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!