realize they would end up being a key component of my PPG. In WI part of Educator Effectiveness (how we are evaluated as teachers) involved writing a PPG.

I've copied and pasted a portion of my PPG below so you can see how the Friday Letters are used to assess student understanding of math concepts, as well as, to uncover misconceptions.

Identify related Danielson Framework for Teaching domain/component(s):

Educator:       3d Using Assessment in Instruction

Focusing on:  Taking the pulse of the class by monitoring student understanding and using strategies to elicit that information.

Evaluator comments:       

Describe applicable instructional or non-instructional activities:

Educator:       

Using formative data to drive my classroom instruction:

• Daily warm ups
• Check ins during collaborative group work time
• Students self correct homework via google classroom
• Homework assignment questions/discussions posed by students
• Exit slips
• Formative assessments
• Friday Letters- student self reflection on learning

I will provide individual feedback to students through their Friday letters and pull small groups based on any misconceptions I discover.  Students will use Google Classroom to correct their own assignments.  This allows them to assess their own work. I check in with students every day to make sure assignment are completed and that I answer any question for clarification.  Students may be pulled in small groups or individually based on this formative feedback.  Students are required to fill out a google form if they plan to reassess any standard,  This form requires students to reflect on their study habits and areas of difficulty.  They also decide on when they will reassess and what they need for me before reassessing.

Students write their Friday Letter reflections every Friday.  I usually provide a prompt and they respond to the given prompt in the format of a letter to me.  When I want to comment back to a student I highlight the date of the letter and then comment from there.  This is an easy way to comment back to the entire letter instead of highlighting bits and pieces and responding that way.  I have about 120 students and the commenting back to them is the hardest thing to manage.  I spent over 2 hours commenting back to every student in just one of my four classes.  Students know that I do not comment back every week.  They do love to ask me questions and sometimes my comment will spark a side conversation with them.

As I read through their letters I jot down notes of things I need to clarify or really focus on due to misconceptions that I see.  This may be something I address with all my students, just one class, or I may pull small groups, or even conference with a student individually.  It depends on what I'm seeing in the Friday letters that week.  I'm also really trying to give them ownership of their learning and assessment, by having them self assess understanding and reflect on their own learning.

I've talked about the whys of the Friday Letters, now onto the hows.  I set up a google doc Friday Letter template that I shared with students in Google Classroom.  Each student made a copy of the Friday Letter template and then bookmarked it in their math folder.  That way every week they just go to their math folder and click on the link to their Friday letter.

 This shows you what a student's Friday letter document looks like.  That formatting box at the top always stays.  Every Friday students write the new letter at the top of the doc, right under the Friday letter formatting box.  Students sign their names to each Friday letter, even though you don't see that here.

When I want to comment on a Friday letter I highlight the date of the letter (or the most recent dated letter if I want to give comments about more than one letter).  I type in my comments and they show up to the student as you see below.  Very important...tell students to NOT RESOLVE the comments you make, otherwise you will get an email that the comment was resolved.  I've told my students that if they want to respond to my comment, just add it to their next Friday letter.  The comments stay next to the letter so it won't clutter things up.

Most of the prompts I give students are designed for them to reflect on their learning that week and so I can see where they are at in their understanding of the math concepts. I'm also trying to get them to be more self reflective so they can see the impact of their own actions on their learning.

Some topics we've covered:

• Introduce yourself to me
• Tell me what you understand about ratios, rates, and proportions
• What is the difference between discrete and continuous data?
• Tell me everything you know about direct variation
• Give me feedback and suggestions on math workshop: opener, mini lesson, group work time, sharing and reflection, small group lessons/individual conferences
• How does homework help you learn?
• How do you prepare for assessments so you are able to demonstrate your understanding of the math content and skills?

I'm really enjoying reading students Friday letters.  Not only am I getting a very clear picture on where students are regarding the math content, but I am finding out what their likes and dislikes are and how they spend their time out of school.  I feel like I am getting to know students much better on a personal level thanks to the Friday Letters.

Intentional Talk Book Study- Chapter 4 "Why? Let's Justify

This summer I am participating in the Summer Book Study on Twitter hosted by @BridgetDunbar

I joined this book study because I really want to learn "how to structure and lead productive mathematical discussions" in my 7th grade math classes this coming school year.  I use the workshop model of delivery and students already do a wonderful job of working collaboratively.  I would like to improve the mathematical discourse during group work time and during whole class discussions.

We use a lot of Disciplinary Literacy Strategies in our 7th grade math classes.  Below is an example of one of those strategies, called the "Do/What" Strategy.  We use this with our students to get them to give a good and complete justification of a problem they solve.  We start using this strategy right away with our first chapter.

Question 1:  What are some math rules or tricks your students use that you would want them to better make sense of and justify?  When we are dividing fractions and we need to make the divisor a whole number I make sure they explain that moving the decimal the same number of spaces to the right to make the divisor a whole number, we are multiplying the divisor and dividend by 10, 100, etc.  I always make them explain that the decimal moves right or left because of multiplication or division.

Question 2:  What classroom routines or structures do you incorporate that encourage students to notice patterns in which to justify? We are constantly looking for patterns in our math class.  An example is when multiplying integers.  Multiplication is like repeated addition. Ex) -3 x -4 Means "the opposite of three groups of -4", " the opposite of -4 + -4 + -4" which would be 12.  
Another way is to have students extend the pattern:
-5 x 5 = -25
-5 x 4 = -20
-5 x 3 = -15
-5 x 2 = -10
-5 x 1 = -5
-5 x 0 = 0
-5 x -1 = 5
-5 x -2 = 10
-5 x -3 = 15


Question 3:  What is the most common form of justification you hear/see from students?  Why do you think they justify that way?  I think I really have to move students beyond just showing their work/procedures when solving problems, to a deeper level of reasoning mathematically.  I want them to have a conceptual understanding, not just procedural fluency.

Question 4:  Reflecting on the Why? Let's Justify Template, How do you support student thinking during justification?  If they say _____ I may ask _____.  
I tend to ask questions like:
How do you know that?
Can you explain that with more detail?
Can you give me another example of what that would look like? 
I think it is really important to make sure students focus on using correct mathematical language. They need to use correct vocabulary in the context of the problems.  Students often have to be pushed to specify thinking with strong math terms instead of vague language.

Question 5:  What next steps would you like to take in facilitating discussions that incorporate justification?  
I think it's really important for me to model what a good justification answer sounds like.  I want them to justify reasoning and their mathematical thinking, not just the procedural steps in solving a problem.

I really enjoyed this chapter.  We focus quite a bit on justification in our math classes, as it is one of our three report card standard we use with Standards Based Grading.  I really like the strategies presented for encouraging better justification during class discussions.

Intentional Talk Book Study- Chapter 3 "Compare and Connect"

This summer I am participating in the Summer Book Study on Twitter hosted by @BridgetDunbar

I joined this book study because I really want to learn "how to structure and lead productive mathematical discussions" in my 7th grade math classes this coming school year.  I use the workshop model of delivery and students already do a wonderful job of working collaboratively.  I would like to improve the mathematical discourse during group work time and during whole class discussions.

Better photo of the planning template.

Question 1:  Can you think back to a lesson where students really benefitted from sharing two solutions? Sketch out the solutions and snap a picture.  There are several lessons in my Carnegie curriculum where we look at different ways to solve a problem.  My book calls it "Peer Analysis".  This sometimes shows two different methods for solving the same problem.  Sometimes it shows how two students solve the using the same method, however, one has a misconception in their solution so they are incorrect.  This is a very powerful tool for students analyzing worked examples of others. 

Question 2:  Do you find it useful to think what your board will look like as a result of a discussion? Why or why not? I think it is very useful to anticipate student solutions of problems in advance.  It can help you to place in certain order to show progression in thinking and strategy.

Question 3:  One idea for "Compare and Connect" is to link notation used in a standard algorithm to notations of invented ones.  Can you share a photo of what that might look like?  If you do -8 + 2, 8 + (-2), -8 + (-2), and 8 +2 all represented with a number line model (or you could also do a +/- counter model).  Students begin to see that when you add a negative and a positive number the sum ends up being the difference between the absolute values of the two numbers and the sign will be of the number farther away from zero on the number line.

Question 4:  Compare and Connect can be used to compare strategies, representations, tools.  What's an important connection students at your grade level need to make?  When we are talking about direct variation it's important for students to understand how the equation, table, and graph all represent the same thing and how those different representations look when it's a direct variation vs. when it's not a direct variation.

Question 5:  How do we know if students are understanding the goals we set for discussion?  What do you do to help students stay in the discussion?  We need to be checking in with individuals students and groups during discussion to hear their thinking.  We can also look at their work shown to see if they are making the connections we want them to make.  Having a sharing and reflection at the end with a problem that wraps up the goal of the days lesson can help us see which students really got it and are ready to move on and which students may need a small group lesson or individual conference.

Sorry I was unable to snap any photos of actual problems I do with students.  I am currently unable to access my shared folders where my SMARTBoard files are located.  Technical difficulties are a pain.

Intentional Talk Book Study-Chapter 2 "Open Strategy Sharing"

This summer I am participating in the Summer Book Study on Twitter hosted by @BridgetDunbar

You can follow #intenttalk to see all the posts on Twitter about this book study.

I really enjoyed Chapter 2 "Open Strategy Sharing" and am looking forward to starting my school year off using this method to help us establish class norms for our mathematical discussions.  Students spend lots of time working in collaborative groups and having discussions in those small groups.  I want to create a classroom culture from Day that values the ideas and opinions of everyone.  I also want them to take risks and not be afraid of making mistakes.  It's important that each student feels comfortable contributing their thoughts and ideas.  I want my classroom to be a safe space for that. 

Twitter Questions:

Question 1:  Do you make an effort to know what strategies students have used before sharing in discussion? How do you do it?  I do try and make an effort to look at the strategies used so I can highlight different strategies when solving a problem.  I also like to try and scaffold the strategies when possible so we start out with the basic conceptual understanding and build to a more abstract solution (that may involves an algorithm).  This requires me to move about the room listening in on student thinking.

Question 2:  Do you ask students to summarize or rephrase other students' ideas?  How do you do it? How do students receive it? I do have students summarize other students's ideas.  Often when students give a correct answer, yet struggle to explain their thinking, another student will jump in to help try and clarify what the student means.  If a student struggles to articulate their thinking a peer will often try and clarify.  Students generally receive this well.

Question 3:  What is an example of a problem you would use for an "Open Strategy Sharing" discussion? Why would you choose it?    I'm really trying to think of a good problem to use at the beginning of the year when we start our first chapter on Ratio and Proportional Relationships.  I would like to use Open Strategy Sharing right away in order to establish our norms for classroom discussions.

Question 4:  Norm: "Agree and disagree with mathematical ideas, not with each other." How can teachers make this happen?  I think it's starts from Day 1 when you are establishing a culture of collaboration and mutual respect in your classroom.  Students need to feel safe and realize it's OK to make mistakes and take risks when sharing ideas.  Also it's important to build student confidence so they don't automatically think they have the wrong answer because they got something different than another student.  Students need to focus on the math when having a mathematical argument and not make comments about the person they disagree with.

Question 5:  How do you respond to an incorrect strategy during an open strategy sharing discussion? Why?  I prefer to ask other students if they agree or disagree with the strategy shared.  I actually love when students share wrong strategies because it's a great way to discuss misconceptions.  It's important for me not to jump in and save them when they are struggling because they need to develop the habits of saving themselves and I can facilitate that through the Talk Moves.

Intentional Talk Book Study-Chapter 1 "Introduction

This summer I am participating in the Summer Book Study on Twitter hosted by @BridgetDunbar

I'm joining this book study because I really want to learn "how to structure and lead productive mathematical discussions" in my 7th grade math classes this coming school year.  I use the workshop model of delivery and students already do a wonderful job of working collaboratively.  I would like to improve the mathematical discourse during group work time and during whole class discussions. The book study started a week ago and I pretty much took week 1 of my summer vacation to catch my breath and spend some quality time with my family.  I did not join the twitter chat for chapter 1, but posted my answers below.

Question 1:  What steps do you take to set up a classroom environment where students see the importance of classroom discussions?  During the first five days of school I set up the expectations that discussion is an important part of our workshop model, both in collaborative table groups and whole class sharing/reflection.  We model this during our team building activities the first few days.  We also discuss norms and expectations for classroom discussions.

Question 2:  What moves as a teacher do you make to encourage students with low math confidence? How do you engage these reluctant students in classroom discussions?  I really try and build student confidence through pre or reteaching concepts during Core Plus or small group lessons during class.  Sometimes we will have a discussion prior to a class (during Core Plus) about upcoming concepts and students will have the confidence to then contribute in class.  Letting students pair-share or share at table groups prior to having whole class discussions also helps reluctant students to participate more.

Question 3:  What strategy do you use the most?  Which do you want to know more about?  We spend a lot of time having students justify their thinking and answers.  Justification is one of our three report card standards so we model this all the time in class.  We also use the Disciplinary Literacy strategy of Do/What to help students set up good justification of problem solving.  I'm very much interested in learning more about helping students focus on What's Best and Why.  I think it's important for students to realize that some strategies are more efficient than others when problem solving and getting students to discern what is a more efficient strategy will help them become better mathematicians.

Question 4:  As we are ES, MS, HS teachers looking for discussion strategies...How might we support this process at each grade level?  Including the support of students with special needs and ELL...  I think modeling is very important at the middle school level.  Also pre-teaching any requisite skills and vocabulary will help to front load for special needs or ELL students.  Often just making students understand the context of any new vocabulary will be helpful.

Question 5:  What questions about discussions in the math classroom are you hoping to get answered throughout this book study?  I'm just hoping to get tips and strategies or making this sustainable in my classroom.  I'm also looking to gain confidence in my ability to make connections between student thinking.  I also need to hold back and let students make the discoveries together.  I am used to modeling my thinking during the mini lesson portion of workshop so it will be different for me to not jump in and save them if they begin to struggle during a discussion.

I'm really looking forward to spending some time this summer, reflecting on how to improve mathematical discussions in my classroom this coming school year.

#5Practices Book Study Begins January 13th

I'm really excited to be hosting another online book study that will be starting on January 13th.  I delayed the start time a couple weeks so anyone who needs to pick up a copy of the book has time to do that.  We will be reading and discussing 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein.

I hate to go all Charlotte Danielson on you all, but that is my reality and my PPG this year is Component 3b:Using Questioning and Discussion Techniques
Elements include:
› Quality of questions/prompts
› Discussion techniques
› Student participation

I'm really hoping this book study will help me improve both questioning and discussion techniques in my math classroom.  It is my goal to enrich my collaborative classroom culture to include student initiated higher order questions and thoughtful student led discussions prompted by rich mathematical tasks.

Each Tuesday morning I will post a chapter summary with discussion questions, reflections, and a link up for you to share your blog post. Please make sure you read and share comments on others' posts.  Don't feel you have to follow the structure as set up when writing your post.  If you prefer to just blog about what you read, do that.  The discussion questions will be prompts for anyone looking for some guidance as to what to blog about. There is no right or wrong way to participate.  Use #5practices on Twitter to also share your blog post.  Any twitter discussion about the reading should include the same hashtag.  If there is interest in a scheduled twitter chat time to discuss the reading, we can decide on that as we go.  If you are not active on twitter now is a great time to start, or you can just link up with your blog posts if you prefer.

Hopefully as the book study continues we will all be able to share stories and examples of how we are improving our discussions in our own classrooms.

Please feel free to leave any questions in the comments section or you can reach me on twitter @luvbcd  I'm looking forward to learning from and sharing with all of you!