ED 411/518 Teaching Children Mathematics
Fall 2003
Designing, Teaching, and Analyzing a Mathematics Lesson
Project #2
The second project focuses on designing, teaching, and analyzing a mathematics lesson. It has three parts. In the first part you will examine a specific textbook lesson that you will teach your class, and consider where your particular students are with respect to the content and skills of that lesson. In the second part of the project you will design your plan for teaching the lesson. In the third you will teach your lesson and analyze how it goes.
Note that this project extends and elaborates the work involved in teaching a lesson beyond what you can do most of the time as a teacher. However, the thinking involved is thinking that is important to do for all lessons. The point is to work in detail on aspects of teaching that you will then learn to do much more fluently.
Part 1—Figure out the mathematical learning goals of a lesson, and set a learning goal for yourself.
(a) Select a lesson. With the assistance of your cooperating teacher and your classroom situation in mind, choose a textbook lesson on place value or computation that you can teach sometime between November 3 and 14.[1]
(b) Clarify the mathematics learning goal(s) for your students. Use the following questions to size up the mathematics of the lesson. You do not have to write out answers to each of these questions one by one; you could instead design and experiment with a way to consider each of these aspects of the lesson and make some record of your appraisal (e.g., a chart or table).
- What is this lesson about? What is the mathematics that students are supposed to be learning?
- What are crucial things that students would have to already know or be able to do to work on this?
- What do the problems or exercises seem to intend students to do?
- Are the tasks for students well aligned with what the lesson is supposed to be about? (Do the problems or tasks yourself to get a concrete idea of what will be involved, and to uncover possible surprises.)
- What implicit assumptions are being made about students –– about their prior experience, their out-of-school lives, their interests and values, their language? How might any of these assumptions create barriers for some students?
- Is this work appropriate for all your students? In what ways is it, and in what ways might it not be?
- What can you anticipate about what students might do in response to the questions and tasks in this lesson? What difficulties might students have? In how many different ways might they approach the work?
(c) Set a learning goal for yourselfas a teacher. In conjunction with your analysis of the lesson, choose a recent experienceyou had as a teacher working with students on mathematics. This could be a lesson you taught sometime during the semester, one you observed your cooperating teacher teach, a lesson from a video we watched, an experience you had with a student or group of students, or an experience from Project 1. Use your experience to define a goal for yourself as a teacher in this lesson. What do you want to try to do, to work on, to learn? Why is this goal important to you, and what are you drawing on in setting this goal for yourself?
Your write-up for Part 1 should include the following two sections:
1)A summary of your sizing up of the lesson from part 1(b). Be sure to include a description of the mathematical learning goal(s) of the lesson and how you think it will work with your students.
2)A description of your learning goal for your teaching from part 1(c), including an explanation of why you have chosen to focus on this goal and what you hope to learn.
Your write-up for Part 1 is due by: Thursday, November 6, in class.
Part 2—Design the lesson.
In detail, map out the segments of the lesson, including (a) designing the opening and setting up of the lesson, and (b) how you will bring the lesson to a stopping point, and how you will “tie” it up for students.
Consider each of the following as you design your lesson:
a)the mathematical learning goals (see Part 1(b));
b)the representations you choose (manipulatives, diagrams, etc.) and your considerations in choosing one over another representation;
c)ways to rescale or modify the work in light of the content and your own students (you should develop some “back pocket” ideas for alternative versions, extensions, and probes that you might have ready just in case); and
d)how you are attending actively to issues of equity in: the tasks you use in the lesson, with special attention to whether or not to contextualize the mathematics in some sort of situation; and how you are prepared to scaffold your students’ learning, with special attention to how to make the work learnable and yet still challenging.
For Part 2, turn in any written preparation you do, including specific descriptions of how you designed for the considerations above. You can design a format for writing your lesson plan that works for you. I will offer some possibilities for you to experiment with as well. What you consciously prepare, and the form in which you set up your plan can make a big difference to your ability to navigate the lesson.
Your written work for Part 2 is due no later than Thursday, November 13, in class.
Part 3--Teach your lesson and analyze how it goes.
Document what happened and gather artifacts or records of the experience, such as videotape, audiotape, written reflections, students’ work, and other people’s observations. Use these records, to write a description of what happened and to reflect on three crucial features of the experience: the mathematics, the students, and the teacher (yourself). The following questions are to help probe your thinking and assist you in your reflection; you do not need to answer each question individually:
Mathematics: What mathematical ideas came up as students worked during this lesson? Did anything surprise you? What aspects of the work seemed to cause students some difficulty? What new ideas did children seem to get from the lesson, and what is your evidence?
Students: What surprised you about students’ responses or participation? Who participated, and in what ways? Did you notice any patterns in who participated, who seemed interested, who was successful with this lesson? What do you think might explain this? Were there other equity issues that arose?
Sample a few different students’ work to show what the students were doing. Be sure to look at evidence of students’ mathematical thinking as represented by their work.
The teacher: What did you do well? Why? What was harder to do? Why?
How well did you do in using the task to make it a constructive opportunity for students to learn mathematics? How well were you able to anticipate how students would respond to the task? How did you feel about trying to probe students' thinking? What was the most challenging aspect of the lesson for you? What were the other on-the-job demands of the situation? Did anything feel easy?
Your write-up for Part 3 should include the following three sections:
1)Description of what happened: What did you and the students actually end up doing (talking about, working on, discussing, getting stuck on)? Try to make your description vivid, and if possible, include excerpts from the talk.
2)Reflection on the mathematics, the students, and the teacher (yourself).
3)Overall comments: What went well, and why? What did not work out so well and why? What progress did you make toward your own learning goal? Based on this experience, what goals do you have for your next experience teaching mathematics this year?
Your write-up for Part 3 is due by: Wednesday, November 26, at 3 p.m.
Ball/Bass/Gilbert/Oonk/Siedel/SleepPage 1 of 3
[1] If you cannot do a lesson that involves some aspect of these ideas, please confer with me about your topic choice. Your cooperating teacher should be comfortable with what you intend to teach and it should be practically related to something that makes sense to be working on with your students now, whether precisely following on what they are doing at this moment or not.