Goal- Help our students become more comfortable with algebraic expressions. Background/Rationale-
Our students come from a low economic background and lack a lot of resources. Our students have performed below proficient in Algebra and Math in general in the NMSBA. They lack basic skills when they get to our school. When it comes to Algebra, which the students think is a new concept, but in actuality they have seen it long before, they are afraid to break away from numbers.
Our students have mentioned that learning Algebra is like learning a new language. We want to help our students become more comfortable with algebraic expressions by using the representations provided in the lesson. We choose to do the 8th grade unit Say it with Symbols because it gives they students representations that will help them become comfortable with variables and what they represent. By doing the lesson study on this unit we feel that this will help us meet our goal. Some of the teachers have taught this unit before and have agreed that this has always been a problem area to teach. We are really looking forward to the learning that will take place.
Comment from Blake: Here are a few thoughts to consider. When you say that you want them to be more “comfortable” with algebraic expressions, can you give a little more detail about what you mean by that? If you can think of a few specific understandings that you would like them to gain, then you will be able to look back at the end and decide whether or not they have actually reached their goal. In other words, list some measurable characteristics of “comfortable.” Do you want them to be good at manipulating them or just good at understanding what they represent?
I would think that “comfortable” is likely related to an understanding of variables. What do they need to understand about variable in order for them to be “comfortable” with algebraic expressions. Response
"What we mean is that students do not understand that a variable represents changing numbers. We notice that they want to automatically put a value on that value and not think about it anymore. Putting a value helps them to see a pattern, but then they stick with that value. We want them to become familiar with variables as representations of changing values." Comment from Blake:
That helps clarify a lot. It would be helpful for those who will observe your lesson to include some of that detail in the statement of the goal. Since the goal is what will drive the lesson, the more clear it is, the better. Comment from Susana
Blake, we have been talking about different kinds of goals. An overarching goal that schools or the team may have for their students. and specific goals for the lesson. The Chaparral team has another one for their lesson. I am looking at what Rina, the leader of the team sent me as a first draft of their lesson and I am adding a couple of comments/questions and will add it to this Wiki page in a little bit. Here is what we have been doing
December 16, 2009 1 hour
Discuss Lesson Study.
Discuss our goal as a team and research question.
Pick our lesson.
Homework: Read the Mathematics of unit and the teacher notes. Complete Investigation 1 in Say it with Symbols 8th grade CMP as if you were a student.
January 19, 2010 2 hours
Discuss the Math and the different responses that were available. We need to anticipate student responses.
Discuss the learning goal(s) of our lesson.
Write our lesson Plan for our lesson and Unit.
Discuss how to organize our summary and integrate Cornell Notes.
Homework: Write a reflection of what was discussed and how we are working towards our goal.
January 27, 2010 3 hours
Continue to work on our lesson plan.
Script teacher and student responses.
One person will teach lesson to the teachers.
watch lesson study video.
Homework: Read the page on observation. Write reflection of the meeting.
Blake thank you for your comments. We decided to put the equations that students came up with on the board and then put up one that was not equivalent so that the students can compare and find the one that is not equivalent.
In the pool problem the equations were given to them but in this problem the students come up with their own equations.
February 26, 2010
Public lesson given by Ms. Mariscal
February 27, 2010
Debrief of lesson
Discussed whether the lesson was not open enough
4/8 and 4/14
Continue to discuss debrief and changes needed in the lesson plan
We will give the groups the strips to put on the board.
4/28/10
Meet to discuss changes to the lesson plan.
The changes are highlighted in yellow. We will not be doing 1.2 our lesson will replace that lesson.
Blake-Our team was wondering what you meant about changing our goal. I can't remember exactly what I might have been thinking when I said this previously but I just read the most recent lesson plan and have made several comments on it relative to the goal. Here are a couple of the general ideas. The current goal is basically "two linear equations can be shown to be equivalent by checking more than one value." I am concerned about this goal because it is only true when you are looking at linear equations and I think students might overgeneralize this. An alternative to this is mentioned when considering tables and graphs of equivalent equations namely "all of the inputs and outputs will be the same in equivalent equations." This goal would have students plugging in several values into pairs of equations to see if they are equivalent. Since many of the students had troubles when they had to evaluate the expressions by plugging in values, this different goal might address their weaknesses better. I also have several other comments along these lines in the file itself which I have attached below. My comments are highlighted in blue.
Goal- Help our students become more comfortable with algebraic expressions.
Background/Rationale-
Our students come from a low economic background and lack a lot of resources. Our students have performed below proficient in Algebra and Math in general in the NMSBA. They lack basic skills when they get to our school. When it comes to Algebra, which the students think is a new concept, but in actuality they have seen it long before, they are afraid to break away from numbers.
Our students have mentioned that learning Algebra is like learning a new language. We want to help our students become more comfortable with algebraic expressions by using the representations provided in the lesson. We choose to do the 8th grade unit Say it with Symbols because it gives they students representations that will help them become comfortable with variables and what they represent. By doing the lesson study on this unit we feel that this will help us meet our goal. Some of the teachers have taught this unit before and have agreed that this has always been a problem area to teach. We are really looking forward to the learning that will take place.
Comment from Blake: Here are a few thoughts to consider.
When you say that you want them to be more “comfortable” with algebraic expressions, can you give a little more detail about what you mean by that? If you can think of a few specific understandings that you would like them to gain, then you will be able to look back at the end and decide whether or not they have actually reached their goal. In other words, list some measurable characteristics of “comfortable.” Do you want them to be good at manipulating them or just good at understanding what they represent?
I would think that “comfortable” is likely related to an understanding of variables. What do they need to understand about variable in order for them to be “comfortable” with algebraic expressions.
Response
"What we mean is that students do not understand that a variable represents changing numbers. We notice that they want to automatically put a value on that value and not think about it anymore. Putting a value helps them to see a pattern, but then they stick with that value. We want them to become familiar with variables as representations of changing values."
Comment from Blake:
That helps clarify a lot. It would be helpful for those who will observe your lesson to include some of that detail in the statement of the goal. Since the goal is what will drive the lesson, the more clear it is, the better.
Comment from Susana
Blake, we have been talking about different kinds of goals. An overarching goal that schools or the team may have for their students. and specific goals for the lesson. The Chaparral team has another one for their lesson. I am looking at what Rina, the leader of the team sent me as a first draft of their lesson and I am adding a couple of comments/questions and will add it to this Wiki page in a little bit.
Here is what we have been doing
December 16, 2009 1 hour
- Discuss Lesson Study.
- Discuss our goal as a team and research question.
- Pick our lesson.
- Homework: Read the Mathematics of unit and the teacher notes. Complete Investigation 1 in Say it with Symbols 8th grade CMP as if you were a student.
January 19, 2010 2 hoursDiscuss the Math and the different responses that were available. We need to anticipate student responses.
- Discuss the learning goal(s) of our lesson.
- Write our lesson Plan for our lesson and Unit.
- Discuss how to organize our summary and integrate Cornell Notes.
- Homework: Write a reflection of what was discussed and how we are working towards our goal.
January 27, 2010 3 hours- Continue to work on our lesson plan.
- Script teacher and student responses.
- One person will teach lesson to the teachers.
- watch lesson study video.
- Homework: Read the page on observation. Write reflection of the meeting.
February 1, 2010 1 hour and 20 minChaparral First draft of the Lesson Plan
February 3, 2010
Second draft
Blake's Comments on Second Draft
Blake thank you for your comments. We decided to put the equations that students came up with on the board and then put up one that was not equivalent so that the students can compare and find the one that is not equivalent.
In the pool problem the equations were given to them but in this problem the students come up with their own equations.
February 26, 2010
- Public lesson given by Ms. Mariscal
February 27, 2010- Debrief of lesson
- Discussed whether the lesson was not open enough
4/8 and 4/144/28/10
Meet to discuss changes to the lesson plan.
The changes are highlighted in yellow. We will not be doing 1.2 our lesson will replace that lesson.
Revised 3rd Draft
Blake-Our team was wondering what you meant about changing our goal. I can't remember exactly what I might have been thinking when I said this previously but I just read the most recent lesson plan and have made several comments on it relative to the goal. Here are a couple of the general ideas. The current goal is basically "two linear equations can be shown to be equivalent by checking more than one value." I am concerned about this goal because it is only true when you are looking at linear equations and I think students might overgeneralize this. An alternative to this is mentioned when considering tables and graphs of equivalent equations namely "all of the inputs and outputs will be the same in equivalent equations." This goal would have students plugging in several values into pairs of equations to see if they are equivalent. Since many of the students had troubles when they had to evaluate the expressions by plugging in values, this different goal might address their weaknesses better. I also have several other comments along these lines in the file itself which I have attached below. My comments are highlighted in blue.
Comments by Susana. I also had added some comments to your last draft. Some I think are solved by Blake's. But here it is anyway.