T&L 564
TEACHING EXPERIENCE

Objective:  Plan, teach, and reflect on a mathematics lesson with a whole class of students.

You will plan a mathematics lesson that will meet certain specifications to be defined. You will teach your lessons at a time mutually agreeable to you and the classroom teacher concerned - the lesson must be videotaped. You will use this videotape to aid your recall and perceptions in writing a paper reflecting on the whole experience. Four products will be submitted for grading purposes:

Rough draft of your lesson plans, due Week 7
Final version of your lesson plans, due Week 9
Written rationale for your lesson plans, also due Week 9
Reflection paper, due no later than Week 15

Note that this timeline gives you a 6-week window in which to teach and tape your lessons, reflect and analyze what happened, and write the reflection paper. You are encouraged to write the paper within a week or two of doing the teaching so that the experience will be fresh in your mind. You will probably also learn the most about yourself and your teaching if you do the reflecting at that time.

Your lesson plans and rationale should be approximately 15 pages in length, with reasonable type size and margins. Please note that this is an approximation; some of you will need more pages, and that is perfectly fine. On the other hand, please do not "fill up" 15 pages just to meet this length.

Lesson Plan Guidelines
Provide a detailed account of the moment-to-moment activity of your lesson. I am NOT requiring a specific lesson plan format - you are free to write this any way you choose. I would recommend that you provide a lesson plan that is narrative and descriptive in nature - error on the side of too much detail. While the PPA format is an option, be sure that it will allow you to fully address the requirements outlined below. The PPA format has worked well in some past cases, but made things difficult in others. Please use a format that works for you.

Please keep in mind that I am requiring a STUDENT-CENTERED lesson plan. This means that students should take an active role in developing mathematical skills and understandings, that you have plenty of planned interactions with the students, and that the students are allowed to take some degree of ownership in what and how they learn.

In some cases your placement might make it difficult for you to stray from "covering pages 71 and 72" or deviating at all from a set curriculum, or even developing a truly student-centered lesson. Because you are still a student, and because the purpose of this assignment is for you to grow as a professional, it is very important that you try to work within your placement to create as much freedom as you can to create a lesson plan that you can call your own and that is student-centered. You are certainly allowed to borrow ideas, and even materials, but the spirit of this assignment is NOT for you to IMPLEMENT a set day of mathematics instruction; the purpose is for you to think deeply about how you will develop certain mathematical understandings in your students, and then construct a lesson plan that you think will do this. I ,and especially your supervisor, will be happy to help you negotiate this aspect of this assignment.

I will look for the following in the DESCRIPTION of the lesson:

Details on the way in which the classroom will be physically set up.
Detailed description of lesson goals - don't use labels and short phrases here. Focus on mathematical content, mathematical process (communication, problem solving, etc.), and other important goals (affective, dispositional, connection to past or future content, etc.).
Moment-to-moment description of what you are plannning to do and say.
Simultaneous description of what you are plannning for your students to do, say, and think about.

In addition, provide the following:
The problem(s) you will use during the lesson
Any tasks you plan to use
Sample questions you will ask your students during interactive aspects of the lesson
Sample student responses you expect to receive
The ways in which you plan to assess student progress through the lesson
The ways in which you will more formally assess or evaluate your students' performance

In key points of the lesson, it is also vital that you plan for contingencies based on potential student reactions and construct different paths through the lesson accordingly. However, you could literally do this forever - please think through the lesson and construct contingencies to the point where you are quite confident that you are ready to interact with your students about the goals you have established.

Written Rationale Guidelines
The rationale is intended to provide an opportunity for to lay bare your reflections on the instructional decisions found in the lesson plan. You will do two main things in your rationale: 1) communicate why you are doing what you are doing in the lessons, and 2) communicate the basis for your thinking.

In constructing your rationale, please use as a basis of your thinking:
1. your own thinking (including 2. your experiences with these students)
3. your cooperating teacher's thinking and advice
4. other teachers' thinking and advice
5. theory
6. research

Your rationale will be much stronger if you draw from multiple bases. Don't rely exclusively on the literature and class readings, but also don't only rely on your own limited experience. My master teacher thinks it's best should also not be the sole basis for your decision-making. Be sure to cite references when using outside support for your thinking (this doesn't just pertain to quotes - if you were informed by a reading that you feel you should credit, then put the reference in parentheses after making your point).

You have two choices in writing your lesson plans and rationale. You can include the rationale as a separate document, or you can embed it within the lesson plan document. If you choose the latter, separate the bits that are rationale from the actual lesson plan by using italics. You also might find it helpful to begin with an "overview rationale" that targets general approaches and big picture things, and then embed "targeted rationale" to the details and specifics of the lesson.

The following questions may help guide your thinking and writing, as these are the kinds of questions I will have in mind when reading your paper.

About your goals
What is the primary purpose for my lesson? What are other purposes?
Why are my specific goals and objectives important? Why am I trying to do these particular things?
What makes me think these goals are achievable in the given time frame? To what extent are they achievable in the given time frame? Have I clearly laid out the specific time frame for the segments/activities in each of my lessons.

About the Activities
What did the students learn? What didn't they learn? How do I know that the students did or did not learn? Why did or didn't the students learn? Why am I using the formats (direct instruction, small groups, whole group discussion, individual work) in the ways I am using them?
Why do I think the activities I am using will help achieve my goals?
Why am I using these activities rather than others which might achieve the same goals?
Why am I sequencing my activities in just this way?
Why these materials? What are the advantages and disadvantages of the materials I am using?
Have I given students opportunity to communicate their thinking? In what ways have I done this? In what modes or representations will they be able to do this? Why have I chosen these particular ways?
Is there evidence of contingency thinking - Where are the possible places I may need to make changes in my lessons? Why would I make changes? What might I do differently, and how and when will I make that decision?
Is there evidence of classroom management - Why am I distributing materials this way? Why am I communicating my instructions in this way? Why am I moving the students around the room in this way?
Am I making efforts to reach all kinds of learners - oral/visual/tactile students, shy/daring students, students who hold varying levels of understanding of the topic at hand, ESL students, etc.?

About evaluation
Why have I chosen these modes of assessment?
Why are these forms of assessment appropriate to the students? to the activities? to the content? to my goals?
How will these assessments tell me the degree to which I have achieved my goals and objectives?
What parts of the lessons are likely to be most difficult for the students, and why? What trouble signs or other cues from students should I be looking for?

About closure
Why have I chosen this type of closure (e.g., integrating, extending, summarizing, connecting, questioning) for my lessons?
Why did I choose this particular closure activity at this particular time?
Why does this closure support the next day(s)' lesson?

About the content
What concepts and procedures do I hope the students learn?
What math do these lessons connect with (both before and after)? If integrating, what other subjects does this math connect with?
Why is it important that the students learn these mathematical ideas and/or processes?

Grading criteria
In order to form a summative grade for the rationale and lesson plans, the following rubric will be used (1-4 relate to the lesson plan, 5-8 relate to the rationale):

(12 pts) Powerful and appropriate mathematics is addressed.
(12 pts) Contingency thinking is displayed; efforts are made to reach all learners; possible sources of student difficulty are identified and discussed, lesson difficulties are anticipated and alternate lesson paths/stimulants are clearly outlined.
(12 pts) Details on the above aspects of the lesson description are fully provided.
(12 pts) Opportunities for students to take active roles in the lesson are provided; details of how the lesson is student-centered are provided.
(12 pts) Discussion of pedagogy and reasons for decisions, addresses why and not just what.
(12 pts) Sound basis of thinking; reasonable decisions are made.
(12 pts) Well-grounded rationale; multiple bases and sources are used.
(12 pts) Rationale is detailed; support for general approach as well as lesson details are provided.
(4 pts) Something extra.

REFLECTION PAPER GUIDELINES
The purpose of this 10-12 page paper is to complete the loop - i.e., reflect on your experiences. The focus will be on what you learned from planning and teaching the lesson, with the added benefit of having captured the experience on tape to aid your reflection. Please try to focus on the mathematical aspects of the teaching and learning process in your reflection, even when addressing more general issues such as classroom management.

NOTE:  Include a very brief reminder of what your lessons were about and the grade level of your students.

Your paper should address the following questions (write in a way that makes sense to you - you don't need to simply go down the list, but do make sure you address EACH question area):

What do you think went well with your lesson? What was it about that part of the lesson that makes you feel this way? What do you think caused it to go well? What did you learn from this? How can you build on this success in your future teaching?
What do you think did not go well with your lesson? What was it about that part of the lesson that makes you feel this way? What do you think caused it to go badly? What did you learn from this?
What did not go as expected - either anticipated or contrary to your expectations? What did you learn as a result of the unexpected? (Some of these things may have been discussed in 1) and 2). If so do not repeat.)
How would you characterize the mathematical activity that occurred in the lesson? Did this go as you planned? Are you satisfied with this? Was powerful mathematics explored by the students?
How would you characterize the classroom discourse? Was it productive? balanced? powerful?
What did you change from your plan while you were conducting the lessons, and why? (Again, some of these things may have been discussed before. If so do not repeat.)
In retrospect, how do you feel about your planning process? You can (but don't have to) consider several things - preparedness, connectedness, mathematically powerful, sequencing, use of materials, transitions, closure, assessment, management.
What might you do differently the next time you teach this or a related topic? Why? (If addressed before, don't repeat.)
What did you learn from watching your tape that you hadn't realized just from teaching the lesson? What long-term implications does this have for you? What have you learned about yourself as a teacher? Will this change the way you teach? If so, how?
What do you think the students got out of the lesson? How do you know this? How, if any, was this different from what you hoped they would get out of it? Do you think your students knew what the point of the lesson was? What could you have done differently to gain additional information on what the students learned?
Choose one or more students who did something interesting or puzzling (whether or not its on tape), and describe what they did. Why do you think they did what they did? What does this tell you about their thinking? goals? motivations? feelings? What did you learn from what they did?
How did the course readings and discussion relate to anything that you did? Conversely, how does what you did relate to the course readings?

Grading criteria
In order to form a summative grade for the rationale and lesson plans, the following rubric will be used:

(20 pts) Were all questions addressed in sufficient depth?
(20 pts) Is there depth in the reflection on the pedagogy and planning, or is this just superficial (is there reflection and not just description)?
(20 pts) Is there insight into your perception of the relationship between the planning process and what actually occurred in the classroom, particularly in regard to the mathematical goals?
(20 pts) Is there detailed discussion of specific student reactions and responses to the lesson, particularly in regard to the mathematical goals?
(20 pts) Did you adequately discuss what and how you learned from this experience?

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