# My first #ObserveMe went poorly

Well, I was really looking forward to being observed using the #ObserveMe rubric from Robert Kaplinsky. I’ve really been consciously aware of elements from the rubric and want to make sure that in every class I am allowing time for students to work together, to ask questions, use diagrams and discuss strategies. I want them to do partner work, individual work, and participate in full class discussions.

Today, I had a colleague scheduled to visit me and do an observation for 30 minutes. I was trying to accomplish two things today:

• Connect intercepts of a graph of polynomial functions to the factored form of the equation
• Teach how to factor after creating a desire to use factored form

I’ve noticed that most of my students struggle with factoring. This year it seems to be that more students struggle with it than in the past. So, I don’t think they struggle, really, I think they just haven’t practiced it enough. Maybe it’s just not as emphasized as it used to be. No problem. But, for polynomial functions, factored form is pretty nice.

I’ve seen that most of my students can factor using GCF really well and they can factor quadratics really well when a is 1 and some do well when a is something other than one. They are good with the box method and the diamond method. Some are using the box method to factor higher order polynomials too (third degree, mostly). But, most struggle if they are used to the diamond method and a isn’t 1. Many also have a hard time recognizing a difference of two squares. So, lots to review and lots to learn.

Because we just finished a grading period last Friday, I spent much of the weekend grading and planning. I had some trouble finding what I was looking for for today’s actual focus. Polynomials: graphing, factored form, factoring. There’s actually a lot out there, but I can be picky and I didn’t want to create my own. I ended up purchasing a bundle on Teachers Pay Teachers. There was a good assortment of problems, note templates and it was well organized, covering all of the concepts and factoring that I was looking for.

Anyhow, for the observation, I had thought to focus our class discussion and activities on multiple representations of polynomials – equations, tables and graphs. Then, with the help of Desmos, students worked together to complete an assortment of questions. Some were lower level fill in the blank, others were more big picture, “How do you know when you are done factoring?” I’m still thinking about that. I can’t wait to see what they say.

Well, in the last 30 minutes of our 90 minute class, it was time to focus on factoring rules and patterns. Using what I thought was a pretty nice set of sample problems and a nice set of practice problems, I projected my note sheet so that we could all go through the problems together. But, suddenly it’s was 9:05. I had 5 factoring concepts to get through in 25 minutes. So, I pretty much grabbed the reigns, led/dominated the conversation and worked through the examples (too quickly), with students mostly following my lead.

First set: Factoring with GCF, difference of two squares, then together. Ideally, those were review, right? So, going quickly through those is okay, right? (No, Laurie, not right. The whole reason I was doing it was because there some people who needed to learn/relearn that.)

Next: Hurry, gotta get to the sum and difference of cubes!

We got there, and I really just told them the rule, did a couple of sample problems (which weren’t super easy) and gave them the assignment. I didn’t get to the fifth concept, so cut the assignment short. No problem, we can go over that next time. Class ends…

Observation wise, my colleague was there for the last 30 minutes – the transition, then the ‘I lead, you follow’ method of instruction. Not my finest. She gave me all zeros.

Well, as much as it hurt my pride, it was really good feedback. I’m glad that I know I don’t usually teach like that. And, my students are actually doing really well this year. Things are generally really good. That is not meant to be a deflection or me trying to give myself a pass. I took that feedback to heart and immediately tried to find better ways to teach it.

To be honest, on some of the nuts and bolts stuff, I default to direct instruction. I would have been complacent about that and never changed had it not been for that rubric. I never expected to be an all zeros teacher. I know part of the problem was getting stressed about the time. Usually, I don’t care about that. But, overall, I feel like I am behind schedule, so I was feeling pressured to get that factoring happening.

As I’ve had the day to think about it, the direct instruction was okay, the notes and practice problems were all fine. It was the way I organized the discussion that left no room for student input, problem solving, strategy analysis, practice or interactions with each other, much less with me.

I might have run my next class the same as the first had it not been for that feedback. Instead, I gave more time for the factoring, and had students suggest first steps. We tried various methods. I had students talk to each other and work on a problems together.

Time was a factor today, certainly. However, my conscious decision to organize the conversation around student input and interactions in my second class, allowed students to have more time to think and express their reasoning. More time to ask questions of each other and answer questions. Those processes lead to better retention and interest.

On the upside, I’m glad that I know where my students are with factoring and was taking steps to improve what they know and expand on it at the Algebra 2 level. I look forward to seeing my first class again in two days, to better address those concepts and get some meaningful conversations and practice happening. That’s one of the great things about teaching. You get to see them again and fix what you did wrong.

Thanks, Robert Kaplinsky for that rubric. Thanks, my dear Colleague, for your time and feedback.

# Creating a culture of observation and sharing

I’m really interested in trying to perpetuate a culture of classroom observations with my colleagues at school. I think most of us value the opportunity to observe and be observed, but we are all soooooo busy!

Fortunately, we have had some funds become available for instructional coaching in our district. One of the ways this can manifest is through release time to observe other teachers. I’d be happy to do it during some of my prep time, but not everyone feels the same way or is able to do it during that time.

After some discussion with the coaches, and knowing we have two new teachers this year who would probably enthusiastically sign up for this, I’ve just sent the email, hoping to get back some positive responses. Oh wait… my email just dinged… YES my first yes, “I am interested.” Now, just a few more and we can get this going, right?

What could go wrong? Well, a lot if people aren’t on the same page about observing and reflecting and respecting the vulnerable position of the observed. For help with learning how to be observed and how to be a good observer, check out this Education World article.

I’m really excited about getting this going. I think it can really transform our teaching and our sense of collegiality and support. The main thing is that it’s really best for students when it’s done well.

I can’t wait to write about how it goes…

PS. Check out Robert Kaplinsky’s #Observe Me post

# Partner Quiz + Evaluation = Fingers Crossed!

Last week I gave a partner quiz to my Algebra II classes.They liked the quiz and seemed to be highly engaged. The rules were simple. Work with a partner – open note, open book, scientific calculator – all allowed. I was also being observed and evaluated by one of our Assistant Principals. So, I had my fingers crossed that everything would go well.

My job was in the partnering and in giving feedback during the quiz. My goal was to give each partnership feedback as they worked. The feedback came in the form of green dot (correct) or pink dot (not quite correct). Or no dot, if a problem was in progress or not started.

As I moved through the tables with my two highlighters, kids were very excited and filled with anticipation as I examined their quizzes and marked either green or pink. Some errors were small – losing track of a negative or not writing the plus/minus symbols in front of the answer to a square root problem. Those things they could find themselves usually. Other errors were bigger, more along the lines of not fully understanding the question or how to start a solution.

When students were not understanding how to start on a solution or not understanding the language of the problem, I was able to discover this gap and then help out. All students were getting feedback and I was learning who needed more help. The nice part, was that I was able to check in with every student multiple times during class and help them where they were. It felt like a pretty good differentiation strategy on hindsight. I didn’t realize that going in to this activity.

The first round of me going through the room was just to give green or pink dots. I didn’t give much help or feedback beyond that for most pairs. I would approach each pair of students and look only at one person’s quiz. The next round I would look at the other person’s quiz and give deeper feedback as needed.

By the end, I had several pairs of students who had completed every problem correctly. I asked them to help out certain students who were having questions or just wanted to know if they were getting green dots on the rest of the problems I hadn’t checked or on any pink dots that needed to be looked at again. By the end of class, everyone had reached 100% green. Well, almost everyone. Two students returned during our study hour to get some more help and finish up. Then everyone had green dots.

I did ask for feedback about the quiz process. The students seemed to like it and wanted to do it again. I got a couple of suggestions for improving the system of checking at the end. Next time, I’ll give the students who finish early a green and pink highlighter just like mine so they can officially check quizzes of students who are finished and waiting.

So, while I didn’t want to give a quiz during an observation lesson, this type to be good for an evaluation. Overall, I think it was an engaged class period where students and teacher learned in a formative way about mastery of concepts. It was low risk and ended in better understandings for all students. A couple of students reported that they learned from the quiz. Excellent.

As far as the evaluation part, my Assistant Principal gave me some ideas for managing the quiz differently next time. One suggestion that I liked was about having each student in the partnership have a different version of the questions and the other one have the solutions. That way they could coach each other. I think that would work well for a maximum of 5-10 problems and would be a good idea to use as an assessment activity after a few lessons. I could circulate and listen to conversations and help out with guiding how students could coach each other. I think it would have been too long of an activity during midterm level review (which this was), covering  good deal of content. But, I will use that idea sometime in the next month. It sounds like a great way to have students use and learn the vocabulary, too.

It was a great day for learning in my classroom.

# The kids were a bit unruly today…

I take that unruliness as a challenge to work on a more engaging experience for them. Today I was teaching polynomial expression operations, which is, admittedly, one of the more nuts and bolts type of topics and not terribly exciting math. This blog post is about how to find ways to raise the engagement on some of the dryer topics that we cover.

And, what’s ‘dry’ to me means that I can’t readily think of great activities, applications, or problems that engage.

To create a higher level of interest is to create a higher engagement level. This means less need for a disciplined atmosphere centered on direct instruction when the kids are just not in the mood. Which is often in my 5th period (after lunch) class.

The kids are energetic, they are social and they are comfortable enough that they interrupt, throw stuff and eat candy, throwing the wrappers on the floor, sometimes near the garbage can. God bless ’em. 🙂 I really do love these kids and I have fun with them. BUT, I do have a hard time getting through direct instruction for 20-30 minutes, so it drags out longer, which makes it even tougher for me and for them. Way too much!! Especially for the half of the class that is quietly waiting to get through a concept or problem.

Let me say, direct instruction has it’s place, but it’s not working well for me with this group. So, I need options. First stop: Desmos. What great activities already exist for us?

So many! Here’s a link to the classroom activities that come up when I search on Polynomial Functions: http://bit.ly/2drqtGd and a screen shot of the list. If you haven’t already, please set up a teacher account at Create Desmos Teacher Account and get inspired!

It think for polynomial function operations, though, I’m not really seeing anything that I could use. Bummer. Hmm… Let me think about a flipped approach.

At the site, you can click the Semester 2 tab, then click polynomial functions, there’s a lesson for operations. The site provides a student note page that students can print and fill out while they watch the video. This way, they have guided notes, they can go at their own pace, and they can ask questions when they get to class. In class, we can quickly summarize the key concepts and ask questions. They can do that in groups, or as a whole class.

Would this really help in terms of engagement? Well, hard to say, but at least I wouldn’t be trying to hold their attention so long when it’s just physically hard for them to stay tuned. They would get a very similar experience of direct instruction, just when they are not in a group with their friends after lunch on a warm day. So, I think it’s an improvement, but it’s not exactly innovative or exciting.

Next, if I do the flipped math for instruction, what activity could I have this energetic group do during class? One option is some sort of matching activity. But, wouldn’t it be better to do a live matching activity where they are the variables? Like, everyone gets to be a cubed-x or a squared-x or a single-x or a constant term? Then, I could write problems on the board and they could group themselves as the equation and solution, and maybe make a video, and maybe put it on YouTube and maybe I could tweet it and blog about it. 🙂 Wow, I’m gonna do that next time.

Another option is to create some open questions. Ways to do this include using some closed questions, like most of the text book questions and simply withholding some of the information and/or instructions, then ask students what are we going to try to solve and what information do you need?

If only I had thought ahead. Well, for me, next time as I look ahead in my planning, I’m going to be a bit more proactive for the sake of this particular class.

Direct instruction + Dry topic = Headache by the end of the block. Never again. 🙂

# My Classroom Culture Is Shifting

Well, it looks like the past six weeks of having students sit in groups and emphasizing that they work together is possibly paying off. Today, instead of hearing, “I have a question…” I heard “We have a question…”

That was beautiful to me. I had just rearranged the seating chart. At our school, we have moved into our second of three grading periods for the semester. These kids knew to work together with their new partners, and they were doing it. They knew I was pretty much only answering questions no one in the group could answer. They are learning to check in with the other students in the group before asking me for individual help.

I highly recommend this type of group seating and emphasis on student-to-student communication. It’s been so helpful to have students talking to each other about math. This should happen during warm-ups, work times, activities, and class discussions. To get them to start talking to each other, I sometimes ask why something works a certain way and ask them to discuss it with each other. Then, I might walk from group to group to check in with the group. Then I might summarize for the class what I learned from the groups.

Full disclosure: I used to be afraid to have them “Discuss at your tables…” because I was afraid they would talk about other things. And, that was often true because I was letting them sit with their friends. Better to mix them up. I first made a seating chart that was alphabetical. That was helpful to get to know their names and faces and to check off homework and take attendance quickly. Now that I know them better, I mix up the seating thinking about male/female, test scores, personalities, etc. I plan to change the seating every grading period. We have six throughout the year.

Groups are working better than two partners. I think it’s because students have more people to talk to who might know the answer. It’s important for me as the teacher to circulate to each group several times during the class period. I ask if the table has any questions. If there are questions, I ask if anyone at the table can answer. Then, if so, I’ll listen to that discussion and help if needed. Or, I’ll walk to the next group and repeat. I try to only answer what students can’t answer.

Students learn that I’m available and want to help, but can’t take the time to answer every single question from every single student. It’s like an economic situation where the teacher’s time is the scarce resource. Students are learning to make their questions be worthwhile to their group.

# Demonstrating the Structure of Quadratic Functions with Desmos

I am a big fan of empowering students to look for and make use of structure in Algebra 2. This is most true for me as we work with functions, parabolas, and quadratics.  I’m writing this post about what I’m finding to be an indispensable tool for helping students quickly learn about the structure of the equations of quadratic functions. This tool is easy to use. Simply project the Desmos calculator (use the links below) and activate the sliders.

One of the many great things about Desmos is some of their built in functions on the calculator. Like this one, using vertex form of a parabola:

In this window, you can activate the sliders* individually to demonstrate to students (and share with your math team)  how a, h, and k affect the parabola. You may want to stop the slider and manually slide a to values you want to emphasize with the class (a = 2, 1, 1/2, 1/3, 0, -1/3, -1/2, -1, -2 for instance).

*To activate the sliders, click on the arrow buttons in rows 2, 3 and 4. To stop them, click again, or manually move the slider to any spot.

Next, move to standard form, which is really interesting.

I suggest you first let c slide and have students watch as the parabola moves up and down. Ask them whether the shape is changing. Some will think it is, but it’s just an optical illusion. Tell them to look again.

Then, stop c and let a slide. Kids can see how the parabola stretches, shrinks and reflects just as it did with vertex form.

Last, the fun one. Ask them to predict and then tell their partner/group what they think will happen when b slides. Will the shape change? Will it move up, down, left, right? Then, activate the slider.

This is where the math just gets cool. Ask them, as they watch the motion, “What is the path of the vertex?” (it travels along a parabolic path); “What is happening to shape of the graph?” (nothing, it stays the same); and, “What is happening to the y-intercept?’ (the parabola travels through the point (0, c) and the intercept doesn’t change).

I found this to be so helpful to me as a teacher and to students to see quickly what the structure of these equations do. To get to them and many others, just click on the bars at the top left corner of the window for the desmos calculator. There are all kinds of great functions to work with. Here’s a picture I made in paint – screen shot, save in paint, edit with brush – to help you find the drop down menu.

P.S. I need to create a note sheet for this where they summarize these structures and the impact of the key components. Next week. Yep, next week. 🙂

# Last minute quiz inspiration

Yesterday, I suddenly decided on a new quiz format. I had been writing a quiz for my Honors Algebra 2 class and I just didn’t like it. It wasn’t interesting or challenging. I really didn’t want to make a second version (my kids sit at tables), and was hoping for several days that some inspiration would hit. Our text has a set of alternate assessment questions, but they are a bit involved.

So, in the 5 minutes before class started, inspiration hit like a tons of bricks.

I let them use the alternate questions, and work in pairs. There are 6 students at a table group and we were covering two chapters. I gave them packets of the questions. There were about 7 questions for Chapter 1 and 6 questions for chapter 2. The guidelines were that they had to answer one question from each packet and couldn’t answer the same questions as the people at the table group. So, that’s a total of 6 questions for the table, three from each chapter, two for each pair of students.

To make it an actual quiz, they couldn’t use notes. They also couldn’t ask me questions. Actually, they could, but they would lose a point. Each question was worth 10 points, for 20 points total. Asking one question would still yield an A. But, no one asked any questions. The kids were engaged and worked steadily for about 35-40 minutes. Most finished, no problem.

I called time at 45 minutes. Some students hadn’t finished. I gave 5 more minutes. However, a couple of groups didn’t get to the second question or had just started it. Uh-oh.

So, as this is a group of motivated, grade-stressed students, I allowed them to come back at lunch or after school or during our tutorial time to finish. They appreciated it, so we were good.

The best part, was in the ask for feedback about the quiz format.

I gave them three prompts:

• Partner quiz again? yes/no
• This would have been better if…
• This was good for…

They unanimously liked the partner quiz because they had another brain to work with. Asking for feedback is gold! Making myself vulnerable was scary. Here I had changed up the quiz in the last few minutes, kids didn’t finish, they were afraid to ask a question even when it would have gotten them to the finish.

Would I do it again? Yes! Overall, it was a positive practice for them and for me. In fact, I’m doing it again today with my other section of that class. I’m happily incorporating their feedback with what I observed to make the following changes for the next class and next partner quiz. Here’s my list:

1. Make more copies of the questions – it slowed them down to have to share.Yes. Done. Easy.
2. Allow questions. Well, I’m thinking no on that, because I think they will ask me a million questions. So, modified practice: they can ask the question. If it’s a fair question, I will guide with no point deduction. If it’s a question about not understanding the content, then I will take a point if I answer. They can ask the question, then I will answer or respond with, “Yes, I’ll answer, but it will cost a point.” Then they can decide if they want the answer.
3. Give more time. No, but I will advise students to read the entire question before choosing (most have multiple parts) and remind them that they can change the question if they get really stuck. Also, I will be more active in making sure everyone is employing strategies to finish on time.
4. No one mentioned this in the feedback, but I didn’t give them a time frame before they started. I wasn’t sure how long it would take. When half the class was finished, I announced 10 more minutes. I should have circulated a bit to check on their progress at around 20 minutes to let students know they should start on their second question within 5 minutes, so they have time to finish.

Now, I just have to grade them. That’s nice too, because I only half the number of quizzes to grade. Another teacher benefit from the partner quiz.

Please comment below with questions or ideas or practices you have tried. If you want to know more about the course or text, send me an email.

One of the toughest things about grading is when the students with 79% or 89% ask/plead/argue for the B- or the A-. I do round an 89.5% or higher, to the 90%. I think that’s just doing proper rounding, as I like to teach in my classes, as opposed to truncating the grades. [Don’t know what truncating is? You can find out here] . But then, the 89.2% kid asks for the A-, too. I would be inclined if their test scores were in the A range, but they weren’t completing all the assignments, and so homework was dragging the grade down. But, if the test scores are in the B range, and homework completion is bringing the grade up to B+, I think that’s good enough.

I have several students who’ve missed a lot of school, or have ADHD and just don’t complete every assignment, or just never are there or aren’t organized enough to present the assignments for credit. If they have high test scores, I’m inclined to round their grades towards those test scores. However, high homework scores with lower test scores are not a compelling argument for me to round the grades higher, even though that’s the request I get a lot.

My grading policies and decisions around tests versus homework and semester grade versus final exam grade are pretty generous in my opinion. Many teachers let the computer calculate the grade based on the settings for the weights they decided at the start of the semester. Many others make exceptions, too.

In addition to the above rules of thumb around my grading decisions at the end of the semester, during the semester I’ve been known to drop some low scores when the class doesn’t do well on a quiz. I think that I didn’t teach them very well when that happens, and we revisit the material.

Algebra 2 is a hard class and not everyone will get an A, even if they usually get As in other classes or in prior math classes. This is one of the tougher lessons for high school students to learn. They are hitting a level of math that really requires studying, critical thinking and perseverance for the longer, more involved problems. They aren’t all ready for that level of problem solving. Even if they are, the course is content rich, meaning there is a lot to learn and a set amount of time in which to learn it.

Students are busy with tough course loads, sports, hobbies or jobs, and social and family activities. Many students don’t have adequate time outside of school to study as much as they need to in order to get the grade they want. Others make sacrifices and get every assignment done every day. They come in and ask questions after they’ve tried to figure things out on their own. Some ask questions immediately without giving themselves time to try a solution, because they are used to the quick answer or they feel pressed to get the questions answered quickly, without a deeper understanding for when the next question comes. In learning math, you learn so much from making mistakes and trying new approaches. Especially at this level. But, I think that requires a level of calm and concentration that many teens aren’t used to. Trial and error are involved. I try to talk abut this to my students when I can.

Some people may wonder about the purpose of the final. Well, I think it’s important to review what they learned over the year. I think it’s important to have a idea of what they’ve retained and to remind students what they need to know for the next course. I think it’s good for them to have an idea of what they remember and what they may need to re-study. And, I don’t let the final exam kill their grade. I think that’s the bad part about finals, which is why I have some of the policies listed above. A final exam can bring a student’s semester grade down much more than it can raise it.

I plan to include these grading philosophies and practices, and study tips and techniques for retention and deeper understanding in my beginning of the year mini-unit next year. I introduced the idea in my blog post  Summer reading, relaxing and revamping…. and will post it when it’s done.

# Summer reading, relaxing and revamping….

For Summer 2016, I plan to do a lot of relaxing, enjoying time my family, cleaning out closets and thinking about next year. I also plan to revamp my grading and record keeping. And overhaul my unit plans. I want to think about making things easy for students in terms of being able to understand what’s expected of them and what their grade depends on.

For next year, I’d like to make unit packets for students that consist of

• Pre-requisite skills questions
• Sample test problems
• Practice Sets
• A portfolio project
• Open questions
• Note organizers
• Formulas
• Reflection prompts
• Spiraled review questions

I know, that’s an ambitious list. Well, I’m an ambitious gal. But, I’ll leave myself some wiggle room. I may not include everything on every plan. Or, it may turn out that some things aren’t needed while other things are, depending on the topics. Some spaces will be blank, allowing students to fill-in as we go. After all, I don’t want to toss all the cool open questions out in a lump. I want to use those to set a low entry point, an opportunity to engage students and an opportunity to talk to the class about options. Those will likely be saved for openers during block periods.

I also think, it will get easier as I get through the first couple of units. I’d like to have the first two units ready to go before school starts. That’s my summer goal.

I want to start the year with a mini-unit on study skills for math. I want to talk with them about passive versus active learning and how that makes wanting success and high grades either a wish or a goal. If you are passive, then your goals are more like wishes. If you are active, your goals are more likely to be achieved. I want them to know what working towards a goal is versus doing the minimum and hoping for a high grade.

Another part of that mini-unit will include how to handle absences. We have a lot of absences at my school. I kept a record in May/June (see photo) because it was really getting to be too much to compensate for. We have block periods, so when kids are absent, they miss a lot. However, I think these unit packets will help them when they are absent too.

The top display is for my Tuesday/Thursday classes, the bottom is for my Wed/Fri classes. Everyone meets on Monday. Some of those percents are pretty high and there are perhaps too many days with more than 10% absent. I didn’t even include senior ditch day.

So, the absences are driving my desire to make things really clear at the start of the unit and have a packet so that kids can know what’s coming and when. I don’t plan to give them a 50 page booklet, but at least an outline, a schedule, a grade tracker, etc. I think I may handout homework packets on Mondays and collect them the following Monday, too.

Part of my planning will be doing some reading and research. I’m looking forward to re-reading some books and finding some new ones. Teaching Struggling Students in Math is my newest acquisition and should be a good one. Check out my new and ever growing list of favorite books for teaching, especially teaching high school math.  My Favorite Books on Teaching Math