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