Each student will spend six hours in an elementary school classroom, three periods observing and three periods working with one or two children in the classroom. You may already know a teacher with whom you can work. If not, choose a school that will be convenient for you to visit. You should do your practicum at a different grade level than last year (semester) so that you may gain exposure to a variety of grade levels, teachers, and techniques. Speak to the principal and explain that you are studying to be an elementary school teacher and would like permission to visit a classroom, observing a math lesson three times and then working with 1 or 2 students for three lessons. Briefly describe what you would like to do and give her/him the attached letter. If you have difficulty in finding a teacher to work with or a teacher who will allow you to complete your practicum as specified in the letter they receive from you, let me know as soon as possible. To a certain extent, we may need to be flexible to the needs of the teacher, but in order to write an analysis paper you will need the opportunity to evaluate students and teach a lesson to the same group. If the teacher wishes you to help students correct errors in worksheets or tests (or anything of this nature), you should work with a different teacher.
The first part of the classroom experience will involve observing three math lessons. These observations may take place in different classrooms. During these lessons you want to consider the observation questions attached below and the assessment questions presented in a video shown in class. Give a lot of attention to the children’s mathematical thinking and note any questions you have about particular student’s understanding of the lesson topics. This classroom observation will be the subject of some class discussion and an assignment. The signature sheet and observation write-up are due October 5.
Observation questions:
What are the class characteristics? (For example: grade, number of children, special interests or considerations.)
What was the mathematics topic under discussion? What was the particular focus of the lesson? Was the focus on a particular concept or on developing a particular skill? Was there some overlap?
What are the prerequisites for the topic in this math lesson? Where does this math lesson lead and are there connections to others topics in math or to other subject areas that you might explore?
Describe how a few students of interest to you worked on the math topic; what they seemed to grasp; what their level of understanding might be, where their confusions seemed to be. Be able to document each case by providing an example of a student question or comment.
The second part of the classroom experience will be your work with 1 to 3 children in the classroom. In this part, during the first meeting with the children, you will explore the children’s understanding of a topic in area or measurement. For the last two meetings you will carry out lessons planned by you which are intended to further develop the children’s understanding of the topic you are considering.
Finally, you will write a typewritten analysis of your mathematical work with the children. Be sure to keep careful notes from your work with the children in order to have the information available when you write your practicum report. This report is due November 25 and will be discussed in detail in class.
Investigating your student’s understanding is an important part of preparing to teach. Although it is not realistic that you (or any teacher) do extensive interviews with each of your students before embarking on teaching a new topic, the information you glean from conducting this interview should provide you insight into the possible ways to listen to student ‘mathematically’ by tuning in to their mathematical ideas. The information gained from this sort of listening will help you make decisions about your teaching.
Before interviewing the student, go through the questions and tasks in the interview. Review the purpose (s) of each, asking yourself what you expect to learn about the student from their responses. This will help you plan questions to follow-up and probe what the student says.
Conduct your interview. Remember that your goal will be to ask questions that help you gain understandings about the student’s mathematical reasoning. Take notes about what the student says and does. Keep anything the student writes down or draws during the interview (this means you should provide paper and pencil for the student if needed.)
As soon as possible after the interview, jot down any insights that occurred to you, including your present hunches about what the student understands and what types of problem solving strategies they used. Develop a plan for the next stage in the student’s mathematical development as a result of your assessment. Have several back-up plans for the next two hours of teaching so that you can be flexible enough to follow the student’s needs.
What The Practicum Report Should Include:
Class characteristics such as school, grade level, number in class, special interests or considerations.
A brief mention of your observations in the class, including the behaviors of your student(s).
Your evaluation of the student’s understanding of the operation or concept considered based on the student’s comments and work
Your plan for the next stage in the student’s mathematical development with a brief outline and rationale for the lessons or work that you plan to present to the student. Be sure to state your goal very clearly. Include some examples you used.
A description of the mathematical discussion and learning that took place during the lesson or work outlined above along with the student’s dialogue and questions/responses to the mathematical discussion. Was the lesson teacher or student focused? How could you tell the student was engaged? Did the work focus on an algorithm, a concept, a model or an application?
An analysis of the student’s response including a discussion of how the student’s understanding appeared to change during the lesson or work and why this change took place, or a discussion as to why the student’s understanding did not appear to change and why; what worked or didn’t work mathematically in the lesson and how the lesson might be improved. What did the student take away from this experience? What did you take away from it? What would you do differently next time?
The grading on the Practicum Report will be based on the depth of your analysis of the child’s mathematical thinking and interaction during the lessons presented.