Imagined Classroom

1. Imagine the surrounding in your classroom. What does the room look like? What resources are available for students? How are the resources used during the lesson?

• First of all, here's a diagram of what I think could be a really effective layout for a classroom. I like it because the desks are grouped in a way that three students can work together, which I think is a good number for initial group work. Then there's the groups of 5-6, as indicated by color, that are good for larger groups if necessary. All the desks are facing the front of the room, but the desks on the sides are also tilted in, so that there's more central focus. There are calculators available for use to each of the students, crates of manipulatives, and colored pencils if students want to use them. Because I'm going to focus primarily on task-based instruction, I'm planning on having those resources available for virtually all activities. Different tools can bring out different images of mathematical concepts that are very useful. There will also be math quotes and posters on the wall like displayed on this page. 
2. Describe the students in your classroom. What are their backgrounds? What are their interests? What are they doing during the lesson?

• The background of my students is something I don't think I've really thought much about. They all have different experiences in life and with math. Each of them have had so many messages sent to them about who they are and what they can accomplish. They are probably all very interested in their friends, in their phones, and things they find interesting. I think that can be influenced. What they're doing during the lesson depends on the time in the class period. Each person will be expected to participate, especially if they're not sure they're understanding things. During tasks, they'll be working individually, as groups, and with the rest of the class.
3. Describe you classroom policies. What are you classroom rules? What is your discipline plan? What are your homework policies?

• Classroom rules will include will include being engaged in the task at all times, owning what you understand and do not understand, and making the classroom a safe space for others to explore mathematics. That includes respecting their ideas, allowing them to speak, and being committed to the mathematics enough to work with others so everyone learns. Math, contrary popular belief, has a lot to do with communities. I will do my best to create a community. My discipline plan is not very developed. I think it will depend a bit on the school administration, but most of it will be up to me. I think it will have a system of warnings, with consequences including speaking to administrators and parents. Homework policies will include grading of completion and mastery. Late work will be accepted through the end of the unit, but there will be penalties. There will also be rewards for turning in homework on time consistently. 
4. Describe a typical lesson you will teach in your classroom. What will you teach? What is the topic? Why did you choose this topic? How will you teach it? What is the main thing you want students to learn during this lesson?
• First of all, math. Lots and lots of math. Math in context with real questions that take reasoning and work to solve. For a specific topic, probably quadratic functions. I chose that because I'm learning about them right now. They're full of amazing mathematical concepts, including calculus. I'll teach it using a task that talks about quadratic rates of change--specifically that a quadratic's rate of rate of change is constant. Also, quadratics are a representation of an area created by the multiplication of two linear expressions. 
5. Imagine your work as a teacher during this lesson. What are you doing during the lesson?

• I'm going around and looking at student work, what they're thinking and how they're coming to conclusions. I'm selecting student work that highlights principles that lead to the fundamental mathematical concept I'm using and my overall goals for the lesson. I'm asking questions to individual students or groups to scaffold or extend. I'm sequencing in my mind the work I want to highlight when we come together as a class.
6. Imagine your students again, what are they doing during the lesson?
• They're engaged in the class--doing their own work, critiquing their own work and the work of others. They're sharing their ideas and reasoning and helping each other make corrections. They're using the manipulatives and tools provided as needed. They're asking questions and answering each others questions. 
7. Imagine how you will assess your students' learning and achievement. How will you know they have learned?

• I will know when they will be able to explain to me what is going on. They should have an image that helps them understand how to engage in the mathematics properly. They should be able to reason through disconfirming evidence. They should gain procedural fluency as a result of their conceptual understanding.