Your personal experience with groping for an answer with this activity is the base for understanding. What helped you to find solutions? How is your "algebraic" mind interpreting the trains differently from the students in the video?

What kind of questions did the teacher use to facilitate the students thinking about perimeter?

The environment in Steve's class is open to investigation. How does he sustain the inquiry? What strategies do you see him using? How is student dialogue encouraged?

A Field Expert will join your online discussion.

What's a Field Expert?

1. What understanding of "perimeter" did Semhar, Ben, and Reeves start out with?
2. Ben struggles for understanding of the +2 at the overhead. What is the center of his confusion?
3. Reeves, the third student at the overhead, suggests a "pop up" theory of the origin of the +2. What would you do to encourage deeper reflection on this hypothesis?
4. The student interaction in the small group is very rich. Can you comment on it?
5. How can you, as the teacher, intervene to promote discussion and reflection? How could the lesson be improved to work better with your students?

Read the comments of others and post two of your own in the Algebra discussion area. Look for the Tools: Algebra Activity 1 thread.

What is the reason for this second reflection?

In the first reflection, you probably thought mostly about the activity itself. In this round, you will react to others' comments, and try to step back and look at the big picture:

• How can a geometric perimeter activity contribute to learning algebra?
  

• Understanding of variable and the need for such a concept is a key transition for students. How can a geometric or manipulative model help?

One hour to post your ideas.

One hour to comment on postings and other reflections.

1. Content issues:

• The abstraction immanent in algebra is made concrete and contextualized using the perimeter relationships in the pattern blocks microworld. How do students make the transition from a domain like pattern blocks to a level of comfort and self-confidence with manipulation of symbols?

2. Issues relating to psychological set:

• Steve's class presented an interesting atmosphere. How does one develop support for hypothesizing?
• Students possibly came to this class with expectations about math that were very different from the way they are studying math right now. How does one develop a schoolwide atmosphere of inquiry?

3. Issues relating to pedagogy:

• Steve has some strategies for questioning and encouraging discourse. What are they? What similar strategies do you use in your class?

Go to the Algebra Discussion Area.