Formative Assessment & Quizster

As I referenced in my Personalized PD post, I've been trying to make more of an effort to be on Twitter and connect with the amazing teachers of the Math Twitter Blog-o-Sphere (#MTBoS).  Last weekend, while grading papers, I tweeted out this question:

The question was born partly out of frustration of my limitations due to time, etc.  I believe strongly in the power of formative assessment but I quickly get overwhelmed by all of the paper that comes with exit tickets, warmup slips, etc.  I also believe in the power of feedback and I don't want my students to get their first feedback on a topic from a quiz/test, so I fight through all of those paper slips, write comments and individualized feedback on each one, and pass them back.  (Thankfully via their table folders!!)

Many people chimed in with responses to my question - Thank you #MTBoS!! - But the one that stood out to me was this tweet from Kate

Quizster is a new app by a long-time math blogger and her husband.  After checking it out and securing permission from our district director to try it out, I decided to test out Quizster with my AP Stat kiddos and a FRAPPY (aka an AP Free Response problem)

Set up was a breeze.  Quizster walks you through the set-up, plus encourages you to create a student account so that you can see what the kids see.  I tested it with both my cell phone and the webcam of my computer and it worked well with both.  Finally it was time to test it out with my kiddos!

On block day, my kids are used to starting the day with a FRAPPY, but often I have them turn it in via their table folder and hopefully they will get it back within the next few days, depending on how behind I am on grading.  With the Quizster app, the students did their work in their notebook, then snapped a photo to upload via the app's webpage on their cell phone browser / Chromebook.  (They are working on a mobile app right now).  Within minutes, I started getting notifications that I had papers to grade!

On the left, you can see my list of "to be graded" as denoted by the red circle.  When I click on a student's name, their work appears (middle photo) and I choose 'Annotate'.  On the right, you can see me writing the student feedback directly on their paper, just like I would traditionally.  After clicking the "X" at the top right, my annotations are saved and there's a button to send my feedback to the student, then back to the "to be graded" list I go! :)

Some features I really like...

• Flexibility on grading - I can easily grade on the patio without papers flying everywhere!
• Flexibility in the classroom - After students submitted their photos, we were able to go over the AP rubric right away as a class, yet I was still able to later give personalized feedback to each student.
• Responsiveness - I really didn't know how easy the app would be to use or how well it would read my writing... it's extremely user friendly!

One drawback is that you do need to be connected to the internet and for students, that may mean use of their data plan if your school doesn't have accessible wifi for student devices.  I had one student that chose to use the Chromebook camera and it worked just fine, but most kids just used their cell phones.  

I'm really excited to use Quizster as we go into AP review.  So far, my students have had very positive feedback as well! :)

Making a difference - One Good Thing

Shoutout to Glenn Waddell (@gwaddellnvhs) - a friend of mine from Nevada.  Glenn and I struck up a friendship over our mutual love of teaching AP Statistics.  Thank you, Glenn for encouraging me to try this strategy!

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There are only 4 more Fridays in this school year.  Part of me is happy and excited for Summer Break, but a huge part of me is sad because that means there are only 4 more 'High Five Fridays' left in the school year! :(

If you've been around the #MTBoS for a while, you've probably heard about Glenn and his High Fives.  If not, go read his post here or watch the Global Math Departmet webinar.

Glenn first shared his idea at #TMC15 and I quickly heard about it through all of the live-tweeting.  I mulled it over and dismissed the thought almost immediately.  I am a VERY introverted person and putting myself out there in the hallway to high five my students was extremely intimidating.  My kids would never guess how introverted I really am because I can fake it pretty well in the classroom.  However, the hallway was a totally different matter!  Through a ton of encouraging tweets, Glenn talked me down from my fears and I agreed to try it out on Fridays during the 2015-16 school year.

I.LOVED.IT

My kids loved it too!

It's hard to be in a bad mood or frown when you are getting a high five... just sayin' :)

But this year (2016-17) is where I've really seen the power of the High Five.

There's a young lady that I've seen walking down the hall this year.  I don't know her, I don't have her in class.  In early March, as she walked by my room, she shyly asked "Can I have a High Five too?".  This has continued each week until last Friday, and I did not see her.  On this past Monday, she was back and as she walked by, she again asked very shyly for a High Five.  I said, "Of course!  I missed getting my High Five from you on Friday!".  Her eyes brightened and she went on down the hallway to her class.  Yesterday, I wasn't in the hallway yet, I was standing just inside my door with a student and as this young lady walked by, she reached into my room with her hand held up and said "Happy Friday, Mrs. T!"

It's amazing how one little thing can make such a huge impact on a person's attitude as well as classroom culture.

Personalized PD - A Renewed Committment

I might just be on a blogging streak.. 2 posts in one day! :)

Years ago, I was extremely active in the #MTBoS. I blogged regularly and was an active contributor on Twitter. I spear-headed the #Made4Math challenge and actively participated and coordinated many Twitter chats and book clubs.

But then, life happened.

Three of the past 4 years, I've had a new prep - and all of them have had their own challenges and struggles. This year, it's pre-calculus and while I am so blessed to have amazing students that I adore, I will be the first to admit that I'm not enjoying the curriculum due to its disjointed nature. The daily struggles and challenges have created a situation where I have pushed away from the MTBoS world and broke ties with people I used to converse with daily. Sometimes change is good - sometimes it bites you in the rear.

For me, it was the latter. As a result of my self-isolation, I have lost a richness in my life that I miss. I miss having people to reach out to to share ideas, triumphs, and frustrations. The #MTBoS has moved well beyond me and I am standing still, just watching their plume of dust in the distance. I'm not sad that I was left behind, but I am sad that I chose to stand still instead of continuing forward, even if I was moving at a snail's pace.

So I am making a public commitment to move forward - to stop standing still. I don't like being stagnant. I don't like the lack of personal growth that I have experienced.

My goals:

• Engage in Twitter at least once per week.  This may be an organized chat or just informal, but I need the mental stimulation that comes with working with other #MTBoS teachers
• Read more blog posts.  I miss the excitement that I get from reading about a really cool idea from a follow teacher.  I need to update my blog roll and blog reader and find new bloggers that are sharing the awesome and not-so-awesome days in their classroom.  
• Blog.  I need to be vulnerable and allow myself to share those same days.  
• Read professionally.  I love summer and the opportunity to read books that challenge my thinking.  This year, after struggling so much, I think my focus needs to turn back to formative assessment and pedagogy because those are things I definitely let slide this year

I know this is ambitious and I need your help.  I need an accountability partner (or 2 or 10) to make sure I stay on this path.  If you are willing, please leave a comment or tweet me :)

Crunch Time

(Note:  I know I should probably make some sort of statement about being gone for so long, but every time I try, it just sounds awkward and weird and I erase the screen and shut down my blogging screen for another several weeks, so we're going to just skip past all that, k?  We're just going to pretend like blogging is a regular occurrence around here and that it hasn't been 7 months since I last wrote...:)  )

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It's crunch time.  The AP exam is in just under 3 weeks and I'm not ready.  My kids are mostly ready, but what I wouldn't give for another week of teaching time to really solidify some concepts!  I've taught AP Stat for 17 years and one would think that I would get better and more efficient at it, but one would be wrong.  I like hands-on activities and that takes time.  With each new released AP exam, I find things that I could tweak or should emphasize more and that takes time.  Curriculum changes in the courses leading up to mine have forced intro stat/probability out the window, so filling in the gaps takes time. Classroom management of 32-33 kiddos, even when they are great kiddos, takes time.  As a result, I have to play triage and decide which topics to teach deeply, which topics to skim over to hit the high points, and which topics to move to the very end of the course and hope I get there before Exam Day comes.

This week was crazy in terms of time.  After school review sessions have started and I'm trying to figure out every little possible thing that I can do to help my students be more successful.  I love teaching seniors, but seniors after spring break can be tiring.  I'm so blessed that my students this year are a fabulous group of kids, but they are tired and I understand that completely.

Skills Check
Last week, on Pinterest, I ran across Bowman's post on Skill Drills in AP Calculus.  While AP Calc and AP Stat are both considered AP math classes, they are vastly different in terms of subject matter and needed skills, but I really liked this idea, so last Sunday, I started typing up my own version of 5 minute quick checks for AP Stat in nice little quarter-sized pieces of paper :)

I've been using them this week as exit tickets and my students have responded very well!  I don't claim ownership of these problems - in fact most of them are based on AP released exams, but you are welcome to them if you want them.

Review Flipper
Last year, I had my students make an AP Review Flipper, but this year, I just ran out of time.  The idea is that each day my students would write an index card "cliffs notes" version of a chapter of material that we could assemble into a review tool.  I got through the first 6 chapters when time just got away from me and it didn't happen this year.  I know that last year's students felt it was very useful, so I felt guilty for not getting it done this year.  With no time left and AP review about to start, I spent many hours this week transcribing my cards to send to the copy shop for each of my students.  This week, we will take a day to highlight each "card" and assemble our flippers and pray that it works okay.  I know it's not ideal - I would rather have them write the cards themselves, but.... :)

My hand was cramping for a good while after this... :)

Now I need to figure out the best way to maximize the next few weeks... In an ideal world, I could give my students some free time to work on old questions, but I've found that in general, that doesn't work well with seniors in May :)  What strategies do you use to help your students?

Formative Feedback

I've been thinking a lot about feedback lately. It started with this tweet:

@MrAbend I would be really curious as to what the Math learning/cognitive science research says about error types. Does @mpershan know?

— Anna Blinstein (@Borschtwithanna) April 15, 2017

@mpershan was kind enough to respond with an email and sent me down a rabbit hole of articles and blog posts about the usefulness of feedback. Since Michael was the inspiration for this journey, it's only fitting that I try to imitate his style of writing out loud to try to organize my thoughts on this topic (sorry, Michael - reading this back after I've finished the blog post has shown me that you are inimitable. Also, I should probably avoid writing blog posts at 11 pm in the future).

The central question we discussed was: what is the purpose of feedback? Clearly, it is only useful if it changes a person's thinking. Does pointing out a mistake do this? Does categorizing the mistake do this? Does indicating a student's level of understanding of a topic ala Standards-Based-Grading do this? Do questions do this better than statements? Do students need to reflect on the feedback or do another problem related to the feedback received or implement it in some other way in order to get more benefit from it? Written vs. oral? Immediate vs. delayed?

Feedback while kids are working in class:

This is the type of feedback I think I know how to do the best. When kids are working on a task, either on their own or with someone else, I am usually able to ask questions, point out features of their work, or connect them with other students' thinking so they can make progress, identify and correct errors, and clarify their own ideas. The one blind spot that I think I still have in this area is when a student thinks about a problem in a way that is really, really different from methods I understand or have seen and thought about before. This doesn't happen very often, but when it does, I'm really stumped. I can help them verify that their answer is incorrect. I can ignore their method and show them a way to think about the problem correctly or point them to another student in the class with a different approach. But if I don't understand it, I can't help them resolve the cognitive dissonance of their incorrect approach, which means that my work is not complete.

But in general, this is the type of feedback that seems to pay the most dividends. The kid is right there with their work, we can have a conversation, I can see if they are able to implement my feedback and give more or of a different kind, as needed, or ask them to work on a related problem. This is really the best case scenario in feedback world for me.

Feedback on homework:

Things start to get real hazy real quick when I'm looking at a kid's work outside of class and my feedback is now provided in written form or via a conversation with them the next day. Will they have time/inclination to do anything about my feedback? Without the option of a conversation, I have to make a guess, which I suspect is often not great, about their thinking and the amount/level of information to provide back and how to do that in a way that opens thinking rather than closes it. Honestly, I don't have any evidence that students get a ton out of the written feedback on their homework assignments. I've thought about building in class time to have students read the feedback on their assignment from the previous day and do something with it (since homework is turned in digitally and feedback is provided digitally, I have no idea how thoroughly students would be reading my feedback otherwise), but it seems like I could just use this time to talk to students of concern about their work or have the class do a problem related to an issue that I saw on many papers. We already go over homework questions in class before it's turned in and the answers are provided in advance, so presumably, they know if they are understanding the material. If I'm very concerned, I would rather email a student or talk to them in class or ask them to work with me outside of class. Spending lots of time writing comments and then flinging them into a black hole of ??? doesn't seem like the best use of my limited time. But not providing feedback on homework also seems wrong. So I'm at a bit of an impasse here. I've moved some of my homework grading (especially for bigger projects) to in-person conversation and in an ideal world, I would be able to do that for all of my grading, but time with students is a precious commodity.

Feedback on assessments:

This type of written feedback seems to go better than homework. I think that there are a few components that have made it more successful:

1. Students perceive assessments to be more summative and take feedback on them more seriously. They know it's a check of their understanding that will more directly be reflected in their grade (grades as motivation.... laaaaaame, but I'm not sure how to get around this... I have to produce some sort of grade at the end, and I like homework to be purely for feedback so that leaves assessments for grading). As a result, they read comments more carefully and are more motivated to figure out their mistakes and learn from them so that they can show more understanding on the reassessment.


2. I separate the feedback and grading parts to help students focus more on the feedback initially. When I grade assessments, I only write comments/questions (and try not to say too much since I know I'll be there in person to continue the conversation). I record their SBG grades on the assessment in the online gradebook only a day or so later, based on the research that showed that when students receive written comments and a grade on an assessment, they basically ignore the comments and only look at the grade, and that this is not helpful for learning. Getting back their assessments with comments only helps to keep the conversations on concepts and learning only, not on grades, as well as encourages students to work together with less comparison to others. 


3. We spend class time correcting quizzes, usually in groups that are either assigned randomly or by common error types. The quiz corrections are an assignment that is collected, they are not for "earning back points" (I don't actually understand what that means), but they are required in order to reassess. I ask students to analyze their error (did they misunderstand an aspect of the concept? execute a procedure incorrectly? make a careless mechanical error?), as well as redo the problems on which they made errors. Based on my thinking around this issue, going forward, I'd like them to also state what they plan to do to make progress on the issue identified. Michael seemed to think that identifying the type of error is not particularly helpful to students, but I think that when followed up with a "next step," it is maybe more useful?


4. I think that more students actually know what they should do to make progress with assessment feedback. They've done a lot of work with the concepts being assessed. They can talk to peers to understand other approaches, they can talk to me, we can schedule a meeting outside of class to work together, they can refer to online resources organized by content topic to review a concept or procedure, they can do practice problems from homework assignments and previous reviews related to this concept so the feedback is both more closely connected to a concrete goal and to ways of reaching that goal. 

So my main questions right now are:

1. How can I make feedback on homework more useful in helping students change their thinking?
2. Are there ways to improve both my in-class and assessment feedback?
3. How can I move more of my feedback to conversation and away from enigmatic notes that try to strike just the right balance of tantalizing hint/information-giving and hook to motivate kids to want to look at their homework again and rethink their approach, but that mostly get ignored or scanned quickly and not attended to? Did I mention that writing tons of feedback on homework assignments takes a lot of time???
4. Are there aspects of feedback that I'm not considering?

Using Canvas to coordinate written feedback

Yesterday, @druinok asked for suggestions on providing more written feedback to many students quickly.

I wish I had the time to give my students more written feedback without a grade attached. How do you fit it all in?

— Druin (@druinok) April 15, 2017

It turns out that we both use Canvas, an LMS, at our schools. There are a lot of features about Canvas that are not the most user-friendly, but in terms of giving feedback to students quickly and easily, it's been really helpful. Here's how I use it:

1. All work that I collect from students passes through Canvas, including work that is not graded, but is just for feedback. I create an assignment with either a link to a pdf for problem sets or to a Google doc for projects/written reflections
   
   
   

2. Students complete the work either in their Math notebook or in a Google doc (for projects/written reflections). But all work is submitted digitally. The student's view has an electronic submission button. Most of my students have the Canvas app on their phones and can submit by snapping a photo of their written work. Those that don't have the app take a picture with their computer camera and submit it via the web version of Canvas. I remind students to submit their homework to Canvas after we go over homework questions in class.
   
   
   




3. In grading mode, I see the photo each student took, mark the assignment Complete or Incomplete, and type written feedback. If the assignment is graded, I indicate their level of proficiency and sometimes comment on the specific objectives graded (we use Standards Based Grading so students don't see points, only learning objectives and levels of proficiency).
   

4. The system is quick - I can go through all the work submitted by students, type or copy and paste comments, and click on levels of proficiency if I'm grading the assignment. Students see the feedback on individual assignments and can also look at feedback from past work, chronologically or organized by learning objective.
   
   
   
5. I love the fact that students have access to all of their Math work in their notebook at all times - there's no longer the loss of time in turning it in, waiting for me to write feedback, and then getting it back, accompanied by the inevitable loss of someone's work and of me lugging piles of papers back and forth from school. There's no longer a question of whether something was turned in or what the feedback on that work was. We can both always easily see a chronological record of the feedback given over the course of the year and track progress. If I ever create a portfolio system for summative assessment, all of the student's submitted work is already digital and organized.
   
   
6. The one drawback that I wish Canvas provided is the ability to annotate directly on student work. If I want to draw a student's attention to a particular problem, I have to write a note that says, "In question #2, look at..." instead of just circling question #2 on their paper. When students upload their files in pdf format, Canvas has an internal marking system that activates and allows you to annotate, highlight, and type directly on the page. But for most students, this would add an extra step of converting their picture to a pdf and uploading it in that format, and I would rather make homework submission as simple as possible. So for now, this is my system.

Hidden Figures

Last Friday, every student at the arts-focused public middle school where I teach math walked to a nearby theater to see Hidden Figures, the 2016 movie about African-American women who were essential to the success of the early US space program, based on the book by Margot Lee Shetterly. We were accompanied by most of the school staff, including our principal and assistant principal, as well as dozens of family chaperone volunteers, a crowd totaling more than 400 people. Seeing the film together and talking about it afterwards with one of my classes were some of the most meaningful and fulfilling experiences I've had as a teacher, and I feel so much love and pride for my whole school community.

A lot of people made that field trip happen, but I was the main force behind it and grew almost obsessed with it, and I want to write about why. As a math teacher, I've become more and more focused on equity in math education and passionate about inclusion and empowerment, and this event sprang from that passion. I love helping my students love math and become confident and competent mathematicians and problem solvers, but I've never lost the memory of what it feels like to know others think you don't belong in math or science and to wonder if maybe they are right. I know that having good intentions and promoting logical thought isn't enough by itself to counteract the fog of racism we all live in, and that STEM fields are still unstable territory for girls and women in our culture. As a math teacher, I have the responsibility and the privilege to help make things better. Sometimes I manage it, and sometimes I still fall short of where I would like to be, but I have to believe that if I keep caring and educating myself, I will be more and more effective at raising everyone up as mathematicians, students, and citizens. I'm fortunate to teach in a time when we can collect and share resources to do that.

As soon as I started seeing information about Hidden Figures last fall, I was hooked. It sounded almost too good to be true — a fun, feel-good, PG film that brings STEM and civil rights achievements by Black women in the early 1960s into the light, shows the excitement of the intellectual accomplishments behind the space program, features stellar actors, and puts a mathematician center stage as a heroine — wow! I read a blog post by a fellow member of the "MathTwitterBlogosphere" (#MTBoS), Delaware physics and math teacher John Burk, with the subject "Let's Start a Movement for Hidden Figures," and thought a school field trip would be a fantastic idea if the movie turned out to be as terrific as it looked. Teachers in my professional learning community at school were intrigued with the idea and interested in working on it, and the school administrators, the school Site Council, the Equity and Climate and Culture Committees, and every other teacher who heard about it were positive and supportive.

As more previews were posted and early rave reviews came out in the media and from STEM educators, I got more and more eager to have my students see this story of courage and accomplishment. I made my screensaver into the picture of Dorothy Vaughan (Octavia Spencer) and her coworkers marching down the hall, posted about it on Twitter, and got an "I LOVE THIS!!" retweet from one of the actors in the picture (fun!!). The week Hidden Figures came out in local theaters, I showed all my math classes previews and a brief clip of the real mathematician Katherine Johnson (now 98) and told them about my own excitement. One African-American girl had seen it before the regular release date, and had watched the previews enough that she was mouthing along to all the words... about women doing math and engineering! A Black mom of another girl later told me the family went to see the movie and thanked me, saying, "I think it’s great that she’s being exposed to careers that require a good math knowledge." Several Black and multiracial girls told me about doing their Social Studies current event assignments on the real-life figures from the movie. White students and boys also went to see it and told me how much they loved it. After a snow-related delay, I finally saw it myself with my own teenage son and we both found it incredibly moving and thought-provoking (and the whole, full theater cheered at the end). As I had expected to be, I was struck by the main characters' heroism as individuals, but I was also impressed with how well the movie showed teamwork and support, how accurately it portrayed math as problem solving, and by the complicated story line about Dorothy Vaughan promoting her whole group's skills and successes and anticipating how the IBM computer would change their workplace.

It was around this point that my enthusiasm for a whole-school field trip moved to determination, especially when our principal went to see Hidden Figures and became one of the strongest proponents of a whole-school field trip, and when our school counselor encouraged me to follow through with planning and generously shared materials, tips, and work from her experience on similar trips. The whole thing took a ton of planning and support: honestly, I might have hesitated more if I had realized how much I was asking from our secretaries and counselor, especially. But I could not have asked for a more positive, can-do attitude from the whole community, and it made the whole thing stay fun and inspiring. Just about the entire staff worked on organizing permission forms and payments and sponsorships, even the school nurse, who wouldn't even be at our site that day. For our professional learning community (PLC) one afternoon, a dance teacher, a social studies teacher, the principal and I had one of my favorite school meetings ever, as we brainstormed about curriculum for teachers to use the afternoon of the movie viewing. Staff, students, and parents thanked me so many times for leading this effort that I lost count, and it was so encouraging to know they were happy about it. Even the National Council of Teachers of Mathematics president, Matt Larson, was talking about Hidden Figures on his NCTM blog the same week as our trip!

The day of the trip, I was a little edgy as our large crowd walked to the theater, wondering how it would go, but the kids were in excellent spirits and great fun, and I don't think I heard any complaints on the 3/4 mile walk, even though it rained all the way (our native Portlanders were completely unphased by that). We actually split across two theaters, and it was pretty awe-inspiring to see how many people were there in each. I loved seeing the movie just as much the second time. The kids seemed totally absorbed during the movie, though in our theater they were quieter and more solemn than I expected (except with Octavia Spencer's line to the white supervisor, "I'm sure you believe that."... that got a vocal reaction!). I was delighted and a little relieved when they clapped as the credits rolled. It seemed fitting that the sun unexpectedly came out for our walk back. Everybody seemed happy to have this experience together and I heard such a positive response to the movie from those who had seen it for the first time, both students and adults.

After lunch, we split up into our sixth period classes, and using our PLC's discussion guide which was a lot like this one (in which I edited out a few questions that originated elsewhere), we talked through these questions:

• What did you think of the movie? Did you enjoy it? 
• What questions or feelings did it leave you with?
• Why do you think we spent school time seeing this movie?
• What does the term “Hidden Figures” refer to?
• In the movie, we saw many times characters were treated unfairly because they were Black. Which three examples stood out most to you?
• What character attributes and/or actions did you admire most about Katherine Johnson (the mathematician), Dorothy Vaughan (the manager who taught herself how to program the computer), and/or Mary Jackson (the engineer)? [I also ended up asking them which was their favorite; as I expected, Mary, played by the glamorous and fun Janelle Monáe, was in the lead, but I was surprised that at least a third of them picked serious, ultra-competent Dorothy Vaughan.]
• In the film, Space Task group director Al Harrison (Kevin Costner) was depicted as a heroic breaker of boundaries when he smashed down the “Colored Women” restroom sign. Unlike many of the dramatic moments in the movie, this incident was entirely made up. In real life, Katherine Johnson herself chose to use the restroom white women used. Why do you think the screenwriter and filmmakers added this incident? Do you think adding this incident improved the movie? Why or why not?
• What was most striking to you about how men treated women in this movie, and how women treated each other? What aspects of how women were treated do you think seem similar to our times, and what seemed different?

Just two hours before spring break, almost all of my sixth grade class members were intent on considering weighty questions and issues about history and justice and racism and sexism. One girl wondered, "Why were these women 'hidden'? Why didn't we all know this history?" These eleven- and twelve-year-old students were so insightful, intelligent, and empathetic that I couldn't possibly do justice to the whole discussion here. I was so incredibly proud of them. I did write down their answers to the question, "What examples of characters being treated unfairly because they were Black stood out to you?" so you can get an idea of how observant and thoughtful they were. This list was generated not just by a few kids, but from a majority of kids in the room:

• Dorothy Vaughan and her kids were chased out of the library by the security guard (and she pays taxes for libraries!).
• Katherine Johnson's coworkers set up a "Colored" coffee pot for her... and it was empty.
• The bathrooms and drinking fountains were segregated, and the courthouse and bus had "colored seats in back." Separate was NOT equal: the things labeled "colored" were dirtier and cheaper. White people acted like this segregation was right, using words like "your kind". 
• Mary Jackson couldn't access the class she needed to because of the segregated night school.
• Katherine Johnson's new coworkers assumed she was the custodian.
• Paul Stafford kept telling Katherine Johnson that computers can't be authors of technical papers. [Actually, I think the way she was restricted to being a computer was more about her being a woman, but it wasn't completely clear.]
• Mrs. Mitchell claimed to Dorothy Vaughan that "I don't have anything against you all," which was obviously false (and even the way she talked about black women as if they weren't people like her was insulting).
• Dorothy Vaughan was doing a supervisor's work, but without the credit or pay.
• When the police officer approached the women by their broken-down car, he assumed they were doing something wrong, and they were scared of what he would do.

We had been afraid that the hour would drag by as we teachers tried to convince kids to have a serious conversation when their minds would be on the Talent Show that followed it and, of course, on the start of spring break right after the show. Instead, we had a fascinating and vigorous discussion that I was sorry to cut short. Kids even asked if we could continue it the Monday after spring break!

I went to the Talent Show full of fondness for my own class around me, the wonderful performers who included my present and past students, and the adults that support them in their arts and in their studies. Da Vinci teachers regularly go so far beyond classroom teaching. Our drama, dance, visual arts, music, and writing teachers do incredible work to bring our students' art to the wider community and bring professionals to the students; a math teacher is one of the Talent Show organizers and a mentor to the student rock band; a language arts teacher organizes a yearly trip to the Oregon Shakespeare Festival in southern Oregon; our science teachers have kids work on community projects; our social studies teachers have them engage with the broader world as citizens in so many ways; our librarian just spent many lunchtimes and a Saturday with kids doing Oregon Battle of the the Books; the list just goes on and on. I volunteer to assist with some of these events, but usually I feel like my community contributions are limited to my classroom role and General Adult Help. It was inspirational to have my own idea and to be supported and given the freedom to carry it through, which was an experience that makes me appreciate my school and its administration and staff even more. And although it's nothing new for me to get resources and ideas from my online math teacher community, this was yet another time that they helped me create something better than I ever could have on my own.

I was already elated with the entire day, but it got even better when the assistant principal thanked me from stage during the Talent Show for organizing it, and the whole school cheered — what an incredible feeling! From what I heard from teachers at lunch and after school, they also loved the whole event, both the movie and the discussion afterwards in their classrooms. As if all that weren't enough, one of those teachers sent the most amazing email the next day to me and the counselor and the secretaries. Here's the part that brought tears to my eyes: "Of everything I've been involved in at dV, this was the most rewarding and was true community building from the heart. [...] Overall, what amazing kiddos we have!! Thank you guys again.....it was so meaningful."

So I started spring break with a full heart, in the best way. It felt good to contribute to community building, good to do a little bit to move society forward, and absolutely fantastic to have 389 kids see this movie and love it. I am so proud of our kids and our community, and grateful to Hidden Figures that we are all more educated on this story than we were last year. What will happen next with our community discourse on race, gender, workplaces, schools, justice, film, math, science, technology, engineering, heck, the whole world? I don't know, but I can't wait to see where we go.

Task Makeover

We've all been there... you find a task that seems awesome. You start reading it and you get excited. There are so many different strategies that can be tried. There's a visual and algebraic aspect to it and a chance to try specific examples, make generalizations and predictions, test them, and build and justify a model. You spend a bunch of time exploring the different paths you think students might take, how you're going to give them feedback and what you'll assess with this task, how it fits with the rest of your curriculum, how you'll structure individual work time, collaboration and class discussion, how you think the lesson will flow, and how much time you plan to give to each component. Mostly, you're excited because you think it will be engaging and fun for students and will also bring up really interesting and important math ideas and practices. You introduce the task in class, eyes aglow with that special teacher light reserved for days like this, rubbing your hands in anticipation for the awesomeness about to unfold.

Except that it doesn't. At all. Kids seem confused. Then, frustrated. Heads start to go down onto desks along with pencils. Silent think/work time becomes sad, frustrated time, then out-loud complaining time as you slowly realize that this task is bombing and how. The kids you'd especially hoped and planned to engage, the ones who only sometimes engage, are the first ones to go. You try to rally the troops, but it's a lost cause, and you end the class demoralized and humbled. X years into this thing and every day still has the potential for catastrophe and epic failing (you may or may not be exaggerating the dramatic nature of the experience, most kids probably shrugged their shoulders and went on with their lives, but it was a hard 30 minutes for me, dammit!)

Where do you go for solace and a sympathetic ear? To the Math Twitter-Blog-o-Sphere, of course!

That feeling when you spend hours planning an awesome investigation for students and they hate it... pic.twitter.com/0xg8yIPcrh

— Anna Blinstein (@Borschtwithanna) March 21, 2017

Thanks to the advice and thoughtful questions of all you fine folks, I was able to reflect on the task design and recognize that the sheer wordiness and immediate jumping into very abstract ideas was a huge turn-off for many students.

Students had been doing so well with open investigations that even though it had been a little while since we had done one, I had completely abandoned the normal structures that coax kids who are not super sold on this Math thing just yet to try things, engage, take guesses, get a foot in the door, and progress towards increasing abstraction and formality at their own pace.

Fortunately, I had another class the next day with which I had planned to try this task. Back to the drawing board.

I started with a story. It's my birthday, but I'm really, really obsessed with all things square. My entire party has a square theme. Of course, I demand a square cake and that all pieces served to guests are perfect squares too. I can have my own party and eat the entire square cake myself. I can be a bit more generous and have a party for 4 since I can cut the cake into 4 perfect square slices. I can be even more generous and throw a party for 7 by cutting the cake further. 

This was a natural segue to asking students what they noticed and wondered, which brought out all the key features of the problem that in the earlier version were laid out in many, many words. Namely - is it possible to throw a party of any size if the slices must be square (but don't need to be of equal size)?

Students immediately had gut reactions and strong opinions. Some were ready to look for patterns right away, but for most, an opening question of: can you make another arrangement that we don't already have on the board? sent them on their way. 

Students quickly determined that they could make 1, 4, 9, 16, 25, etc pieces and that they could always add three to the number of pieces by cutting one of them into 4 and add 8 to the number of pieces by cutting them into 9.

There was another breakthrough when a student presented a convincing case for 6 pieces (as well as 11) and others realized that they could always add 5 more pieces by putting another layer on the outside.

This was the class I'd been hoping and prepping for when I found this task. Engaged, arguing, changing their minds, kids working past the end of class and needing to figure this out. 

Take-aways for me? Don't assume that kids have graduated past scaffolds that help them get started and build up to abstraction. If you're going to take them away, be aware and think deeply about how to do that carefully and thoughtfully. It's hard to reclaim a class that's lost its confidence so pay attention to this part.

I went back to the first class and tried again. With the reformulated question, things went much better. One of the students who had struggled the most the first day came up with a great organizational chart (that she said was inspired by Pascal's triangle) for tracking possible party sizes. 

She did have to amend it when another student came up with the 6 and 11 square versions since her version only assumed you could have perfect squares and add either 3 or 8.

Next step for both classes - helping them transform the patterns and ideas they have into more formal written explanations and justifications.

More ideas on working with students who really, really don't like mathematical exploration

As I've blogged before, the area in which our program has perhaps received the most criticism is in the challenge that open tasks, labs, mathematical explorations, and group problem solving pose for students who crave a more structured, algorithmic, and predictable approach. I met with a student (new to me this semester) last week who told me that she was incredibly frustrated with her current Math class (I am the teacher) because in her prior Math class, homework was 1 through whatever odd and both homework and quizzes were repeat versions of what the teacher had shown students in class. She had found this prior class soothing and comfortable and was an excellent student in this environment, whereas now, she felt that every facet of class was constantly asking her to figure out problems she hadn't seen before and she never knew if she really understood or felt like she was on solid, comfortable ground. She was worried that her confidence was slipping and that she wasn't learning as well as she had in the more traditional environment.

My initial internal reaction was to try to convince her that my pedagogy was sound, that it would indeed be better for her long term to struggle and make sense of novel situations, apply and stretch herself, learn how to tinker and problem solve rather than regurgitate algorithms repeatedly, but I felt that this would be minimizing her experience and negating her sense of her learning and mathematical identity. She had clearly stated that things make sense to her after she is given a method and does a lot of similar problems - only then does she believe that she is able to generalize and form an underlying concept. This isn't how our program is designed and I absolutely believe that it is better for most students to experiment and play first, forming conjectures and identifying patterns before coming to or seeing more formal methods (if needed), but maybe it's not better for her. At the very least, if she is convinced that this is the wrong way for her to learn, then it will be very difficult for her to interpret her experience otherwise, thus creating a self-perpetuating cycle. 

So I'm trying something new, and I'm not sure how well it's going to work. Every week, I'm going to email her a list of concepts that we will be working on next week, along with resources either in the textbook or online for her to see these concepts explained and practice problems for her to work on. A preview, if you will. Class will then not be a time for her to explore and invent, like it is for other students, but a time for her to generalize and prove the patterns that have already been revealed and practiced. In exchange, she has agreed that in a few weeks, she will again try exploring a new topic and be open to coaching by me in order to also get better at this way of learning. 

I'm hoping that by engaging in good faith, I am able to bridge the divide in expectations and meet this student at her current level of need and that she is able to grow over time in the mathematical habits of mind that I believe are just as important as, if not more than, content knowledge. It is certainly possible that she will continue preferring doing math in predictable and routine ways, following a pattern shown to her by someone else, on mathematical autopilot. I really hope that I can convince her that she can be successful and that it's worthwhile to engage in math in a different way than she has in the past. But it's okay if that's not where she is right now. I have a whole semester to build a relationship of trust and forment and celebrate moments of mathematical success for her.

Have you had students who actively and eloquently resisted your view of math or ways of teaching? What are some ways that you've made progress over time in their willingness to go there with you? Are there students who never changed their minds? Any and all advice welcome, as always :)

#DITL Friday, February 10th, 2017 Homecoming!

{It's Homecoming Week! I'm the student council sponsor and I have the smallest group ever with only 11 students. We are responsible for decorating the stage for the coronation, organizing the actual ceremony, dress up days, Spirit Assembly and games, and Homecoming Dance}


6:00 Wake up and began my busiest and longest day of the year.

1st Hour: I walk in and a sub is in my room. I have never had a sub on this day ever. I almost can't believe it. Basically I lucked out that no one was absent and they had to send our permanent sub somewhere. I had nothing planned but students just finished a handout that they started the day before. I am off to the gym for Homecoming rehearsal. We lift down a stair case and two platforms from the stage to the floor, set up giant cardboard pumpkins and glass slippers {can you guess our theme?}, turn on blue lights, and start organizing the 26 students involved in the coronation ceremony. Lights out, mics on, spotlight shining, and....go!

2nd Hour: I go check on students in the home ec room who are making jello and pudding for the Spirit Assembly games. We have some missing pans so I go out to my car and find them. We wrap up the first run through. Adjust and start over. We have to finish by 10:00 because we have a fire drill which they were already nice enough to move back from 9:00. At the end of this second time we have to put every thing back up and clear the gym.

3rd Hour: Fire drill. We come back inside and send students to class. We tried a new idea of a meme contest but I never figured out how to pick a winner and didn't even have them turned in until Thursday afternoon. I brainstorm with principal and he decides I should hang them in the lobby and have middle school students vote. I proceed to tape them up and individually visit each middle school classroom to ask for their votes. Back to the principal's office to brainstorm the cafeteria set up for the dance tonight.

4th Hour: Check on students in home ec room who are baking 8 dozen cupcakes and making pink lemonade for the dance tonight. I plan with students who are decorating for the dance on how and when to set things up since the concession stand for the two basketball games that happen before the Homecoming coronation and dance. I go round up the supplies: napkins, tablecloths, cups, lights, and deliver to home ec room. Back to principal's office to brainstorm how to set up a t-shirt table to raise money for Student Council.

5th Hour: He finds me an awesome cart so I go organize the shirts into piles by size, then make and print signs to hang in front of each pile. Ironically, the mom who has volunteered to help me sell them e-mails me and we hash out the time and plan for the night. Student Council also does a big fundraiser for Valentine's Day so all morning I've been tracking an order from Sam's Club for 300 carnations, hoping they will come in before lunch. After lunch I am booked every minute until midnight. I start getting supplies ready for the Spirit Assembly that starts immediately after lunch. {I already have 12,000 steps by this time.}

Lunch: On my way to get my lunch, the district secretary calls me to let me know the carnations just came in. She has volunteered to open them for me and get them organized into buckets with water and solution. I almost cry at this offer since I have zero minutes to spare. After I finish eating, the elementary school secretary catches me in the hallway- the florist is on the line saying that she gave the wrong order of flowers to my dad. While she stays on the line, I call my dad and send him back to the florist to get the Queen's rose bouquet. Lucky timing? I think not. Jesus has my back.

12:45 My student council meets to get our tubs of supplies and lay out a game plan for the assembly.

1:00-3:10 Let the games begin! During our assembly we play tug-of-war, 3-legged race, 4 corners, hungry hungry hippos, scavenger hunt, hunger games relay race, jell-o eating contest, inch worm race, chariot race, and 3-point shootout. While I am tallying the points, the cheerleaders getting ready for their dance. We announce the winning class- seniors- and hurry to get everything cleaned up before the bell rings.

3:15-4:15 Even though I need to get home and get ready to come back, I still have last minute jobs to finish. I have to proof 14 pages that my mistresses of  ceremonies will be reading and print out final copies. Print out pictures of the court. Deliver last minute dance supplies that I forgot earlier to the home ec room. Finally head home.

4:15-5:30 Go home to grab some food. Laminate the pictures of the court as last minute gifts. Curl my hair. Change my clothes. Sync my phone so that the cheerleader's dance song is on my phone so the girls can practice one last time. Back to school I go!

5:30-6:00 I'm back to school carrying my own Christmas lights to use for dance decorations as well as the Queen's bouquet. I go to the dressing room for the boys and girls. I lay out pictures, programs, and the engraved keychains we've ordered as gifts as long with the flowers each girl will carry. I need a box to put the rest of my programs in so I dump out a box from my cabinet and finally head down to the gym. I'm also the cheerleading coach and the game starts at 6:00. Luckily I walk in the gym and there is an extra 10 minutes on the clock. My girls are warmed up and ready to go.

6:00-8:45 I am now wearing my cheerleading coach hat and at halftimes and between JV and Varsity games, I am circulating to make sure no one needs anything and to check on my t-shirt selling volunteers. Between games I record my girls doing their Illinois loyalty dance. At halftime I record them doing their hip hop dance....and the crowd goes wild. We win 83-44! As soon as the games end, I switch back to my Student Council sponsor hat. My teacher bestie heads down to herd the cats while I open up the stage and the dads in the crowd help me lift down the steps and platform and so on. We get everything ready to go in about 12 minutes. Let's get this show on the road!

9:00 The ceremony begins. I stand by the mistresses of ceremonies during the coronation. At one point, I realize I've forgotten to take the crowns out of the display case. I literally run down the hallway to the lobby just to see that my teacher bestie already had everything under control.

9:45 The ceremony ends. As the crowd mingles, takes pictures, and celebrates, I rush to the cafeteria to get the dance started. My student have already plugged up the lights, poured balloons everywhere, and set up the food and snack table. I turn on the music and then head back to the gym to herd the cats toward the dance.

10:00-11:00 I hide in my little closet in the back of the cafeteria playing DJ on my laptop and iTunes while the 30ish kids who stayed are having a great time.

11:05 I hit the lights and start kicking people out, asking them to take cupcakes and pop balloons on the way out. We get the cafeteria cleaned up pretty quickly but then we have to put all 20 tables back. There are 4 student council kids left at this point and their boyfriends who help. Next we go back to the stage to pop all those balloons and unplug everything.

11:30 All the kids and the superintendent are gone. It's just me and the janitors. I push a cart of random leftover supplies back to my room. I have to print out blank bell ringer templates for my students because I can't be trusted to get to school early enough on Monday morning to do it.

11:45 I'm home. I am cleaning my makeup brushes while I cook chicken strips for a late night dinner.

12:00 I crash on the couch with my chicken strips and "This Is Us" playing. I chase that down with cookies and milk and fall asleep to the joy of having no alarm set.

I ended the day with 28,040 steps which is my personal best and is a total of 12.47 miles.

P.S. It took me an hour just to type all of this! And teachers everywhere know how many millions of tiny things I left out!

Digging Deep Wells

After my post about feeling basic, I got a lot of comments, tweets, and messages of others who are feeling the same. We are not alone! Thank you so much for your feedback and for always pushing me to dig deeper, even to write this follow up post.

I had a great conversation with a few of my longest Twitter teacher friends about this and they also encouraged me to narrow it down to something I can work on and actually change.

Tom had a great comment, especially for a super-logical-organized-planner-rule-follower like myself, which was to use the Charlotte Danielson rubric, which my school uses as an evaluation instrument, to pick some areas to work on. This is exactly what I need to give myself some focus.

As I read through the 4 domains, I was encouraged that I feel like I am rocking Domain 2 and my recent post-observation meeting confirmed that. She pointed how students came in and got their binders and start working, knew where supplies were and got them out when needed, discussed their work with each other without prompting, helped each other pick up stuff when a student dropped a drawer out of the cart, and that my procedures are in place. I thought those were things that came naturally....because they do come naturally...to me. Cue Annie's on point comment. It also follows with how I see I'm a great teacher but not a great mathematician. Domain 1 scares me and I'm floating on sea level in Domains 3 and 4 with plenty of room to grow.

I picked a few things that I thought were doable and I noticed an interesting pattern...

• The teacher’s plans demonstrate awareness of possible student misconceptions and how they can be addressed
• The teacher’s plans reference curricular frameworks or blueprints to ensure accurate sequencing. 
• The teacher connects outcomes to previous and future learning.
• Assessments provide opportunities for student choice.
• The teacher uses rich language, offering brief vocabulary lessons where appropriate, both for general vocabulary and for the discipline.
• Students have an opportunity for reflection and closure on the lesson to consolidate their understanding
• The teacher’s assessment of the lesson is thoughtful and includes specific indicators of effectiveness.
• The teacher seeks regular opportunities for continued professional development, including initiating action research.

These are all things I can create! I am a creator at heart. Now that my curriculum is aligned, I'd like to write some nice unit plans. 3 out of 8 on my list have to do with plans.

I have provided student choice on assessments by giving them 6 questions and asking them to choose 5. What other ways can I give student choice?

I included the one about rich vocabulary because I am bad about breaking things down so much that I don't used academic vocabulary like I should- a student pointed that out in our semester reflections and I know she is right.

I was including some reflection questions on quizzes and tests thanks to @pamjwilson's suggestion. I need to do this consistently. I also need to remind students about shading their colored circles in their INB table of contents.

Sadly I just completed my post-observation assessment but I love the idea of 'specific indicators of effectiveness'. I need to think about that for each lesson- what do I want to achieve and how will I know if I achieved it? I think that also ties back to plans.

But the last one got me really excited- action research! I learned about it and did it during my master's program but never used it since. Once again, it's something I can create. I don't even know what to do but it sounds fun!

I already feel like this post is rambling but this is me explaining my brain.

I think what makes me a good teacher is that I am very observant and I think very logically. I want to enhance those traits in my students. I think Number Talks and WODB are great tools for that so I am committing to reading Number Talks books and researching it in depth during this year and this summer.

I also think I ask good questions and while I get better at it every year, I'm definitely not asking those higher order questions like synthesizing and application.

Shelly @druinok brought up a good book we read a while ago and so I dug it out.

I'm also committing to reading these throughout this semester and this summer. My goal is to come up with one good question a week for the rest of the school year. It can be for any content area and it might come word for word from one of these books but that's okay. My plan as of now is to maybe just add a slide at the end of a lesson with a 'challenge' question for students to discuss and maybe something like it will also show up on the study guide or as a bonus question on a test. The idea of asking questions and adding one here and there doesn't overwhelm me- even though making them up does. I know I have to start before I can get good so this is my plan.

For those of you who commented on NBCT, I'm applying for funding in February even though it scares the crap out of me. My state no longer has stipends and no one at my school has ever done this so....there's really no financial reward for so I don't see myself pursuing it if I don't get funding from somewhere. Thank you for thinking I can do it!

While this post might seem all over the place, it's better than how I was feeling two weeks ago and it went a long way as far as 'underwhelming' me. Also, I'm giving myself nine months to read two books so that I don't feel rushed and give up.

Anyone have idea for an action project? Formative assessment? Questioning? Vocabulary?

Anyone want to do it with me? :) :) :) :) :)

Why might students be motivated in math class?

At the end of the first semester, as part of students' self-evaluations, I asked them to reflect on their habits of learning, including curiosity and passion, asking, "Do you do work just to get it done? Do you cultivate your mathematical strengths and interests? How motivated/passionate are you and how might you improve here?" I received some pretty interesting responses to this series of questions, many of which boiled down to: I've never been that interested in or motivated by math and I don't know where to start to develop this.

In my reflection on this reflection, I came up with four main categories from my experience that describe why students have been interested in or motivated to study and learn mathematics.

1. Patterns and beauty inherent in mathematical structures

Some students are intrigued by looking for, identifying, and explaining patterns; others enjoy the beauty inherent in visual representations of mathematical objects and relationships. These students appreciate a teacher who encourages and rewards their curiosity, but overall, require the least amount of effort on the teacher's part to motivate and support since they're often speaking the same language as the teacher already.

2. Applications between mathematics and the real world

Other students I have taught were less interested in math in and of itself, but did find the idea of math as a tool to understand, explain, and predict the real world motivating. These were often students with an existing interest in science or social science who saw the usefulness of math in their respective fields of interest. Interesting projects were obvious choices in hooking and motivating these students, as well as a greater emphasis on practice and application than on derivation or justification. 

3. Being a good student

   This third category of student is one that is invested in an image of themselves as a good student. They care about doing well and meeting their goals and are motivated by seeing their progress, exerting effort and seeing it pay off, as well as specific feedback on how to improve and clear objectives for the course. 

4. Relationships

   These students seem to be predominantly motivated by positive interactions with others, whether that's the teacher or their peers. Classroom structures that increase conversations and collaboration between students and that make students feel known and connected to others have been helpful in motivating this group in my experience, as well as putting more of an emphasis on my relationship with them. 

Obviously, most students are some mix of these categories, but for many in my experience, one is more dominant. I think that a classroom that tries to balance between these different student needs will likely result in broader student success than one that caters to only one type. I would love pushback on my preliminary and perhaps too simplified analysis. Are there any categories you see being useful for thinking about student motivation? What other tools and strategies have you used to help students foster their curiosity and interest about math and motivation to exert effort towards the class?

#DITL Tuesday, January 10th, 2017

6:00 Wake up and  get pretty.

7:42 Arrive at school and drop off my lunch in the home ec room so I won't have to walk all the way to the office. Head to my room to get my cooler and race to the cafeteria to fill it with ice and water. (Students aren't allowed to bring food or drinks so we provide water in our rooms.)

1st hour- We are finishing six problems on the right side of our INB about parallel and perpendicular slope. Students seem to be taking each problem in stride and doing well. Glad I already have the next activity prepared....although it takes the majority of the class period to finish those six problems. Now students get out dry erase markers to practice on the desk while we play a game of trashketball. Two problems later and the class is already over.

2nd hour- Students are finishing a handout from yesterday to prepare for a quiz over reciprocal functions. Everyone starts and finishes at different times and I wait for everyone to be finished before starting the next activity. We are making an almost-fortune-teller-cootie-catcher for our INB notes on quadrantal angles. Why does it take 8 upperclassmen 40 years to cut and fold a piece of paper? Even following my verbal directions, with the picture on the board, and my completed example, students still mess up and have to start over. Never give up teaching students to follow directions! We don't even have time to start writing in them before class ends. :(

3rd hour- Algebra I has a quiz today over finding intercepts and graphing horizontal and vertical lines. For practice, all I made was a boring worksheet of 12 problems. I remember an idea from someone's blog post about a buried treasure powerpoint game that I downloaded. Every slide has ships on them and students get to a click a ship to find the treasure. I tell students they get one click after I have checked each set of 4 problems. The winner gets a baby butterfinger. I spend the rest of the class period bouncing back and forth across the room to check answers- I don't even have time to print out an answer key. Students are HIGHLY engaged. As they finish, they start gathering around the board, waiting for the next person to click, in expectation of who might actually find the treasure. It's adorable. I stop the class and handout the quiz. I probably burned more calories traversing the room than I did all day.

4th hour- Almost scripted word for word...thanks for the dry run first hour. I have a class full of boys and basketball players who expect to be awesome at trashketball. It's a very humbling game. All students in each team have to agree on their answer so a lot of good discussion is happening. We also get done with only two problems. Crazy how consistent(ly slow) I can be.

5th hour- Students are finishing a quiz while I make an answer key for the study guide they are about to take. I cleaned out a binder last week that I thought I didn't need so there went a few answer keys. The last page I'm getting all wrong answers but students are starting the study guide and need my help while I'm feeling anxious about the last page. Luckily, nobody gets that far by the end of the class period.

Lunch- The bell rings at 12:10 which means I get down to my food around 12:15 and then have to be back in my classroom and ready to go by 12:30. The healthy lunch plans are  joke at our school and the teachers are having a fit over what is served while I eat the leftovers my mom saved for me. I've been trying to convince these people for two years to just bring their lunch every day...

6th hour-My rowdiest class is finishing the quadratic formula and are taking a quiz today. I put one problem on the board for them to review first. As I'm walking around, the levels range between not knowing the first step, not knowing which numbers are a. b. and c and students who finish the whole problem independently. After the quiz it's time to start the dreaded........word problems!!!!!! It takes forever for students to fold two pieces of paper in half and tape them in their notebook. I give a lecture about how these problems are hard, now is the time to focus, stop playing and distracting others....We finish one problem and class is over.

7th hour- My class of five is taking a quiz over simplifying rational expressions. We just finished trig identities so I feel like this is going to be a piece of cake. By the time we finish reviewing so that they feel prepared, there is only 15 minutes left of class. There are 6 problems and only 1 actually complete the quiz. To be continued. Literally.

8th hour- It's my plan period but I have to sub. I bring the class to my room since no plans were left and they play on chrome books and talk while I grade papers and get things ready to copy.

3:20 It's time for cheerleading practice. There is also an after school BETA club meeting to prepare for state competitions in March. Since my whole squad is in BETA club, we split up time between the two. I'm excited that I will get to go home early.

4:00 Practice is over and I have more papers to grade and copies to make so I don't have to take anything home.

5:15 I guess I won't be going home early...

6:00-10:00 I need to make an answer key but I messed up on it so many times already that I'm too tired and unmotivated to do it. I dread it all night and end up not doing it. I finished walking to get my 12,000+ steps in, I pack my school bag for the next day, and do some scripture journaling.

11:00 I decide to go to bed 'early.'

1) Teachers make a lot of decisions throughout the day. Sometimes we make so many it feels overwhelming. When you think about today, what is a decision/teacher move you made that you are proud of? What is one you are worried wasn’t ideal?

Every day I am worried that my pacing is so far from ideal but I balance in the tension between pacing and giving my students enough time to process and practice. When some students tell me I move too fast, I almost cry with frustration. I'm on unit 3 or 4 in every class with anywhere from 10-12 units on my pacing guide. I'm lucky to do 6 units all year long.

I am proud of how often I ask students to tell me what is different about each new problem and how often I ask them to explain why and how.

2) Every person’s life is full of highs and lows. Share with us some of what that is like for a teacher. What are you looking forward to? What has been a challenge for you lately? 

I'm looking forward to my three day weekend and my upcoming Unit Circle project in trig. Even though we've just had a two week Christmas Break I'm praying for a snow day on Friday so I can have a four day weekend.

A challenge for me lately has been trying to decide a focus for growth this year. I am feeling pretty basic and like I'm at the peak of my math abilities. I want to work on the things that have the most impact on student learning, but how do I decide what those are?

3) We are reminded constantly of how relational teaching is. As teachers we work to build relationships with our coworkers and students. Describe a relational moment you had with someone recently.

 I heard a girl in the hallway call another girl a fat b*****. A few minutes later she came to return my pencil and I pulled her aside and told her I heard her. I told her that as a female, we should never call other female's that word since so many men already do. She nodded and went in the room. That may not be my best response but it was off the top of my head. She walked out and said, "Ms. Miller I am really sorry." That was a moment we wouldn't normally have shared.

Overall, I am having some really funny and interesting conversations with almost every class on a regular basis. We have inside jokes and favorite memes and I just feel really open and close with the majority of the students.

4) Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What is a goal you have for the year?

Reread More Good Questions and work on questioning skills, make answers keys beforehand, continue my work life balance, and blog more often!

#MtbosBlogsplosion - My Favorites

Carl and Julie have kick-started a new blogging initiative, and the timing is perfect, as I'm trying to get myself blogging more often instead of waiting for An Amazing Inspiration. This week's theme is My Favorites, and I wanted to share a really helpful framing for peer editing created by my awesome colleague. We've been working on using peer feedback more productively this year, and her document (shared below) gives a good structure for students to reflect on and give feedback to their peers' write-ups and oh hey, they also learn a lot about what makes for a good write-up and use this understanding to do a better job themselves. Mandy has incorporated a peer feedback step for all write-ups, with that night's assignment for students to revise their own work. I would love to do more structured peer feedback in other components of the class, such as homework assignments, note-taking, and studying for assessments. The setup is very basic - students exchange papers, give each other feedback, get their peer's feedback back, and turn it in with their revised write-up, documenting any revisions that they made.



Here's my first draft for a homework feedback form. Would love any feedback and suggestions for improvement.

Goals for second semester

As I've been wrapping up grading from semester 1 and planning semester 2 for my classes, I'm realizing that I did not set goals at the start of this year the way that I have in the past. Better late than never!

Changes for my personal teaching:

• Get back to individual feedback meetings. I blogged about them here, but the general idea is that I set aside 20 or so minutes to meet with each student approximately every two weeks in order to sit down together and look over their work and have a feedback conversation. I've found these incredibly helpful for students to actually attend to my feedback, understand what I mean and why I think it's important, and explain their thinking to me. This year has been very tricky since the schedule was changed and students lost a floating free period that I used to be able to use for these meetings. I am recommitting to instituting them again, using class time, if needed. It's been the best way for me to get through grading big projects in a timely manner since it's actually fun and rewarding to sit and discuss students' work with them rather than grading on my own after a long day (since, let's face it, grading gets put off and off).
• Be more on top of students who are struggling. I am committing to looking at work that is turned in every week to check up on students who are missing work or need additional support. If anyone has a good system for keeping track of interactions/observations/progress for all students and how they make sure that no one is falling through the cracks, I'd love to chat.
• More nuanced and thoughtful reflection questions - I think that the balance of reflection vs. doing math has been better this year, but I'd like to focus the questions I ask students in order to hone in on specific mathematical practices rather than just general "what's going well? what do you need to work on?" type questions. I also want to bring back, "what's one good thing that happened this week?" - it was a great way to regularly check in and connect with students.
• Collaboration quizzes to give more direct feedback to students on their groupwork and engagement and help them internalize expectations more effectively.
• More peer feedback. I've started doing this more this year, and love how much motivation it creates for students to express themselves more clearly and justify their thinking. I'm hoping to use peer feedback this semester to help students get better at analyzing strategy, getting positive feedback for extensions they create, and to deepen their understanding of different approaches. One of the lesson study groups worked on peer feedback last semester and I'm really excited to learn from them. I would also like to use a Slack channel for classes so that students can discuss and share ideas outside of class more easily.
• Better differentiation. I'd like to meet with students to set individual goals and do more follow up to help them stay on track with these. I think that there's already a fair amount of choice in problem sets and homework assignments, but I'd like to do a better job of teaching students how to use those choices better. One way will be to have them reflect at the end of class on the type of work they need to do to follow up on that day's learning (review of prior concepts, practice, connections, and/or reach problems). I know that they are learning project management skills in their other classes, but in Math, the product is the process, which is more abstract and harder for them to track and plan. 
• Continue and get better at classroom routines that foster reflection and a clear arc from start to finish. 
• I have often used Desmos Activity Builder to start and end class, but would like to do this more consistently and help students get better at constructing meaning from problem-based lessons by selecting useful reflections and comments to share. I still have work to do on making sure that meaning and connection emerges from students' own thinking and not ignoring times when they don't emerge or simply telling students what they should have learned. One way is to do more planning of student responses and how to connect these and have the main ideas of the lesson emerge from them, sharing methods and responses that did not emerge as part of that process. 
• This also connects to better note-taking. I have given feedback to students once or twice on their note-taking and organization and definitely need to do this again. I haven't really figured out a solution for sharing board work and "notes" from class since I've emphasized process and individual needs. I do share presentations, if they were used, but those generally do not contain worked solutions. If anyone has good ideas on this, I'm all ears. 
• I would also like to do this on a unit-level rather than just lesson-by-lesson by using student-generated essential questions, concept maps, and study-guides more this semester. There is still a fair amount of tension between student-generated conclusions/connections and teacher-generated ones that are more "efficient" and feel more comfortable and structured for students, especially if they're oriented towards maximizing content acquisition. I am working to help students get better at this and at understanding why I think that it's important, both of which are necessary to get more buy-in for the process and rewards that actualize when students do more of this work. One way is to be more transparent about the structures that I'm using and why - I observed a teacher recently giving an intro to a lesson by explaining the groupwork structure that he would be using and what he hoped it would achieve, and I think that enlisting students as teammates in this process is hugely beneficial. 
• Continue the following changes I implemented last year:
• Each assessment includes reassessment of previous content
• Visibly Random Groupings (new groups daily) and whiteboarding
• Homework that's spiraled and includes Retention, Review, Reflect, and Reach sections; students self-select problems to do (should sometimes group students by homework problems completed the next day though)
• Students submit all work digitally, all feedback is recorded digitally in one place (online gradebook)

Big Picture Curriculum:

• Decide on mathematical practices and habits that should be emphasized within a given year/semester/unit and link them to specific lessons and activities. I've been doing a much better job this year of giving students regular feedback on these, but haven't been very intentional about which habits will be emphasized when, noticing which ones students are making progress on and which ones need more work, and how (besides getting feedback) they might get better at them.
• Create more opportunities for interdisciplinary connections. I've put out some feelers to Science teachers and will do the same for Computer Science, English, and History to see where we can join forces and create projects that can support and enrich both disciplines.
• Formulate a more cohesive picture of our curriculum and mission so that our core sequence is less content-driven and so that we can explain to students and families why acceleration is not necessary or desirable. This will require a reducing/reworking of our acceleration pathways, enriching/differentiating core classes, and deciding how electives should support the overall program. 
• Start developing a portfolio assessment for one Math course. It might not be ready to go this semester, but if I can pilot a beta version in one class, I can work on tweaking/developing it more over the summer so that it's ready to go in more classes next year.
• Work on developing group assessments (and other differentiated assessments) for at least one unit in each class.

Professional Development:

• Continue lesson study this semester and figure out good systems for sharing the results that each group has found, both within the discipline team and with the school community more broadly. Possibly help other disciplines/divisions begin the lesson study process. Think about presenting about lesson study next year and the types of resources and supports teachers would need to get started with this.
• Figure out what I want to work on over the summer. Major contenders currently are:
• Attending PCMI
• Teaching at summer institutes for teachers
• Start compiling our existing curriculum into a more easily shared and edited form for students, families, and teachers
• Curriculum development for my school, focusing on alignment between courses, portfolio assessment, projects that connect to other disciplines and class trips, parent education, and developing new electives
• Summer math support for students who are doing independent work or working more directly on accelerating/remediating/enriching
• Coordinating with the middle school on curriculum, parent education, and development of mathematical practices