Jacob Disston and his students share their insights into the day's lesson and reflect on what they learned.

7th Grade Math - Algebraic Equations, Inequalities, & Properties*Jacob Disston, Willard Middle School, Berkeley Unified School District, Berkeley, California*

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JACOB DISSTON: when you get your six made up and you know what categories they fit in, what I want you to do is write the symbol string on one side and then tell me what it is on the back. Four minutes...

STUDENT: Do I do one on each category? Can I do the property of equation and solving for the unknown?

JACOB DISSTON: If you like. I mean I like to see if you can do the variety but...

STUDENT: We are supposed to write out our equations. We have to figure out what we are going to write. I'll do the expressions.

STUDENT: I'll do the equations.

STUDENT: Okay, so I guess you'll do the inequalities.

STUDENT: What can we write about equations?

STUDENT: (inaudible)

STUDENT: In separate cards right?

STUDENT: No, it says list them here and write each one of them on the front of an index card with a description of the subcategory on the...oh, I messed it up so bad.

JACOB DISSTON: What I'm going to do is ask you to reflect on the lesson. I'm going to ask you some questions and just have you write about it. You're going to write this right here in this last box; the open box on the back. I want you to think about when you came into this room and you started, I gave you this orange card. I want you to think about what you knew about these things, these symbol strings, these inequalities, these expressions, these equations when you came in. I want you to think about what you know about them now. I just want you to write a sentence or two of what you learned today. Is anybody willing to share the sentence of what they learned?

STUDENT: I learned that not all equations equal a number, some equal a variable.

STUDENT: I learned how equations, inequalities and expressions work.

STUDENT: I learned that there can also be different types of groups within groups.

STUDENT: What would you call equations, inequalities and expressions as a group?

JACOB DISSTON: Good question. What would we call the big group of these things?

STUDENT: Math.

STUDENT: Algebra.

JACOB DISSTON: Well I call them things, math things and then we came up with the name symbol strings, so we're calling them symbol strings.

STUDENT: Big groups of symbol strings can be broken into smaller groups.

JACOB DISSTON: Okay, so here's what I want you to write now. I just asked you "what did you learn," so I want you to think "how did you know you actually learned it?" Last thing I want you to write is how do you feel about it? How do you feel about this class that we just had? You guys are now the critics. You get to write anything you want about how the movie was. Put your papers in a pile and make sure your names on it. Put the cards in a pile on top of that. Clean up your table tops before you go back to your regular seats. I really want to thank you guys. You guys did an amazing job thinking and doing that with all the people and cameras in here. Bye, thank you.

COMMENTARY BY COACH LINDA FISHER: During the closure, Jake spends time discussing various ways that groups sorted equations. This part seemed like an opportunity to make all the knowledge or thinking from the groups public. It also honored the idea that there could be different categories. Once the equations were discussed, he didn’t choose to delve into the categories for the other two groups. Is it always necessary to have a group discussion about everything? Why or why not?

As I watch the lesson, I see that there are several built in places for assessment. In the first problem, students are given chances to write about their thinking so far (See the student artifacts – questions 1 and 2.) In the lesson closure, students are assessed by being asked to create new examples. Why is this a significant process for assessment? What does it tell you about how students are learning?