Sense of Urgency? (5-22-08)

Do you remember finals week in college? A ridiculously stressful time when everyone grinds to get it done. From final papers to class presentations to exams, finals week is great for one reason. It prepares you for the future high-stress situations that you're bound to face in your career. Whether it's a deadline for an article or a last minute creation of a partnership proposal for a business...every high-stress experience that you come out on top of builds a sense of confidence and assurance for the next encounter. Like the way Tiger Woods pulls on all of his previous victories to push through to the podium in each of his new successes we need a foundation of positive encounters to act as a catalyst for success in our future.

In our last week of school I am finding myself disappointed with a large group of students who are failing to rise to the occasion. Rather than just providing them with a traditional final assessment I've chose to break their final into two parts...a written component (30% of their final grade) and a presentation on what they know and how did they grow (70% of their final grade). The reason behind this decision was that they have an opportunity to pick any topic from the year that they feel confident in and share their expertise with us. It's unreasonable to think that every kid will be highly proficient at every content topic that we've covered this year. It seems highly reasonable that every student can pick one area that they are comfortable with and demonstrate to the class that they really know their stuff. Thus, I put more weight on the component of their final in which they have freedom of choice and more likelihood of success.

On Monday I provided students with a schedule of their presentation times with each of their time slots clearly mapped out. Today is Thursday and one out of the 6 scheduled students presented. It was like watching the Power of 1...what happened to 17? I guess I'm just disappointed in the seriousness in which our students approach these opportunities to perform in a high-stakes situation. Rather than recognize that they might need to stay after school or sacrifice a couple of lunches to be prepared they choose to fail. A notion that I simply don't get. This is not true for all students as some such as Ron and Armando did what it took to make sure they were ready. Our school's motto and guiding vision is quite simple, "WE WILL DO WHATEVER IT TAKES..." How can we get our students to adopt this vision rather than it simply being a guiding force for the staff?

Today I must say that I am more DEPRESSED than I am IMPRESSED.

Discourse Time Baby! (5-16-08)

Discourse Time (DT) is a chance for students to debate mathematics. We so often forget that students need a chance to share ideas, listen to other peoples opinions and change their own thinking based on what they hear and see. The beauty of DT is that it brings mathematics to life. Students often get a bit heated as they argue their points and try to convince others of their position. The goal for DT is for students to really demonstrate their problem solving skills, showing how they attack the problem, articulating where their solutions are coming from, and dealing with counter arguments to their thinking.

During DT a group of students ( 4 - 6) sit at a table in the middle of the class and debate the problem at hand. While they're involved in their discourse the rest of the students have one of two jobs. 1.) Taking "I notice" and "I wonder" notes - observational notes of what they're seeing and hearing from the group on the inside. 2.) Scoring participants - this includes giving them points for such actions as stating an opinion relevant to the question, supporting a position with factual evidence and drawing someone else into the conversation.

Below is a scribing of today's Discourse Time. It may be difficult to follow, but you'll get the idea that kids really get into solving the problem and persuading each other. Prior to the documented dialogue is a copy of the problem that the students were solving. Following the dialogue you will see a set of I Notice and I Wonder notes that students and I observed.

THE PROBLEM
Camilla threw a softball straight up in the air. The table at the right shows the height of the ball in feet at different times after she released it. (ex. 0.4 sec - 19.44 ft, 1.0 sec - 30.0 ft, 1.2 sec - 30.96 ft.)
Tell whether each statement is true orf false and explain how you know. (Hint: Find the equqtion for the height of Camilla's ball, using the fact that the general equation for the height, y, of a thrown ball x seconds after it is released is y = - 16x^2 + bx + c)

"Discourse Time Starts Now!"

I said false, true, false, false...Jordy
Wrong, I said false, true, false true...Benito
Hold up, let me see your graph...Jordy
Why was it released from a height of 6 feet?...Saul
Look, my graph shows it that she throws at 4 feet...Jordy
How can there be 19 ft. in a split second? She's not superman...YELLED BENITO

Time Out - CALM DOWN...it's difficult to have a conversation when someone is aggressively yelling...Singer

Would you care to explain your equation to us that backs up what you're saying?...Josh
I got a question...if you don't have your equation how are you proving what you're saying?....Saul
My guess is that 3 out of the 4 are true...Josh
There will be two times when the ball will hit 4 feet, that has to be false...Saul
I guess it's true then...Jordy
What do you have to say about it Josh...Saul
I'm guessing B is false man because I'm looking at the table and there's no value when the height is at 4 feet...Josh
If you throw a ball it's going to pass four feet when it comes down, it can't avoid 4 feet...Saul
How old is the girl, is she tall or short?...Jordy
Does it matter?...Singer
What if you just used your equation to determine at what height the ball was thrown?...Singer
What is our equation?...Jordy
What did you get for b?...Jordy
I got what I told you I got...Benito
You don't need to use the graph to find the C value you could just use the table...Josh
What do you say Jordy?...Saul
I say false, look, you see my graph, it don't get to 3...Jordy
Wait...I messed up right there, I think you guys are right...Jordy
I say true cause as you said on your graph it shows that it doesn't even get to 3 so it has to be less than 3 seconds that the ball is in the air...Saul
Can you guys please draw your graph on the board so we can see it...Singer
Based on the parabola it's clear to see that the curve comes back to the ground before 3 seconds so C has to be true...Saul
The maximum height of the ball is less than 35 ft. has to be true because of the vertex...Benito
Look at the table, you can see that between 1.2 and 1.4 it hits its highest point...Saul
For B what do you guys say...Benito
I say true for B because when she throws the ball it could be below 4 ft. and then when it comes back down it's going to pass 4 ft. again...Saul
What do you think Josh, we need another opinion...Benito
When you throw a ball in the air it's got to be 4 feet of the ground and then basically when it comes back down you've got 4 ft, I think true...Josh
Do you guys realize how tall is 4 ft.? ...Jordy
I change my answer to true for part B...Jordy
I still believe it's false, it's only common sense...Benito
(getting up from the table) Look guys, watch as I throw this ball, you can see that I'm releasing it from below 4 ft...Saul
Look how fast the ball is travelling...Benito
But wait, we only know height from the ground, not the distance it's travelling...Singer
Look at the change from .4 seconds to 1.0 seconds, that's .6 seconds and it's moved 20 ft....it's going pretty fast...Saul
This is my equation...y = -16x^2 + 38.4x + 9.2...Benito
That's the same equation that I got...Iaisha (from the audience)
In . 4 seconds it grew 13 and some change so if you have .6 seconds it's like 26 and if you keep going I think it will be 30 roughly....Saul
Wait...what if you use Benito's equation to test things out...Singer
So when I put 0 in I get 9.2 ft which means that she throws the ball from 9.2 ft. which means that Benito is right...Jordy
She's tall, she threw the ball like that...Jordy
She might have thrown the ball from a platform or a chair...Benito
Or on top of a building...Saul
Unless she's taking steroids...Ron
So B is false...Jordy
And then A is false, has to be because we just solved it and she doesn't release the ball from 6 ft...Jordy
False, False, True, True...GROUP DECISION


I NOTICE
I notice that Josh didn't challenge other peoples opinions...Jessica
I notice that Saul was trying to get in the conversation...Angel
I notice that Benito was acting like he was the only one who knew the answers...Angel

I WONDER
I wonder why people didn't bring Jordy into the conversation...Angel
I wonder why Benito was being so aggressive and angry...Singer
I wonder why the class wasn't all doing their jobs outside of the Discourse Time...Singer
I wonder if Benito was just talking or if he really knew what he was talking about...Sir

The End is Near! (5-13-08)

The end of the school year is a tricky time to be a teacher. You want the kids to continue to learn and your expectations are in some ways higher then ever. After spending a year setting the tone and making professionalism a top priority in your classroom it's hard to accept anything less. On the flip side you have the students who are ready to forget all about everything you've worked for all year...a professional, collaborative learning community.

The Power of 17 is unfortunately no different. Some students, Mahkena, Armando and a few others still demonstrate immature behaviors and difficulty with their impulse control. In some ways it seems as though some of our freshman have actually gotten less mature through out the year (something that I'm not particularly proud of). At the same time, some students are still struggling to engage in learning. Ron refused to work yesterday and Bonnie spent about an hour outside of class doing God knows what. Meanwhile, despite the unavoidable struggles, we continue to push forward as a class.

Beyond the classroom behavior and focus issues teachers face other dilemmas at the end of the year. With two weeks left should I continue to provide the students with new learning and new information or should I spend the time making sure that they really, deeply understand the big ideas that we've spent a year developing. Having taught for almost 5 full years now I tend to opt for the later of the two. Ensuring that kids really comprehend the essential learning from the year and that they're able to draw connections between what they've learned is more important to me than anything else. As a result, we're focusing on two major end of the year projects/tasks.

The first is a chance for the Power of 17 to analyze three major kinds of data that they've been dealing with all year...Linear, Exponential and Quadratic. Since these types of functions aren't going away from their math education anytime soon I believe it will do them a great service to solidify their thinking and make any possible concrete connections between the three types of data. Since this group of students are the only ones who have spent time with Quadratics it is important that they really see how they're related to the other two types of functions.

The second is an opportunity for kids to show what they know and how they grow. In other words, students will be asked to come up with an end of the year presentation that convinces me and their peers that they have retained some crucial information from this year's course. Moreover, they need to describe how they've grown as a person and as a student. It's my belief that students need opportunities to think about how they've changed and reflect on their own learning. Otherwise school becomes a go, go, go environment with no pauses to stop and really think..."what do I know, how have I changed."

I'll be sure to keep you posted as we work through these last weeks of school. On a side note, I need to give some props to Ladon, Benito and Torian. Ladon and Benito did a great job in the staff-student basketball game. I was really impressed with how they play the game in a professional way and how much hustle they bring to the court. They're also really skilled (much more than me although I will say that I was impressed by my 18 points in our 54-51 victory). Torian deserves props for his coaching of the student team in which he really did his best to help them stay in the game.

True Learners (5/1/08)

It was a welcomed break from the norm. Only 30 % of our kids were in the school building. A large group had chosen to attend the protest downtown for immigration and another big chunk of kids were at the JROTC district wide reception. Sarah (our English Teacher) and I decided to join our classes rather than teach little groups of 8 or 9 students. So there I was on a bizarrely snowy day in May with a combined class of 17 in which very few students were interested in learning. "I'm not feeling it today Mr. Singer...no one else is here...why should I have to learn...come on, we work here everyday." These were the comments I was hearing from many as I tried to encourage some positive work time. Not to discredit the whole class as there were a chunk of kids engaged in learning. Ron comes to mind as he worked on finding an equation to represent a parabola he was dealing with. Josh was his usual self, taking care of business the way he knows how. Ask questions, get support, move forward. He loves getting it done. Beyond these pockets of students who chose the right path to follow there were two who I must discuss in more detail, Iaisha and Sir.

Teaching Iaisha and Sir reminds me of my own learning experience in college when I would sit in my Discrete Mathematics Professor's office and get help with creating complex proofs. I would sit there asking questions and getting support while Dr. McGivney would hand me different materials to look at that might clue me in on some new information or show me an example of how what I was dealing with might look in a different context. He never gave me answers, but always helped guide me to what I needed to find my own solutions. The same is true for the experiences that I occasionally get the opportunity to bask in with Iaisha and Sir. Two extremely bright students with a passion for new knowledge, Sir and Iaisha bring the same attitude about learning to the table that I did as a college sophomore.

Working as a team (the 3 of us) we were trying to find a way to solve for the exponent in an exponential equation. How do you get the power down from there? was really the question. If you have an equation that represents investing money like y = 12,550(1.13)^t where y is your output, $ in the account, and t is your time than how could you solve the equation for t when given a specific amount of money. For example, if asked when your investment would reach $25,000.00 then how could you solve the equation 25,000 = 12,550(1.13)^t? As we discussed this mathematical dilemma I mentioned to my two math whizes that there is a thing called a logarithm that might help us do just that. Opening a college text book we began to explore what these logarithms were all about and how they might help us crack the case wide open like a young Angela Lansbery. As we went through examples and discussed what all of this new terminology meant we soon realized that nothing we were looking at was getting us too close to our needed support. "Why don't we move a few sections ahead in the text," remarked Sir. "These are just simple examples...I'll bet they'll show us how to use it with equations later in the book." Sure enough Sir was right on the money. A few sections later we found exactly what we needed to answer our initial question.

Over a near 1 hour period of time the three of us were engaged in learning and doing mathematics as colleagues. I simply kept suggesting, questioning and supporting, but never giving solutions. It's amazing how much we can underestimate the talents, intelligence and interest level of our students if we don't allow for these types of opportunities. Think about it. How many 9th graders would be interested in reading through a college math text to discover how logarithms might support them in solving exponential equations for the power variable? How many for that matter have the ability to accomplish this task with minimal guidance from their teacher? I was so proud of Sir and Iaisha as they came to their solution and discovered an entirely new area of mathematics that they may not have even known existed prior to today. Awesome stuff...just awesome!