Re-Imagined Classroom

As I edit my "Imagined Classroom" text that is added in red (Like this) is how I would now envision my classroom. Text that is white is what I had already previously written. Text/ideas I want to completely get rid of now will be crossed out. (Like this)

As I begin imagining my future classroom, the first thing that comes to mind is the physical aspect. As far as lay-out goes, I would like my desks to me arranged in groups, allowing for sufficient classroom discussion. Something like the following:

(This is how I'd like my classroom to be set up. With bright colors and the students in groups of 4)

Source: http://blog.edmentum.com/what-your-room-setup-says-about-you

However, I'm also a strong proponent that all students should personally get to know each of their classmates. I plan to accomplish this is a couple of different ways. First, on the first day of school, I would have each student introduce themselves to the class, say what they did that summer, and that whole bit. Then, the students would shuffle themselves and try to remember each other's names. And again... and again... and possibly again just for good measure. Assuming they're semi-familiar with each other due to attending the same school, I don't think it's unrealistic to have every student know every other student's name by the end of the first day.
As far as the getting to know each other part goes, that's a little more tricky. I once had a math teacher who used a deck of cards to "shuffle" her students' seating arrangement each day and I've grown very fond of that idea.

For example, on the second day of class, I would stand at the door and greet each student, handing them a random card from my deck. Then, another card of the same number would be taped to the pod of desks. So, for example, all students who receive a card with a number "3" on it, would sit at pod 3. Not actually as complex as it sounds, but it's a great way to "force" students to sit together without having to make a physical seating chart every day.

http://itembrowser.com/item.php?id=353

(These are the types of cards I would use each day to assign my students their seats. By doing it this way, I don't have to come up with a new seating chart all the time, and yet, they get to meet new people)

When it comes to deciding where each students will sit, I want to have each student decorate an index card in any way they want. This index card represents their "seat." Each index card is then pinned to the wall in a specific seating arrangement and that's how the students know where to sit. Periodically, I would go and rearrange the index cards on the wall so that students can get to know each other. I wanted to use the index cards because I wanted to involve them more in the decoration of the classroom. I want to have them and their ideas/personalities represented in my classroom to help each individual student feel more included. I felt like this is something that needed to change from my original imagined classroom because my entire classroom was what I wanted. It excluded my students and focused on me and that needed to change. 

I decided to change the way I did my seating chart because I didn't want it to be random anymore. Before, I didn't consider that my students may speak different languages or may not feel comfortable not sitting with strangers. With my new seating chart, I can put students near others who I know can help/uplift them or with students with whom they can communicate clearly. 

I've also thought a lot about how I can help my students feel represented and express themselves in the classroom. I've decided to leave one of the walls in my classroom completely blank. Instead, I would simply have a long, white sheet of butcher paper. My students are allowed to come in (during lunch, before/after school, or during passing periods) and doodle or write anything they'd like. I'll call it my "graffiti wall." Obviously this "graffiti" needs to be school appropriate, but I think it will help my students feel like they're part of the classroom community.

Now that my students have sufficiently awkwardly introduced themselves, we would dive into the classroom policies. In my opinion, the first day of school is by far the most important. It sets the tone for the entire rest of the year. I want them to know a couple of things but mainly I want to create an open, safe environment. I have no idea where I'll end up teaching (due to my husband attending medical school in the near future), but wherever I end up, I can almost guarantee that I will have students from multiple backgrounds (ethnically, financially, geographically, intellectually...) and yet, I want them all to feel safe and comfortable making mistakes. Saying that now as a confident college student sounds easy, but making mistakes as a high schooler is practically the end of the world. Unfortunately, something as simple as that can tarnish a student's opinion of math (one of the already most hated subjects). This is why classroom policies are so important on the first day of school.

The first thing I would want to go over is the syllabus. This is because the syllabus (regardless of how the class itself is run) will contain important topics I want to cover on the first day of class. These topics include:

Inappropriate language. I imagine the conversation going like this: "In our classroom, we don't use any type of language that would offend anyone of any race, gender, sexual orientation, religion, disability, culture, class/poverty, etc... If you are not sure if something is offensive or not, feel free toc come and ask me. But I'll tell you right now, if you're unsure, it's probably best to not say it. I understand that some of you may be used to this language already and not think much of it. I just want you to know, though, if I hear it, I will address it immediately. I may address it privately or to the class as a whole, but it's that important that I won't let even one instance slide."

Homework policy: I'm pretty lenient when it comes to grades. Here's how I imagine the discussion about homework going. "In my class, homework is graded by you based on your participation, completion, and effort. So, if you feel like you did your best work and attempted each problem, you should give yourself a 10/10. Homework should be used as an assessment for me and for you to know how well you understand each concept. If I looks at the homework and realize every student missed #2, this means I didn't do my job as a teacher. I expect you and me to both adjust our efforts as needed."

I wanted to include these two additional discussions of language and homework for a couple of reasons. First, I wanted my students to expect how I would react when I hear inappropriate language. I also want them to begin becoming aware of the impact their words can have on others. I also was worried about how to teach tolerance in a math classroom where we don't usually have discussions about things like this and realized that bringing it up directly on the first day of school would be the best way. 

As for the homework discussion, I wanted to focus on the idea that my students are responsible for their own work and that I'm going to treat them as adults. I don't need to be on their backs about every little assignment. I want to change the way they view their education - the burden of learning should be shared between the teacher and them. It's not just the teacher's fault if they don't succeed. My class requires effort, but as I'll talk about later, the learning is much deeper and will last a lifetime.

After looking online on google, pinterest, etc... I came up with some policies of my own. Ideally, we would review/update these often and have them posted on the classroom wall.


Other classroom policies would include:
Be Present: Physically and mentally be present in class. No cell phones or other electronics (besides calculators of course). Participation is Key.
Take Responsibility: Your work is your work. Your actions are your actions. You choose how to act and how to respond and no other option will be accepted.
Learn how to fail: There is a difference between failing repeatedly and being a failure. There are no failures in my classroom. We learn only by experience and that's okay.

A couple of other thoughts about these classroom policies. For the "participation is key" part, I've realized that high schoolers aren't super motivated to participate without some type of reward. However, I also don't want to punish those students who are introverts or have anxiety about sharing answers. But, after all, this is a safe zone so hopefully that wouldn't happen. I would definitely be willing to bump up a student's grade who actively participates in class and simply didn't do well on a couple of assignments. I believe by making this known to the students early on would encourage classroom discussion/participation.

Honestly, I don't care about grades. Having been someone who learned and attended class only to maintain my gpa, I now believe they're worthless. The student cares plenty enough about their own grade for the both of us. That being said, I am very very passionate about understanding. If a student can on their own accord demonstrate understanding to me, I would be very flexible regarding their physical grade.

I'm imagining a "C" student coming to me and saying "Mrs. Garland, look. I can conceptually demonstrate to you what slope means...." And I will adamantly argue against anyway who says that doesn't deserve an A but claiming that being able to regurgitate "rise over run" does.

(If a student can come to me and present this type of graph with a conceptual understanding, why shouldn't they get an A?)

https://www.montereyinstitute.org/courses/Algebra1/COURSE_TEXT_RESOURCE/U04_L1_T1_text_final.html

This idea also connects to my homework policy. I like to follow the 4-2-2 rule. There will be 8 problems assigned each night. Four of them will be on what we learned that day in class, two will be review, and two will be foreshadowing, exploratory, challenging questions on what we will learn the next day. Homework will be a formative assessment around which I will need to adjust the next day's lessons. By making both of these standpoints known to the class on the first day of school I can hopefully encourage students to learn conceptually and not procedurally.

Which brings me to my other probably debateable philosophy of teaching mathematics. This idea comes mainly from Dr. Teuscher, but I refuse to teach procedures. They're not needed. I will never say to my class "The formula to find the area of a rectangle is length time width." Like, what is the point of that? That demonstrates the thinking of a robot. Instead, I will ask my students to see how many unit squares can fit into this rectangular shape and to then find a way to generalize that to any size of rectangle. THE FORMULA WILL COME UP ON ITS OWN I PROMISE. After that point, I can guarantee you that none of my students will forget or use the wrong formula. That's not what happens when concepts are understood. Obviously this is more easily said than done, but I'm working towards zero procedures and I'm sure I'll get there eventually.

One other aspect I decided to implement on the first day of school was "Get to Know You" forms. I talked about the fact that I wanted to have good relationships with my students, but never really was specific about how to do that (probably because I was unsure myself). However, I realized that in order for my students to trust me and vice versa, I need to better get to know them. Because of this, I want to have them fill out "Get to Know You" forms. Some questions on this form may include:

What do you want to learn in this class besides math?
What are you interested in?
Are you involved in any extracurricular activities at school?
What is your home language?
Do you have access to a computer?
What is your parent/guardian's contact information and the best way to reach them?
What is something you want me to know about you?
Are you comfortable answering questions on the board/presenting in front of the class?

This form now serves two purposes. 1) It helps me get to know what my students are interested/involved in. By knowing this I can apply math to things they care about as well as attend any of their activities to show I care about them. 2) It also helps me understand what kind of background the students are coming from. I can learn what their home life is like and if there are any concerns I should be aware of.

I also wanted to make sure my students feel comfortable in my classroom which includes realizing that they may come from a culture where working as a group or presenting in front of the class isn't widely accepted. If this is the case, I, as the teacher, would want to be aware of it.

With this form I hope my students realize that I care about their lives, not just about their learning of math. I think I had left this important fact out of my original imagined classroom and I'm feeling better about how I can create this open, safe environment in my classroom.

Now, as I imagine the physical layout of my classroom, I'm reminded of the countless mathematics classrooms I've stepped foot in. They're usually covered with symbols, equations, formula, or anything numbers related really. I'm a big believe of surrounding yourself with goodness. So, that is exactly what I will do. I plan on having motivational posters, quotes, sayings, etc. all over my classroom; sayings that truly make my students think and want to become better. I previously had imagined quotes (all in English) and math posters, but realized that I'm assuming everyone speaks English and has an interest in math. Because of this, I now plan to have inspirational quotes in different languages as well as quotes from inspirational people from all different cultures. In my brain, my posters were all going to be from white males which isn't the type of model I want to set for my students. I want them to have positive role models from their own culture/gender/ethnicity/sexual orientation which means I need to incorporate these role models into my classroom. Basically I've now changed my imagined classroom to include all of these.

I imagine having this poster up on my wall and hoping the students see me as a mentor and not a judge when it comes to grades and tests

https://s-media-cache-ak0.pinimg.com/236x/c6/8d/16/c68d16845c4e062c3f3317ab431b1d85.jpg

(I want my students to realize that they're smart regardless or what they get on a test. I think teaching that to my kids and having this poster up to remind them would be a great thing in my classroom)

As well as these posters, I also want to include a safe space poster (or a couple) in my classroom. I want to emphasize though that this safe space goes broader than just gender and sexual orientation. I want my classroom to be a safe space for everyone. An example of one of these posters is:

https://dribbble.com/shots/2389989-Safe-Space-Poster-Typography

Although we would have already had an open discussion about safe spaces on the first day of school, I want this poster to serve as a reminder that I'm going to continue to enforce the inclusion of everyone.

One thing I realized I've left out of my imagined classroom is the physical needs of my students. So, on the first day of school, I would let my students know that they can come to me with any concerns, physical or otherwise. I would let them know that if they ever need a snack, tampon, bandaid, jacket (for ripped pants or period stains), or any general necessity like that, they could come ask me for them, no questions asked. I've realized that students can't focus or learn if they have other physical needs distracting them. I had left this out of my previous plan, but I think that having a desk full of supplies is a good way to address it.

After the first day is successfully over, here's what a normal lesson would go like. I would greet each student in the doorway and hand them a card (remember our seating arrangement). 

After everyone has found their seat, our warm-up would begin. There would be one problem similar to the homework to ensure everyone is on the same page and a second problem a little more about what we're doing that day. 

They would share and discuss answers and strategies in groups while I go around monitoring, selecting, and sequencing. I'm monitoring their work, selecting those I want to share, and sequencing the order they should share in. Then, I would have two students per problem come up and share on the board. This is my main opportunity to correct any misconceptions and ensure no one is falling behind before moving on to the next lesson. (I hope to teach in an A-day/B-day school so the class periods are long enough to accomplish all of this.) 

Next, I would have the students give themselves a grade out of ten. Once again, the change in this homework policy is mainly to not punish students who don't graph concepts after seeing them only once (not punishing them on their ability) as well as to have them hold some responsibility for their own learning.

Next, I would review the homework. Once again, having them only check their answers for the first 4 problems and then share their strategies and attempts for the last two problems. Those two problems are key. They're my segue into the day's lesson. I'm not expecting the students to fully be able to answer these questions. They will be pretty open-ended and are intended to push the students to explore more concepts. 

Today's lesson is on "system of equations". The two exploratory questions from the homework are the first two questions of the following worksheet: (Shown to me by Dr. Hendrickson)

(This is the worksheet I would hand out to the kids)

http://www.mathematicsvisionproject.org/secondary-mathematics-iii.html

We would then launch into a discussion of this problem. How is this possible to solve? We have two variables, have we ever done that before? What are the different ways of approaching and solving this problem? Is there more than one answer?

During this time, the students will be discussing with their groups and then sharing with the class as I go around monitoring, selecting, and sequencing again. 

This lesson, as well as the majority of the lessons I will teach, have a lot of back and forth teaching. Ideally, the students would be teaching each other and answering each other's questions/misconceptions way more than I would ever be. This is how I would know if they've truly learned the concept. "While we teach, we learn" - Seneca

As I wrote this lesson, I didn't consider that some students may not speak the same language. Whether they don't speak English or don't speak "math", they will struggle completing this part of the assignment. Because of this, during the lesson I would emphasize that you can solve the problem ANY WAY YOU LIKE (Yes, even in Spanish or French or with pictures). 

Throughout this entire process, the main thing I want my students to learn is that the x and y solution is the same in both equations. This seems to be an easily fixed, but common misconception. Assuming nothing weird happens at the store, a bag of dog food can't cost some amount for one person and a different amount for another. They need to understand conceptually what these numbers are we're solving for, where they come from, and how we can verify they're correct.

I would love to be able to quickly evaluate my students as I walk around peaking over shoulders at their work. In general, I believe in formative assessment. I want to see how my students are doing and not punish them along the way if they're not understanding. For example, If I send this "Shopping for Cats and Dogs" worksheet home with my students and they completely get the wrong answer, they don't all deserve a "C" or a "D" or whatever it may be. If this is the case, clearly I need to reteach the concept and reevaluate the lesson. When multiple students fail, the blame should be on the teacher. Because of this, homework/classwork isn't graded, but I can still use their correct answers to evaluate their learning. 

Then, as a class, we would discuss the problem. During this discussion, I would have my students "translate" their work from whatever they originally wrote into the language of math. In this case, that means representing the word problem as a system of equations with numbers and symbols. So whatever "language" you started out solving the problem in, we would all end up on the same page. Hopefully this discussing and solving together would solve the problem of students coming from different language background literally (like not speaking a lot of English) or simply a different language background since they're not used to expressing words with numbers. This enables me to teach to the entire class and not exclude anyone due to their lack of knowledge or language experience.

I also am a strong believer of personal feedback and would have the students self-evaluate themselves for each major topic. For example, this could be a possible rubric for the formative self-assessment:

(This is the type of self-evaluation I would have the students do at the end of each concept taught.)

http://teachingaheadofthecurve.blogspot.com/2012/10/formative-assessment-ideas-for-math.html

At the end of the unit/chapter when there has been plenty of time to correct misconceptions, I will give a summative assessment. On the unlikely chance that the majority of the students fail the summative assessment, I once again would need to evaluate my teaching. 

In summary, I've changed a lot about my now imagined classroom from what I wrote about at the beginning of the year. I had stated that my students might not all come from the same background, but the physical layout of my classroom and my lesson plan didn't reflect that. Now I've actually taken my students' differences into consideration. Also, previously I had spoken a lot about how I wanted to create an "open, trusting environment" without actually giving specifics on how I would do that. I've now included some new aspects such as attending my students extracurricular activities, applying math to their interests, having quotes/posters from different languages/religions/cultures, as well as allowing the students to solve the problem in whatever "language" they want before translating it together as a class. These changes as well as the others discussed in the rest of my post actually create an open environment in which my students feel safe instead of just talking about it.

In summary, My classroom is open, safe, comfortable. Lots of sharing and lots of mistakes. Students participate in the teaching while the teacher facilitates, monitors, and directs. Students are motivated by a desire to learn because they understand the benefit it is to them. 

Once again, obviously this is in a super ideal situation, but if I can even focus on one thing each year I teach and improve from there, I'm making a difference and that's what really counts.