I just finished the first two weeks of school, and I have had more fun with this beginning than any I can remember. Last year, I was too busy trying to figure out how teaching worked again, but this year, I am again comfortable with what I am doing. (But not complacent!) I've had the chance to collaborate with other teachers, and I have learned the names of all 100+ of my students. All of my classes are fun; the students are pretty engaged (even after a rough quiz or two); and I'm happy with the climate for learning we are building.

I don't know too much about the students beyond their names, yet. Some are really engaged, and vocal about their excitement. One student blurted out in the middle of class, "This is really fun!". Many others dive into the problems and seek out suggestions from classmates. I am really thankful for their energy, enthusiasm, and willingness to engage with others they may have just met. There are also a handful of kids who appear to be having some sort of difficulty, and others who have not said much at all. I will need to spend next week attempting to reach out to them, so they don't get lost.

I'm looking forward to learning more about my students, and helping them see why I think math is fun, beautiful, and power. (Yes, the noun is purposeful; more on that later.)

## Friday, September 4, 2015

## Sunday, August 23, 2015

### First Day of School!

I get so excited at this time of year, I can hardly sleep! This is the same feeling I used to have as a kid on Christmas Eve, anticipating the family visits, the food, and, of course, the presents. Although there are no actual presents or special dinner tomorrow, the first day of school never gets old for me, despite the fact that I've had over 25 first school days as a teacher. My wife tells me my inner teaching geek is showing, but I can't help wondering who my students are this year and thinking up ways to help them learn (and maybe even get excited about) math.

If you are reading this because you are one of my students, Welcome! This is going to be a great year! I really believe that you can get better at math this year, and most of my job is helping you be the best person, student, and mathematician that you can be.

If you are the parent or guardian of one of my students, know that I feel blessed to have the chance to know your child. I know that as a core class, math is really important, and I will do my best to help each of my students succeed. If you ever have a question, concern, or suggestion, please call or email me.

See you tomorrow!

If you are reading this because you are one of my students, Welcome! This is going to be a great year! I really believe that you can get better at math this year, and most of my job is helping you be the best person, student, and mathematician that you can be.

If you are the parent or guardian of one of my students, know that I feel blessed to have the chance to know your child. I know that as a core class, math is really important, and I will do my best to help each of my students succeed. If you ever have a question, concern, or suggestion, please call or email me.

See you tomorrow!

## Friday, August 14, 2015

### What Am I Grading? (Part 3)

After talking to a colleague about my grading policy, I found that she has a similar grading policy, but states the weights of the categories a little differently. Rather than 75% tests, she states that the homework and quiz grades together count as a test grade. This works the same as my system, but her students seemed to respond more positively to the system. (Am I giving away too much to my students by telling this?)

We also talked about how to cue students to important problems in the homework, and how to give students choice about which homework problems to focus on. Additionally, we brainstormed ideas about how to have students practice writing about their thinking, and how we might provide feedback (not necessarily a grade) to this work. Lots of ideas, but I am not yet sure which I will incorporate into my classes. It was really exciting, thought-provoking, and satisfying to talk to another teacher about our work. (Thanks, Cory!) I think I was missing that last year.

Finally, I saw a really short article today, "Is grading killing learning for our students?" which raises issues about grading and learning that I continue to worry about. In particular, how do I create (or balance?) a culture of learning and a culture of performance?

As this year starts, I want to work on few things regarding grading:

We also talked about how to cue students to important problems in the homework, and how to give students choice about which homework problems to focus on. Additionally, we brainstormed ideas about how to have students practice writing about their thinking, and how we might provide feedback (not necessarily a grade) to this work. Lots of ideas, but I am not yet sure which I will incorporate into my classes. It was really exciting, thought-provoking, and satisfying to talk to another teacher about our work. (Thanks, Cory!) I think I was missing that last year.

Finally, I saw a really short article today, "Is grading killing learning for our students?" which raises issues about grading and learning that I continue to worry about. In particular, how do I create (or balance?) a culture of learning and a culture of performance?

As this year starts, I want to work on few things regarding grading:

- providing growth mindset messages to my students
- providing helpful and actionable feedback (not necessarily a grade) to my students about their work (balancing learning and performance)
- making sure my expectations for good work are clear.

I'll have to revisit my thinking as this year goes along.

## Wednesday, August 5, 2015

### What Am I Grading? (Part 2)

At the end of last year, I talked to another teacher about the "standards-based" grading policy. For this, students are given a list of the things they are expected to know and be able to do by the end of the unit, and instead of putting a grade on a quiz or test, the teacher gives them a score for each standard, which gets translated into a letter grade by the end of the quarter. This is intriguing to me because I want the students to focus on the skills and understandings of math rather than on the grades. I also tried this method of grading a number of years ago (almost ten years, I think), but the system seemed more confusing to students since they were not entirely sure how their grade was calculated. (I also don't recall how I made this calculation.) Now that we have an online grading program, parents and students can track their grades on a daily basis, and I'm really not sure how to make the calculations or how to make the calculations clear to the users.

Having some system through which it is clear to students (and parents) how well they are understanding the topics is important to me, so I am thinking about how to include aspects of standards-based grading into my classes.

One thing I tried over the summer, and plan to continue this year, is having a unit outline of four to six big ideas I would like the students to learn over the course of the unit. I'm hoping to keep the number of these to four "skills" like "identify the important features (domain, range, vertex) of quadratic functions based on their graphs and equations", and one or two practices like "construct clear critiques of possible solutions". I'm figuring that the practices will appear across multiple units, but the skills belong in only one unit. The idea here is to alert the students to the important information I want them to learn, to provide me with reminders about what understanding I want to check (via exit slips, short ungraded quizzes), and to cue students to self-assess their understanding. So I'm creating a set of "sample problems" to go with each big idea, and providing space for students to monitor their understanding over the course of the unit. I'll still give graded quizzes (and allow retakes) and a graded unit test.

Having some system through which it is clear to students (and parents) how well they are understanding the topics is important to me, so I am thinking about how to include aspects of standards-based grading into my classes.

One thing I tried over the summer, and plan to continue this year, is having a unit outline of four to six big ideas I would like the students to learn over the course of the unit. I'm hoping to keep the number of these to four "skills" like "identify the important features (domain, range, vertex) of quadratic functions based on their graphs and equations", and one or two practices like "construct clear critiques of possible solutions". I'm figuring that the practices will appear across multiple units, but the skills belong in only one unit. The idea here is to alert the students to the important information I want them to learn, to provide me with reminders about what understanding I want to check (via exit slips, short ungraded quizzes), and to cue students to self-assess their understanding. So I'm creating a set of "sample problems" to go with each big idea, and providing space for students to monitor their understanding over the course of the unit. I'll still give graded quizzes (and allow retakes) and a graded unit test.

## Monday, August 3, 2015

### What Am I Grading?

As the summer is starting to wind down, and I have two weeks before the staff meetings start up, I am thinking about how I structure the grading systems of my classes. Lately, I have been dividing up quarter grades based on the following weights: homework is 10%, quizzes are 15%, and tests are 75% of the quarter grade. I don't penalize students for late homework, although I pester students who are not turning it in on the due date. I also allow students to retake quizzes once they have corrected the original quiz and reviewed the material with me, and I only count the higher grade. Finally, the last test of each quarter covers all the material from the quarter, and if a student gets a higher grade on this test than on a test from earlier in the quarter, this test grade also replaces that earlier, worse test grade. My intent for this system is to try to assign grades based on a student's understanding of the material over the long term rather than his/her ability to turn in homework on time, to cram (or not) for a test, or to quickly perform well with new material versus needing time to practice. (I don't think catching on quickly to new material and keeping oneself organized should be the criteria for getting an "A".)

The positive outcomes from this grading policy include:

The positive outcomes from this grading policy include:

- more homework is getting done
- fewer students report copying homework from classmates
- more students spend time reviewing quizzes
- more students reporting that they understand the material better.

The negative outcomes from this grading policy include:

- students report feeling stressed about tests since they are weighted so heavily
- the students who perform the worst on the quizzes were not taking advantage of the retakes
- the students who turned in the least amount of homework by the due date were least likely to turn in assignments at all or appeared to spend very little time on assignments they did make up
- some students seemed more concerned about making up homework (without really trying to learn the material) than about retaking quizzes, and expected their grades to improve more than they really would given the relative weights.
- most of the students described in the last three bullet points were Black or Hispanic.

I should note that on the end of the year surveys last year, only two students said the homework policy encouraged them to procrastinate and the quiz policy encouraged them to not study for the quizzes.

I'm happy about the positives; I think the policy matches the growth mindset I try to maintain for myself and engender in the students. The negatives concern me in that I don't think they are a direct result of the grading policy, but probably have more to do with the way I sell the students on growth mindset and how I talk to, work with, and connect to the students of color in my classes.

More reflecting to come ...

## Friday, July 24, 2015

### There and Back Again

Last week, I saw this blog post from Pernille Ripp about the apparent divide between teachers and administrators, and it got me thinking about my journey from teacher to department chair and back to teacher. Pernille talks about the need for trust, and I completely agree with that need, but I also think the divide is a result of differences in perspective. I know mine has changed quite a bit in the last few years.

As a “pre-department chair” high school math teacher, I had anywhere from 80 to 140 kids in my classes, depending on what I was teaching. I had to answer to the students, their parents, my department chair, and teachers with whom I was collaborating. My responsibilities included creating lessons to meet the needs of my kids (each and every one of them), providing them with encouragement, feedback, coaching, and occasionally discipline, and working on unit plans and curricula with teachers on my team. I sometimes questioned the administrators’ decisions, as they did not make sense from where I was standing. My perspective was necessarily narrow based on my experience and “sphere of influence.”

When I became the department chair, I no longer taught any classes, but met with lots of different students on a daily basis and had to answer to and work with students, parents, teachers, counselors, the principal and other administrators, the math coordinators at the public and private middle schools, and the other department chairs in my building. I had primary responsibility for hiring, evaluating, and developing the teachers in my department, placement of incoming students, course changes for current students, department course curriculum, scheduling and budgets. I had to address complaints and compliments about teachers from all the players (including other teachers), and adjudicate a few cheating and disciplinary situations. My sphere of influence was much bigger as a department chair than it was when I was a teacher, and my perspective had to change to accommodate all the new information. I couldn’t make decisions based on a narrow focus.

I enjoyed being the department chair, and I think I did a pretty good job of it. The hard part for me was that I continued to see myself as a teacher, and felt I was losing the ability to focus on the things that have kept me in the profession for over 25 years: my relationships with the students and the joy of sharing my content area. So I went back to the classroom.

And now, as a “post-department-chair” teacher, my perspective has again changed. In some ways, I had to relearn how to use my classroom lens this past year, to keep a tight focus on my students and let go of some of the “administrator worries” I had developed. But knowing that wider perspective has helped me fine-tune my classroom perspective. For example, having seen more examples of teaching as I observed classrooms has helped me better understand the rubric on which I am now evaluated, and how my actions as a teacher affect the students. (We’ll see how much this helps as I go through the observation and evaluation process this coming year.)

Trust is important, and I have had to work to build it as a teacher and as an administrator with a variety of people. Part of that trust is recognizing that my perspective will be different from my colleagues’ and different from our administrators’. Walking the administrator path for a while has taught me again the importance of walking in someone else’s shoes for a while. I’m glad I went there, and I’m glad to be back again.

## Tuesday, June 9, 2015

### End of the year reflection

Another school year just ended, and I thought I would take a few minutes to reflect on how it went ...

First, I'm glad I made it through. Being back in the classroom after three years out was a lot harder than I thought it was, but as the second semester went on, I started to feel more like my old self.

Second, while I don't really regret anything I did, there are a number of things I will do differently next year. (See my last post ...) I also want to do a better job of catching and supporting kids who are running into trouble with the material. I missed some important clues at the beginning of the year, and did not intervene as I should have.

Although some things could have been better, I am proud of a few things as well. The end of year surveys indicated I did a good job of building a positive classroom climate. Most students really appreciated my homework policy (no late penalties) and indicated that they completed at least as much if not more homework than they would have if there were late penalties, and learned more as well. Most also said that they would not copy, or were less inclined to copy homework. I am also proud of my students and the work they did. While not everyone did as well as they wanted grade-wise, they were all excellent, exciting, and engaging human beings, and if I had some small part in helping them keep moving in that direction, then I have done good work.

Finally, I have several plans for next year. First, I want to be more aware of and make better connections with my students, especially those who are struggling, early on in the school year. I will make the time to call home and introduce myself to parents and family members within the first two weeks. Also, this summer, I am working on integrating the Chromebooks into my lessons, and I hope in the fall to be able to create some online self-checks for students using Google Forms. We'll see how that goes. I also want to experiment with "standards-based" grading; more on that some other time ...

That's about it for now. Summer School starts tomorrow, and I need to get ready! I'm looking forward to meeting more new students!

First, I'm glad I made it through. Being back in the classroom after three years out was a lot harder than I thought it was, but as the second semester went on, I started to feel more like my old self.

Second, while I don't really regret anything I did, there are a number of things I will do differently next year. (See my last post ...) I also want to do a better job of catching and supporting kids who are running into trouble with the material. I missed some important clues at the beginning of the year, and did not intervene as I should have.

Although some things could have been better, I am proud of a few things as well. The end of year surveys indicated I did a good job of building a positive classroom climate. Most students really appreciated my homework policy (no late penalties) and indicated that they completed at least as much if not more homework than they would have if there were late penalties, and learned more as well. Most also said that they would not copy, or were less inclined to copy homework. I am also proud of my students and the work they did. While not everyone did as well as they wanted grade-wise, they were all excellent, exciting, and engaging human beings, and if I had some small part in helping them keep moving in that direction, then I have done good work.

Finally, I have several plans for next year. First, I want to be more aware of and make better connections with my students, especially those who are struggling, early on in the school year. I will make the time to call home and introduce myself to parents and family members within the first two weeks. Also, this summer, I am working on integrating the Chromebooks into my lessons, and I hope in the fall to be able to create some online self-checks for students using Google Forms. We'll see how that goes. I also want to experiment with "standards-based" grading; more on that some other time ...

That's about it for now. Summer School starts tomorrow, and I need to get ready! I'm looking forward to meeting more new students!

## Saturday, April 11, 2015

### Doing It Wrong ...

Just before Spring Break, we were finishing up a unit on sequences and series in my pre-calculus classes, and I started thinking about review problems. I thought about the Handshake problem, the diagonals of a convex n-gon, constructing a Sierpinski Gasket and related figures, patterns in Pascal's Triangle, and a few other "puzzle-style" problems. Some of these showed up in some form in the homework problems I had assigned during the unit, but I realized that I had not really used them in class. Looking back through my plans for the unit, I found I had pretty much followed the textbook, and in the process probably reduced a really important set of ideas to a bunch of formulas, and lost some of the excitement I usually had for the subject.

I had taught the unit wrong.

I didn't teach any of the content incorrectly. I didn't leave out important ideas that the students will need as they move into the next course. I tried to make sure everyone learned the content, I checked for understanding as we went along, and I gave opportunities for students to process new ideas.

But I had lost the "story" of the unit. A colleague once told me that she did a lot of up-front planning on a unit, and on a course, because she really wanted to understand the content as a story, with a beginning, middle, and end, including plot twists and cliff-hangers. My sequences and series unit had all the important pieces, but lacked any narrative thread to bring the ideas to life. The result was I had students really worried about memorizing formulas, asking "Is this on the test?" or panicking because they were having trouble with patterns outside the typical arithmetic or geometric ones.

I can't go back and reteach the unit a better way. We don't have time left for that in the school year, and once the students have seen the major plot points, rearranging them or weaving in story details isn't going to make the story more coherent. So, I now have a big note on the first page of my planning notes for the unit to get back to the story. And I'm working on the narration for our next unit.

I had taught the unit wrong.

I didn't teach any of the content incorrectly. I didn't leave out important ideas that the students will need as they move into the next course. I tried to make sure everyone learned the content, I checked for understanding as we went along, and I gave opportunities for students to process new ideas.

But I had lost the "story" of the unit. A colleague once told me that she did a lot of up-front planning on a unit, and on a course, because she really wanted to understand the content as a story, with a beginning, middle, and end, including plot twists and cliff-hangers. My sequences and series unit had all the important pieces, but lacked any narrative thread to bring the ideas to life. The result was I had students really worried about memorizing formulas, asking "Is this on the test?" or panicking because they were having trouble with patterns outside the typical arithmetic or geometric ones.

I can't go back and reteach the unit a better way. We don't have time left for that in the school year, and once the students have seen the major plot points, rearranging them or weaving in story details isn't going to make the story more coherent. So, I now have a big note on the first page of my planning notes for the unit to get back to the story. And I'm working on the narration for our next unit.

## Saturday, March 14, 2015

### Musical Chairs

If you'd seen my classroom in the last many years, you saw that I have my students sitting in groups of three or four, with their desks turned inward, toward each other, or even sitting at tables rather than desks. I set my classroom up like this a few times when I taught junior high back in the early 1990s, then went back to rows for the most part until I decided that having students talk, a lot, in class was the best way for them to learn math. So I got tables and desks that could easily be arranged in pods, and that became my standard room arrangement. I did not completely know what I would do to make the situation work, but I thought that if I did not force the issue, I would probably continue to put off really using the collaborative work that I knew would be good for my students.

So the first couple of years there were lots of bumps and scrapes, with plenty for me and the students to learn. I realized that I needed to do more ice-breaker activities, because if I wanted students to work together, they had to know each others' names and get comfortable with each other. I had to write lesson plans that included some pretty significant problems that would insure the students would not be able to complete them on their own. I had to let go of some of my more controlling impulses, and allow for varieties of solutions. I also had to come to terms with some off-task behavior; after all, if the students were going to talk to each other, it was unreasonable to think they would talk about nothing but the math. Logistically, I had to write different versions of quizzes, and move the desks apart when it came time for tests. I also had to think about how to divide the students into groups: randomly? based on their current abilities? their ability to get along with each other? their comfort level with each other? (In the end, I usually used random group assignments, and let the students know that I expected and believed that they could learn from and work with anyone. But I also rearranged the home-groups from time to time, and regrouped students for individual lessons as needed.)

Fast-forward to this year, and visitors to my room now see that I have the students sitting in a kind of double-'U' shape, with the open end of the 'U' facing the screen at the front of the room. I can still quickly group them as needed, with a pair from the inner 'U' matched with a pair from the outer 'U'. Why the change? I was not as happy with the students' interactions or their focus on the lessons while sitting in their pods. Also, I was having trouble getting a discussion going across the room, as students tended to focus on their small groups, and ignore students in other groups. I spent part of the semester break thinking about what was happening, and why this year was different. Perhaps I was out of practice with orchestrating collaborative learning. Perhaps the attached chairs and desks made it more difficult for the students to comfortably see what their group-mates were doing. Perhaps the problems I was asking the students to work on were not as engaging as they needed to be. I wasn't sure of the reason, but I knew that I needed to do something different; I thought all of us could benefit from shaking things up a bit.

The students were a little surprised by the change, but adapted quickly. Their focus is more on the math and less on social topics, I think. I do have to be very specific about when I want them to talk to each other, and prompt them to discuss their work with their group-mates. Whole class discussions seem a bit more focused, and students are starting to respond to each other, even across the room. I am worried that spontaneous collaboration will suffer, but I have noticed that some groups will start working together without prompting; I need to think about how to encourage that with other groups. Some students have commented that they like the new arrangement.

I really have three take-aways from my game of musical chairs. First, the seating chart is a powerful tool that can reinforce the big lessons I want to teach. Second, just because one strategy has worked well for a long time, it doesn’t mean that it will work forever, or that there isn’t a more appropriate or effective strategy. And finally, just like my mother used to move the furniture around in the living room when she felt like life was getting a little dull, creating a very visible change in the classroom can shake up an atmosphere that might be starting to feel old and tired.

I might go back to pods eventually, but I want to play with this arrangement a little more. I also want to get one of the instructional coaches in so I can get another pair of eyes on what’s happening now.

By the way, thanks to Tools for Teaching by Fred Jones, The Skillful Teacher by Jon Saphier, and two colleagues who have been using the double-’U’ for their inspiration and guidance.

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