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!

More volatile than the Dow Jones (4/17/08)

How powerful is the "power of 17?" I'm not really sure. Right now it doesn't really have the feel of a solid collaborative learning community that I had envisioned when we set out on a mission to create the ultimate class. Today was a great example of just how all over the place we are.

A group of students who initially detested the rules of exponents used to simplify expressions did an amazing job on their quiz to demonstrate their knowledge. At the same time, Ladon took a nap and completed two of the questions and Torian turned in his quiz while demanding to be switched into a different class and proclaiming, "that's it! I give up on math, I'm done." It was certainly a volatile day (not unusual).

Of the 17 or so kids in the class a handful received a grade of "In Progress" on their quiz, which means that they're showing some understanding, but they're not quite there yet. Rather than review the quiz with the whole class and bore the majority with information they already know I decided to split the class into groups. Iaisha volunteered to work with a small group of kids who are struggling with the quiz material while I took the rest of the class so that we could move on with our learning.

It was great because everyone's needs were being met. Everyone that is except for Ladon who was sleeping, Torian who has "given up on math" and Bonnie who ditched for nth time in a row. In one class period you can experience such a variety of successes and failures. It's really amazing how volatile the inner-city teaching profession can be. On the positive side you have a group of students choosing to work with a student leader to clarify their confusion. You have another group of kids ready to move on and learn new material (in this case we've just begun looking at how to use exponential growth to make money). On the negative side you've got one student who's done, another who's sleeping and one more who's way more into her own personal life drama then getting a high school diploma.

Today the "Power of 17" was more like the Power of 12 or maybe 13, but I guess one could argue that we still have the power and that's not so bad in and of itself.

Hip Hop and Math (4/14/08)

Learning the rules of working with exponential expressions can be a tedious learning experience. 7 properties ranging from what to do when multiplying powers with the same base to how to handle negative exponents. Although not terribly difficult, there's certainly nothing inherently engaging about developing your skills around how to handle (x^3 * x^5)/x^4. As a result, I decided to come up with a way to really get the kids going on learning these properties.

Our kids love music. Whether it's hip hop, alternative, or Latino, they just really seem to love music. As a result I thought why not bring music into the classroom? What if the kids were asked to take a song that they really like and change the lyrics to teach the properties? That was the task I assigned the kids. Making sure you use all 7 properties we've learned change the lyrics to teach the listener how to use the rules.

The beauty of teaching is that just because an idea sounds great doesn't mean it will actually work. As I discovered for the umpteenth time in my career. First of all, my assumption that because my kids love hip-hop means that they could produce hip-hop lyrics was false. Putting the constraint on them by saying your song needs to teach the properties of exponents became too much of a daunting task for many groups. Creating rhythm and rhyme with a set amount of material really is tougher for students than I anticipated. In addition, it takes a long time...something that we are always worried about in the teaching profession. If it's going to take a while then it better be a valuable experience that ensures the learning outcomes are being met. In this case, as two days passed, I realized that it was too much time for too little learning. Like recognizing when to take a loss on a stock that's continuously dropping it was time to sell. I scrapped the project.

As disappointed as I was that the groups were unable to really come up with some amazing songs I was pleased to see Ladon and Torian really take to the challenge. Moving into their third day of writing they have been fully engaged in the activity and it seems as though this project suits their interests and learning needs. We know that all kids learn differently and enjoy engaging with materials in different ways. It's clear that these two appreciate the musical side of things and are able to transfer their knowledge into meaningful lyrics. I'm really excited to hear their final version. If you're curious, their song choice was the rap song that starts "I wish I was a little bit taller...I wish I was a baller..." They're new version starts with "I wish I was a product of a power...it took my nearly an hour..."

What did I learn from my mistake...
1.) Just cause kids love music doesn't mean they all want to create it. The same holds true for video games. Just cause kids love to play them doesn't mean they all want to learn how to make them. (False assumption)
2.) An activity like this one can be really powerful for some, and therefor should not be put in the closet just because it didn't work for everybody. In the future, I should just make it an option in a list of many choices on how students can demonstrate what they know.
3.) As one of my more astute students, Jamel, suggested to me yesterday afternoon, I should have started the activity later on when the kids had more familiarity with the rules and how to work with them. "Hey Mr. Singer, we should have done this after we were already comfortable with the properties...it would have been easier to work with them and write lyrics about them." He was absolutely right...it's far easier write about things you know.

As teachers it is essential that we experiment in our classrooms with any ideas that we believe will further engage students in learning. Sometimes our experiments work and other times they fail, but that doesn't mean we stop experimenting.

Stop Pushing Me So Hard! (4-3-08)

Although not a part of the Power of 17 I feel compelled to share a story from yesterday.

After two consecutive days of receiving a completely "nasty" attitude from one of my female students I felt the need to ask why. I had enough of "you're not my mommy or daddy...don't tell me what to do...don't ever talk to me again." Here's how the conversation went.

Me: Hey _________, what's going on? Be honest with me. I don't think I've done anything to you to deserve the kind of treatment your giving me. So what's going on?

Student: You really want to know?

Me: Yeah, come on...we have a relationship, tell me what's up.

Student: I'm sick of you pushing me.

Me: What?

Student: I'm sick of you expecting so much from me and challenging me so much. You push me too hard.

Me: (a blank stare with the thought "are your f'n serious?")

Never in my long, illustrious career (just kidding, this is my 5th year) have I heard a student say something like that. "Don't push me so hard!" What am I supposed to do? When I have a student who I really care about who isn't achieving or isn't working to their potential it is my natural response to say "hey, let's get it going...let's make it happen...come on, you can do this...I believe in you." I've always looked at my job as wearing multiple hats. One of which is that of a cheerleader. I'm not just here to teach or facilitate learning, I'm also here to motivate and encourage. Maybe when I'm working with this particular student I'll have to take that specific hat off and be sure just to teach. God forbid I encourage her to achieve great heights and pressure her to be successful.

The more I think about it the more I realize that I assume too much. Not every kid is motivated in the same ways, and this particular student gave me a great wake up call to this understanding.

Farewell to Carlos (3-20-08) You will be missed (?)

As I've written this blog through out the semester Carlos' name has certainly appeared more than once. Always involved in our class (although not always positively), Carlos has entertained, impressed and annoyed. Demonstrating that he is without a doubt one of the more intelligent individuals I have ever taught, Carlos will certainly be missed. Tomorrow is his last day with us as his family has moved and he will be heading to new school. In some ways I'm happy as a teacher to not have to deal with his "mischevious" behaviors or constant need for engagement (god forbid you ask him to chill for a couple minutes!), but in others I am sad to see him go. I know he's going to be an amazing student one day and that his maturity will catch up with his intelligence so it's a bit sad to only see the 14 year old Carols and not the Senior in High School dawning a cap and gown Carlos. Either way, he's one of those kids that you just don't forget.

As a farewell to our audience Carlos has written a brief story for us that occured on March 3.
He writes...

It was 3/3/08 and I cut my finger with a razor blade. I went to the hospital and there were some seanyers (seniors) ther for cretites (credits) they have to do. Somehow we started talking about math and I started telling them about quadratic equations. I got a piece of paper and showed them (-b +/- radical (b^2 - 4ac)) / (2a). They were like "is your school rich or something? We don't learn stuff like that at my school." I made a graph and found a, b, and c and showed them how it worked with the equation y = ax^2 + bx + c. They were amazed and wanted to konw how to do it at their school.

Carlos told me this story the day after it happened and I remember just feeling pride. Here's a freshmen who causes our school all sorts of trouble who opened a conversation about quadratic equations in an ER at the hospital with a group of Seniors from other schools. How do I know Carlos is going to make it? I know because of three things...1.) He loves learning new things 2.) He has amazing retention abilities. and 3.) He loves sharing what he knows and showing his thinking.

Good luck Carlos...we know you're going to do great things.

It's March! (3-10-08) An update

I can't believe the school year is 75% done. It seems like just yesterday I was learning the names of my students and all of the sudden I know about their family dynamics, their learning styles, their likes and dislikes and their abilities with mathematics. What happened? As a teacher you are so buried in the day to day survival that you loose sight of the big picture. Like a caveman constantly searching for food its easy to forget that you've got bigger goals than your next meal or in our case, your next lesson plan. What has happened to the "Power of 17?" Did I loose track of the big goals? Let me get you up to speed on what we're working on and then we'll answer the bigger question.

As individuals the students are working hard (mostly). Currently engaged in an extensive project framed around theoretical and experimental probability the students have been using a lot of originality and creativity to complete their tasks. Creating their own game of chance (i.e. I bet I can roll three 7's before you roll a 3,4, and 5) students were then asked to calculate the theoretical probabilities of both positions in order to choose the most favorable stance. (SIDE NOTE: Probability Theory and that entire field of mathematics originated from wealthy noblemen gambling in the 17th century and asking mathematicians like Pierre de Fermat for help - what an opportunity to bring something fun into learning Algebra) Unfortunately, I wasn't sure how to teach the process behind calculating these figures. I had some ideas, but needed some support form others to finalize my thinking. (what a funny notion, a math teacher who doesn't have all the answers)

Posing the problem to a group of colleagues I myself engaged in some pretty rough mathematical arguing. It wasn't quite a Tyson vs. Holyfield rematch, but it certainly had some sweat and a few jabs. After nearly two hours of discourse between the group of math teachers I decided that our findings weren't conclusive enough to say "hey kids, here's the way to do it." Instead, I decided to pose the two perspectives that we narrowed it down to and let my students decide which approach they wanted to use in calculating their probabilities. The exciting part was sharing the work of the math teachers with my students so they could get a sense of how a person trained in working with mathematics approaches a problem. Here were the two schools of thought that came out of the conversations with the math teachers that the student had to choose from (or make up their own).

THE PASCHAL APPROACH
Although each roll of a set of dice is independent a game involving multiple sums that you're trying to obtain has some dependent factors. For example, if I want to roll a 3,4, and 5 then the probability of my second roll depends on which number I get first.
i.e. The 1st roll has a probability of how ever many outcomes there are for 3, 4, and 5 out of the total outcomes possible for rolling a set of dice.
P(3, 4, and 5) = (2 + 3 + 4) / 36 = 9/36
The 2nd roll then depends on what you've already rolled. So if a 4 came up first than you're now looking for a 3 or 5.
P(3 or 5) = (2 + 4) / 36 = 6 / 36
Assuming that we next get the 3 we've been looking for we now have to hope for the 5.
P(5) = 4/36
Using what we know about the probability of multiple events we simply multiply each probability together to get the overall probability of rolling a 3,4, and 5
9/36 * 6/36 * 4/36 = (216)/(36^3) = .0046 = .46 %

Using this school of thought there are a series of scenarios to consider when determining the overall probability. i.e. 3 then 4 then 5 or 4 then 5 then 3 or .... and all of them have to be considered when finalizing your solution. Perhaps finding the average probability of all scenarios is the way to go or maybe just providing the range of probabilities is a better option. Either way, the Paschal method, named after my colleague here at Manual, uses the notion of dependence and scenarios to drive its calculations.

THE JIMMY METHOD
According to Jimmy, an old friend and colleague who is currently back in school studying mathematics education (he's neither old nor is our friendship, but I've worked with him since nearly the beginning of my career so it seems like an old friendship and since he's fairly wise when it comes to math instruction I have to consider him to be "older") the probabilities are not based on multiple scenarios as Pashcal would suggest. Rather, when we look at the probabilities of each scenario the outcome is always the same.

Consider this table.

Ways to win the game, # of ways to roll each number, Prob. of Mult. Events (*)
(3, 4, 5) , (2, 3, 4) , 2*3*4 = 24
(3, 5, 4) , (2, 4, 3) , 2*4*3 = 24
(4, 3, 5) , (3, 2, 4) , 3*2*4 = 24
(4, 5, 3) , (3, 4, 2) , 3*4*2 = 24
(5, 4, 3) , (4, 3, 2) , 4*3*2 = 24
(5, 3, 4) , (4, 3, 2) , 4*3*2 = 24

According to Jimmy's theory the order of the rolls is unimportant since the properties of multiplication will show that there's always the same total number of ways for your favorable outcome to be produced. In the end, Jimmy's thinking states that there are 6 winning outcomes each of which has 24 ways of happening. Therefore, he concludes the probability to be...
P(3, 4, and 5) = (24 * 6)/(36^3) = 144/(36^3) = .0031 = .31 %

The key to student engagement in the project has been its open-endedness. Moving away from simply right and wrong, the project goes on from these calculations to ask student to construct a set of new dice that will favor their position even greater. Whether that means constructing a die that looks like a loaf of bread (Carlos' idea) or simply creating a lopsided pencil, which is really a hexagonal prism (Latha's idea), the students are thinking, creating and problem solving. That's what it's all about. Sometimes I worry so much about kids solidifying procedural knowledge that I forget what being a mathematician or a scientist is all about. Testing ideas, experimenting, drawing conclusions, sharing your thinking and dealing with counter-arguments. This is the stuff!

As we are currently in the midst of CSAP, our state tests, (something I'll discuss in a later blog) I have a chance to stop searching for food and to remember my larger goals; Creating a collaborative learning community (who can think!) Hey, we're engaged in a project that does just that. Although I need to get back to my die hard effort of creating an effective classroom of collaborative learners at the moment I am pleased with the mere fact that we're engaging in real mathematics. Solving problems using multiple pathways and bringing our own thinking and creativity to the table in order to produce something new. Struggling alongside one another, teacher and student, to answer questions and produce work that neither of us know the outcome to. That's collaboration!