It's an important question to consider...are our class demographics representative of the entire school population. As we continue to study ratios and proportions we're making the move from exploring similar figures to looking at the world of sampling; the idea that data from an entire population can be determined by examining a small random sample. Thus, the question for today...does our class represent the entire school population?
1.) How many boys are in our school?
2.) How many girls are in our school?
3.) How many Hispanic students are in our school?
4.) How many Black students are in our school?
5.) How many Hispanic female students are in our school?
6.) How many Black female students are in our school?
7.) How many Hispanic male students are in our school?
8.) How many Black male students are in our school?
By setting up a series of proportions we can discover whether or not we actually represent the school. Only time will tell as we've just started the activity, but I have a hunch that the results will be disproportional. If that's the case, I'm hoping we can have an open conversation about why that might be. Who says math is only about numbers?
Thursday, January 31, 2008
Wednesday, January 30, 2008
I'm Proud of my Kids (1-30-08)
Today I feel proud of my students. We worked hard, collaborated effectively, and got the job done. Today we "made it happen." The question...what made the difference?
I think the biggest difference was the grouping of students. Randomly arranging them in groups of 3 for our problem solving session they seemed resistant at first, but then did a great job of working with one another. By the end of class Carlos, who was paired with Josh and Lulu, told me that he should keep his group forever. "We did great! We're so smart," he stated proudly. Beyond Carlos' triumphant feeling, Saul also found the power in his group. "Iaisha's so smart...she really explains things clearly," he told me. What I started to realize is that our class doesn't really know each other. If Saul hadn't been paired with Iaisha he may never have realized how much of an asset she is to our class. If Carlos hadn't been paired with Lulu he may have never discovered how bright she is and how much she can bring to our learning community. Beyond the two groups mentioned above I watched as Sir and Jordy worked together to complete the problems. I also saw Benito work much more positively in his new found environment (no insults today, or at least none that I heard).
Moral of the story...don't get lazy Mr. Singer...simply grouping kids in different ways can make a huge impact on student learning and the classroom culture. When you feel like saying, "go ahead and work with whoever you'd like..." Don't! You'll thank yourself later.
I think the biggest difference was the grouping of students. Randomly arranging them in groups of 3 for our problem solving session they seemed resistant at first, but then did a great job of working with one another. By the end of class Carlos, who was paired with Josh and Lulu, told me that he should keep his group forever. "We did great! We're so smart," he stated proudly. Beyond Carlos' triumphant feeling, Saul also found the power in his group. "Iaisha's so smart...she really explains things clearly," he told me. What I started to realize is that our class doesn't really know each other. If Saul hadn't been paired with Iaisha he may never have realized how much of an asset she is to our class. If Carlos hadn't been paired with Lulu he may have never discovered how bright she is and how much she can bring to our learning community. Beyond the two groups mentioned above I watched as Sir and Jordy worked together to complete the problems. I also saw Benito work much more positively in his new found environment (no insults today, or at least none that I heard).
Moral of the story...don't get lazy Mr. Singer...simply grouping kids in different ways can make a huge impact on student learning and the classroom culture. When you feel like saying, "go ahead and work with whoever you'd like..." Don't! You'll thank yourself later.
Monday, January 28, 2008
I'm just trying to teach math...or am I? (1-28-08)
Benitto and Jessica were really going at it today. So much disrespectful verbal banter. "I'm just gonna keep arguing with you cause if I piss you off enough maybe you'll leave this class," exclaimed Benitto. I'm not sure what Jessica's response was to that one as it's not fresh in my mind at this point, but what is fresh in my mind is the frustration I felt inside as I watched their insults being thrown back and forth like a vicious game of red rover, red rover send another insult over. What do they actually have against each other? Anything? Or, is it just a projection of things that are pissing them off inside and rather than keep the anger bottled in why not let it out...on someone else?
After diffusing the the situation as best I could and encouraging the two students to act as professional as possible while in a classroom environment I realized how innefective my words were. How many times has an adult explained to a child (or young adult) that you're not always going to work with people you like, but you still have to find a way to work in a respectful manner. What a classic speech. A speech that I highly doubt affected either of my intolerant pupils. Benitto even said that he had heard the same thing from his father on repeated instances. I'm pretty sure my words were listened to as much as those spewing from the mouth of Charlie Brown's teacher. Wah, wah, wah and more wah.
The dilemma...how can I put out the fires created by my students, convince them that we should all just "get along," and make sure everyone's learning a challenging level of mathematics, at the same time! Is it possible that not every kid is in a place to engage in learning everyday...most certainly. Is it also possible that teachers aren't in a place to teach everyday, but still find a way to press forward...most certainly. How do adults develop that ability to overcome their "stuff" and still get the job done. Tiger Woods doesn't blame a bad round of golf on the fact that his baby daughter kept him up all night (not that he has a lot of bad rounds). Where does the intellectual perseverance come from and how do we get more of it. "I know I'm having a rough day, I know things in my life aren't perfect, but you know what...I'm gonna get the job done and I'm definitely not gonna stop someone else from doing their job."
After diffusing the the situation as best I could and encouraging the two students to act as professional as possible while in a classroom environment I realized how innefective my words were. How many times has an adult explained to a child (or young adult) that you're not always going to work with people you like, but you still have to find a way to work in a respectful manner. What a classic speech. A speech that I highly doubt affected either of my intolerant pupils. Benitto even said that he had heard the same thing from his father on repeated instances. I'm pretty sure my words were listened to as much as those spewing from the mouth of Charlie Brown's teacher. Wah, wah, wah and more wah.
The dilemma...how can I put out the fires created by my students, convince them that we should all just "get along," and make sure everyone's learning a challenging level of mathematics, at the same time! Is it possible that not every kid is in a place to engage in learning everyday...most certainly. Is it also possible that teachers aren't in a place to teach everyday, but still find a way to press forward...most certainly. How do adults develop that ability to overcome their "stuff" and still get the job done. Tiger Woods doesn't blame a bad round of golf on the fact that his baby daughter kept him up all night (not that he has a lot of bad rounds). Where does the intellectual perseverance come from and how do we get more of it. "I know I'm having a rough day, I know things in my life aren't perfect, but you know what...I'm gonna get the job done and I'm definitely not gonna stop someone else from doing their job."
Thursday, January 24, 2008
We're Pretty Smart! (1-23-08)
As I walked around the room today and watched students engage in the learning activity I had a realization. "We're pretty smart!" The students were actively trying to discover how changing each coefficient, a, b, and c, in the quadratic model, y = ax^2 + bx + c, affects how the parabola looks. As I listened and watched I heard some beautiful thinking...
- "As the b value gets more positive the parabola slides in the southwest direction." (Armando)
- "When b is negative the parabola moves into the fourth quadrant and when b is positive the parabola moves into the third quadrant." (Torian)
- "I don't see a pattern when I'm changing the b value, the shift in the vertex when I change b seems somewhat random. How can I find the pattern?" (Iaisha)
- "If a is large and positive the parabola is skinny and if a is small and positive then the parabola is wide." (Jessica's group)
- "c just shifts the graph up and down. If c is positive the curve just moves up and if c is negative than the curve just moves down." (Saul's group)
Testing a variety of equations in the graphing calculator and exploring how manipulating the number changes the look of the curve, the kids actively pushed to discover mathematics. They still need guidance, support and modeling. They still get stuck from time to time and don't quite know how to get themselves unstuck. But, they're working hard to learn and when I step back for a moment and observe rather than engage I realize that we're actually pretty smart.
- "As the b value gets more positive the parabola slides in the southwest direction." (Armando)
- "When b is negative the parabola moves into the fourth quadrant and when b is positive the parabola moves into the third quadrant." (Torian)
- "I don't see a pattern when I'm changing the b value, the shift in the vertex when I change b seems somewhat random. How can I find the pattern?" (Iaisha)
- "If a is large and positive the parabola is skinny and if a is small and positive then the parabola is wide." (Jessica's group)
- "c just shifts the graph up and down. If c is positive the curve just moves up and if c is negative than the curve just moves down." (Saul's group)
Testing a variety of equations in the graphing calculator and exploring how manipulating the number changes the look of the curve, the kids actively pushed to discover mathematics. They still need guidance, support and modeling. They still get stuck from time to time and don't quite know how to get themselves unstuck. But, they're working hard to learn and when I step back for a moment and observe rather than engage I realize that we're actually pretty smart.
Friday, January 18, 2008
"Quadratics is real simple." (1/18/08) - thoughts by Sir
Today we prepared for a test or assessment on quadratics. When you think about it, quadratics is real simple. Learn how to graph, find a curve of best fit, and use these four equations. y =a(x-h)^2 + k to find a, y = -b/2a to find b, y = ax^2 + bx + c to find c, and x = (-b +- radical b^2 - 4ac)/2a to find roots. With those 4 equations you can answer almost any question about that graph and equation. After achieving an "A" on that test with ease and a calculator I think the power of 17 may be more interesting and easier than WE ALL THOUGHT.
Wednesday, January 16, 2008
"It's cause I'm stupid!" (1-16-08)
"Why am I wrong?" Carlos demanded. "It's cause I'm stupid. That's why." Such a defeatist attitude..."I'm wrong cause I'm stupid." I don't know if he really believes what he's saying, but I sure hope not. After all, he's one of the brightest students we have. "I'm not sure," I replied, "it could be any of your coefficients, a, b, or c. A minor error during any of your calculations could have caused the final equation to be off. Either way, just cause your quadratic model isn't producing the answer we're looking for doesn't make you stupid. Do you realize the intelligence it takes just to put this equation together. Don't sell yourself short Carlos...you're smart."
I really wasn't sure why it was wrong, but something seemed funny to me. Like Columbo finding the last clue before he breaks the case I kept looking at the solution. 18.6 seconds. The rocket would take 18.6 seconds to reach the ground. Based on the parabola on our graphs we were expecting a value somewhere between 30 and 34. Why 18.6? "Wait a second Carlos...let me see your graph...(pause to look at the curve and where it hits the x-axis) ARE YOU KIDDING ME! It's right...it's absolutely right. You were looking at the old data set...LOOK at your graph...WHERE DOES THE CURVE HIT THE X-AXIS?" "At 18," Carlos slowly and quietly rolled off his tongue. "AT 18! Which is damn close to what we got from your quadratic model. You're not stupid, not even close...you're just disorganized and have trouble following directions."
"Now that we've solved that mystery (speaking to the class) use this work (pointing to the modeling I had done with the quadratic formula to find the roots of a parabola) with your a, b, and c values to figure out when you think the rocket ship will reach the ground." As I walked around the room watching the students complete the task I felt a sense of comfort. Nearly everyone was trying to complete it. Nearly everyone demonstrated a desire to succeed. Nearly everyone wanted to engage in learning.
A couple of minutes passed when Josh approached me to share his solution. With a smile strung across his face like a sideways banana and his eyes open wider than a two year old staring at a bowl of ice cream his look said it all. "Check this out Mr. Singer," he said. "31.7 seconds." The evidence of his work was right there in front of me. He was so proud and I was too. Sharing a look of appreciation we hugged it out. Not a womanly type hug, but a man hug with a couple pats on the back. The kind of hug that a tough football coach might give to a player after making a great play. Josh is one of those kids whose just plain hungry for knowledge. How can you not want to give him a hug. How many students do you know that get that happy about performing in math class? He really is a great kid.
Moving away from Josh and continuing around the room my sense of pride and accomplishment grew. I knew I was looking at just 1 class and just 5 minutes and just 17 kids, but everything for that moment felt right. Like we were all learners...like we were all part of a team...like we were a collaborative learning community.
I really wasn't sure why it was wrong, but something seemed funny to me. Like Columbo finding the last clue before he breaks the case I kept looking at the solution. 18.6 seconds. The rocket would take 18.6 seconds to reach the ground. Based on the parabola on our graphs we were expecting a value somewhere between 30 and 34. Why 18.6? "Wait a second Carlos...let me see your graph...(pause to look at the curve and where it hits the x-axis) ARE YOU KIDDING ME! It's right...it's absolutely right. You were looking at the old data set...LOOK at your graph...WHERE DOES THE CURVE HIT THE X-AXIS?" "At 18," Carlos slowly and quietly rolled off his tongue. "AT 18! Which is damn close to what we got from your quadratic model. You're not stupid, not even close...you're just disorganized and have trouble following directions."
"Now that we've solved that mystery (speaking to the class) use this work (pointing to the modeling I had done with the quadratic formula to find the roots of a parabola) with your a, b, and c values to figure out when you think the rocket ship will reach the ground." As I walked around the room watching the students complete the task I felt a sense of comfort. Nearly everyone was trying to complete it. Nearly everyone demonstrated a desire to succeed. Nearly everyone wanted to engage in learning.
A couple of minutes passed when Josh approached me to share his solution. With a smile strung across his face like a sideways banana and his eyes open wider than a two year old staring at a bowl of ice cream his look said it all. "Check this out Mr. Singer," he said. "31.7 seconds." The evidence of his work was right there in front of me. He was so proud and I was too. Sharing a look of appreciation we hugged it out. Not a womanly type hug, but a man hug with a couple pats on the back. The kind of hug that a tough football coach might give to a player after making a great play. Josh is one of those kids whose just plain hungry for knowledge. How can you not want to give him a hug. How many students do you know that get that happy about performing in math class? He really is a great kid.
Moving away from Josh and continuing around the room my sense of pride and accomplishment grew. I knew I was looking at just 1 class and just 5 minutes and just 17 kids, but everything for that moment felt right. Like we were all learners...like we were all part of a team...like we were a collaborative learning community.
Monday, January 14, 2008
Are we there yet?...No we're not (1/14/08)
What a mediocre day. Everything just seems so "stale," as my colleague Darren likes to say. The students were stale, I was stale...it was all stale. After breaking into triads and quads to tackle a problem involving rocket ships and quadratic modeling I encouraged the students to work as mini-teams, working through the problem together, sharing ideas, and showing evidence of their thinking. What I got was silence. I'm not sure if they really know what it looks like to be an effective collaborator. In fact, I'm fairly confident that many of them don't. I need to model it, scaffold it and build it into our routine. When you work with a group of people you contribute. You pose questions to one another. You defend your thinking with evidence. You actively engage in the process of learning alongside one another. These are the things I want...they're not the things I'm getting.
Constantly moving around the room and pushing kids to really work with one another was both tiring and frustrating. "Come on Armando, does Jordy even have a clue what you're working on? Have you shared your thinking with him?" "Why is everyone in this group quiet Benito? Is anyone on the same page? Where's the collaboration?" "LaDon and Torian, how is it going to help you learn a new skill by just watching Iaisha write her work on the poster? Don't you need to involve yourselves in the process?"
After countless reminders, encouragements and suggestions the students finally started to work together. Benitto and Ron showed Angel how to find the a, b, and c values of a quadratic model, y = ax^2 + bx + c. Iaisha coached Torian and LaDon on the process used to get each coefficient as well. Carlos paid close attention as I facilitated his independent work (a success considering that his entire group left him after they became too annoyed by his behavior and attitude). Josh, Jessica and Saul worked alongside one another, trying to decide whose curve of best fit was the highest quality so they could use it as the foundation for deriving their quadratic equation. The students were finally starting to look like a community of learners. The only question is, why did it take us half the class to reach this level of collaboration? How can we make these type of student behaviors the norm without my incessant coaching?
When I look back on it now, maybe the class wasn't so mediocre after all. In fact Jessica demonstrated some beautiful knowledge when she stated that "the reason we work with non-linear data is because everything in the world doesn't follow a linear pattern and if we want to work with real data in real situations we're going to have to get used to other types of equations." As Ladon put it, "we're going to have to leave our comfort zone (linearity)." The class ended strong even though it started weak. Now the big question I'm wondering...How can we start strong, stay strong and finish strong? Maybe I need to give out Power Bars and Redbulls 40 minutes into class, or maybe there's another way. I'll let you know when I figure it out.
Constantly moving around the room and pushing kids to really work with one another was both tiring and frustrating. "Come on Armando, does Jordy even have a clue what you're working on? Have you shared your thinking with him?" "Why is everyone in this group quiet Benito? Is anyone on the same page? Where's the collaboration?" "LaDon and Torian, how is it going to help you learn a new skill by just watching Iaisha write her work on the poster? Don't you need to involve yourselves in the process?"
After countless reminders, encouragements and suggestions the students finally started to work together. Benitto and Ron showed Angel how to find the a, b, and c values of a quadratic model, y = ax^2 + bx + c. Iaisha coached Torian and LaDon on the process used to get each coefficient as well. Carlos paid close attention as I facilitated his independent work (a success considering that his entire group left him after they became too annoyed by his behavior and attitude). Josh, Jessica and Saul worked alongside one another, trying to decide whose curve of best fit was the highest quality so they could use it as the foundation for deriving their quadratic equation. The students were finally starting to look like a community of learners. The only question is, why did it take us half the class to reach this level of collaboration? How can we make these type of student behaviors the norm without my incessant coaching?
When I look back on it now, maybe the class wasn't so mediocre after all. In fact Jessica demonstrated some beautiful knowledge when she stated that "the reason we work with non-linear data is because everything in the world doesn't follow a linear pattern and if we want to work with real data in real situations we're going to have to get used to other types of equations." As Ladon put it, "we're going to have to leave our comfort zone (linearity)." The class ended strong even though it started weak. Now the big question I'm wondering...How can we start strong, stay strong and finish strong? Maybe I need to give out Power Bars and Redbulls 40 minutes into class, or maybe there's another way. I'll let you know when I figure it out.
Friday, January 11, 2008
Iaisha's 1st Blog (1/11/08) - A student's perspective
Being in the upper math class so far is giving me a chance to be with students who share the same qualities of learning as me. The first day back we worked on finding what it means to be in a collaborative learning community. So far I think we are beginning to get what it means. I feel that once we fully understand collaborative learning community we will get even farther in math. Yesterday we worked on Excel and Power Point...I helped Saul with his work, and as I helped him I realized that I am contributing to the collaborative learning community. I helped Saul clarify his work! I felt as if that was a step ahead of building a relationship with another student. I look forward to seeing where this upper math class leads to. Also, to experience a complete collaborative learning community. I have faith in the "Power of 17."
Thursday, January 10, 2008
Day Three (1/10/08) - The Chant
"My mom's gonna kill me if she reads this," erupted Carlos as he listened to me share my latest posting with the class. "Maybe you should watch what you say," I replied, "the public is listening."
Class went smoothly as the students were fairly engaged in their work today. They've been creating PowerPoint presentations for an inter-disciplinary project around examining the culture's of countries. The math component has involved linear and quadratic modeling of population data and using those models to make future predictions. Where's this country's population headed and how is that going to effect the people who live there? All of this work has fallen under the umbrella essential question, "What if the future really isn't a mystery?" Having spent a great deal of time exploring the power of modeling data with functions and using those functions to make predictions I think the kids are starting to realize that maybe the future isn't so mysterious after all.
As exciting as the content of our class is (might depend on your perspective)...the biggest highlight from today didn't come from the curriculum. It came from our first go at our new closing chant. I really wanted to give us something to end with every class that would remind us of our goal, the creation of a true collaborative learning community. Since my exhaustion has recently taken over my originality I pulled from the student's definition of what it means to be part of a collaborative learning community that they created jsut a couple of days ago. And why not? Why not use their words? Here's how it goes...
Teacher: "We Sink"
Students: "We Sink"
Teacher: "We Swim"
Students: "We Swim"
Teacher: "Together"
Students: "Together"
Teacher: "We are"
Students: "We are"
Teacher: "Interdependent"
Students: "Interdependent"
The most positive thing I can say about our first crack at this new ritual was that nearly everyone participated without hesitation. My plan for tomorrow and from here on out. Go through it three times gradually increasing the volume from a whisper to a roar..."We are Interdependent." Can you hear it?
Class went smoothly as the students were fairly engaged in their work today. They've been creating PowerPoint presentations for an inter-disciplinary project around examining the culture's of countries. The math component has involved linear and quadratic modeling of population data and using those models to make future predictions. Where's this country's population headed and how is that going to effect the people who live there? All of this work has fallen under the umbrella essential question, "What if the future really isn't a mystery?" Having spent a great deal of time exploring the power of modeling data with functions and using those functions to make predictions I think the kids are starting to realize that maybe the future isn't so mysterious after all.
As exciting as the content of our class is (might depend on your perspective)...the biggest highlight from today didn't come from the curriculum. It came from our first go at our new closing chant. I really wanted to give us something to end with every class that would remind us of our goal, the creation of a true collaborative learning community. Since my exhaustion has recently taken over my originality I pulled from the student's definition of what it means to be part of a collaborative learning community that they created jsut a couple of days ago. And why not? Why not use their words? Here's how it goes...
Teacher: "We Sink"
Students: "We Sink"
Teacher: "We Swim"
Students: "We Swim"
Teacher: "Together"
Students: "Together"
Teacher: "We are"
Students: "We are"
Teacher: "Interdependent"
Students: "Interdependent"
The most positive thing I can say about our first crack at this new ritual was that nearly everyone participated without hesitation. My plan for tomorrow and from here on out. Go through it three times gradually increasing the volume from a whisper to a roar..."We are Interdependent." Can you hear it?
Wednesday, January 9, 2008
Day Two (1/9/08) - A Little Friction
"Come on Asshole!" blurted Carlos. "You gonna call me an asshole...I'm not helping you." A reasonable response by Eduardo when you stop and think about it. Why would I want to help a student who just called me an asshole and I'm a teacher, not a 15 year old. Moving away from a group of kids who were engaged in a mini-lesson on using Excel to create graphs I felt a bit obligated to speak with the two young men.
"What's going on guys?" "It's simple," replied Carlos,"Eduardo won't help me learn how to do these parabolas." "That's cause he's acting like an ass," immediately snapped Eduardo. "Alright...enough." I just wanted to cut off the banter before it grew out of hand. "We've got a simple dilemma...Carols, there's something you want to and need to learn...Eduardo, there's something you know and have the opportunity to share. You are interdependent...Carlos, you need Eduardo to teach you and Eduardo, you need Carlos so you have a chance to clarify your thinking around quadratics and to solidify what you know. The bottom line, you need to find a way to make this work...you need each other."
As I walked away from the two disgruntled students I wondered what would happen next. I hadn't really finalized things...I left them a bit open (on purpose). At some point during our time together these guys were gonna have to find a way to live in the same house. Forcing boiled chicken down your throat like my grandma used to do wasn't gonna do it. I needed to put it on them.
Ten minutes went by as I continued with the mini-workshop when I glanced over to find Eduardo once again working with Carlos. Eleven minutes went by when I glanced over to find Eduardo and Carlos arguing. Eleven minutes and fifteen seconds went by when I glanced over to find Eduardo angirly moving back to his table with a look of of utter defeat. I guess he knows how it feels to be a frustrated teacher with a stubborn student. God knows I do.
Evidence that we don't yet have a true Collaborative Learning Community...Carlos and Eduardo.
"What's going on guys?" "It's simple," replied Carlos,"Eduardo won't help me learn how to do these parabolas." "That's cause he's acting like an ass," immediately snapped Eduardo. "Alright...enough." I just wanted to cut off the banter before it grew out of hand. "We've got a simple dilemma...Carols, there's something you want to and need to learn...Eduardo, there's something you know and have the opportunity to share. You are interdependent...Carlos, you need Eduardo to teach you and Eduardo, you need Carlos so you have a chance to clarify your thinking around quadratics and to solidify what you know. The bottom line, you need to find a way to make this work...you need each other."
As I walked away from the two disgruntled students I wondered what would happen next. I hadn't really finalized things...I left them a bit open (on purpose). At some point during our time together these guys were gonna have to find a way to live in the same house. Forcing boiled chicken down your throat like my grandma used to do wasn't gonna do it. I needed to put it on them.
Ten minutes went by as I continued with the mini-workshop when I glanced over to find Eduardo once again working with Carlos. Eleven minutes went by when I glanced over to find Eduardo and Carlos arguing. Eleven minutes and fifteen seconds went by when I glanced over to find Eduardo angirly moving back to his table with a look of of utter defeat. I guess he knows how it feels to be a frustrated teacher with a stubborn student. God knows I do.
Evidence that we don't yet have a true Collaborative Learning Community...Carlos and Eduardo.
Tuesday, January 8, 2008
Day One (1/8/08) - Here we go!
Students will create a definition for collaborative learning community and recognize the value of working within one. That was our learning outcome for day one. To reach this desired result we participated in a variety of activities. Starting with a continuum protocol the students had to take a stance on such statements as I learn more when I work alone vs. I learn more working in a group and a basketball team has a better chance winning with one all star versus an entire team working together. Getting their voice on the table it was great to listen to them open up and begin to share their ideas with one another. "I definitely learn more in a group, said Iesha, because I have a chance to share my ideas." "My education comes first," stated Jessica firmly. "I'll help other people, but not if it's getting in my way of learning." What if the roles were reversed I posed to my firmly grounded student? "I guess it would be nice to get some help," she quietly replied. As the continuum protocol came to an end with the basketball metaphor is was beautiful to watch the entire class move to the side of the room that represented "A basketball team has a better chance of winning as an entire team working together." I felt like Moses parting the Dead Sea (even though the wave only went one way). Everyone agreed...our chances for success increase exponentially when we all take responsibility for the greater good...when we all join a collaborative learning community.
Moving on from the continuum activity students were grouped at their tables and asked to read a variety of short texts that described everything from cooperative learning to community to collaboration. Co-constructing a definition of Collaborative Learning Community, the students read the documents, shared the main ideas and synthesized the information to create one, concise and simple definition. As they worked in teams Carlos, an inquisitive young man to say the least, called me over and said, "Mr. Singer, are you saying you want us to be like the army? Leave no man behind?" After pausing to think..."Yeah Carlos, I guess I am." Illustrating Carols' point even more, Aramando's group, made up of Jessica, Bennito and Angel created the stickiest definition I could have imagined. Chip and Dan Heath, authors of Made to Stick, would have been proud of the simplicity in their words. "A Collaborative Learning Community" is interdependence, you sink or swim together."
That was it...the seed had been planted and we even did a little watering. I'm not saying you could see a branch, a leaf, or even a weed...but the seed was in the dirt and I'm confident that it will grow with time.
Moving on from the continuum activity students were grouped at their tables and asked to read a variety of short texts that described everything from cooperative learning to community to collaboration. Co-constructing a definition of Collaborative Learning Community, the students read the documents, shared the main ideas and synthesized the information to create one, concise and simple definition. As they worked in teams Carlos, an inquisitive young man to say the least, called me over and said, "Mr. Singer, are you saying you want us to be like the army? Leave no man behind?" After pausing to think..."Yeah Carlos, I guess I am." Illustrating Carols' point even more, Aramando's group, made up of Jessica, Bennito and Angel created the stickiest definition I could have imagined. Chip and Dan Heath, authors of Made to Stick, would have been proud of the simplicity in their words. "A Collaborative Learning Community" is interdependence, you sink or swim together."
That was it...the seed had been planted and we even did a little watering. I'm not saying you could see a branch, a leaf, or even a weed...but the seed was in the dirt and I'm confident that it will grow with time.
Monday, January 7, 2008
What if your philosophy is wrong? (1/7/08)
Malcom Gladwell, renowned author of national bestsellers The Tipping Point and Blink, does a beautiful job of convincing his readers that word of mouth is one of the essential ingredients in creating epidemics. In a poignant example to illustrate his hypothesis he refers to Paul Revere and his famous ride in which he yelled to the people, "the British are coming." One person acted as a catalyst for creating an epidemic that spread like wild fire. Gladwell, doing a tremendous job of providing countless anecdotal evidence to his theory, shares a multitude of illustrations to illuminate his point. But...what if he had been wrong? What if his beautiful idea about word of mouth epidemics was flat out invalid? What if everything he believed around his theory was proved unsubstantiated when put to the test? What if only one person had listened to Revere's words while everyone went about their business, sipping tea and knitting sweaters (I don't really know what they did in those days)?
That's how I feel at this point in time...like an invalid Gladwell. An amazing theory with no support. My grounding philosophy as a progressive educator framed around heterogeneous grouping has been compromised (to an extent). Although my students have shown growth through out the first semester of school and data from our assessments will support that claim, I still know that their needs have not been met. Sir and Iesha could have accomplished so much more...Milton and Liz learned hardly a thing...McKena did what was expected of him even though he could have rose to greater heights...and Aramis still hasn't proved he can make a prediction using a linear model. I feel like the data that shows student growth is hiding the truth...student's needs were not met to the extent that they could have and should have been.
As a result of this realization we have made changes to our grouping of kids as described in my initial blog. The only way that my mind is able to deal with this shift that goes against my "Wilhelm bottom line" is that it doesn't represent the traditional form of tracking. Why? For two reasons.
1.) Our grouping is fluid. Students can move in and out of the Algebra-X class as well as the Algebra support class and the frontloading elective. Nothing about our sectioning of students is final.
2.) If you examine the Algebra-X class roster closely you start to see that it's not really homogeneous. It's a beautiful mixture of female, male, Black and Hispanic students who encompass a wide range of student categories. Ranging from behavior problems to high performing, mature intellectuals the class really is more of a variety pack than just one flavor.
Perhaps the above is just a cleverly orchestrated excuse in helping me deal with the fact that I've broken my core philosophy, but the objective part of me likes to believe that there is some merit to my argument. If the changes being made create a positive increase in learning for all students then how can such change be deemed unworthy?
Gladwell's theory was right...mine may have been wrong, but...we're doing something about it.
That's how I feel at this point in time...like an invalid Gladwell. An amazing theory with no support. My grounding philosophy as a progressive educator framed around heterogeneous grouping has been compromised (to an extent). Although my students have shown growth through out the first semester of school and data from our assessments will support that claim, I still know that their needs have not been met. Sir and Iesha could have accomplished so much more...Milton and Liz learned hardly a thing...McKena did what was expected of him even though he could have rose to greater heights...and Aramis still hasn't proved he can make a prediction using a linear model. I feel like the data that shows student growth is hiding the truth...student's needs were not met to the extent that they could have and should have been.
As a result of this realization we have made changes to our grouping of kids as described in my initial blog. The only way that my mind is able to deal with this shift that goes against my "Wilhelm bottom line" is that it doesn't represent the traditional form of tracking. Why? For two reasons.
1.) Our grouping is fluid. Students can move in and out of the Algebra-X class as well as the Algebra support class and the frontloading elective. Nothing about our sectioning of students is final.
2.) If you examine the Algebra-X class roster closely you start to see that it's not really homogeneous. It's a beautiful mixture of female, male, Black and Hispanic students who encompass a wide range of student categories. Ranging from behavior problems to high performing, mature intellectuals the class really is more of a variety pack than just one flavor.
Perhaps the above is just a cleverly orchestrated excuse in helping me deal with the fact that I've broken my core philosophy, but the objective part of me likes to believe that there is some merit to my argument. If the changes being made create a positive increase in learning for all students then how can such change be deemed unworthy?
Gladwell's theory was right...mine may have been wrong, but...we're doing something about it.
Budapest, Hungary (1/2/08) - The Power of 17
There I was in a small Hungarian bistro waiting for my bowl of Goulash soup to come out when I left my vacation and traveled back to my classroom. It's amazing how easily teachers can leave their classroom, their school, or even their country, but never escape their profession. The upcoming semester was coming with some substantial changes and I really hadn't spent time digesting how the changes would affect my teaching and the school as a whole.
Finishing our first semester in the newly re-opened Manual High School a group of us realized that we just weren't meeting the needs of our students. The epic question of how wide of a spectrum can be differentiated for in the secondary math classroom was driving us crazy. Students with ability levels ranging from 4th through 9th grade in the same classroom is a daunting task...no question about it. As an experiment and as an effort to meet the needs of our kids we decided to make some changes (using the work of the Denver School of Science and Technology as a model to start from). The major changes were as follows.
1.) A separate class made up of a small group of students would be put together to support kids who just weren't ready for Algebra. These students had been constantly struggling because of the compound number of foundation skills missing from their math background. We wanted to give them a math opportunity where they could feel success and equip themselves with the tools necessary for completion of a rigorous secondary math program.
2.) An elective "frontloading" class would be developed for students who felt like they just need more time to digest the Algebra they're learning. This class would be offered twice a week and would introduce students to upcoming major math concepts before they see them in their Algebra classes. This would mean that students would have their regular Algebra class 85 minutes everyday in addition to two more 85 minute periods of "frontloading." Amazingly, 29 of my 80 students had volunteered for this elective citing that they loved the idea of getting "smarter at mathematics and feeling more confident with the work."
3.) A group of students, as determined by anecdotal evidence and quantitative data, would be placed in an Algebra-X class. Made up of a healthy mix of male, female, Hispanic and Black students (there are no white students on my team), this class would set a higher bar for student learning. Working harder, going deeper and moving faster, this class would challenge a group of 17 to rise to a new level of mathematics learning.
This 3rd change, the creation of the Algebra-X class, is what my mind focused on the most. "The Power of 17" just kept ringing in my head. Over and over and over. "The Power of 17." What could these 17 kids accomplish together. How could they epitomize the mission of our inner city school and act as a model for our beliefs? How could we create a sub-culture of 17 kids who embody what learning looks like in the new Manual High School? So many questions posed and only 5 more days before the start of our journey to answers begins.
Finishing our first semester in the newly re-opened Manual High School a group of us realized that we just weren't meeting the needs of our students. The epic question of how wide of a spectrum can be differentiated for in the secondary math classroom was driving us crazy. Students with ability levels ranging from 4th through 9th grade in the same classroom is a daunting task...no question about it. As an experiment and as an effort to meet the needs of our kids we decided to make some changes (using the work of the Denver School of Science and Technology as a model to start from). The major changes were as follows.
1.) A separate class made up of a small group of students would be put together to support kids who just weren't ready for Algebra. These students had been constantly struggling because of the compound number of foundation skills missing from their math background. We wanted to give them a math opportunity where they could feel success and equip themselves with the tools necessary for completion of a rigorous secondary math program.
2.) An elective "frontloading" class would be developed for students who felt like they just need more time to digest the Algebra they're learning. This class would be offered twice a week and would introduce students to upcoming major math concepts before they see them in their Algebra classes. This would mean that students would have their regular Algebra class 85 minutes everyday in addition to two more 85 minute periods of "frontloading." Amazingly, 29 of my 80 students had volunteered for this elective citing that they loved the idea of getting "smarter at mathematics and feeling more confident with the work."
3.) A group of students, as determined by anecdotal evidence and quantitative data, would be placed in an Algebra-X class. Made up of a healthy mix of male, female, Hispanic and Black students (there are no white students on my team), this class would set a higher bar for student learning. Working harder, going deeper and moving faster, this class would challenge a group of 17 to rise to a new level of mathematics learning.
This 3rd change, the creation of the Algebra-X class, is what my mind focused on the most. "The Power of 17" just kept ringing in my head. Over and over and over. "The Power of 17." What could these 17 kids accomplish together. How could they epitomize the mission of our inner city school and act as a model for our beliefs? How could we create a sub-culture of 17 kids who embody what learning looks like in the new Manual High School? So many questions posed and only 5 more days before the start of our journey to answers begins.
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