(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-youHowever, 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)
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. 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.
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?)
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.
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 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)
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 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
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.
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, 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.
