## Saturday, August 25, 2012

Our Middle School has a fairly developed advisory program in the 6th - 8th grades. This will be my seventh year as an advisor, and I really, really love it. Which is very surprising to me because it was the thing I was most nervous about when starting at this school - I know math, I don't necessarily know adolescents and their crazy thinking and feelings and struggles. But it's turned out much, much better than I had feared, and I would not like to go back to just being a classroom teacher like I was before. I really enjoy the close relationships that I develop with advisees and the community that advisory becomes as the year progresses.

Some aspects of the program:

• Advisors welcome students to a new year with either a phone call or a letter sent home before school starts. Here is my letter that I'm sending out in a few days, but I hand wrote each one on a cute notecard. Kids love getting mail!
• Advisory meets first thing every morning for 10 minutes to go through announcements and check in with students and for 45 minutes twice a week ("extended advisory").
• Advisors meet with students and parents twice a year for Parent-Advisor-Student conferences, led by the student. They discuss the student's progress and other issues that are affecting them. 8th grade advisors (that's me!) also help students register for high school classes if they are continuing into our high school.
• The advisor is basically the touch point between the student and family and the school. The advisor keeps tabs on how the student is doing academically (via other teachers), behaviorally (via the assistant principal), and emotionally (via the counselor). Concerns about the student are supposed to go to the advisor first, either from other teachers or from parents.
• During extended advisory, we do activities that are related to the advisory curriculum (more on that below), play games, play outside, or meet one-on-one with advisees. Two big things that the 8th graders also do during advisory is participate in a Little Buddies program with a younger class and do community service projects, like helping out at a food pantry. One of the extended advisories takes place on a Friday morning and students take turns bringing in breakfast so that the advisory can sit down and eat breakfast together.
• The curriculum is pretty loose, but tries to hit the following topics:
• Learning/study strategies, goal setting, other academic type skills, including preparing to lead conferences
• Executive functioning, organization (a lot of our students struggle with this)
• Risky behaviors (sex, drugs, and rock & roll)
• Relationships (navigating friendships & dating, cliques and excluding others)
• Bullying & aggressive behavior
• Online stuff (navigating social media, safety, civility in a digital world)
• Media literacy, including being a smart consumer
• Body image & eating disorders
• Diversity & inclusion
• 8th grade advisors select a book for each of their advisees as a graduation gift (the school pays for this). This is one of my fave traditions, but it takes me forever to come up with the perfect book for each kid.
I'm currently organizing all of the 8th grade advisory resources into digital form since we've had physical binders & folders for a long time, and will post an update once they have been migrated to the web in case anyone would like to use them.

### NBI Post #2: Something That I'm Proud Of

Seems like the New Blogger Initiative has gotten started with a bang... my Google Reader is bursting at the seams and I'm seeing lots of new faces on Twitter. So here we go with entry #2. I chose the first prompt:

Find one worksheet or activity or test or unit or question or powerpoint slide or syllabus or anything that you are proud of. Share it.

I cheated because I couldn't pick just one, and had to settle for two that are very connected. So my favorite sequence of lessons to teach are on the topic of slope-intercept form of a linear equation. I feel like there's so much richness there, in terms of patterns, real-world applications, and connections to previous and future topics that I've always enjoyed teaching it. My main problem has been time constraints hitting against my desire to do a million different activities with this topic. Last year, this was the sequence that I used:

1) Introduce patterns that grow in a linear fashion. Students are in groups and need to predict the previous and the next figures in the pattern. Then, they need to explain the pattern - what changes? what stays the same? Then, they describe the 100th figure in the pattern and generalize to the xth figure. Repeat for a few more patterns that are still linear, but either grow faster or slower or start with a different number of tiles. We make a table showing the data (figure # versus # of tiles), graph it, and then all the awesomeness gets even more so when we start connecting and comparing all of the different representations and finally discuss the equation for each pattern and how it shows this information.
Intro to Slope-Intercept Form

I really like this activity because it is so group-focused - all I need to do is moderate the discussions, and all of the discovery and thinking comes from the students. The tasks are also low-entry and kids that maybe typically don't participate much seem to enjoy the visual patterns and predictions. I love days when I feel like the students are running the classroom and I see intrinsic engagement.

2) The next day, students complete a lab-type activity in groups, called "Linear Walks." They use motion detectors to visualize the relationship between time and distance and better understand why the graph of an equation in slope-intercept form looks the way that it does. This was adapted from the Discovering Algebra textbook, but I've seen versions of it in lots of places.

Linear Walks Lab

This is also a super fun day for me because there's such a clear connection for students between the algebraic reality (variables and equations and such) and what's actually going on in front of them. It's so clear why the graph of y = 0.5x + 2 looks the way that it does since it represents someone standing 2 meters away from the motion detector and increasing their distance by 0.5 meters every second. It also connects nicely to when we discuss point-slope form of an equation a few lessons later. An equation like y = 0.5(x – 1) + 2 now means that someone standing 2 meters away from the motion detector waited 1 second (so they lost 1 second of time, hence we subtract 1 from x) and then started increasing their distance by 0.5 meters every second.

I love that these two lessons make sense of an abstract concept like y = mx + b without memorization or "tricks," but rather through understanding of patterns and physical concepts like movement over time. It gives me a nice contextual handle to refer back to throughout the chapter: "If your graph represented someone walking, would their distance be increasing or decreasing over time?" "If your equation represented a pattern, how many tiles would it have started with?"

I'd love to hear how others teach this topic and if you have any feedback or criticism of these lessons.

## Tuesday, August 21, 2012

### New Blogger Initiative - Post #1 on First Week Goals

Super excited for the New Blogger Initiative that @samjshah has started up! I'm fairly new to blogging (started about 3 months ago), and it's wonderful to be initiated into the mathtwitterblogosphere and to be harangued & threatened with whacking if I don't keep up with my blog! Umm, I think it's with love?

Anyway, without further ado, here is my big goal for the first week of school, which is in about two and a half weeks:

## Create a positive classroom culture where students feel comfortable, confident, and cared for by me and each other.

Yup, that's a raccoon group hug.

Many of my students have struggled with math in the past or have learned that it is a weird, arbitrary set of rules that they have to memorize and regurgitate as best as they can and that their creativity, passion, and intellect don't have much of a place. Yes, it's a bit of a tall order for the first week, but I want students to have a sense of our classroom as a place where things make sense, where they are smart and capable, and where people care about each other. Since the first unit for all of my sections will focus on review, it gives me lots of opportunities for activities that emphasize collaboration, creativity, and engaging thinking. I also want to be sure to create a sense of order and safety in how the class is run, both in terms of procedures that simplify our day-to-day structures and in terms of how mistakes are received and feedback is given. Obviously, as the year goes on, I'm going to be looking at students' learning and ability to communicate mathematically, and all of the big goals that I outlined for myself earlier, but for the start of the year, I would love to just see students feeling positive.

## Sunday, August 19, 2012

### msSunFun #3: Goals for the School Year

I'm so glad that the theme for this week was changed to goal-setting for the new school year because this is something that I've needed to sit down and write for a while now, and this was the perfect kick-in-the-butt to get myself to do it. I have set goals for a few years now, but this year, I'd like to go back and you know, actually see how I'm doing. So maybe there will be a prompt later in the year to check in on our goals?

I have two overarching goals this year:

1. Richer Mathematics
2. I would like to deepen the curriculum, to push for understanding that is more abiding and less surface-level or focused on discrete skills. The specific ways that I hope to achieve this are by having students do more:  
• writing, processing, reflecting, and explaining

We already do a lot of this in class and I've required students to do journal writing for two years now, but I want to make this part of daily homework assignments and incorporate into assessments. I don't want writing and reflecting to be an add-on that happens every week or two, but incorporated into the fabric of the class. To that end, I will be asking students to respond orally and in writing to prompts at the end of most class periods and as part of most homework assignments. I will be asking students to make videos where they explain their approach to a problem. I would also like to put more "explain this" type questions on tests.

• problem-solving

In my previous post, I wrote about the various different approaches that I've tried to incorporate rich problems and tasks into my classrooms, and how I plan to use them this year. The basic gist is that I want to use more problems that are content-related in the classroom, pose more problems for kids to think about outside of the classroom, and continue to provide extra, "fun" problems to interested kids. I think that the group-sized whiteboards I made this year will help encourage better groupwork and communication about problems between students. I'm still thinking about how to assess students' work when assigning more difficult, open-ended problems, both in terms of giving good feedback and in terms of coming up with a grade of some sort at the end.

3. Communication
4. I would like for there to be more dialog between myself and students, more opportunities for them to give feedback on how they are doing and what they need and for me to communicate more clearly and more often back to them how they are doing in the class and what they should be working on to improve.
Last year, I had time to meet with students in the two-year Algebra sequence about once a week to discuss how they were doing and what I wanted to them to work on, but it wasn't until the end of the year that I realized that I was doing a lot of the work for them (keeping track of missing assignments & assignments that should be corrected, as well as assessments that needed to be retested) and that they were depending on me to tell them what to do. Last year, I started making them keep track of this themselves and even gave points for having a pretty clear picture of where they were at when I checked in with them. I want to start this much earlier this year.
I was also very unsystematic about reassessing - there wasn't a clear schedule and I didn't always follow up with students who blew it off. I would like to be more organized this year - I will have a calendar where students who miss assessments or those who are reassessing will sign up, and keep better track of students who need to reassess but avoid doing so.
I would also like to encourage students to communicate with me about their needs. I'll be using Edmodo for the first time this year, which will allow me to periodically post surveys or questionnaires to get more feedback from students. I'm planning on taking more pictures and notes during class and sharing my observations with students throughout the year rather than just at report card time. I'm also toying with the idea of involving parents more, either through Edmodo (which allows for parent accounts) or by using Evernote to keep track of the student photos and notes and emailing them to families. I need to think about this a bit more - I'd love to hear how others choose to involve (or not involve) parents and why.

## Wednesday, August 15, 2012

### Integrating problem solving into the curriculum

Like many others (@fawnpnguyen posted recently about her approach and there were some great discussions in the comments), I have wrestled with the question of how to integrate problem solving into my teaching. The master's program through which I was trained as a teacher heavily emphasized students engaging with rich, multi-entry tasks that promoted collaboration, writing, and connections between different approaches and ideas. I strongly believe this type of work should be a vital part of every math class. At some point soon, I hope that the Global Math Department will have a presentation on how to lead/organize problem solving in the classroom. Here are the different ways that I've used rich problems in the past:

1. Found problems that connected directly with the content material that was already part of the course.
There are many problems that lend themselves to the content found in traditional MS and HS classes. For example, many of the problems in the Interactive Mathematics Program, Years 1 and 2, lead to students creating rules for specific scenarios or functions, including linear, exponential, and inverse ones. The Mathematics in Context and Connected Mathematics series have some great problems that can be integrated into traditional Pre-Algebra and Algebra 1 classes. The drawback with trying to connect everything back to the traditional content is that there's lots of material for which I have not found good problems, such as factoring, operations with rational expressions, and radical functions and expressions. Back when I taught Algebra 2 and Pre-Calculus, I had similar difficulties finding rich problems for much of the content. There's also the issue of time - I'd like to ideally have at least one rich problem every week or two, which eats up a lot of my class time if done well. Finally, using only problems that have a clear connection to the traditional curriculum leaves out a lot of rich, awesome problems that I still want to include.

2. Assigned problems to be completed outside of class. Some were connected to the traditional content, some were not.
This gave me a lot more flexibility in terms of good problems to use and took up much less class time. But I never found a good way to support struggling students, develop the writing and problem-solving skills that are at the core of this type of work, and make explicit the connections between the assigned problems and the rest of the curriculum. The problems gradually petered out as both I and the students lost steam and assigning the problems became stressful and unproductive. If I do this again, I will need to spend some class time teaching students how to wrestle productively with open problems and will probably need to do some ramping, with easier problems at the start of the year.

3. Provided problems to interested students outside of class. Not required, problems were usually unconnected to the content.
This was definitely the approach that involved the least amount of work. I had a pretty straightforward system: a folder with copies of the current "Problem of the Week" stapled to the wall outside of my classroom and another folder stapled just below that where students put their completed write-ups. At the end of the week, I would read through the submitted work, write feedback, and award candy to those students who demonstrated good work on the problem. I had a spreadsheet where I kept track of students who completed these. Some positives were that I got kids who weren't even my students to participate, just because they thought it might be interesting, and because it was not required, it was very stress-free and emphasized the "fun" aspect of figuring out math problems. The cons were that there was little connection to the curriculum and the students who participated were those who already enjoyed math and the students who could stand the most to gain from this type of experience avoided it altogether.
So, my thoughts for this school year are that I would like to do all three of these options (hooray for overachievers!). A mix of #1 and #2 make the most sense for my class - doing those problems that have a clear content connection in class & spending more time on them, while reserving those awesome, random problems for the times when I can't find anything good that connects to what we're studying. Option #3 can co-exist as optional, more challenging or more "fun" type problems for students to do just because they want more. My biggest enemy right now is time: time in class for students to discuss and time outside of school for students to think and do math and write up their thinking and mathing. Oh, and did I mention that my students only have math for 45 minutes four days a week??? Clearly, I can't just add on more stuff without cutting anything, so I'm wondering how others have found time to do this - what do you cut?

## Saturday, August 11, 2012

### MS SunFun - Math Class Binders

The theme this week is Student Math Class Notebooks. Instead of notebooks, however, I like for my students to keep a 1 inch 3-ring binder. My reasons for this rather than an Interactive Notebook is that there is no cutting or gluing necessary, which cuts down on supplies needed for class as well as time to cut & glue stuff into the notebook. Instead, all handouts are hole-punched and students have blank hole-punched lined and graph paper to use. The other benefit is that the order can be changed and new pages inserted at any time. If a student is absent, they can just continue with their class work and if they later work on an assignment that happened while they were gone, they can just insert it into the right place. Homework or classwork can be turned in to me and then easily returned to the binder. Students' binders go back and forth between home and school.

The binder is organized into three sections with dividers:

1. Notes/In-class projects (basically, everything that happens in class, but isn't a quiz or test)
2. Homework/Journaling (all assignments that get taken home)
3. Quizzes/Tests, along with corrections and retakes
This year, I will be using Left Hand Page and a Right Hand Page designations for notes, as described by Megan on her blog. Students will use the RHP to write down and work out problems and take notes, and they will use the LHP to process the material, mostly through reflective journaling questions that I will ask at the end of class, as well as a general summary of the day's lesson and a list of any questions that they still have.

Another change for this year is that I will ask students to number the pages in each section and make a table of contents at the front of the In-class section. Since I give them an assignment sheet that lists all of the homework assignments for the unit, that page can be their table of contents for the homework section. I do a binder check every so often (more if the kids seem especially disorganized) where I look to see that they have the three sections organized and that they have blank lined and graph paper, as well as the required supplies for class. During the binder check, I also check in with students to see if they know what assignments, if any, they are missing, and what assignments they have not received full credit on and that they need to correct before the end of the unit. It's part of the grade for the binder check that students have a pretty accurate view of any outstanding work that they need to complete and know what concepts/topics they need to review or correct. My hope is that this helps them see the benefit of having an organized binder and puts more of the responsibility of knowing what they are supposed to do on them.

My other little tip for keeping a binder is that at the end of each unit, students clean out each section, staple them together, and put them in a file folder that I keep for each student in a crate in my classroom. This year, I may ask them to reflect on the unit and create a summary sheet of the most important concepts and skills, which they will put at the front of the packet. At the end of the year, students have a nice folder of review materials that is organized by chapter. I'm not sure yet how to effectively help them use it to review for final exams, so if you have any good ideas about that, I'd love to hear them.

(This is not from my class, but since all of my classroom stuff is still put away for the summer, it will have to do)

## Saturday, August 4, 2012

### Counseling conference thoughts

I've been super busy the last few days attending a counseling conference for teachers and advisors in Colorado. It's been amazingly powerful. We have been working on the skills that will help me be more than just an advisor ("Let's see how we're going to fix this problem..." "Have you tried...?" "When I was a student...") and moving towards real listening and building deeper relationships that will allow students to feel truly connected and understood. This will sometimes result in them processing through their feelings and coming to a solution of some sort. Sometimes, it will mean that "the relationship is the solution," which is a new idea for me. The conference is run by the Stanley H. King Counseling Institute, and I have a few more days in which to practice these newfound skills.

On the first day, we learned about "real listening," which basically involves me talking as little as possible, only saying a few words or a question here or there to continue encouraging the speaker to go deeper and talk more. The next day, we learned about specific skills that would help us do this type of listening. I am actually thinking of making a small handout to post for myself listing these types of responses until they become more internalized:

• Summary: a broadbrush overview of what was said, used to convey that you've got the main idea
• Paraphrase: rephrases what the speaker has said into your own words, this allows the speaker to correct or clarify the listener's misunderstanding (basically, a more detailed version of summarizing)
• Feeling and source: identifies the feeling underlying the speaker's words and the perceived cause of this feeling (can be helpful in pushing the speaker to dig deeper, but have to be careful not to assume or jump too far)
• Clarifying question or statement: helps the speaker better understand what he or she is feeling. This is NOT to satisfy the listener's curiosity - the focus is on the speaker and what he or she needs
• Joining: a statement that shows empathy or shared connection with the speaker's feelings without moving attention away from his or her story (so don't say, "I had a similar experience too," but instead say, "It's really tough when x happens.")
We've done a few role plays channeling students that we struggled to advise over the years, and it was amazing how helpful these techniques were in understanding where the student was coming from and in deepening the listener's relationship with them. I was struck by the difference between this type of relationship building and the type that I usually engage in: discussing common interests, asking kids about their hobbies and athletic pursuits, sharing music or funny videos, etc. These are also good, but they don't promote deep processing and working through issues, which quite a few of my students would benefit from. I also really appreciated the importance of not placating the student or denying their feelings ("I'm sure it's not that bad." "It's okay." "Don't be sad."), which is something I'm certainly guilty of doing. I thought that I was doing a weepy student a kindness by releasing them to go to the bathroom and come back "when they're feeling better and ready for class" (I let them bring a friend! What am I - some kind of monster?), but now I see that I just couldn't handle sitting with their pain and uncomfortable with processing it with them together. This conference is helping me realize that much of what I was doing with my advising and relationship building before was about me, not about the student.